Kristof Risse

Preliminary Overall Aircraft Design with Hybrid Laminar Flow Control

Luft- und Raumfahrttechnik

Preliminary Overall Aircraft Designwith Hybrid Laminar Flow Control

Vorentwurf von Flugzeugen mithybrider laminarer Strömungskontrolle

Von der Fakultät für Maschinenwesen der Rheinisch-WestfälischenTechnischen Hochschule Aachen zur Erlangung des akademischen Grades

eines Doktors der Ingenieurwissenschaften genehmigte Dissertation

vorgelegt von

Kristof Risse

Berichter: Universitätsprofessor Dr.-Ing. Eike StumpfUniversitätsprofessor Dr.-Ing. Wolfgang Schröder

Tag der mündlichen Prüfung: 23. August 2016

Diese Dissertation ist auf den Internetseitender Universitätsbibliothek online verfügbar.

Shaker VerlagAachen 2016

Berichte aus der Luft- und Raumfahrttechnik

Kristof Risse

Preliminary Overall Aircraft Designwith Hybrid Laminar Flow Control

WICHTIG: D 82 überprüfen !!!

Bibliographic information published by the Deutsche NationalbibliothekThe Deutsche Nationalbibliothek lists this publication in the DeutscheNationalbibliografie; detailed bibliographic data are available in the Internet athttp://dnb.d-nb.de.

Zugl.: D 82 (Diss. RWTH Aachen University, 2016)

Copyright Shaker Verlag 2016All rights reserved. No part of this publication may be reproduced, stored in aretrieval system, or transmitted, in any form or by any means, electronic,mechanical, photocopying, recording or otherwise, without the prior permissionof the publishers.

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Abstract

This thesis deals with preliminary overall aircraft design including hybrid laminarflow control (HLFC) on wings and tails. An integrated methodology and software

framework is developed that closes the gap between conceptual aircraft design capabilitiesand the detailed design tasks of HLFC aerodynamic wing design and HLFC system sizing.The key new achievement of the proposed approach compared to the current state ofthe art is its capability to perform overall aircraft design studies, while simultaneouslycapturing the specific influences of different transition mechanisms and transonic drag onswept-tapered wings, as well as the integration of the suction system into the wing.

TheMultidisciplinary Integrated Conceptual Aircraft Design and Optimization (MICADO)framework constitutes the basis for this integrated approach. MICADO consists of a con-sistent and flexible software architecture, a requirement-driven overall design philosophy,and several loosely-coupled program modules. Most significant elements for HLFC air-craft design are a thermodynamic engine model including secondary power extraction,overall-aircraft drag and mass prediction, and detailed mission performance simulation.

The incorporation of HLFC aerodynamics into overall aircraft design is solved by a quasi-three-dimensional wing design approach, and a database containing multi-point optimizedHLFC airfoils at different design conditions. An Euler/boundary-layer and a transitionprediction code (including cross-flow instabilities) are combined with appropriate sweep-taper transformations into an iterative and robust drag prediction method for transonicHLFC wings. Both pressure and suction distributions are taken into account for auto-mated estimation of power requirements and component masses of the suction system.

Applicability and validity of the proposed HLFC aircraft design approach are demon-strated for a long range passenger aircraft. Influences of mass snowball effect, componentresizing, and conservative fuel planning for in-flight loss of laminarity are quantified interms of block fuel and other key design parameters. The significant fuel saving potentialof HLFC is confirmed, and further exploited by the integrated design and optimization ofHLFC wing geometries for maximum overall aircraft benefit.

III

Kurzfassung

Die vorliegende Arbeit befasst sich mit dem Flugzeuggesamtentwurf und der An-wendung hybrider laminarer Strömungskontrolle (HLFC) auf Flügel und Leitwerke.

Hierzu wird eine rechnergestützte Methodik vorgestellt, die die bestehende Lücke zwischendem Flugzeugvorentwurf und den detaillierten Aufgaben des aerodynamischen Laminar-flügelentwurfs und der Auslegung des Absaugsystems schließt. Verglichen mit dem Standder Technik ergibt sich die wichtige neue Fähigkeit, im Zuge automatisierter Flugzeugent-wurfsstudien die spezifischen Einflüsse von Transitionsmechanismen und transsonischemWiderstand zugespitzter Pfeilflügel sowie der Systemintegration mitzuberücksichtigen.

Die entwickelte Flugzeugentwurfsumgebung MICADO (Multidisciplinary Integrated Con-ceptual Aircraft Design and Optimization) basiert auf einer flexiblen Softwarearchitek-tur mit verschiedenen Programmen, die nach einer konsistenten Entwurfslogik ablaufen.Wichtige Elemente für den HLFC-Flugzeugentwurf sind ein thermodynamisches Trieb-werksmodell mit Sekundärleistungsentnahme, Berechnungsmethoden für Aerodynamikund Massen des Gesamtflugzeugs sowie ein detailliertes Modell zur Missionssimulation.

Zur Einbindung des aerodynamischen HLFC-Flügelentwurfs in den Gesamtentwurf wer-den ein quasi-dreidimensionaler Ansatz und eine Datenbank mit für verschiedene Entwurfs-punkte voroptimierten HLFC-Profilen kombiniert. Die iterative robuste Widerstands-berechnung verbindet ein Euler-Grenzschicht-Verfahren und eine Transitionsvorhersage-methode (einschließlich Querströmungsinstabilitäten) mit geeigneten Transformationenfür den zugespitzten Pfeilflügel. Ausgelegte Druck- und Absaugverteilungen werden fürdie Bestimmung der benötigten Leistung und der Masse des Absaugsystems verwendet.

Die Gültigkeit der Gesamtmethodik wird anhand ihrer Anwendung zur Auslegung einesLangstreckenflugzeugs demonstriert. Hierbei werden die wichtigen Einflüsse iterativerMassenzunahme und Komponentenauslegung sowie der Treibstoffplanung für den Aus-fall der Laminarität während des Fluges quantifiziert. Das bedeutende Treibstoffeinspar-potential der HLFC-Technologie wird durch die Entwurfsstudien bestätigt; es kann außer-dem weiter ausgeschöpft werden durch die integrierte Optimierung von HLFC-Flügel-geometrien für einen maximalen Nutzen im Sinne des Gesamtentwurfs.

V

Acknowledgments

The research presented within this thesis was conducted at the Institute of AerospaceSystems (ILR) of the RWTH Aachen University. First of all, I would like to express

my deep gratitude to Prof. Dr. Eike Stumpf, for supervising my thesis, and reviewing itwith great care and important advices; further, for providing a research environment, inwhich I always enjoyed to work. Secondly, I would like to thank Prof. Rolf Henke, underwhose guidance I started my work at ILR. It was him to pave the way for this thesis, byestablishing both aircraft design and hybrid laminar flow control as research topics at theILR. I further thank Prof. Dr. Wolfgang Schröder for kindly being the second examinerof my thesis, which I especially appreciate due to his expert knowledge in aerodynamics.

I thank the academic counselors Dr. Günther Neuwerth and Dr. Ralf Hörnschemeyer fortheir continuous encouragement at the beginning and final phase of my thesis. I couldnot have enjoyed my time in Aachen so much without so great colleagues and friends. Ithank Eckhard Anton, for teaching me so many things, from which I still profit, for thecountless programming sessions, and particularly, for his fundamental work and persistingideas on MICADO. I thank Katharina Schäfer who accompanied me already from thebeginning of my studies; I cannot imagine a better combination of office colleague, friend,and discussion partner than her. I am further thankful to Dr. Tim Lammering, FlorianSchültke, and Fabian Peter for a great collaboration in aircraft design, and for manycommon working hours and after-hours. This certainly also includes all other colleagues,friends, and several student workers who contributed in different ways to this thesis, thedevelopment of MICADO, and in general to my time at ILR.

This research originated from the German LuFo projects HIGHER-LE and VER2SUS; Ithank all involved people for the great cooperation within these projects. In particular, Ithank Dr. Geza Schrauf, Airbus Bremen, for sharing his transition prediction programs,and especially his expert knowledge and experience in laminar flow with me. I also like tothank my new colleagues at the DLR in Braunschweig for important technical discussionsand feedback at the end of my thesis.

I deeply thank my parents and my sister for their enduring support throughout the years.Finally, but most gratefully, I thank you, Anna, for your patience, love, and encourage-ment in all the hours that I spent on this thesis instead of spending them with you.

VII

Contents

List of figures XI

List of tables XV

List of symbols XVII

1 Introduction 11.1 Motivation and problem statement . . . . . . . . . . . . . . . . . . . . . . 11.2 Related work in laminar aircraft design . . . . . . . . . . . . . . . . . . . . 41.3 Thesis objectives and approach . . . . . . . . . . . . . . . . . . . . . . . . 7

2 Fundamentals and state of the art 92.1 Fundamentals of preliminary aircraft design . . . . . . . . . . . . . . . . . 92.2 Laminar flow theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.2.1 Viscous flows and boundary-layer theory . . . . . . . . . . . . . . . 122.2.2 Laminar-turbulent transition . . . . . . . . . . . . . . . . . . . . . . 162.2.3 Linear stability theory . . . . . . . . . . . . . . . . . . . . . . . . . 172.2.4 Transition prediction . . . . . . . . . . . . . . . . . . . . . . . . . . 202.2.5 Instability mechanisms and transition on swept wings . . . . . . . . 262.2.6 Laminarization techniques (NLF, LFC, and HLFC) . . . . . . . . . 32

2.3 HLFC design and integration aspects . . . . . . . . . . . . . . . . . . . . . 352.3.1 HLFC aerodynamic wing design . . . . . . . . . . . . . . . . . . . . 352.3.2 HLFC system and structural integration aspects . . . . . . . . . . . 382.3.3 HLFC operational aspects . . . . . . . . . . . . . . . . . . . . . . . 40

3 Method for aircraft design with hybrid laminar flow control 433.1 Integrated aircraft design environment MICADO . . . . . . . . . . . . . . 43

3.1.1 Software architecture . . . . . . . . . . . . . . . . . . . . . . . . . . 453.1.2 Overall aircraft design approach . . . . . . . . . . . . . . . . . . . . 503.1.3 Integration of HLFC methods into MICADO . . . . . . . . . . . . . 533.1.4 Design interactions: mass snowball effect and aircraft resizing . . . 54

IX

X Contents

3.2 Conventional aircraft design and analysis methods . . . . . . . . . . . . . . 563.2.1 Component sizing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 593.2.2 Engine modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 603.2.3 Full-configuration aerodynamic analysis . . . . . . . . . . . . . . . . 613.2.4 Mass estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 673.2.5 Systems sizing and power distribution . . . . . . . . . . . . . . . . . 693.2.6 Mission analysis and fuel planning . . . . . . . . . . . . . . . . . . . 713.2.7 Design evaluation: performance and cost analysis . . . . . . . . . . 76

3.3 HLFC aerodynamic wing design method . . . . . . . . . . . . . . . . . . . 783.3.1 Design approach and integration into MICADO . . . . . . . . . . . 813.3.2 Assumptions and relations for conical 2.5D approach . . . . . . . . 833.3.3 Validation case for conical 2.5D wing drag prediction method . . . . 883.3.4 2D transonic flow solver (MSES) . . . . . . . . . . . . . . . . . . . 903.3.5 Transition prediction modules (STABTOOL) . . . . . . . . . . . . . 923.3.6 HLFC airfoil analysis process . . . . . . . . . . . . . . . . . . . . . 963.3.7 HLFC airfoil design and optimization procedure . . . . . . . . . . . 1063.3.8 HLFC airfoil aerodynamic database . . . . . . . . . . . . . . . . . . 112

3.4 HLFC system design method . . . . . . . . . . . . . . . . . . . . . . . . . . 120

4 Application of developed method to HLFC overall aircraft design 1254.1 Design and validation of long range reference aircraft . . . . . . . . . . . . 1264.2 Design sensitivities and HLFC integration potential . . . . . . . . . . . . . 1404.3 HLFC aircraft design and optimization . . . . . . . . . . . . . . . . . . . . 144

4.3.1 HLFC aircraft design: single point evaluation . . . . . . . . . . . . 1454.3.2 HLFC overall aircraft design studies . . . . . . . . . . . . . . . . . . 1554.3.3 HLFC overall aircraft design optimization . . . . . . . . . . . . . . 158

5 Conclusions and outlook 161

Bibliography 165

A MICADO parameters and methods 191

B Conical-flow equations 193

C Supplementary data of MICADO long range reference aircraft design 195

List of figures

1.1 Motivation, potential, and applicability of laminar flow technologies . . . . 2

2.1 Mission with top-level aircraft requirements and cruise force equilibrium(schematic, not to scale) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2 Schematic of boundary layer on a flat plate with parallel flow, after Schlicht-ing and Gersten [250] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.3 Laminar-turbulent transition in the boundary layer on a flat plate at zeroincidence [250, 319] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.4 Schematic of neutral curve in a stability diagram (temporal theory) . . . . 202.5 Principle of eN method: relation between stability diagram and amplifica-

tion ratios, after Arnal [17] . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.6 Principle of transition prediction using the two N -factor method . . . . . . 252.7 Instability mechanisms for three-dimensional flow around a swept wing,

adapted from Redeker and Wichmann [216] . . . . . . . . . . . . . . . . . 272.8 Criteria for attachment-line transition including suction . . . . . . . . . . . 312.9 Typical characteristics of HLFC pressure and suction distribution (schematic),

following Ref. [124] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.1 Principle of control and data flow of the MICADO environment . . . . . . 463.2 Principle of MICADO geometry modeling: C++ geometry classes create 3D

model based on parametric description in AiX XML file. . . . . . . . . . . 483.3 Principle and implementation of MICADO parameter study manager . . . 493.4 Process overview and design methodology of the MICADO environment . . 513.5 Extract of MICADO process with integrated data flow for HLFC aircraft

design and assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533.6 Initial sizing diagram: influence of variation inMTOW on compliance with

TLARs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553.7 Principle of MICADO engine model . . . . . . . . . . . . . . . . . . . . . . 603.8 Schematic model of MICADO conventional systems architecture based on

network of sources, sinks, and conductors . . . . . . . . . . . . . . . . . . . 693.9 Climb profile for A320 type aircraft compared with data from Ref. [8] . . . 75

XI

XII List of figures

3.10 Process of HLFC airfoil aerodynamics integration into MICADO, with in-terconnection of geometry, methods, and aerodynamic data . . . . . . . . . 81

3.11 Conical-flow assumption on a tapered wing segment . . . . . . . . . . . . . 843.12 Deviation in drag transformation as a function of ϕref and rf , see Eq. (3.31);

sample points computed at M = 0.85, Cl = 0.3 – 0.7 . . . . . . . . . . . . . 883.13 Validation of conical 2.5D drag prediction method for wing data in ta-

ble 3.4; 3D Navier–Stokes solutions computed with DLR TAU code [92] . . 893.14 Governing equations of CFD methods, after Schröder [275] . . . . . . . . . 913.15 HYLFAS flow chart for HLFC conical 2.5D airfoil analysis, including MSES,

STABTOOL, and nested iteration for (x/c)ref and (x/c)trans . . . . . . . . 973.16 Results of iterative HYLFAS analysis process for HLFC airfoil example and

comparison of pressure distribution with Navier–Stokes solution . . . . . . 993.17 Results of conical compressible boundary-layer analysis with COCO . . . . 1003.18 Tollmien–Schlichting and cross-flow N -factors calculated with local linear

stability solver LILO, including variation of suction distribution Cq (x) . . 1013.19 Correlated transition location using HLFC limiting curve . . . . . . . . . . 1023.20 Construction of adapted Cp,3D distribution around stagnation point for

specified ϕeff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1033.21 Results of automated HYLFAS drag polar prediction process for validation

case (see design parameters in table 3.6) . . . . . . . . . . . . . . . . . . . 1053.22 Off-design points for HLFC airfoil multi-point optimization . . . . . . . . . 1073.23 Results of HYLFAS inverse design and multi-point optimization process for

example case with target design conditions listed in table 3.8 . . . . . . . . 1093.24 History of HYLFAS airfoil design and optimization procedure . . . . . . . 1093.25 Influence of altitude and suction intensity Cq,max on transition and drag

characteristics at constant design conditions (M = 0.80, Cl = 0.645) . . . . 1103.26 Principle of HLFC airfoil and aerodynamic database . . . . . . . . . . . . . 1143.27 Comparison of selected HLFC airfoil database designs . . . . . . . . . . . . 1173.28 Validation of drag polar interpolation in HLFC airfoil database . . . . . . . 1193.29 Principle of simplified suction system inside wing leading edge, after Ref. [129]121

4.1 MICADO initial sizing diagram for TLARs given in table 4.1 . . . . . . . . 1274.2 3D view of MICADO design of long range reference configuration . . . . . 1284.3 Performance characteristics of MICADO baseline engine model . . . . . . . 1294.4 Geometrical, aerodynamic, and structural wing characteristics . . . . . . . 1314.5 Aerodynamic characteristics of full aircraft (clean) configuration . . . . . . 1334.6 Breakdown of mass groups and relative share in OWE . . . . . . . . . . . 1354.7 Total systems power and bleed air requirements (8150 NM mission) . . . . 1364.8 Mission simulation results for 8150 NM SPP design mission . . . . . . . . . 137

List of figures XIII

4.9 Altitude, CL, and block fuel profiles for 4000 NM study mission . . . . . . 1384.10 Take-off and landing performance characteristics . . . . . . . . . . . . . . . 1384.11 Comparison of payload-range diagram with Airbus reference data . . . . . 1394.12 Retrofit and resizing approach for design change evaluation in MICADO . 1414.13 Generic analysis and validation of HLFC integration impact on block fuel . 1424.14 HLFC aerodynamic wing design results for design points in table 4.5 . . . 1464.15 Schematic layout of HLFC systems architecture for retrofitted baseline de-

sign (HLFD-0) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1494.16 HLFC system mass and power requirements as function of design Mach

number M , altitude h, and suction distribution Cq (x/c) . . . . . . . . . . 1504.17 Overall aircraft design evaluation of HLFD points in table 4.5, including

reserve fuel estimation and resizing for in-flight loss of laminarity . . . . . 1524.18 HLFC overall aircraft aerodynamics and mission simulation results . . . . . 1544.19 HLFC aircraft designs for variations in wing loading and wing span . . . . 1564.20 HLFC aircraft designs for variations in Mach number and wing sweep . . . 1574.21 Fuel-optimized aircraft geometries (gray: turbulent; blue: HLFC) . . . . . 159

C.1 Characteristics of GasTurb engine model for long range aircraft as functionof Mach number and altitude (ISA conditions, without offtakes) . . . . . . 197

C.2 Overall aircraft design variations for turbulent baseline design . . . . . . . 200

List of tables

1.1 Overview of aircraft design methods including NLF or HLFC . . . . . . . . 6

3.1 Method overview for prediction of aerodynamic coefficients in MICADO . . 623.2 Sensitivities of MICADO mass estimation methods . . . . . . . . . . . . . 683.3 Basic flight segment types of MICADO flight performance model . . . . . . 723.4 Reference wing parameters for validation of drag prediction method . . . . 883.5 Overview of STABTOOL modules . . . . . . . . . . . . . . . . . . . . . . . 933.6 Geometry and design conditions for HLFC airfoil validation case [114] . . . 983.7 Comparison of results for effective sweep angle ϕeff and Cp,3D,stag . . . . . 1033.8 Reference and target conditions for HLFC airfoil design example . . . . . . 1083.9 2D design points for HLFC airfoil database with corresponding 3D cases . 116

4.1 Selected TLARs for MICADO design of long range reference aircraft . . . . 1274.2 Accommodation specifications for reference design . . . . . . . . . . . . . . 1284.3 Key aircraft characteristics of reference design . . . . . . . . . . . . . . . . 1284.4 Mass breakdown for reference design . . . . . . . . . . . . . . . . . . . . . 1354.5 Selected HLF design points [247] . . . . . . . . . . . . . . . . . . . . . . . 1454.6 Comparison of HLFC system design results . . . . . . . . . . . . . . . . . . 1494.7 Design variables for HLFC overall aircraft optimization . . . . . . . . . . . 1594.8 HLFC overall aircraft design optimization results . . . . . . . . . . . . . . 159

A.1 Block composition and contents of Aircraft Exchange (AiX) XML file . . . 191A.2 Overview of mass estimation methods implemented in MICADO . . . . . . 192

C.1 Top-level aircraft requirements used for MICADO reference design [114] . . 195C.2 Key aircraft parameters of MICADO reference design (suppl. to table 4.3) 196C.3 Wing geometry parameters of MICADO reference design (see Fig. 4.4a) . . 196C.4 Aerodynamic coefficients of MICADO reference design (see Fig. 4.5) . . . . 197C.5 Mass breakdown of MICADO reference design (suppl. to table 4.4) . . . . 198C.6 Mission specifications and simulation results (see Figs. 4.8 and 4.9) . . . . 199C.7 Comparison of performance parameters with TLARs from tables 4.1/ C.1 . 199C.8 Results of HLFC aircraft design optimizations (suppl. to table 4.8) . . . . 200

XV

List of symbols

A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cross-sectional area, m2

A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . disturbance amplitude

A . . . . . . . . . . . . . . . . . . . porosity factor for pressure drop through suction surface, N s/m3

a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . speed of sound, m/s

A, B, C . . . . . . . . . . . . . . . . (5× 5)-matrices in linear stability differential equation system

A0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . initial disturbance amplitude

B . . . . . . . . . . . . . . . . . . porosity factor for pressure drop through suction surface, N s2/m4

b . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . wing span, m

BF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . block fuel, kg

BFdm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . block fuel on design mission, kg

BFsm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . block fuel on study mission, kg

bi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . boundary condition function

c . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . chord length, m

c . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . phase velocity of a wave, m/s

CAS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . calibrated airspeed, m/s

Ccrew . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . crew costs, $/ASK

Cfees . . . . . . . . . . . . . . . . . costs for ground handling, landing, and navigation fees, $/ASK

Cfuel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . fuel costs, $/ASK

Cinsurance, depreciation . . . . . . . . . . . . . . . . . . . . . . costs for insurance and depreciation, $/ASK

Cmaintenance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . maintenance costs, $/ASK

COC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cash operating costs, $/ASK

cp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . specific heat capacity, J/ (kg K)

D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . drag force, N

d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . diameter, m

DOC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . direct operating costs, $/ASK

e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Euler’s number

XVII

XVIII List of symbols

EGT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . exhaust gas temperature, K

f . . . . . . . . . . factor in Lock’s equivalence law relating 3D and 2D pressure distributions

f . . . . . . . . . . . . . . . . . . fineness ratio of slender bodies (e.g., fuselage or nacelles), f = d/l

f . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . frequency, Hz

FF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . form factor

FN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . net thrust (per engine), N

Fz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (wing) shear force, N

g . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . acceleration of Earth’s gravity, 9.80665 m/s2

H . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . total enthalpy, J

h . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . flight altitude, ft

h . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . specific enthalpy, J/kg

H12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . boundary-layer shape factor

hICA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . initial cruise altitude, ft

hOEI,max . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . one-engine-inoperative net ceiling, ft

hop,max . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . maximum operating altitude, ft

i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . imaginary unit (i2 = −1)

ihtp . . . . . . . . . . . . . . . . . . . . . . . . . . . . incidence angle of (all-movable) horizontal tailplane, ◦

K . . . . . . . . . . . . . . . . . . . . . . . . nondimensional suction velocity (parameter in K-criterion)

k . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . thermal conductivity, W/ (m K)

kA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . airfoil technology factor

L . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . lift force, N

l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (characteristic) length, m

L/D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . lift-to-drag ratio

LDL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . landing distance limit, m

LFL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . landing field length, m

M . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mach number

m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . mass flow, kg/s

m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . mass, kg

M∞ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . freestream Mach number

ma/c . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (current) total aircraft mass, kg

MAC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . mean aerodynamic chord, m

mAF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . alternate fuel (mass), kg

List of symbols XIX

mBF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . block fuel (mass), kg

mbleed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . bleed air flow (from the engines), kg/s

mCF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . contingency fuel (mass), kg

Mcl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . climb Mach number

mcmp . . . . . . . . . . . . . . . . . . . . mass of compressors, motors, and VFDs (HLFC system), kg

Mcr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (design) cruise Mach number

Mcrit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . critical Mach number

MDD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . drag divergence Mach number

mduc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ducting mass (HLFC system), kg

mel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . electric wiring mass (HLFC system), kg

mf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . fuel flow, kg/s

mf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . fuel mass (unit), kg

mFRF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . final reserve fuel (mass), kg

mfurnishings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . mass of furnishings group, kg

MFW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . maximum fuel weight, kg

mhlfc,tot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . total mass of HLFC system, kg

MLW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . maximum landing weight, kg

mMF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . mission fuel (mass), kg

MMO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . maximum operating Mach number

moperator items . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . mass of operator items group, kg

mPL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . payload (mass), kg

mPL,max . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . maximum payload (mass), kg

mpower unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . mass of power unit group, kg

mRF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . reserve fuel (mass), kg

Msh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mach number at local shock position (x/c)shmSPP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . standard passenger payload (mass), kg

mstructures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . mass of structures group, kg

msystems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . mass of systems group, kg

mTF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . trip fuel (mass), kg

MTOW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . maximum take-off weight, kg

mTXF, in . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . taxi-in fuel (mass) at landing, kg

mTXF, out . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . taxi-out fuel (mass) at take-off, kg

XX List of symbols

MWE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . manufacturing weight empty, kg

Mx . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (wing) bending moment, N m

MZFW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . maximum zero fuel weight, kg

N . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . N -factor

N1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . rotational speed of low-pressure shaft, min−1

NCF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . N -factor of cross-flow instability

neng . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . number of engines

NTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . N -factor of Tollmien–Schlichting instability

O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . conical wing apex

OWE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . operating weight empty, kg

p . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pressure, N/m2

p3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . burner inlet pressure (GasTurb terminology), N/m2

Pcmp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . compressor shaft power (HLFC system), W

Phlfc,tot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . total power required by HLFC system, W

Pshaft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . shaft power offtake (from the engines), W

Q . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . interference factor

q . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . flow quantity

R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . range, NM

R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . specific gas constant of dry air, 287 J/ (kg K)

r . . . . . . . . . . . . . . absolute value or magnitude of a complex number in polar form (reiφ)

r . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . radial distance (from cone apex O), m

r . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . recovery factor

r0 . . . . . . . . . . . . . . . . . . . . . . . . . . . radial distance (from cone apex O to conical section), m

Rdes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . design range, NM

Re . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Reynolds number

Reδ∗ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . displacement thickness Reynolds number

Reθ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . momentum-thickness Reynolds number

Reθ,AL . . . . . . . . . . . . . . . . . . . . . . . attachment-line momentum-thickness Reynolds number

ReAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . attachment-line Reynolds number

Rec . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . chord Reynolds number

Recrit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . critical Reynolds number

Reind . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . indifference Reynolds number

List of symbols XXI

Rex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Reynolds number with respect to x station

rf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ratio of friction drag to viscous drag

ROC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . rate of climb, m/s

ROD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . rate of descent, m/s

S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . surface area, m2

S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . total entropy, J/K

s . . . . . . . . . . . . . . . . . . . . . curvilinear (arc-length) coordinate along airfoil/wing surface, m

s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . distance covered, m

s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . spanwise width of wing segment, m

SAR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . specific (air) range, m/kg

SFC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (thrust-)specific fuel consumption, kg/ (N s)

SLST . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . sea-level static thrust, N

Sref . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . wing reference area, m2

Swet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . wetted area, m2

T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . temperature, K

T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . thrust force, N

t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . time, s

t/c . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . thickness-to-chord ratio

T/W . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . thrust-to-weight ratio

TAS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . true airspeed, m/s

TOFL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . take-off field length, m

TTC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . time to climb, min

Tu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . turbulence intensity

u . . . . . . . . . . . . . . . velocity component in x direction (Cartesian coordinate system), m/s

U∞ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . freestream velocity, m/s

uθ . . . . . . . . . . . . . . . . . . velocity component in θ direction (polar coordinate system), m/s

V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . flight velocity (current true airspeed), m/s

v . . . . . . . . . . . . . . . velocity component in y direction (Cartesian coordinate system), m/s

Vapp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . approach speed, m/s

VMO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . maximum operating speed, m/s

vr . . . . . . . . . . . . . . . . . . velocity component in r direction (polar coordinate system), m/s

W . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . weight force (aircraft gross weight), N

XXII List of symbols

W . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . work, N m

w . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . specific work, N m/kg

w . . . . . . . . velocity component in z direction (Cartesian/polar coordinate system), m/s

W/S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . wing loading, kg/m2

ww . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . wall-normal suction velocity, m/s

x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x coordinate, m

(x/c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . relative chord position

(x/c)lam,sep . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . relative chord position of laminar separation

(x/c)ref . . . . . . . . . . . . . . . . . . . relative chord position for 3D/2D transformation reference

(x/c)sh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . relative chord position of shock

(x/c)trans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . relative chord position of transition

(x, y, z)CG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . center of gravity coordinates, m

xi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . input parameter / free variable

Y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . specific energy transfer, J/kg

y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . y coordinate, m

yi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . output parameter / objective

z . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . z coordinate, m

Greek symbols

α . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . angle of attack, ◦

αi, βi . . . . . . . . . . . . . . . . . . . . . . . . . spatial amplification numbers in x and y direction, m−1

αr, βr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . wave numbers in x and y direction, m−1

β . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Prandtl–Glauert factor (β =√

1−M2)

γ . . . . . . . . . . . . . . . . . . auxiliary variable in 3D Orr–Sommerfeld equation (γ =√α2 + β2)

γ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . flight path angle, ◦

γ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ratio of specific heats (γair = 1.4)

∆ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . difference operator

δ, δ99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . boundary-layer thickness, m

δ′ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . nondimensional boundary-layer thickness

δ∗ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . displacement thickness, m

ε . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (wing section) twist angle, ◦

εref . . . . . . . . . . . . . . . . residual for iteration of transformation reference location (x/c)refεtrans . . . . . . . . . . . . . . . . . . . . . . . . . . . . residual for iteration of transition location (x/c)trans

List of symbols XXIII

η . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . energy conversion efficiency

η . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Levy (or similarity) transformation variable

η . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . relative spanwise coordinate

θ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . momentum thickness, m

θ . . . . . . . . polar angle in developed conical wing plane (measured from stagnation line)

θ∗AL . . . . . . . . . . . . . . . . . . nondimensional attachment-line momentum-thickness parameter

Λ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . wing aspect ratio

λ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . wave length, m

λ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . wing taper ratio

µ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . dynamic viscosity, N s/m2

µbrake . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . braking coefficient

µroll . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . rolling coefficient

ν . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . dihedral angle, ◦

ν . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kinematic viscosity, m2/s

ξ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Levy (or similarity) transformation variable

π . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pi

ρ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . density, kg/m3

Σ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . summation operator

τ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . shear stress, N/m2

φ . . . . . . . . . . . . . . . . . . . . . . . . argument or phase of a complex number in polar form (reiφ)

ϕ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . sweep angle (at local chord position), ◦

ϕ25 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . quarter-chord sweep angle, ◦

ϕ50 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . mid-chord sweep angle, ◦

ϕeff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . effective sweep angle, ◦

ϕLE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . leading-edge sweep angle, ◦

ϕref . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . sweep angle for 3D/2D transformation reference, ◦

ϕsh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . sweep angle at local shock position (x/c)sh, ◦

ϕTE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . trailing-edge sweep angle, ◦

ψ . . . . . . . . . . . . . . angle of wave number vector (with respect to streamwise direction), ◦

ψmax . . . . . . . . . . . . . . . . . . . . wave number direction ψ with most unstable disturbances, ◦

ωi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . temporal amplification rate, s−1

ωr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . circular frequency, s−1

XXIV List of symbols

Subscripts

∞ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . infinity (freestream conditions)

0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . initial

0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . reference

2D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . two-dimensional

3D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . three-dimensional

a/c . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . aircraft

AL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . attachment line

avg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . average

bkt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . bucket

c . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . chamber

c . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . chord

c . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . component

c . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . conical

CF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cross-flow

cmp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . compressor

crit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . critical

d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (suction) duct

des . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . design

dm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . design mission

duc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (pipe) ducting

e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . edge of boundary layer

eng . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . engine(s)

FP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . flat plate

fric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . friction

htp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . horizontal tailplane

IB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . inboard (wing)

in . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . inlet

ind . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . indifference

ind . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . induced

lam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . laminar

LE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . leading edge

List of symbols XXV

low . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . lower (airfoil) side

max . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . maximum

max ct . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . maximum continuous

mot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . motor

n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . normal

OB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . outboard (wing)

opt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . optimum

ov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . outflow valve

pres . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pressure

prof . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . profile

ref . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . reference

sm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . study mission

stag . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . stagnation point

T/O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . take-off

TE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . trailing edge

th . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . threshold

tot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . total

trans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . transition

TS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tollmien–Schlichting

turb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . turbulent

upp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . upper (airfoil) side

vfd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . variable-frequency drive

visc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viscous

w . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . wall (body surface)

w . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . wing

wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . wave

Superscripts

u . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . amplitude function

u . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . base flow quantity

u′ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . disturbance quantity

u′ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . nondimensionalized quantity

u′ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . wall-normal derivative ( ′ = ddz

)

XXVI List of symbols

Coefficients

Cd,airf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . airfoil (total) drag coefficient

CD,fric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . aircraft friction drag coefficient

Cd,fric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . airfoil friction drag coefficient

CD,ind . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . aircraft induced drag coefficient

CD,ind,w . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . wing induced drag coefficient

CD,misc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . aircraft miscellaneous drag coefficient

Cd,pres . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . airfoil pressure drag coefficient

CD,prof,w . . . . . . . . . . . . . . . . wing transonic profile drag coefficient (= Cd,visc,w + Cd,wave,w)

CD,total . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . aircraft (total) drag coefficient

CD,visc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . aircraft viscous drag coefficient

Cd,visc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . airfoil viscous drag coefficient

Cd,visc -p . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . airfoil viscous pressure drag coefficient

CD,visc,w . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . wing viscous drag coefficient

CD,w . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . wing (total) drag coefficient

CD,wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . aircraft wave drag coefficient

Cd,wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . airfoil wave drag coefficient

CD,wave,w . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . wing wave drag coefficient

cf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (local) skin friction coefficient

CL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . aircraft lift coefficient

Cl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . airfoil (or wing section) lift coefficient

CL,avg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . average cruise lift coefficient

CL,des . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . design lift coefficient

CL,htp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . horizontal tailplane lift coefficient

CL,max . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . maximum lift coefficient

CL,max,LDG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . maximum lift coefficient at landing

CL,max,T/O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . maximum lift coefficient at take-off

CL,opt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . optimum lift coefficient (at maximum L/D)

CL,w . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . wing lift coefficient

CM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . aircraft pitching moment coefficient

Cp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pressure coefficient

Cp,stag . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pressure coefficient at stagnation point

List of symbols XXVII

Cq . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . suction coefficient

Abbreviations

2.5Dc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . conical 2.5-dimensional

2D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . two-dimensional

3D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . three-dimensional

a/c . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . aircraft

ACN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . aircraft classification number

AFR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . additional fuel reserves

AiX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Aircraft Exchange (XML parameter file)

ALT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . attachment-line transition

ALTTA . . . . . . . Application of Hybrid Laminar Flow Technology on Transport Aircraft

App. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . appendix

APU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . auxiliary power unit

ATA . . . . . . . . . . . . . . . . . . . . Air Transport Association (now: Airlines for America, A4A)

ATC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . air traffic control

avg. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . average

BADA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Base of Aircraft Data

BC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . business class

BR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . brake release

CAD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . computer-aided design

CeRAS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Central Reference Aircraft data System

cf. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . compare (Lat.: confer)

CFD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . computational fluid dynamics

CFI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cross-flow instabilities

CFRP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . carbon fiber-reinforced plastic (or polymer)

CG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . center of gravity

Chap. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . chapter

CO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . carbon dioxide

COCO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . STABTOOL module for boundary-layer analysis

CSM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . computational structural mechanics

CSV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . comma-separated values

COC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . cash operating costs

XXVIII List of symbols

D1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . design approach 1 (retrofit design)

D2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . design approach 2 (component resizing)

DES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . detached eddy simulation

DLR . . . . . . . German Aerospace Center (Deutsches Zentrum für Luft- und Raumfahrt)

DNS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . direct numerical simulation

DOC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . direct operating costs

E/E bay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . electronic and equipment bay

EC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . economy class

ECS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . environmental control system

e.g. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . for example (Lat.: exempli gratia)

Eq. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . equation

EU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . European Union

Fig. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . figure

FL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . flight level

HIGHER-LE . . . . . . . . . . . . . . . . . . . . . . . . . . HIGH-lift Enhanced Research – Leading Edge

HLF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . hybrid laminar flow

HLFC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . hybrid laminar flow control

HLFD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . hybrid laminar flow (aircraft) design

HTP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . horizontal tailplane

HYLFAS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . HYbrid Laminar Flow Airfoil Suite

IATA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . International Air Transport Association

ICAO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . International Civil Aviation Organization

i.e. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . that is (Lat.: id est)

ILR . . . . . . . Institute of Aerospace Systems (Institut für Luft- und Raumfahrtsysteme)

ISA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . International Standard Atmosphere

ISO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . International Organization for Standardization

LEC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . leading-edge contamination

LES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . large eddy simulation

LFC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . laminar flow control

LILI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . LIFTING_LINE

LILO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . STABTOOL module for linear stability analysis

LINDOP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . MSES module for airfoil shape optimization

List of symbols XXIX

LuFo . . . . . . . . German Aeronautical Research Program (Luftfahrtforschungsprogramm)

NCFNTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . STABTOOL module for N -factor correlation

PrepCPCQ . . . . . . . . . . STABTOOL module for preprocessing of Cp and Cq distribution

MADS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . mesh adaptive direct search (algorithm)

MDO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . multidisciplinary design optimization

MEDP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . MSES module for semi-inverse airfoil design

MICADO . Multidisciplinary Integrated Conceptual Aircraft Design and Optimization

MLW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . maximum landing weight

MPI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Message Passing Interface

MSES . . . . . . . . . . . . . . . . . . . . multielement airfoil design/analysis system (2D flow solver)

MTOW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . maximum take-off weight

MWE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . manufacturing weight empty

NaN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . not a number

NASA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . National Aeronautics and Space Administration

NLF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . natural laminar flow

No. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . number

NOMAD . . . . . . . . . . . . . . . . . . . . Nonlinear Optimization by Mesh Adaptive Direct Search

OAD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . overall aircraft design

OEI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . one engine inoperative

ONERA . . . . . . . . . . . . . . . . . . . . . Office National d’Etudes et de Recherches Aérospatiales

OpenMP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Open Multi-Processing

OT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . offtake(s)

OWE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . operating weight empty

PAX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . passenger(s)

PSE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . parabolized stability equations

PSM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . parameter study manager

Q3D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . quasi-three-dimensional

RANS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Reynolds-averaged Navier–Stokes

Ref./ref. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . reference

Sec. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . section

SL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . sea level

SPP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . standard passenger payload

XXX List of symbols

SQL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Structured Query Language

SST . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . simple sweep theory

STABTOOL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Stability Tool

std. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . standard

TLAR(s) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . top-level aircraft requirement(s)

TOC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . top of climb

TOD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . top of descent

TS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tollmien–Schlichting

TSI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tollmien–Schlichting instabilities

Turb. BL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . turbulent baseline (aircraft design)

USAF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . United States Air Force

VFD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . variable-frequency drive

VLM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vortex-lattice method

VTP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vertical tailplane

W3C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . World Wide Web Consortium

XML . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Extensible Markup Language

XSD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XML Schema Definition

Imperial and other non-SI units

ASK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . available seat kilometer

dc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . drag count, 1 dc = 0.0001 CDft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . foot, 1 ft = 0.3048 m

kt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . knot, 1 kt ≈ 0.5144 m/s

lbf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pound force, 1 lbf ≈ 4.448 N

NM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . nautical mile, 1 NM = 1852 m

pp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . percentage point

1 Introduction

This thesis presents an integrated overall design approach for transport aircraft withhybrid laminar flow control (HLFC). Though facing a long history of research and

testing, as well as showing one of the greatest fuel saving potentials for conventionalcommercial aircraft, the HLFC technology has yet remained unfinished in exploiting itsfull potential within airline operations. However, with the first in-service operation of apassive HLFC system on the Boeing 787-9 empennage, and the currently highly increasingindustry and research development efforts, the way of the HLFC technology seems to bepaved for its most promising application, that is, the wings of future aircraft programs.

1.1 Motivation and problem statement

In the recent years and decades, highly ambitious goals have been proclaimed by differentstakeholders of the aviation industry to reduce its global environmental impact [72, 74].For instance, the “Flightpath 2050” objective to reduce CO2 emissions by 75 % until theyear 2050 (with reference to 2000) [74] poses strong requirements to manufacturers andoperators to increase aircraft fuel efficiency. For airlines, this is certainly accompaniedby the incentive of reduced operating costs due to lower fuel consumption. While airlinestogether with local and global authorities also focus on improvements of operational andair traffic management procedures, airframe and engine manufactures are elaborating oncontinuous efficiency improvements of the aircraft itself.

Yet, no radical configurational changes have been carried out or seriously scheduled,though some unconventional configurations (e.g., blended/hybrid wing bodies, or nonpla-nar wings) may promise leaps in fuel savings in the more distant future (2050+). For theclassical “tube-and-wing” configurations, the significant steps in fuel efficiency during thelast years could primarily be achieved by improved engine concepts (e.g., geared turbo-fans), where further improvements are still expectable (e.g., by open rotor concepts). Theother two main drivers to improve aircraft efficiency—i.e., reduced component masses andimproved aerodynamics—have rather faced an evolutionary improvement process overthe last decades. Literally speaking, this process is asymptotically approaching its opti-mum with the current state-of-the-art technologies. Aerodynamics, however, still offersan unredeemed promise for significant fuel burn reduction on today’s transport aircraft,which is the laminarization of aircraft surfaces to reduce friction drag.

The principle and high potential of this approach is getting obvious by looking at a typi-cal drag breakdown of a transport aircraft as exemplified in Fig. 1.1a. The left column of

1

2 Chapter 1. Introduction

the bar chart shows a typical drag breakdown, where the major contributors are viscous(friction plus form) drag as well as induced drag, which amount to more than half andto around one third of total aircraft cruise drag, respectively [264]. The viscous drag isfurther split up in the right column, showing which proportions originate from which air-craft component (see highlighted colors in the upper aircraft figure). One key to reducethis large drag share lies in maintaining the laminar state of the boundary layer, whichis usually fully turbulent under typical aircraft cruise conditions. The motivation behindthis laminarization is the significantly reduced friction drag in laminar boundary layerscompared to turbulent boundary layers. For the simple flow case around a flat plate,Fig. 1.1b illustrates this difference by showing the laminar and turbulent friction drag co-efficient1 Cd,fric as a function of Reynolds number. A friction drag reduction potential ofmore than 40 % is indicated, even if only half of the surface is laminarized2.

0

25

50

75

100

total drag breakdownby drag components

viscous drag breakdownby aircraft components

rela

tive

shar

e of

tot

al a

ircra

ft cr

uise

dra

g, %

friction drag

viscous pressure/form drag

induced drag

wave dragparasitic, interference

wing

horizontal tailplanevertical tailplane

nacellespylons, fairings

fuselage

appl

icab

ility

of

lam

inar

flow

tec

hnol

ogie

s

(a) Typical transport aircraft drag break-down and estimated potential for ap-plication of laminar flow technology, af-ter Schrauf [264]

0.000

0.001

0.002

0.003

0.004

0.005

0 10 20 30 40 50

frict

ion

drag

coe

ffici

ent

(flat

pla

te)

Cd,f

ric

Reynolds number Re, 106

-44% Cd,fric

fully turbulent boundary layer 50% lam. BL / 50% turb. BL fully laminar boundary layer

(b) Friction drag coefficient in laminar andturbulent boundary layers

0

10

20

30

40

0 10 20 30 40 50 60 70

lead

ing

edge

sw

eep

angl

e ϕ L

E, d

eg

Reynolds number Re, 106

NLF HLFC / LFC

NLF limitregion Tollmien−Schlichting

instability

cross-flowinstability

attachmentline transition

Flight testsA320 NLF LFC HLFC

757

AC data(wing MAC, FL330)

VFW-614

F-100

A320 fin

Falcon 50

Falcon 50+900

X-21AJetstar

787

(c) Laminar flow boundaries, instabilityregions [214], and flight tests [142]

Figure 1.1: Motivation, potential, and applicability of laminar flow technologies

The objective is thus to delay the transition from laminar to turbulent flow over the air-craft. This can reasonably be achieved on wing and tail surfaces as well as engine na-celles, while it is practically infeasible on the fuselage due to its high Reynolds numbersas well as on smaller components exposed to “unsmooth” flow such as pylons or fairings.The wing obviously offers the highest saving potential, but also involves very complex de-sign challenges. If—under favorable aerodynamic conditions—laminar flow can be estab-

1Though other notations are common in pure aerodynamic contexts (e.g., Cf or Cdf ), the friction dragcoefficient is herein denoted by Cd,fric to support distinct and consistent nomenclature for various com-binations and breakdowns of drag coefficients used throughout this thesis (see, e.g., Sec. 3.2.3 or Sec 3.3).

2The viscous pressure drag is additionally influenced via the boundary-layer thickness. Fundamentalaspects and relations of laminar flow and boundary-layer theory are discussed in more detail in Sec. 2.2.

1.1 Motivation and problem statement 3

lished on half of all prospected surfaces, the full drag reduction potential can roughly beestimated to 14 % from Figs. 1.1a and 1.1b, as it is similarly indicated in Refs. [233, 246].

On swept wings of transport aircraft, transition from laminar to turbulent flow is mainlygoverned by the following three phenomena: Tollmien–Schlichting instabilities (TSI),cross-flow instabilities (CFI), and attachment-line transition (ALT) [216]. They can oc-cur separately or in combination, which is strongly influenced by Reynolds number andwing sweep angle, as illustrated in Fig. 1.1c. If these key parameters take sufficiently lowvalues, transition can be passively delayed by means of airfoil shaping, which is callednatural laminar flow (NLF). However, susceptibility towards CFI/ALT and TSI becomesmore critical with increasing sweep angles and Reynolds numbers, respectively. The grayshaded band in Fig. 1.1c roughly represents the resulting NLF limit region, beyond whichpassive laminarization is no longer possible. However, remedy has early been found in thepossibility to actively stabilize the boundary layer by means of suction, which is calledlaminar flow control (LFC). As a more practicable approach, hybrid laminar flow control(HLFC) integrates the NLF and LFC concepts, by applying both airfoil tailoring as wellas suction, but the latter only ahead of the front spar. The different laminarization tech-niques will be explained in more detail in Sec. 2.2.6.

For most transport aircraft, the large dimensions and high transonic cruise Mach num-bers imply wing parameter combinations of sweep angle and Reynolds number, which arebeyond the applicability limits of NLF (see black circles in Fig. 1.1c). This underlines thestrong past and current interest of aviation industry in the HLFC technology. Fig. 1.1calso summarizes important NLF, LFC, and HLFC flight tests conducted over the lastdecades. One early key milestone in the realization of LFC was the X-21A flight test pro-gram conducted by the USAF and Northrop in the 1960s [202]. The interest in fuel ef-ficient technologies dramatically increased after the oil crises in the 1970s, followed by alarge number of LFC research and flight tests, including the HLFC patent in 1986 [101].Most relevant in the United States were the LFC flight tests on a Lockheed C-140 (Jetstar)testbed [81, 161], and the HLFC flight tests with a Boeing 757 [174]. In Europe, extensiveNLF flight tests have been conducted with the DLR VFW 614 / ATTAS aircraft [127], aFokker F-100 [313], and a Dassault Falcon 50 [40]. HLFC activities started at the end ofthe 1980s with successful flight tests on the Dassault Falcon 50 and 900 demonstrators, fol-lowed by the Airbus A320 HLF fin tests at the end of the 1990s [116]. Representative flightconditions of the mentioned test programs are marked in Fig. 1.1c, effectively showingthat no HLFC tests have yet been performed in the very high Reynolds number region oflarge passenger aircraft wings. Comprehensive overviews and results of laminar flow flighttests as well as wind tunnel test campaigns are, e.g., given in Refs. [38, 50, 111, 142, 261].

While decreasing oil prices during the 1990s were followed by a decline of industry ac-tivities and research programs, the realization of in-service laminar flow applications hasstrongly regained interest during the last decade. Boeing succeeded in bringing a passiveHLFC system on the vertical tailplane of the 787-9 [146], and is conducting further laminarflow tests on its 737 and 757 ecoDemonstrator testbeds [140]. However, it recently droppedthe HLFC system for its 777X program [191]. Airbus is also planning and conductingseveral laminar flow flight test campaigns, e.g., within the EU programs AFLoNext andCleanSky (A340 testbed) [267, 318]. To exploit the full potential of HLFC, it is predomi-

4 Chapter 1. Introduction

nantly applied to long range aircraft, because HLFC is primarily operated during cruise,and long range aircraft offer a very high ratio of cruise fuel to total mission fuel [233].

Though HLFC is clearly an aerodynamically driven concept, its realization is a highlyinterdisciplinary task. Especially the application of HLFC to the wing requires close designinteractions between aerodynamicists, as well as structural, systems, and overall aircraftdesigners. The central task of the aircraft designer is to design an aircraft for a given setof top-level requirements and optimally integrate and trade off different disciplines andconflicting requirements. Key measures to evaluate the net benefit of a new design or aninnovative technology are the consumed (block) fuel or the operating costs for the airline.For aircraft design with HLFC, the benefit due to viscous drag reduction is lowered by therequired suction system integration into wing (and tails) to enable active boundary-layercontrol. It results in both additional systems mass and electrical power requirement toestablish the suction mass flow through the outer surface. The required power is ultimatelyextracted as secondary shaft power offtakes from engines, which implicitly increases theirspecific fuel consumption. Further, laminar aerodynamic airfoil shaping and wing designcan impact wing structural mass, fuel storage capabilities, or trim characteristics.

An integrated treatment of this strongly multidisciplinary design task has to be (and canprobably only be) fulfilled at a preliminary design stage, before all aspects undergo de-tailed investigation. The significance of preliminary design within this context is under-lined by the IATA 2013 technology roadmap [135], which groups promising technologiesinto five categories with different time horizons3, where HLFC is assigned to the category“new design after 2020”. The entry into service of aircraft with HLFC wings can thus beprojected certainly after 2020, and probably even not before 2030. The possibility or eventhe need for a new design requires close cooperation between an integrated preliminaryoverall aircraft design and the different detailed design disciplines. This highly motivatesto develop an integrated preliminary overall design framework that allows efficient design,assessment, and optimization of HLFC aircraft for given requirements and objectives.

1.2 Related work in laminar aircraft design

The introductory discussion revealed both the high fuel saving potential and the com-plexity of applying (hybrid) laminar flow control to commercial aircraft. This is also re-flected by the large number of flight tests on the one hand, but the still missing in-serviceoperation of HLFC wings on the other hand. Key arguments to convince an airline of ap-plying HLFC are the promised fuel and cost savings. Numerous studies have been con-ducted to predict the benefits and design impacts of HLFC for different aircraft configu-rations. A comprehensive overview and discussion of results for relevant studies is givenby Joslin [142]. Predicted fuel savings mostly range between 10 and 20 %, while savingsin direct operating costs (DOC) stay below 10 %. The saving potential can differ stronglywith the specific aircraft configuration, mission requirements, and the extent of laminarflow achieved on different surfaces. Most of the studies focus on a retrofit design, which

3The 5 categories are: (1) retrofit, (2) production upgrade, (3) new design before 2020, (4) new designafter 2020, and (5) breakthrough technologies after 2030.

1.2 Related work in laminar aircraft design 5

means to analyze the impact of HLFC integration for a given (turbulent) baseline con-figuration. For example, Hood et al. [124] present an elaborated retrofit investigation forthe Boeing 757 aircraft, which was later followed by the 757 HLFC flight tests. The ap-plication of HLFC to the Airbus A310, A320, and A340 aircraft are studied by Bieler andSwan [30] and by Robert [233].

Though the retrofit design is important for a reliable evaluation of the HLFC potentialfor existing commercial aircraft, an integrated design procedure is required to exploit thefull HLFC potential by quickly performing investigations within a larger parameter space.This is especially important, because the specific properties of laminar aircraft implydifferent design trends, hence resulting in different optimum configurations [39, 205]. Thisthesis follows the motivation to identify these trends by an integrated HLFC aircraft designapproach on conceptual to preliminary design level, which requires combining classicalaircraft design capabilities with the following detailed HLFC design tasks:

• HLFC aerodynamic wing design (including transition prediction)

• HLFC system design and integration

• HLFC operational aspects

A detailed discussion on these HLFC-specific topics, including references with relevantapplications, will be given in Sec. 2.3. Fundamentals and state of the art of laminar flowtheory and transition prediction on swept wings will be provided in Sec. 2.2. Further,related work on the herein proposed (conventional) aircraft design methods will be givenin the course of Sec. 3.2. Let us here focus on related preliminary design approachesincluding elements of HLFC (or laminar flow in general) to identify and underline theneed for a new integrated HLFC aircraft design approach.

Table 1.1 presents four different approaches or applications, in which elements of bothaircraft design and laminar flow are considered (for brevity, the table only contains thefirst authors). In the table rows, different requirements for an integrated HLFC aircraftdesign are listed; the ticks indicate which methods comply with these requirements. Thisoverview is certainly not exhaustive, but covers the range of existing approaches, withapplication to both HLFC and NLF, and with different levels of detail.

Arcara Jr. et al. [15] used the NASA Flight Optimization System (FLOPS) [181] to studythe application of HLFC to a 300 passenger twin-engine aircraft. FLOPS contains relevantconceptual to preliminary design elements for mass estimation, aerodynamic analysis, andmission simulation. Also, mass and power consumption of the HLFC system are estimatedand considered for prediction of savings in block fuel and direct operating costs (DOC).However, the transition line on the wing is not predicted, but assumed to be fixed at 50 %relative chord on the wing upper surface and on the tails.

A comprehensive work on HLFC aircraft and its operational effectiveness is given by Young[325] (also discussing on results presented by Wilson [320]). Though several detailed as-pects are included (e.g., HLFC system design), the focus lies on retrofit application ofHLFC and operational investigations (including a computer code for block fuel prediction),

6 Chapter 1. Introduction

rather than on integrated aircraft or aerodynamic wing design. In his conclusions, Youngexplicitly mentions the need for an integrated sizing approach to specifically design HLFCaircraft for their optimum overall benefit and to exploit the aircraft resizing potential.

A recent work on the application of LFC to flying wing configurations, which is not listedin the table, is presented by Saeed [237]. Besides the application of different conceptualdesign methods, some of the required HLFC aspects are covered (e.g., an engine model, 2Dtransition prediction, or the suction system). However, crucial aspects for the applicationof (H)LFC to long range aircraft in terms of transonic drag prediction and transitionprediction on swept wings (including cross-flow instabilities) are not included.

Table 1.1: Overview of aircraft design methodsincluding NLF or HLFC

Arcara[15]

Youn

g[325]

Allison[9]

Seitz

[282]

HLFC X XNLF X X

Laminar flow design capabilitiesTransition prediction X XTransonic drag X

HLFC power/mass X XHLFC system design X

Overall aircraft design capabilitiesEngine model X X XMission analysis X X X XIntegrated design X

A more sophisticated and promising ap-proach in terms of integrated sizing ispresented by Allison et al. [9]. To in-clude natural laminar flow (NLF) into theirconceptual design framework PASS [152],they parameterize the airfoil pressure dis-tribution by several control points; tran-sition is predicted based on a quasi-three-dimensional boundary layer code. The in-tegration of laminar airfoil characteristicsinto conceptual design allows for rapid in-vestigation of different aircraft configura-tions and to implicitly design for optimumlaminar flow benefit. Still, the consideredconfigurations offer moderate Mach num-bers and sweep angles. The applicationof HLFC to long range aircraft, however,implies transonic laminar design of highlyswept wings, including the difficult bal-ance between viscous drag reduction andwave drag penalties, as well as betweenTollmien–Schlichting and cross-flow insta-bilities. The required careful shaping ofsuction and especially pressure distribution(see Sec. 2.3.1) cannot be fulfilled anymore by a simple parameterization. Further, HLFCinvolves the additional complexity of suction system sizing and integration. Nevertheless,the approach by Allison et al. [9] is outstanding in its integrated sizing approach.

The application of NLF to a short-range aircraft with forward-swept wings was investi-gated in the DLR LamAiR project [282]. Among the approaches in table 1.1, it coversthe most detailed design aspects, for example, Navier-Stokes computations, inverse wingdesign, 3D transition prediction (including TSI, CFI, and ALT), and aeroelastic tailoring.The preliminary design of the overall aircraft configuration is performed with the softwarePrADO [115]. However, despite (or because of) the high level of detail, aerodynamic wingdesign and transition prediction are decoupled from the aircraft design framework, so that

1.3 Thesis objectives and approach 7

no integrated sizing is allowed. Further NLF and HLFC design applications with a similarlevel of detail and the main focus on aerodynamic wing design are given in Refs. [103, 281].

The approaches by Allison et al. [9] and Seitz et al. [282] both underline the importanceof laminar wing design, which is also considered by the author as crucial missing elementin HLFC preliminary aircraft design. Several detailed laminar wing design methods existincluding automated transition prediction and optimization of wing geometry (see, e.g.,Refs. [296, 167, 209]). However, the presented approaches are not included in an aircraftdesign context, and therefore not further discussed.

From table 1.1 and the discussions above, it is evident that a complete solution of theintegrated HLFC aircraft design task is not existing yet. Though the presented approachespartly fulfill the specified requirements, they either focus on conceptual design and handlecrucial aspects by rough assumptions (e.g., constant transition location) [237, 325, 15];or, detailed methods (e.g., for 3D transition prediction) are included, but they are notapplicable to HLFC [9], or they are not included into an integrated sizing process [282].

The latter aspects exactly concern the main crux and complexity, which have yet impededa successful solution of the integrated HLFC aircraft design task: that is, any variation inkey conceptual design parameters (such as cruise Mach number or wing sweep angle) im-plies a change in design requirements for both HLFC aerodynamic wing design and sys-tem sizing. The complexity of instability mechanisms for three-dimensional flows aroundswept wings requires sophisticated transition prediction codes, which are usually not ap-plicable to automated conceptual or preliminary design. Further, HLFC system designrequires knowledge about pressure and suction distributions, which are also not availablein preliminary design. Therefore, both (aerodynamic and system design) tasks are so farsubject to detailed design and performed manually; subsequently, the computed aerody-namic benefits or system mass and offtakes can be applied to the preliminary design. Sucha decoupled approach still allows performing retrofit or stepwise designs. However, over-all design parameter variations to exploit the full potential of HLFC, including resizingof the overall aircraft configuration, can only be performed by a fully integrated HLFCaircraft design approach.

1.3 Thesis objectives and approach

It is the main task and objective of this thesis to fill the identified gap between detailedHLFC design and preliminary overall aircraft design. This requires a sophisticated solu-tion that covers all relevant overall aircraft design disciplines and interdependencies, aswell as the capability to perform accurate and consistent transition and laminar drag pre-diction, and to integrate a proper suction system. To develop a suitable method, the fol-lowing (intermediate) objectives are stated for the present thesis:

1. development of a flexible preliminary overall aircraft design environment, includingall relevant disciplines and interfaces for integrated HLFC aerodynamic wing designand suction system sizing

8 Chapter 1. Introduction

2. development of robust methods for HLFC transonic aerodynamic design of swept-tapered wings (including transition prediction), as well as for HLFC suction systemcomponent sizing and integration

3. creation of inherent connections between the enhanced HLFC aerodynamic andsystem design methods and the overall aircraft design platform

4. demonstration of method validity and applicability by performing parameter studiesto find overall design optima for long range aircraft with integrated HLFC systems

Thus, the integrated HLFC aircraft design framework is developed to solve the followingtwo central tasks:

• retrofit design and assessment for optimum integration of HLFC systems

• integrated overall aircraft design for maximum benefit of HLFC on aircraft level

As discussed above, the second task has yet remained unsolved, and therefore representsthe outstanding feature of the proposed integrated HLFC aircraft design method andframework. More detailed discussions on these design tasks and on further requirementsto the specific included methods will be discussed in the course of the following chapters.To achieve the stated objectives, the thesis follows the approach and structure shortlyoutlined below.

Since HLFC aircraft design requires profound understanding of laminar flow theory aswell as HLFC design principles and challenges, fundamental aspects along with compre-hensive literature for further reading are reviewed in Chap. 2. In Chap. 3, the developedHLFC aircraft design method is described in detail. The proposed MICADO4 framework(Sec. 3.1) is based on a flexible and modern software architecture and comprises designand analysis methods for all relevant disciplines (Sec. 3.2). The enhancement of MICADOby the more detailed HLFC aerodynamic wing and system design methods is discussed inSecs. 3.3 and 3.4, respectively. The developed HLFC aerodynamic wing design methodHYLFAS5 and its interconnection to MICADO via a quasi-three-dimensional approachand an HLFC airfoil database constitute a key achievement of this thesis. The includedEuler/boundary-layer flow solver MSES (Sec. 3.3.4) and the STABTOOL suite for tran-sition prediction (Sec. 3.3.5) provide reliable coverage of instability mechanisms and suc-tion distribution for robust and consistent prediction of laminar drag polars and pressuredistributions. Chapter 4 demonstrates applicability and validity of the integrated HLFCaircraft design method, including single-point design evaluations as well as overall designstudies and optimizations. First, a turbulent design of a long range baseline configurationis presented. Successively, HLFC retrofit and resizing studies at selected design pointsare investigated. Finally, integrated HLFC aircraft design studies are presented, to ana-lyze overall HLFC aircraft optima and thus address the above formulated objective. Mostimportant achievements and results are recapitulated and concluded in Chap. 5, finallyfollowed by an outlook including recommendations for related future work.

4Multidisciplinary Integrated Conceptual Aircraft Design and Optimization5HYbrid Laminar Flow Airfoil Suite

2 Fundamentals and state of the art

This thesis presents a holistic approach towards overall aircraft design with hybridlaminar flow control. The discussion of the developed method in Chap. 3 requires

a profound understanding both of the relevant preliminary aircraft design disciplines, aswell as of HLFC physics and integration aspects.

In this sense, this chapter first introduces some fundamental principles of preliminaryaircraft design in Sec. 2.1. More detailed aspects of the different disciplines are discussedin the context of the implemented aircraft design and analysis methods in Sec. 3.2.

The fundamentals of boundary-layer transition and linear stability theory are introducedin Secs. 2.2.1 to 2.2.3, with two main purposes: first, to give an understanding of theapplied eN method for transition prediction (Sec. 2.2.4), to which linear stability theoryis immanent; second, to explain the physical origins and mechanisms of the instabilitiesleading to transition on swept wings (Sec. 2.2.5), as well as suitable techniques to controlthem (Sec. 2.2.6).

From the fundamentals of laminar flow theory, concrete guidelines for the aerodynamic de-sign of hybrid laminar flow wings can be derived. These are shortly discussed in Sec. 2.3.1and later applied for the proposed HLFC wing design methodology (Sec. 3.3). Apart froma well-balanced aerodynamic design, it is very important to consider HLFC integrationand operational aspects, which can significantly complicate the overall design and reduceits net benefit. This first involves the sizing of HLFC system components and their spaceallocation in the wing nose section, together with a suitable high-lift system (Sec. 2.3.2).Further, appropriate devices to fight ice and insect contamination have to be integrated,which otherwise can cause premature transition during aircraft operations (Sec. 2.3.3).

2.1 Fundamentals of preliminary aircraft design

The central task in preliminary (commercial) aircraft design is to size an aircraft towardsa given set of top-level aircraft requirements (TLARs). The two main TLARs, which areinitially derived during market analyses (e.g., by studies of desired city pairs), are thedesign range R and a standard passenger payload (mass) mSPP . Speaking in terms ofphysical work, it is thus the task of the aircraft to transport a given payload over a givenmission range, or to do the transport work1 W = mSPP g R.

1The physical work is here denoted by W to distinguish it from the weight force W . Further, g denotesthe acceleration of Earth’s gravity with the constant value of g = 9.80665 m/s2 throughout this thesis.

9

10 Chapter 2. Fundamentals and state of the art

take-off requirements

cruise requirements

climb requirements

approach and landing requirements

Figure 2.1: Mission with top-level aircraft re-quirements and cruise force equi-librium (schematic, not to scale)

On the design mission, further TLARshave to be fulfilled according to the differ-ent mission phases as shown in Fig. 2.1.The key requirement for cruise is the initialcruise Mach number2 Mcr, which is usuallymaintained during the whole cruise phase.For the take-off phase, the take-off fieldlength (TOFL) requirement has to be re-spected, as well as minimum climb gradi-ents in different take-off segments as speci-fied by the certification authorities [70, 80].The climb is commonly performed with afixed climb speed schedule3 until reachingthe initial cruise altitude hICA at the topof climb (TOC). The combination of hICAwith a required time to climb to this alti-tude (TTC) implicitly defines the climb capability4 of the aircraft by means of engine per-formance, which can be expressed by the ratio of total engine thrust T to aircraft grossweight W , called thrust-to-weight ratio T/W . This key sizing parameter has to be se-lected such that it also fulfills take-off and cruise requirements, where the strong depen-dence of thrust on flight altitude h and Mach number M has to be considered. The otherkey sizing parameter is the wing loading W/S, which determines the wing reference areaS = Sref . The wing loading is mainly sized by cruise, take-off, as well as approach andlanding requirements, where the latter are given in terms of a minimum approach speedVapp and a landing distance limit LDL.

In addition to these key mission performance requirements, the TLARs can compriselimitations concerning airport operations (e.g., maximum wing span) or the boundariesof the flight envelope (e.g., maximum operating speed VMO and Mach number MMO,maximum operating altitude hop,max). From the TLARs and specifications, more specificstructural (e.g., dive speed) or aerodynamic (e.g., stall speed, buffet onset) requirementscan then be derived for preliminary component design. It may be noted that the specificlist of TLARs is not unique and parameters may be defined in different ways; however,they should always allow initiating the aircraft design process. More precise definitionsand boundary conditions of the herein used TLAR parameters [114] will be given in thecontext of the proposed design methods and applications, see Chaps. 3 and 4.

The initial sizing process can be summarized as the task to determine a combinationof the key sizing parameters W/S and T/W such that all TLARs are fulfilled. A firstselection (out of many possible) can be done using the well-known sizing charts in terms ofT/W = f (W/S), in which the limiting lines represent the different TLARs. The objectiveof the subsequent aircraft design process is to find combinations of W/S, T/W , and other

2The Mach number (M = Va ) is defined as the ratio of the aircraft speed V to the local speed of sound a.

3The climb speed schedule is commonly segmented into: (1) a constant calibrated airspeed (CAS) below10000 ft, which is limited by air traffic control (ATC), (2) an increased CAS above 10000 ft, and (3) theclimb Mach number Mcl above crossover altitude (i.e., where Mcl corresponds to the second CAS) [8].

4Another climb requirement concerns the reachable altitude with one engine inoperative hOEI,max.

2.1 Fundamentals of preliminary aircraft design 11

key design parameters that are optimal with respect to a selected evaluation measure,e.g., the block fuel5 (BF = mBF ) or the cash or direct operating costs (COC, DOC). Adetailed discussion on how this design task is solved and implemented within the proposedaircraft design method is given in Secs. 3.1 and 3.2.

To only roughly expose the main drivers to optimize an aircraft design with respect tominimum block fuel, the aircraft can be considered as fuel efficient if it performs thementioned transport work W with a minimum amount of fuel, i.e., if the specific workw = mSPP gR

mBFis maximized. Similarly, the specific (air) range SAR is a commonly used

measure to continuously maximize fuel efficiency during flight (for a given aircraft withconstant payload). It is hence defined as the covered distance s per fuel mass unitmf [248];i.e., for an infinitesimally small time t, it is SAR = ds/dt

dmf/dt= V

mf, with the aircraft speed

V and the rate of decrease in fuel mass mf . Applying the equilibria of thrust and dragforce (T = D) and of lift force and weight (L = W ) during cruise (see Fig. 2.1), as wellas the definition of specific fuel consumption (SFC = mf

T), SAR can be rewritten as

SAR =

ISA︷︸︸︷a

aerodynamics︷ ︸︸ ︷M L/D

SFC︸ ︷︷ ︸engine

W︸︷︷︸weight

. (2.1)

Interestingly, this equation identifies the three basic modifiers to maximize SAR and thusfuel efficiency: (1) an improvement of aircraft aerodynamics in terms of an increased prod-uct of Mach number and lift-to-drag ratio M L/D, (2) a more efficient engine in terms ofa reduced SFC, and (3) a reduced gross weight W , e.g., by applying lighter structures.Further, atmospheric influences have to be taken into account, which are represented bythe International Standard Atmosphere (ISA) model6 [136, 189] throughout this thesis.The SAR parameter will be revisited in the context of optimum selection of cruise alti-tudes in Sec. 3.2.6. The same design drivers as in Eq. (2.1) can be identified from the well-known Breguet range equation. Evidently, behind these simple but useful equations, thecomplex dependencies of the key parameters on aircraft geometry, engine thermodynam-ics, flow conditions, etc., open up a multidisciplinary design optimization (MDO) prob-lem. An efficient solution of this MDO problem requires a flexible and modular softwarearchitecture, as it is established for the proposed aircraft design method (see Sec. 3.1.1).Further, sizing of airframe components and engines, as well as analyses within differentdisciplines (e.g., aerodynamics, masses, performance) have to implemented into appropri-ate methods (see Sec. 3.2). The automated execution of different program modules ac-cording to a specific overall design logic (see Sec. 3.1.2) completes the framework for effi-cient aircraft design parameter studies and optimizations.

Compared to the classical overall aircraft design (OAD) problem, the design towards anoptimally integrated HLFC system introduces additional complexities. First, HLFC inte-gration affects all disciplines given in Eq. (2.1), because the aerodynamic benefit achieved

5The term block fuel is defined in analogy to the block time, which is the time from brake release at thedeparture airport (“off blocks”) to the engine shut-down at the destination airport (“on blocks”).

6The U.S. [189], ICAO, and ISO [136] standard atmosphere models are identical for altitudes h < 32 km.

12 Chapter 2. Fundamentals and state of the art

by laminarization is lessened due to the integration of the HLFC system components, in-volving additional weight and power requirements (thus increased SFC). Second, cap-turing these effects requires the implementation of methods that are usually not availablein preliminary aircraft design. This concerns the sizing and integration of the HLFC sys-tem, and, most notably, the aerodynamic design and analysis of laminar wings, includingtransition prediction. The following sections introduce the theoretical background to ap-ply suitable methods to consider laminar wings within preliminary aircraft design.

2.2 Laminar flow theory

The motivation for the application of the HLFC technology to wings of transport aircraftis the high fuel saving potential through the reduction of friction drag. This is achieved bydelaying transition to maximize the area of laminar flow around the wing. It is thereforeimportant for the designer to understand the flow physics behind the phenomena of thelaminar-turbulent transition process, and to know suitable mathematical models to de-scribe it. The following sections provide both physical and mathematical insight into thesubject of laminar flows and transition. Since transition is inherently related to viscousflows and boundary layers, the respective fundamentals and equations are introduced first.

It may generally be noted that—facing the long history of research on the subject oflaminar flow control—only a very short summary can be provided in the scope of thisthesis. For a more detailed investigation, the reader may refer to the references citedduring the following discussions. Very comprehensive insights and overviews for the topicsof boundary-layer theory, transition prediction, and laminar flow control are, for example,given by Schlichting and Gersten [250], Arnal [17], and Joslin [142], respectively.

2.2.1 Viscous flows and boundary-layer theory

edge of boundary layer

Figure 2.2: Schematic of boundary layer on aflat plate with parallel flow, af-ter Schlichting and Gersten [250]

In inviscid, incompressible, irrotationalflow, a closed two-dimensional body7 expe-riences zero drag, as stated by d’Alembertin his well-known paradox. The finite dragof a body measured in reality, however, canonly be predicted using viscous flow the-ory [11]. Compared to inviscid flows, whereonly normal (or pressure) forces are consid-ered, the main difference of viscous flows isthe additional presence of shear forces dueto the frictional interaction between bodyand fluid. The second important character-istic of viscous flows is the so-called no-slipcondition, that is, the flow velocity is zero exactly at the body surface [11]. The thin layer

7This section exclusively treats external flows over bodies; internal flows are, e.g., discussed in Ref. [11].

2.2 Laminar flow theory 13

close to the wall, in which the velocity develops a certain profile—from zero at the wall tothe finite freestream velocity U∞—is called the boundary layer, as introduced by Prandtlin 1904 [210]. For the two-dimensional flow around a flat plate with the freestream velocityU∞, the development of the boundary-layer thickness8 δ(x) and the boundary-layer veloc-ity profile u(x,z) at a fixed x position are schematically illustrated in Fig. 2.2. It is impor-tant to see the thickening of the boundary layer with increasing x position, and that u(x,z)asymptotically approaches the freestream velocity at the edge of the boundary layer, i.e.,ue = u (x, δ(x)) = U∞. Because of this asymptotic behavior, the boundary-layer thick-ness is virtually defined as δ99, which is the distance from the wall, where u = 0.99ue [11].

According to Newton’s friction law, the shear stress at the wall τw results from the pre-vailing velocity gradient

(dudz

)w[250],

τw (x) = µ

(du

dz

)w

, (2.2)

where the proportionality factor µ is the dynamic viscosity of the fluid. In addition tothe freestream velocity U∞ and the viscosity µ, a viscous flow is physically characterizedby its density ρ and a characteristic length l. The dimensionless Reynolds number [224]combines these parameters by the following expression:

Re = ρU∞l

µ= U∞l

ν, (2.3)

where ν = µρdenotes the kinematic viscosity. The Reynolds number can be interpreted as

the ratio of the inertia force to the friction force of a viscous fluid, which has to be keptconstant to maintain mechanical similarity between two incompressible flows around twogeometrically similar bodies. Further, the Reynolds number strongly influences whethera viscous flow is laminar or turbulent (see Sec. 2.2.2) [250].

As relation for the laminar boundary-layer thickness, the equilibrium of inertia and vis-cous forces yields δ (x) ∼

√νxU∞

, where the proportionality factor approximately equals5 according to the Blasius (flat-plate) solution for δ99, thus δ99(x)

x≈ 5√

Rex[250]. Further

characteristic boundary-layer parameters, which are more commonly used due to theirdistinct definitions (here written for compressible flows), are the displacement thickness

δ∗ (x) =∞∫

0

(1− ρu

ρeue

)dz (2.4)

and the momentum thickness

θ (x) =∞∫

0

[ρu

ρeue

(1− u

ue

) ]dz. (2.5)

8Correctly speaking, δ(x) denotes the velocity boundary-layer thickness that is mostly smaller than thethermal boundary-layer thickness defined via the development of the temperature profile T (x, z) [11].

14 Chapter 2. Fundamentals and state of the art

Correspondingly, the Reynolds numbers Reδ∗ and Reθ are defined by inserting δ∗ and θas characteristic length l in Eq. (2.3), respectively. The ratio of δ∗ to θ is defined as theso-called shape factor

H12 (x) = δ∗ (x)θ (x) . (2.6)

Since δ∗ and θ are noticeably larger in turbulent than in laminar boundary layers, theparameters introduced in Eqs. (2.4) to (2.6) can be used as measures for the detection oflaminar-turbulent transition (see Sec. 2.2.4). For detailed definitions and explanations,the reader may refer to the standard literature of aerodynamics and boundary-layer theory(see, e.g., Refs. [11, 250, 251]).

Laminar boundary-layer equations

The boundary-layer theory introduced by Prandtl divides viscous flows at high Reynoldsnumbers into two regions: first, the very thin boundary layer close to the wall, where thefluid viscosity has to be considered to guarantee the no-slip condition; second, the inviscidfar-field, where the viscosity is assumed to be small so that it can be neglected [250].

From a mathematical point of view, the introduction of Prandtl’s boundary-layer as-sumptions to the Navier–Stokes equations9 allows deriving a simplified formulation, theboundary-layer equations. The first assumption is that the boundary layer is very thincompared to the characteristic length l (i.e., δ′ = δ/l � 1). Further, boundary-layer the-ory applies to fluids with very large Reynolds numbers (i.e., Re → ∞). Consequently,the terms of order O (δ′) or smaller in the Navier–Stokes equations can be neglected. Fora two-dimensional (2D), steady, compressible flow with the velocity components u and win x and z direction (see Fig. 2.2), the laminar10 boundary-layer equations are obtainedin the following form [11]:

continuity: ∂ (ρu)∂x

+ ∂ (ρw)∂z

= 0 (2.7)

x-momentum: ρ

(u∂u

∂x+ w

∂u

∂z

)= −dp

dx+ ∂

∂z

(µ∂u

∂z

)(2.8)

z-momentum: 0 = −∂p∂z

(2.9)

energy: ρ

(u∂h

∂x+ w

∂h

∂z

)= u

dp

dx+ ∂

∂z

(k∂T

∂z

)+ µ

(∂u

∂z

)2

, (2.10)

9The derivation and formulation of the Navier–Stokes equations is, for example, given by Anderson [11].10Note that in comparison to the laminar boundary-layer equations, the turbulent formulation containsthe time-averaged mean velocity components and additional turbulent stress terms based on Reynolds’shypothesis. The resulting equation system can be closed by the application of a suitable turbulencemodel. The treatment and numerical analysis of the boundary-layer equations is generally much moredifficult for the turbulent case due to the highly complex nature of turbulent flows. [250]

2.2 Laminar flow theory 15

where the viscosity µ(T ) and the thermal conductivity k(T ) are temperature-dependentfluid characteristics.

The zero pressure gradient in wall-normal direction in Eq. (2.9) implies that the freestreampressure remains constant from the boundary-layer edge to the surface wall at a fixed xposition, i.e., p(x) = pe(x) = pw(x). The connection of the two “separate” flow regionsby an inviscid external pressure “impressed” to the boundary layer is significant, as the“outer” flow can be solved using an inviscid approach (e.g., based on the Euler equations),and then be coupled to the “inner” viscous solution of the boundary-layer equations [250].This procedure is implemented in the flow solver MSES, which is applied within thisthesis for the prediction of viscous and wave drag (see Sec. 3.3.4). The principle ofan “impressed” pressure has also practical importance for the design of laminar airfoilsthrough the provision of appropriate geometry shapes, as it will be discussed later in thischapter.

The solution of the boundary-layer equations for the flow variables u, w, ρ, T , and theenthalpy h—by respecting the mentioned boundary conditions at the wall (no slip) andat the boundary-layer edge—yields the temperature and velocity profiles of the laminarboundary-layer flow11. These are especially required for the solution of the linear stabilitydifferential equations introduced in Sec. 2.2.3. Within the proposed HLFC design method,the boundary-layer equations enhanced for three-dimensional (3D), conical flow aroundswept, tapered wings are numerically solved using the program COCO (see Sec. 3.3.5).

Friction drag

The temperature and velocity profiles obtained from the solution of the boundary-layerequations are of further practical importance for the determination of shear stress andheat transfer. Here, we focus on the shear stress τw, which is connected to the wall-normalvelocity gradient via Eq. (2.2), and which yields the local skin friction coefficient [11]

cf (x) = τw (x)12ρU

2∞. (2.11)

As an important result of the boundary-layer theory, the total skin friction drag coefficientCd,fric is finally obtained by integrating the local coefficients cf (x) over the body. Thefriction drag of aircraft surfaces is much higher in turbulent than in laminar boundarylayers. The reasons are an increased shear stress in turbulent boundary layers due to theprevailing “fuller” velocity profiles with stronger gradients near the wall (τw ∼

(dudz

)w),

and an increased particle exchange due to the highly fluctuating turbulent motion. For anincompressible, two-dimensional flow over a flat plate at zero incidence and with the chordReynolds number Rec, for example, the Blasius solution of the laminar boundary-layer

11The two missing equations to achieve a determined equation system for the five unknowns follow fromthe assumption of the air being a calorically perfect gas, i.e., p = ρRT and h = cpT , with the specific gasconstant R ≈ 287 J

kgK and the specific heat capacity cp of dry air at standard conditions [11].

16 Chapter 2. Fundamentals and state of the art

equations (2.7)–(2.9) results in Cd,fric,lam = 1.328 Re−12

c , while for a turbulent boundarylayer, the relation Cd,fric,turb = 0.074Re−

15

c can be derived [274].

The significant difference of friction drag in laminar and turbulent boundary layers leadsto the motivation to maximize the amount of laminar flow, e.g., around a wing. For asatisfactory treatment of this task, the following questions remain, which are discussed inthe following sections:

1. How does a laminar flow develop into a turbulent flow (Sec. 2.2.2)?

2. How can this transition be modeled and predicted (Secs. 2.2.3 and 2.2.4)?

3. How can the transition on a swept wing be controlled and delayed to maximize theextent of laminar flow (Secs. 2.2.5 and 2.2.6)?

2.2.2 Laminar-turbulent transition

The term laminar-turbulent transition denotes the transitional process from a laminar toa turbulent boundary-layer flow. The transition phenomenon was first discovered in 1883by Reynolds [224]; from his famous dye experiments he derived the hypothesis that thetransition from laminar to turbulent flow happens at a certain (critical) Reynolds number.Besides the Reynolds number, the laminar-turbulent transition has been shown to dependon many other parameters, which are predominantly the pressure distribution in theexternal flow, the surface roughness, and the freestream turbulence intensity [250]. Furthersensitivities along with active boundary-layer control techniques to delay transition arediscussed in Sec. 2.2.6.

For the simple case of the flow over a flat plate, Fig. 2.3 shows the different stages and flowphenomena that occur in the boundary layer during the transition process from stablelaminar flow (1) to fully turbulent flow (6).

1 2 3 4 5 6

Laminar TurbulentTransition

(1) stable laminar flow

(2) unstable disturbance waves

(3) nonlinear effects: 3D waves andvortex formation (Λ structures)

(4) 3D vortex breakdown

(5) formation of turbulent spots

(6) fully turbulent flow

Figure 2.3: Laminar-turbulent transition in the boundary layer on a flat plate at zeroincidence [250, 319]

2.2 Laminar flow theory 17

The transition process is initiated by the so-called receptivity [187], that is, external dis-turbances are brought into the developing boundary layer, where they excite disturbancewaves12. The disturbance waves superimpose the laminar base flow and become unstableat the indifference Reynolds number Reind. The linear wave amplification (2) and the be-longing primary instability mechanisms can theoretically be modeled by the linear stabil-ity theory (see Sec. 2.2.3). Farther downstream, secondary instabilities cause the forma-tion of nonlinear, three-dimensional waves and flow interactions forming the characteristicΛ vortex structures (3). The breakdown of these vortices (4) leads to the first occurrenceof turbulent structures in the form of the so-called Emmons spots (5). The turbulent spotsfinally develop into a fully turbulent flow at the critical Reynolds number Recrit [17, 250].

The longitudinal distance of the transition regime between the Reynolds numbers Reindand Recrit (see Fig. 2.3), together with the sensitivity of transition to surface and flowparameters, implies the difficulty to define a distinct streamwise transition location. Areliable and consistent prediction of the transition location, however, is crucial for lam-inar wing and aircraft design applications. Within this thesis, the well-established eN

method is applied for transition prediction. Before this method is described in Sec. 2.2.4,the underlying (primary) linear stability theory is introduced.

2.2.3 Linear stability theory

The described laminar-turbulent transition process can be considered as a stability prob-lem, in which a laminar boundary-layer flow is exposed to external disturbances. At lowReynolds numbers, the excitations of the disturbance waves can be damped by the pre-dominating viscous forces (ν ∼ Re−1); the flow is then considered as stable. With in-creasing Reynolds number, the viscous damping effect reduces, which leads to an unsta-ble wave amplification and finally to laminar-turbulent transition [250].

Disturbance ansatz and Orr–Sommerfeld equation

The primary13 linear stability theory analyzes the stability of a laminar boundary-layerflow by dividing it into a steady base flow, which is superimposed by a flow with unsteadydisturbances. A three-dimensional flow around an arbitrary body may be considered,using a Cartesian or curvilinear coordinate system (x,y,z), with z in wall-normal direction.Any variable q of the resulting superposed flow can then be written as

q (x, y, z, t) = q (z) + q′ (x, y, z, t) , (2.12)

where q can be a velocity component (u, v, w) in (x, y, z) direction, as well as pressurep, density ρ, or temperature T . The bar symbol ¯ refers to base flow quantities and the

12For the 2D flow over a flat plate, these waves are called Tollmien–Schlichting waves. The more complexcase of 3D flows on swept wings along with predominating instability mechanisms is discussed in Sec. 2.2.5.

13The primary stability theory considers the undisturbed boundary-layer flow as base flow, while thesecondary stability theory starts from the disturbed state within the unstable boundary layer [250].

18 Chapter 2. Fundamentals and state of the art

prime symbol ′ represents fluctuating quantities of the unsteady disturbance flow. Sincethe latter are commonly regarded as sinusoidal disturbances, the following ansatz holdsfor three-dimensional flows [17]:

q′ (x, y, z, t) = q (z) ei(αx+βy−ωt), (2.13)

where the complex amplitude function q only depends on the wall-normal coordinate z.The meaning of the complex numbers α, β, ω depends on whether the linear stabilitytheory is considered from the temporal or from the spatial point of view. In the contextof the temporal theory, α and β are real wave number components in x and y direction,and ω = ωr + i ωi is a complex quantity with the temporal amplification rate ωi. Fromthe spatial point of view, the circular frequency ωr is real, and α and β are complex withthe amplification numbers αi and βi [17].

Both the base and the disturbance flow are considered as solutions of the Navier–Stokesor the boundary-layer equations. The disturbances are assumed to be small such that dis-turbance terms of second order O2 can be neglected in the Navier–Stokes equations. An-other important assumption in linear stability theory is the parallel-flow approximation,that is, the vertical velocity component of the base flow w is small compared to the wall-parallel components u, v (thus w = 0), and the derivatives of u, v, p, T with respect tox and y can be neglected (q = q (z), see Eq. (2.12)). The parallel-flow approximationthus neglects nonparallel effects such as the thickening of the boundary layer and im-plies a local consideration of the stability problem [17, 258]. By applying all assumptionsto the Navier–Stokes equations, simplified representations of the momentum equationsare obtained. Eliminating the pressure terms and inserting the harmonic disturbanceansatz (2.13) and its partial derivatives, finally yields the Orr–Sommerfeld [196, 288] equa-tion, a fourth order ordinary differential equation, which is here given for incompressiblethree-dimensional flows [292]14:

(αu+ βv − ω)(w′′ − γ2w

)− (αu′′ + βv′′) w = − i

Re

(w′′′′ − 2γ2w + γ4w

). (2.14)

Note that γ =√α2 + β2 is only used as a short notation and that the prime sign ′ is here

used as an abbreviation for the wall-normal derivative ( ′ = ddz

), and not as a fluctuatingquantity. The Orr–Sommerfeld equation states an eigenvalue problem with the complexvelocity eigenfunction w (z). The left-hand equation terms originate from the inertiaterms and the right-hand terms from the viscous terms of the Navier–Stokes equations.For two-dimensional (β = 0, v = 0), inviscid ( 1

Re→ 0) flows, Eq. (2.14) degenerates to

the Rayleigh equation [250].

An important conclusion from Rayleigh’s frictionless stability equation has been theso-called point-of-inflexion criterion15, saying that velocity profiles are unstable if they

14The 3D Orr–Sommerfeld equation is solved together with the Squire and the continuity equation [292].15The existence of an inflexion point in the velocity profile has been stated by Lord Rayleigh [171] asnecessary—and later by Tollmien [305] as sufficient—condition for (frictionless) instability. It also holdsfor viscous boundary-layer profiles, which, however, can even be unstable without inflexion point. Apartfrom being unstable, velocity profiles with an inflexion point are also susceptible to separation [250].

2.2 Laminar flow theory 19

have an inflexion point, i.e., their wall-normal second derivatives ∂2u∂z2 exhibit a change

of sign [250]. According to the wall condition of the boundary-layer x-momentum equa-tion16 (2.8), this is always true for flows exhibiting a positive pressure gradient ( dp

dx> 0),

since then(∂2u∂z2

)w> 0, while

(∂2u∂z2

)z→ze

< 0 always holds. Conversely, a negative pressuregradient ( dp

dx< 0) is favorable, because the corresponding velocity profile has no inflexion

point, which stabilizes the boundary-layer flow. This makes the point-of-inflexion criterionvery significant for the shaping of pressure distributions in laminar airfoil and wing design(see Sec. 2.3.1). In this context, recall that the inviscid external pressure distribution canbe considered as being impressed to the boundary-layer flow as discussed in Sec. 2.2.1.

Differential equation system for compressible flows

For three-dimensional compressible flows, there is no unique, canonical formulation ofthe linear stability equations due to the additional density parameter. Eliminating thelatter, Schrauf [258] presents a linear system of ordinary differential equations for theamplitude functions u(z), v(z), w(z), p(z), T (z), with four second-order, and one first-order differential equation:

d2

dz2

u(z)v(z)w(z)

0T (z)

+ A(α, β) d

dz

u(z)v(z)w(z)p(z)T (z)

+B(α, β)

u(z)v(z)w(z)p(z)T (z)

= ω C

u(z)v(z)w(z)p(z)T (z)

. (2.15)

The (5× 5)-matrices A, B, C depend on the base flow parameters and the wave numbersα and β. A derivation and a full representation of the differential equation system (2.15)is given by Schrauf in Refs. [254, 256]. The equation system also states a generalizedeigenvalue problem with the complex eigenvalue ω in the framework of the temporaltheory. This eigenvalue problem is numerically solved within the program LILO [265]that is applied within this thesis (see Sec. 3.3.5).

Stability diagram

The physical—i.e., real—parameters involved in the eigenvalue problems (2.14) and (2.15)are basically the real and imaginary parts of the complex numbers α, β and ω, as well asthe Reynolds number Re, where the exact parameter combination depends on the flowtype, and whether the temporal or spatial theory is applied [17]. As simplest case, thetwo-dimensional Orr–Sommerfeld equations (v = 0, β = 0) may be considered from thetemporal point of view. For a given base flow u(z), the equation contains the four realparameters Re, α, ωr, ωi, where the wave number of the disturbance flow (α = αr) resultsfrom the physical wave length λ = 2π

α. With a specified parameter combination (Re, α),

16For constant viscosity µ and zero velocities at the wall (uw = ww = 0), the x-momentum equation (2.8)reduces to

(∂2u∂z2

)w

= 1µdpdx .

20 Chapter 2. Fundamentals and state of the art

the solution of the Orr–Sommerfeld equation yields a complex eigenvalue ω = ωr + i ωi.The sign of the temporal amplification rate ωi now decides whether the disturbances aredamped (ωi < 0, stable flow) or amplified (ωi > 0, unstable flow)17 [250].

unstable

stable

(neutral curve)

Figure 2.4: Schematic of neutral curve in a sta-bility diagram (temporal theory)

For a graphical representation of a linearstability analysis, the correspondence be-tween the parameter combinations (Re, α)and the eigenvalue components (ωr, ωi) canbe compiled in a so-called stability diagram,as schematically illustrated in Fig. 2.4.Exemplary, three amplification curves areshown, on which ωi is constant. The neu-tral curve (ωi = 0) separates the stable(ωi < 0) from the unstable (ωi > 0) flowregion. The stability limit, below which alldisturbance waves decay, is reached at theindifference Reynolds number Reind, thatis, the point on the neutral curve with thesmallest Reynolds number (see dashed tan-gent parallel to α axis). Recall that thepoint at which the transition process is“completed” (Recrit, see Fig. 2.3) is locatedfarther downstream of this theoretical neutral point, and that the distance is influencedby the freestream conditions and the wave amplification within the disturbed boundary-layer flow [250].

Based on Reynolds’s early hypothesis about the instability of a laminar flow, the linearstability theory has first been theoretically worked out by Tollmien [304] and Schlichting[249]. Extensive research and experimental investigation over the years have made ita widely accepted and used theory for the analysis of primary instability mechanisms(Sec. 2.2.5) in the initial stages of the transition process, especially in connection with theeN method (Sec. 2.2.4). The receptivity and the nonlinear transition phases (see Fig. 2.3),however, can obviously not be modeled by the theory. For a comprehensive descriptionand literature review of linear stability theory, the reader may refer to Schlichting andGersten [250] or Arnal [17].

2.2.4 Transition prediction

For laminar flow design applications, a specific transition location is required, at whichthe transition process is completed. The flows upstream and downstream of the transitionpoint can then be considered as pure laminar and pure turbulent, respectively, and thecorresponding flow equations can be applied [292]. Different theoretical and experimentalmethods exist to predict the transition location, the most important of which are sum-

17The phase velocity c = ω/α is also often used as stability criterion within the temporal theory (stable ifci < 0). If the spatial theory is used, the flow is stable for positive amplification numbers (αi > 0), andunstable if αi < 0.

2.2 Laminar flow theory 21

marized below. The theoretical transition prediction methods can be divided into empir-ical, semiempirical, and nonempirical methods. The focus is laid on the semiempirical eNmethod that is applied within this thesis for the proposed laminar wing design method.

Empirical transition prediction

The first empirical methods were derived from a large number of measurements and basedon an observed relation at the transition location xtrans = xcrit between the Reynoldsnumber Rex,trans = uextrans

ν= Recrit (see Fig. 2.3) and the Reynolds number of the

momentum thickness Reθ,trans. Michel [186] used this relation to propose a first simpletransition prediction criterion already in 1952. A refined approach based on the samerelationship is given by Cebeci and Smith [46] as

Reθ,trans ≈ 1.174(

1 + 22400Rex,trans

)Re0.46

x,trans, (2.16)

from which the transition location xtrans can implicitly be determined. The empiricalGranville criterion [99] developed in 1953 correlates the difference between Reθ,trans andthe indifference Reynolds number Reind with an average pressure gradient parameter,based on flight and wind tunnel measurements. It has been shown by Holmes et al. [122]to be applicable for transition prediction on NLF wings in two-dimensional flow. Basedon the Granville approach, the so called C1 and C2 criteria have been developed by Arnalet al. [20], including further parameters such as the shape factor and the freestreamturbulence level [141].

Still, all these criteria are correlated based on extensive empirical observations and mea-surements and only marginally capture the underlying flow physics. Especially the com-plex instability mechanisms on swept wings in compressible flow (see Sec. 2.2.5) requirean approach that takes the external pressure distribution and the boundary-layer flowphysics into account. The eN method discussed in the following section addresses theserequirements as it is based on the above presented linear stability theory.

The eN method

In Sec. 2.2.3, it has been shown how the solution of the linear stability equations yieldsthe stability limit of laminar flows in terms of Reind, below which all disturbance wavesare damped. Between this neutral point and the transition point, the linear stabilitytheory analyzes the temporal and spatial propagation of the unstable disturbance waves;the nonlinear transition phases are not covered. But even the linear stability analysis ofthe wave amplifications cannot directly yield a transition location, because it is unknown,which amount of wave amplification finally leads to transition. This missing boundary isintroduced by the eN method in terms of a statistically derived limit for the amplificationrates as described below.

22 Chapter 2. Fundamentals and state of the art

The growth rates of the disturbance waves can be analyzed using their local amplitudefunctions A (x, z), which can be derived from the (physically relevant) real part of thedisturbance ansatz in Eq. (2.13). With the spatial theory applied to two-dimensional,incompressible flows18, the derivative of A with respect to the streamwise coordinate xcan be expressed as follows [17]:

1A

dA

dx= −αi. (2.17)

The integration of Eq. (2.17) over a certain interval [x1;x2] yields

A2

A1= e

x2∫x1

−αi dx, (2.18)

which is defined as the amplification rate between the two amplitudes A2 and A1.

x

f

x

N-factor en

velope

Figure 2.5: Principle of eN method: relationbetween stability diagram and am-plification ratios, after Arnal [17]

Eq. (2.18) underlines that the linear stabil-ity theory only provides ratios of wave am-plitudes, but neither absolute amplitudevalues nor a limit above which a certainamplitude ratio causes transition. Withthe definition of the amplification rate,however, the principle of transition predic-tion using the eN method can now be ex-plained recalling the stability diagram fromFig. 2.4. In the upper part of Fig. 2.5, aschematic stability diagram (based on thespatial theory) is shown, with the stream-wise position x ∼ Rex on the abscissa, thefrequency f = ω

2π on the ordinate, andthe neutral curve, where αi = 0 holds.Consider a disturbance wave propagatingdownstream in the boundary layer at theconstant frequency f2: it is first beingdamped in the stable region up to x0 (leftof the neutral curve); in the unstable re-gion (between x0 and x1), the oscillationsare amplified before they are damped againfor x > x1. The ordinate of the lower di-agram shows the natural logarithm of theamplification rate ln

(AA0

)at a certain po-

sition x with respect to the initial distur-bance amplitude A0 at x0. Note that the local gradient of these curves is proportional to

18The real part of the two-dimensional form of the disturbance function q′ = q (z) ei(αx−ωt) can be writtenas Re (q′) = re−αix cos (αrx− ωt+ φ), with α = αr + iαi and q (z) = reiφ. For the amplitude functionA = A (x, z) of this disturbance wave, it follows: A (x, z) = r (z) e−iαix.

2.2 Laminar flow theory 23

−αi and thus becomes zero at the stations x0 and x1, which reside on the neutral curvein the upper diagram. The damping of the waves varies with their frequencies, where thewave traveling at f3 exhibits the lowest damping so that the curve does not reenter thestable region within the considered chordwise interval [17].

At every chordwise station x the so-called N -factor is now defined as the envelope of allcurves at different frequencies (see dashed black line in lower diagram), i.e.,

N = maxf

(ln A

A0

). (2.19)

The transition location is finally obtained at the x position at which the local N -factorfirst exceeds a specific limiting N -factor (Ncrit). The amplitude at the critical frequency isthen eNcrit times larger than the initial amplitude A0. Note that the absolute value of theinitial amplitude A0 is strongly influenced by the nonlinear receptivity mechanism [240].

Determination and correlation of N-factors

The limiting N -factors, at which laminar-turbulent transition is expected, has to be de-rived from flight or wind tunnel experiments. The semiempirical approach to correlatemeasured transition data with amplification rates obtained from linear stability theoryhas first been presented by Smith and Gamberoni [284, 285] and van Ingen [311] in the1950s. In their experiments, they observed transition at nearly constant N -factors be-tween 7 to 9, why the eN method was initially named e9 method.

The transition location in experiments is mostly defined at the onset of transition, thatis, where a characteristic parameter or flow quantity significantly deviates from its lami-nar flow behavior. Amongst many, this can be a decrease of the shape factor H12 of themean velocity profile (see Eq. (2.6)), or a strong increase in skin friction or heat trans-fer [19]. Examples for suitable measurement techniques are infrared images, the hot filmtechnique, or sublimation techniques via acenaphthene or naphthalene flow visualizations(see, e.g., Refs. [17, 216]). Despite clear definitions and precise measurement techniques,the detection of distinct transition locations remains difficult due to the complex nature ofthe transition process. This especially holds for three-dimensional flows on swept wings,where the presence of cross-flow instabilities can lead to sawtooth-like transition patterns.The uncertainties and ambiguities in probably scattered transition data have to be keptin mind, when using the derived correlation curves in theoretical design applications [17].

Further, experiments conducted under different conditions can yield different N -factorlimits due to the strong sensitivities of transition towards outer flow conditions. Thedependence on the freestream turbulence intensity Tu has been considered by Mack [172]in a functional relationship N = f (ln(Tu)), which shows applicability to turbulenceintensities in the approximate range of 10−3 < Tu < 10−2 [19]. Due to the increaseddisturbance environment, N -factors derived from wind tunnel experiments are usuallylower than those derived from free-flight, which has to be carefully analyzed and correlatedfor the use of laminar wing designs [17, 281]. Since the proposed method applies to

24 Chapter 2. Fundamentals and state of the art

transport aircraft flying under real operating conditions, the following discussions assumelow freestream turbulence levels as expected in free-flight, and corresponding correlationcurves. It is obvious that generally all parameters that influence the transition (e.g.,external pressure distribution, suction, roughness) also influence the calibration of N -factors in experiments. Therefore, the used correlation curves should be derived fromexperiments with similar conditions to those of the investigated design case.

N-factor integration strategies for three-dimensional flow

The method proposed within this thesis is faced with the increased difficulty of tran-sonic flows around swept wings, where instability mechanisms occur both in longitudi-nal and in cross-flow direction. The eN method that has been discussed above for two-dimensional, incompressible flow, has therefore to be enhanced to three-dimensional, com-pressible flows, as introduced by Arnal et al. [20]. This requires including an additionalspanwise parameter, both for the solution of the eigenvalue problem (see Eq. (2.15)), aswell as for the integration of the growth rates. Commonly used physical parameters arethe spanwise wave number βr, the total wave length λ = 2π√

α2+β2, or the wave num-

ber direction ψ = arctan (βr/αr), which is the angle between the physical wave numbervector and its streamwise direction. For the integration of the amplification rates (seeEq. (2.18)), the additional dimension requires solving a double integral, which implies anambiguity in terms of the selected integration path. Arnal [17] distinguishes three differ-ent classes of integration strategies:

A: envelope method

B: envelope-of-envelopes methods: fixed ω and fixed β, λ, or ψ

C: NCF/NTS methods (two N -factor strategy)

The envelope method (class A) integrates over the growth rates maximized with respectto ψ at each chordwise location and thus only yields one N -factor. It is widely used andwell-accepted for NLF and two-dimensional applications, but shows significant drawbacksfor three-dimensional flows with strong cross-flow instability, since there is no distinctionbetween streamwise and cross-flow instabilities [17]. Within the class B methods, the inte-gration is performed along waves with two fixed parameters, the first of which is always thefrequency ω (or f = ω

2π ), and the second is selected according to the type of instabilities.For streamwise instabilities, a suitable choice is to fix the direction in terms of ψ, while β orλ are commonly fixed for cross-flow instabilities [260]. The instability mechanisms are thusimplicitly separated and the N -factor is determined as the envelope of several envelopecurves. Following the twoN -factor strategy (class C), two explicitly separateN -factors arecalculated, one for Tollmien–Schlichting (TS) instabilities in streamwise direction (NTS),and one in cross-flow direction (NCF ) [19]. The class A or B methods can here be applied assub-strategies. More detailed discussions about advantages and drawbacks of the differentapproaches along with selected application cases can be found in Refs. [17, 19, 261, 273].

2.2 Laminar flow theory 25

The principle of transition prediction with the two N -factor strategy, which is used withinthis thesis, is illustrated in Fig. 2.6, where computed NCF and NTS envelope values areplotted as pairs for the same relative chord stations x/c (see Fig. 2.5).

critical curve(transition criterion)

computed NCF/NTS

envelope values

band of limiting N-factors

Figure 2.6: Principle of transition predictionusing the two N -factor method

The transition location (x/c)trans is definedat the intersection of this computed curvewith an (experimentally derived) criticalcurve, which virtually separates regionsof laminar or turbulent boundary layers19.Certainly, the correlation of N -factor en-velopes with experimentally obtained tran-sition locations does not directly yield adistinct line, but rather a band of limit-ing N -factors [269]. However, for designapplications, a specific choice has to bemade, e.g., by using a best-fit curve. Thesame two N -factor method (with selectedclass B methods as sub-strategies) has beenextensively used by Airbus and the Ger-man Aerospace Center (DLR) for anal-yses of transition experiments and com-parisons with linear stability computations(see Refs. [214, 258, 261, 273]). It is there-fore chosen as suitable approach for theproposed HLFC design method. Detailsabout the specific integration strategiesimplemented in the applied STABTOOLsuite, as well as the correlated NCF/NTS limiting curve used for all HLFC design appli-cations within this thesis will be presented in Secs. 3.3.5 and 3.3.6.

Limitations of the eN method and alternatives

It is obvious that the shortcomings of the eN method correspond to the above-mentionedlimitations of the underlying linear stability theory, i.e., mainly the non-consideration ofreceptivity and nonlinear mechanisms within the transition process [17]. It is neverthelessstill the state-of-the-art method for transition prediction in industrial and academic designapplications [19, 149]. Its main advantages are a reasonable computation effort and thecoverage of the physics represented by the linear stability theory, which provides therelevant sensitivities, e.g., for the proposed HLFC wing design application. Examples forindustrial tool applications of the eN method are given in Sec. 3.3.5.

Within this thesis, the eN method is applied using the local linear stability theory asdiscussed above. Alternatively, the nonlocal theory including the so-called parabolizedstability equations (PSE) could be applied, where the amplitude function q and the wave

19Different shapes of NCF /NTS limiting curves are, for example, discussed by Redeker et al. [214].

26 Chapter 2. Fundamentals and state of the art

number α in the disturbance ansatz (2.13) additionally depend on the chordwise positionx [265]. The PSE thus account for the disturbance history and for streamwise variationsof the base flow (wall curvature, nonparallel effects) [19, 119]. A comparison of resultsobtained with either local or nonlocal linear stability theory is, for example, providedby Schrauf et al. [270].

As alternative to the classical eN method, both simpler and more advanced methods ex-ist. Arnal et al. [19] provide a review of simplified methods, which are either analytical,or apply a database approach with tabulated growth rates from exact stability compu-tations. A comprehensive overview of similar methods is also given by Rajnarayan andSturdza [212] who further combine the database technique with a machine-learning fit-ting approach. The integration of the database techniques into Navier–Stokes solvers hasalready been shown and can provide satisfying results, still if applied to design cases thatare well-represented by the tabulated stability data. Another type of simplified meth-ods are the so-called envelope fitting methods as integrated by Drela in his XFOIL [68]and MSES [65] codes; recent more advanced approaches of this type are, for example, theRATTraP code [53] by Lockheed or the MATTC code [43] code by NASA. [212]

To account for nonlinear transition processes, advanced nonempirical transition predic-tion methods can be applied, e.g., the nonlinear, nonlocal PSE [118, 217, 270], or evendirect numerical simulation (DNS) of the Navier–Stokes equations. Both required mod-eling effort and computation time of these methods, however, are well beyond reasonableapplicability to preliminary aircraft design.

After the theoretical excursus into boundary-layer and linear stability theory as well as anintroduction into transition prediction methods, let us return the focus to the applicationof laminar flow technology to transport aircraft. An overview of the instability mechanismsoccurring on swept wings is given in the next section. Section 2.2.6 discusses appropriatelaminarization techniques to prevent or control these instabilities.

2.2.5 Instability mechanisms and transition on swept wings

In Sec. 2.2.2, the laminar-turbulent transition process has been introduced for the simplecase of a two-dimensional flow around a flat plate. The highly three-dimensional flowaround a tapered swept finite wing of an aircraft implicates additional and much morecomplex transition phenomena. This complexity and the practical relevance motivateda lot of theoretical and experimental investigations of the flow characteristics in three-dimensional boundary layers around swept wings (see, e.g., Refs. [21, 45, 143]).

The primary instabilities and transition mechanisms that predominantly occur on sweptwings are [250]:

• Tollmien–Schlichting instabilities (TSI)

• cross-flow instabilities (CFI)

• attachment-line transition (ALT)

2.2 Laminar flow theory 27

wall streamline

external streamline

TSICFI

ALT

(a) Streamline curvature and predominant regionsof instability mechanisms

external streamline

wall streamline

(b) Inflected cross-flowvelocity profile in a3D boundary layer

Figure 2.7: Instability mechanisms for three-dimensional flow around a swept wing,adapted from Redeker and Wichmann [216]

Figure 2.7a schematically indicates, in which chordwise region on the wing these instabil-ities mainly occur. Further, the streamline curvature and the twisted boundary-layer ve-locity profiles (see Fig. 2.7b) are shown, which are typical for three-dimensional boundarylayers on swept wings. They are key especially to the origin of cross-flow instabilities. Thephysical mechanisms of the three instabilities will be discussed in the following paragraphs.

A fourth type of instability occurring in three-dimensional boundary layers is representedby centrifugal instabilities, namely Taylor-Görtler vortices, which are only shortly dis-cussed below due to their limited practical relevance. A detailed review of instabilitymechanisms, including secondary instabilities and instabilities of nonlocal (nonparallel)flows is, for example, given by Oertel Jr. and Delfs [194].

Tollmien–Schlichting instability

Disturbance waves that travel in streamwise direction are called Tollmien–Schlichtingwaves (TS waves), which were first discovered by Tollmien [304] and Schlichting [249], andlater experimentally confirmed by Schubauer and Skramstad [276]. In a two-dimensionalflow with low turbulence intensity, they are always initiating the transition process [240,250] (see flat-plate flow in Fig. 2.3). Mathematically, the TS waves are described bythe solution of the two-dimensional Orr–Sommerfeld equation that degenerates from Eq.(2.14) if β = 0 [292]. In two-dimensional, incompressible flow, the strongest growthrates occur nearly in streamwise direction (ψmax ≈ 0◦), where for compressible flow, thedirection can have higher values up to around (ψmax ≈ 40◦–70◦) [17].

28 Chapter 2. Fundamentals and state of the art

As shown in flight and wind tunnel experiments, Tollmien–Schlichting instabilities (TSI)predominate on aircraft wings with moderate leading-edge sweep angles (ϕLE . 25◦) [12,141]. Still, they also occur on highly swept wings, where, however, cross-flow instabilitiescan cause premature transition (see next paragraph). Since TS waves are described bylinear stability theory, the described point-of-inflexion criterion holds, that is, the TSdisturbances are damped in case of favorable (negative) pressure gradients and amplifiedthrough positive pressure gradients [142]. Supposing a low-swept wing with a favorablepressure distribution, TSI thus mostly occur in the mid-chord region and transition due toTSI can be delayed up to close behind the point of minimum pressure [243, 250]. Details ofdesired pressure distribution shapes to enable laminar flow will be discussed in Sec. 2.3.1.

Apart from a favorable pressure gradient, the amplification of TS waves strongly dependson the freestream Reynolds number and on the roughness of the wing surface [243]. If localdisturbances (e.g., caused by insects or surface imperfections) occur on the wing in anunstable flow region, sudden transition can be caused in the form of turbulent wedges [250].

Boundary-layer suction has also been shown to stabilize TS disturbances [241, 223, 250],though this influence is secondary compared to a smooth surface and favorable pressuregradients. Also, note that as soon as nonlinear and three-dimensional effects occur, theeffort for a relaminarization of the boundary layer via suction becomes tremendous [243].

Cross-flow instability

Cross-flow instabilities (CFI) are primary instability mechanisms that only occur in three-dimensional boundary layers [250], especially in regions with strong negative pressure gra-dients like near the wing leading edge [244]. CFI originate from the streamline curvaturecharacteristic in three-dimensional boundary layers [286], which has schematically beenshown in Fig. 2.7a for the flow on a swept wing.

Figure 2.7a shows two streamlines on the wing upper side, one at the wall, and an ex-ternal streamline at the outer edge of the boundary layer. Since at the stagnation point(at the wing leading edge) only the spanwise velocity component v∞ is nonzero, the in-viscid external streamline is initially strongly moved outboard. On the wing upper side,the combination of negative pressure gradient and wing sweep then inflects the stream-line inboard. Farther downstream in the pressure recovery region this effect is reverted,leading to the curved external streamline as sketched in Fig. 2.7a [218]. The pressure gra-dient perpendicular to the external streamline also acts on the boundary layer, in whichthe slowed viscous fluid follows this gradient and develops a secondary flow, called cross-flow [194]. The wall streamline is hence inflected even stronger than the external stream-line. The resulting twisted velocity profile in the boundary layer is shown in Fig. 2.7b,where it is decomposed into its components in streamwise direction (u) and perpendicularto it (cross-flow component v). If the coordinate system is linked to the external stream-line20 (xe, ye, ze), the cross-flow component is zero both at the surface (no-slip condition)and at the edge of the boundary layer [286]. From these boundary conditions, it follows

20The coordinate system is Cartesian, with xe in flow direction, and ze normal to the wall.

2.2 Laminar flow theory 29

that cross-flow velocity profiles always exhibit an inflexion point, which has been statedabove to destabilize the boundary layer (see Sec. 2.2.3).

The resulting cross-flow instabilities are characterized by co-rotating vortex structureswith their axes oriented in streamwise direction [104, 244]. The cross-flow vortices andinstabilities have first been discovered by Gray [102] and investigated on swept wings inthe experiments by Saric and Yeates [245] and Bippes and Nitschke-Kowsky [31]. Thetheoretical formulation of CFI has first been given by Gregory et al. [104].

Within linear stability theory, the CFI are described by solutions of the differential equa-tions (2.14) or (2.15) for three-dimensional flows; i.e., the wave number component in ydirection is nonzero (β 6= 0). The most unstable direction ψmax is mostly found close tothe cross-flow direction (ψmax ≈ 85◦–90◦) [17].

If cross-flow occurs, the highly inflectional cross-flow velocity profiles have a much strongertendency to instability than those in streamline direction. CFI predominantly occur in theleading-edge region of swept wings due to high surface and streamline curvature and strongnegative pressure gradients and thus inflectional instability [17, 216]. The instability isalso influenced by the specific shape of the inflectional cross-flow profile. Generally, theoccurrence of CFI strongly depends on the wing leading sweep angle ϕLE. While TSI aredominant at low sweep angles (ϕLE . 25◦), the dominance of CFI over TSI increases withϕLE, often causing transition near the leading edge [141, 250].

To laminarize a swept wing at transonic cruise conditions it is thus the main design goalto suppress both TSI and CFI, which is difficult because the negative pressure gradientsstabilizing TS waves have been shown to support CFI [242, 243]. Appropriate targetpressure distributions will be discussed in Sec. 2.3.1. At very high leading-edge sweepangles—beyond physical boundaries of natural laminarization—boundary-layer suctioncan additionally be applied to suppress CFI (see Sec. 2.2.6).

Attachment-line transition

For three-dimensional flows around swept bodies, boundary-layer transition can alreadyoccur at the attachment line21 (AL). On swept wings of transport aircraft, large distur-bances—e.g., originating from the turbulent boundary layer of the fuselage—can propa-gate along the attachment line and cause transition. This phenomenon is called leading-edge contamination (LEC). If the attachment-line boundary layer is initially laminar orrelaminarized, it can also undergo an instability due to small disturbances (attachment-line stability problem) [218, 269].

The transition and flow phenomena at the attachment line of swept wings were firstdiscovered by Gray [102] and rediscovered by Pfenninger [202] during the X-21 flight tests.Further relevant experimental and theoretical work can be found in Refs. [109, 207, 278].

21On swept bodies (such as cylinders or wings), the attachment line is the streamline at the leading edge,along which the flow separates onto the upper and lower part of the surface. For infinite, symmetricalbodies of constant chord, this corresponds to the isoline of maximum static pressure [17].

30 Chapter 2. Fundamentals and state of the art

Attachment-line transition (ALT) on a swept wing is severe as it causes full turbulentflow over the whole surface and undermines the efforts to control TSI or CFI on thewing. For the design of a laminar flow wing, it is therefore crucial to prevent this form oftransition. To prevent LEC, the so-called Gaster bump [90, 91] can be applied22, whichdiverts the turbulent boundary layer originating from the fuselage and enables a “fresh”laminar boundary to develop [264].

A quantitative criterion exists to evaluate ALT (and LEC) on swept wings, which hasoriginally been formulated by Pfenninger [202]. Since transition at the attachment lineoccurs if the pressure and inertia forces outweigh the viscous forces in the boundary layer,Pfenninger selected the spanwise attachment-line momentum-thickness Reynolds numberReθ,AL = ve θAL

νas suitable measure [203]. Here, the attachment-line momentum thickness

is written as θAL = θ∗AL√

ν(due/ds)s=0

(with θ∗AL = 0.404)23, by analogy to the Blasius lengthscale for the flat-plate boundary layer (see Sec. 2.2.1). The spanwise velocity is definedby ve = v∞ = U∞ sinϕeff , with the effective sweep angle24 ϕeff ; the chordwise velocitygradient (due/ds)s=0 with respect to the curvilinear arc length s at the attachment line(s = 0) characterizes the flow divergence as it draws the disturbances away from theleading edge [206, 260]. The Pfenninger criterion results as follows:

Reθ,AL = 0.404 U∞ sinϕeff√ν ·

(dueds

)s=0

= 0.404ReAL < Reθ,AL,crit, (2.20)

where Reθ,AL has to stay below a certain critical limit Reθ,AL,crit to prevent transitionat the attachment line. From the X-21 flight tests, Pfenninger [203] derived a limit ofReθ,AL,crit ≈ 90−100 (ReAL,crit ≈ 250), below which LEC through the formation of turbu-lent eddies in the boundary layer is suppressed, even for an initially turbulent attachment-line boundary layer25. If the attachment-line boundary layer is initially laminar, or aGaster bump is used to divert the turbulent disturbances, higher values of Reθ,AL can bereached before transition occurs, up to the linear stability limit of Reθ,AL,crit ≈ 240 [109].

According to Eq. (2.20), suitable design measures to obtain acceptably small values ofReθ,AL are a reduced leading-edge sweep angle (sinϕeff ↓), a “sharper” nose in terms ofa smaller leading-edge radius26

((dueds

)s=0↑), or a reduction of the unit Reynolds number

Recc

(U∞ ↓ or ν ↑). For corresponding wing design applications, see, e.g., Refs. [214, 281].

LEC can also be suppressed by applying suction along the wing leading edge (see Sec. 2.2.6).To include the effect of suction into Eq. (2.20), Pfenninger [203] proposed a dependencyof θ∗AL on the nondimensional suction velocity parameter K = ww√

ν (due/ds)s=0, which is rep-

resented by the black diamonds in Fig. 2.8, and which contains the wall-normal suctionvelocity ww < 0. Thus, increasing suction makes K more negative and reduces Reθ,AL (or

22A summary of the Gaster bump and other passive relaminarization devices is given in Ref. [18].23The factor θAL∗ = 0.404 can be derived from tabulated boundary-layer data [203, 206].24The effective sweep angle ϕeff will be treated in Sec. 3.3.6; for infinite swept wings, it is ϕeff = ϕLE .25The Pfenninger criterion has been confirmed experimentally by Poll [207, 208], why it is also calledPfenninger-Poll criterion. A confirmation based on aircraft flight test data is also given in Ref. [260].

26For cylinders of circular or elliptic section with leading-edge radius r, it is(due

ds

)s=0 ∼

1r [17].

2.2 Laminar flow theory 31

ReAL). Introducing the suction coefficient

Cq = wwU∞

, (2.21)

K can be written as K = wwveReAL = Cq

sinϕeff ReAL. Similarly to reducing ReAL, the criticalvalue ReAL,crit can also be raised, as proposed by the so-called K-criterion

ReAL,crit = 250− 150K, (2.22)

i.e., a correlation derived from different wind-tunnel tests conducted at ONERA [22, 221].

0.00.10.20.30.40.5

−14−12−10−8−6−4−20

θ AL*

Re−

AL

,cri

t (K

−crit

.)

suction parameter K

250

400

850

Pfenninger (suction) criterion ONERA K−criterion

Figure 2.8: Criteria for attachment-line tran-sition including suction

That both approaches, i.e., either reducingReAL or increasing ReAL,crit are virtuallyequivalent, is shown in Fig. 2.8, where theblue curve represents Eq. (2.22) in termsof θ∗AL = 0.404 250

250−150K and approximatesvery well the Pfenninger criterion. A dif-ferent relation was suggested by Schrauf[260] based on the A320 HLF fin flighttests, i.e., ReAL,crit = 250 + 4 · 106 C2

q ,which, however, does not consider the in-fluence of sweep angle. The prediction ofattachment-line transition in HLFC applications thus still contains uncertainties andhas to be validated in further flight tests. However, recent experiments [44] confirmedEq. (2.22), why it is herein used as quantitative evaluation criterion (see Sec. 4.3.1).

Görtler vortices

The laminar-turbulent transition can also be triggered by centrifugal forces, which prevailfor shear flows over curved surfaces. While centrifugal forces slightly stabilize boundary-layer flows over convex surfaces, they exert a destabilizing effect on boundary-layer flowsthat develop over concave surfaces. This leads to the formation of pairs of stationary,counter-rotating vortices, with their axes oriented in streamwise direction [17, 250]. Sincethey were first described by Görtler [97], these vortices are called Görtler (or sometimesTaylor-Görtler) vortices, and the underlying instabilities (Taylor-)Görtler instabilities.

Görtler instabilities are herein of low practical relevance, since they can be controlledby appropriate airfoil design [242]. Basically, concave curvature is only used at the rearpressure side of airfoils, where transition delay is not of interest. Also, if centrifugalinstabilities occur in three-dimensional boundary layers on swept wings, they are mostlyof negligible significance compared to TSI or CFI [218]. For a detailed discussion, thereader may, for example, refer to Refs. [239, 250].

32 Chapter 2. Fundamentals and state of the art

2.2.6 Laminarization techniques (NLF, LFC, and HLFC)

The central objective in laminar wing design is to achieve a maximum extent of laminarflow area over the wing to minimize friction drag. Its practical realization is a complextask that has to consider all parameters influencing the transition process in the boundarylayer, including the discussed instability mechanisms and their interactions.

Different laminarization techniques exist, which can be classified according to the phys-ically governing terms in the boundary-layer equations27. Introducing a nonzero suctionvelocity ww through the wall, the two-dimensional x-momentum equation (2.8) at thewall can be rewritten according to Reshotko [222] as:

µw

(∂2u

∂z2

)w

= dp

dx+[ρww −

dµ

dT

(∂T

∂z

)w

](∂u

∂z

)w

. (2.23)

As discussed in the context of the linear stability theory in Sec. 2.2.3, the boundary-layerflow is stabilized if the term

(∂2u∂z2

)w

becomes more negative, corresponding to a fullervelocity profile u (z). The laminarization techniques thus result by analogy to the termsthat make the right-hand side of Eq. (2.23) more negative [242, 319], where

(∂u∂z

)w> 0:

• negative pressure gradient (via shaping): dpdx< 0

• suction of the boundary layer: ww < 0

• wall cooling in gases (e.g., air):(∂T∂z

)w> 0,

(dµdT

)gas

> 0

• wall heating in liquids (e.g., water):(∂T∂z

)w< 0,

(dµdT

)liquid

< 0

Wall cooling is very expensive28 and is rather applied to supersonic Mach numbers; surfaceheating is only effective in liquids. Shaping and suction, however, are of significant prac-tical relevance to delaying transition on subsonic and transonic transport aircraft. Influ-encing the pressure distribution by providing appropriate geometry shapes is regarded asnatural or passive laminarization technique, while boundary-layer suction is an active con-trol technique. Over the past decades, these two techniques have been extensively stud-ied and applied, mainly under the following three laminarization technology names [142]:

• natural laminar flow (NLF)

• laminar flow control (LFC)

27It may be noted that the focus of this thesis is exclusively on boundary-layer control to delay transition.Generally, boundary layers can also be controlled to prevent flow separation, e.g., through motion of thesolid wall, boundary-layer suction, or tangential blowing. Boundary-layer control further includes binaryboundary layers by means of injection of a different gas, which is rather used for thermal protection at highsupersonic velocities. For details, refer, for instance, to White [319] or to Schlichting and Gersten [250].

28Though wall cooling can damp TS disturbances, its potential to suppress CFI at the leading edge ofhighly swept wings is marginal compared to that of suction [141, 242].

2.2 Laminar flow theory 33

• hybrid laminar flow control (HLFC)

These technologies will be shortly discussed in the next paragraphs. Recall that theapplication domains and physical boundaries (in relation to cruise Reynolds numbers andwing sweep angles) have already been introduced in Chap. 1. Important design principlesand aspects for the integration of the HLFC technology into commercial transport aircraftwill be discussed in Sec. 2.3.

Natural laminar flow

With the natural laminar flow (NLF) technology, the boundary-layer transition is tried tobe delayed “naturally” by shaping the surface geometry. One main geometry characteristicof NLF airfoils is the more rearward chordwise position of maximum thickness, which alsoshifts the point of minimum pressure rearwards. Up to this point, a favorable (negative)pressure gradient is applied, which has been shown above to stabilize Tollmien–Schlichtingwaves and thus to delay transition in two-dimensional flows [251].

Doetsch [55] first discovered the positive effect of shifting airfoil maximum thickness rear-wards on maintaining laminar flow. The interrelation of geometrical and aerodynamiccharacteristics of laminar flow airfoils have then intensively been studied at NASA byAbbott et al. [1, 2]. Some experiments and flight tests with NLF gloves and wings havebeen presented in Sec. 1.1.

The main challenge in the practical realization of NLF is the strong requirement forsurface smoothness and quality to prevent transition through roughness, imperfectionsor contamination. The application of NLF is further limited to low-swept wings due tothe increasing dominance of CFI and ALT at larger sweep angles. For moderately sweptwings, ALT can mostly be controlled if the airfoil nose radius is reduced with increasingsweep to fulfill the Pfenninger-Poll criterion (2.20) along the wing span. Still, a carefullybalanced design is required to suppress both TSI and CFI, while TSI mostly dominatesfor ϕLE . 25◦ [141] (see Sec. 2.2.5). NLF design applications are, for example, givenby Redeker et al. [214] or Seitz and Horstmann [281], along with guidelines for suitabletarget pressure distributions. At high wing sweep angles, where CFI and ALT cannotbe controlled anymore by passive laminarization techniques such as NLF, active controlmethods are required, e.g., via boundary-layer suction.

Laminar flow control

Laminar flow control (LFC) is herein understood as active boundary-layer control tech-nique via steady suction to maintain laminar flow [141]. This narrower definition is im-portant, because LFC is sometimes used as a broader term for boundary-layer controltechniques as discussed above [319]. Moreover, wall suction can generally also be appliedto relaminarize a turbulent flow or to prevent separation.

34 Chapter 2. Fundamentals and state of the art

For the laminarization of aircraft surfaces, LFC via suction is especially useful beyond thephysical boundaries of natural or passive laminarization techniques. This is mainly thecase for wings with very high Reynolds numbers and sweep angles, where CFI and ALT arethe dominating transition mechanisms. LFC is realized via suction through either slots orholes, where the latter means continuous suction through a porous or perforated wall [251].Starting already in the 1930s the slot-suction—and later the porous-suction—conceptshave been widely investigated in wind tunnel and flight tests, showing that large regionsof laminar flow (up to full-chord) can be achieved. Still, shortcomings of the slot suctionconcept, which are mainly the loss of slot effectiveness in the leading-edge region andthe disturbance of the flow by the slots, have more and more favored the porous suctionconcept [142, 251]. Detailed experiments and studies have been conducted to find outcritical values below and above which the creation of vortices induced by suction throughthe holes led to undesired turbulent flow [141].

The principle of LFC, which was investigated in the early works by Holstein [123], Ackeretet al. [6], and Pfenninger [201], follows the boundary-layer physics as described above:Wall-normal suction (ww < 0) leads to a thinner boundary layer and, more significantly,a fuller boundary-layer velocity profile. The boundary-layer flow is thus more resistantagainst linear disturbance growth, which delays laminar-turbulent transition [242, 251].Applications of LFC to transport aircraft can, for example, be found in Refs. [315, 204]. Acomprehensive summary of LFC including all relevant design and manufacturing aspectsalong with a historical overview of wind tunnel and flight tests is given by Joslin [142].

Though full-chord laminar flow has been shown to be generally feasible, it requires suc-tion over a long distance. The realization of full-chord LFC implies very high system com-plexity (including compressors, ducting, etc.), fabrication efforts, as well as space alloca-tion and structural integration problems, especially with the wing box between the spars,where the fuel is stored. These hurdles make full-chord LFC very expensive or even im-practicable for the application to transport aircraft.

Hybrid laminar flow control

The hybrid laminar flow control (HLFC) concept combines the LFC with the NLF tech-nology by applying suction only ahead of the front spar and shaping in the mid-chord re-gion. Strong suction in the leading-edge region can suppress both ALT as well as CFI.Further, the limited chordwise extend of suction reduces systems complexity and integra-tion efforts, which are immanent to LFC. Behind the suction panel, the likely occurrenceof early transition due to TSI motivates to establish favorable pressure gradients by ap-propriate geometry shaping. More detailed aspects concerning desired pressure and suc-tion distributions for HLFC airfoil and wing design are discussed in Sec. 2.3.1. Like otherlaminarization techniques, HLFC can reasonably be applied to wings, tails, and nacelles.

The idea of a hybrid approach between NLF and LFC has first been introduced under thename HLFC in a patent by Gratzer [101] at Boeing in the 1980s. Since then it has beenintensively studied and demonstrated in flight and wind tunnel tests, mainly in the UnitedStates and Europe [141]. Still, the complex issues coming with the structural integration

2.3 HLFC design and integration aspects 35

and fabrication of the suction system remain a critical aspect for the acceptance of theHLFC technology by airlines for in-service operations. Further, maintenance and opera-tional uncertainties have to be considered, where the latter mainly concern shortfalls oflaminarity due to systems failures, icing conditions, or insect contamination. Due to thecomplexity of realizing HLFC and its strong impact on overall aircraft design, the mostimportant HLFC design and integration aspects are treated in the following sections.

2.3 HLFC design and integration aspects

This section gives an overview about the design challenges that are implied by the inte-gration of an HLFC system into commercial aircraft. The primary goal of applying HLFCis the aerodynamic drag reduction through laminarization of aircraft surfaces (wing, em-pennage, nacelles). This thesis concentrates on the wing integration, which promises thehighest saving potential due to the large wetted surfaces, but has also the strongest im-pact on overall aircraft design.

The principles of aerodynamic wing design to enable hybrid laminar flow are discussed inSec. 2.3.1, based on the fundamentals introduced in Sec. 2.2. HLFC system and struc-tural integration aspects are discussed in Sec. 2.3.2. Operational considerations includingcontamination due to insects or ice accumulation are presented in Sec. 2.3.3.

Remind that this thesis considers HLFC integration within a conceptual to preliminarydesign context. The focus is therefore placed on those influences with significant impacton overall aircraft design and performance. Very detailed aspects with no appreciableimpact on the overall aircraft are only treated shortly, and the reader may refer to thecited references for more detailed investigations. As an example, this applies to the preciseproduction technique for the suction holes, which—though it is of high importance forthe practical realization of HLFC—has negligible influence from the preliminary designperspective.

2.3.1 HLFC aerodynamic wing design

To integrate HLFC to the wings of commercial aircraft, an efficient wing design is obvi-ously of primary interest and priority. Let us first consider the basic design requirementsthat are generally posed to commercial aircraft wing design. Most notably, these arethe performance requirements in the different flight phases (low- and high-speed perfor-mance), acceptable flying qualities (e.g., handling and stalling characteristics), structuraldesign requirements, as well as storage and integration of fuel and other components andsystems (e.g., landing gear, high-lift devices, flight controls, actuators). More detaileddiscussions can, for example, be found in Torenbeek’s book [306]. Under consideration ofthese requirements, the wing has to be designed for an optimum benefit on overall aircraftlevel, e.g., in terms of minimum fuel or operating costs (see Sec. 2.1). The preliminary

36 Chapter 2. Fundamentals and state of the art

wing design parameters29, which mainly affect aerodynamic performance and structuralweight, are:

• wing (reference) area Sref , according to the aircraft wing loading W/S

• planform parameters (span b or aspect ratio Λ, sweep angle(s) ϕ, taper ratio λ)

• thickness distribution t/c (y) and sectional (airfoil) shapes

• spanwise lift distribution, depending on airfoil shapes and twist distribution ε (y)

• high-lift devices (types and planform arrangement)

These parameters have to be determined and optimized in the conceptual and preliminarydesign phase. The preliminary wing optimization already includes crucial trade-offs, e.g.,between good aerodynamic performance and light structural design, or between favorableaerodynamics during cruise (high L/D at moderate lift coefficients CL) and low-speedflight (low take-off drag, high maximum lift coefficients CL,max at approach and landing).

The realization of HLFC primarily affects the aerodynamic high-speed wing design, sinceHLFC is designated for operation during cruise30. Further, as discussed in the introduc-tion, HLFC is especially applied beyond the physical boundaries of natural laminar flow,see Fig. 1.1c. This concerns aircraft with high Reynolds numbers and wing sweep angles,which are implied by large wing chords and high transonic cruise Mach numbers.

Compared to turbulent transonic wing design, design for hybrid laminar flow additionallyrequires maximizing the extent of laminar flow by delaying transition on the wing upper(and optionally lower) side31. As shown in Secs. 2.2.5 and 2.2.6, this means to suppress thepredominating instability mechanisms by appropriate laminarization techniques. UsingHLFC, suction is applied ahead of the front spar (15–20 % of local chord length) tosuppress ALT32 and CFI, and suitable geometry shaping is applied in the mid-chordregion to cope with TSI and CFI. The contrary effects of negative pressure gradientsstabilizing TS waves, but also promoting CFI, requires a carefully balanced design ofpressure distribution Cp (x) and suction distribution Cq (x) over the wing. The pressurecoefficient Cp is defined as

Cp = p− p∞12ρ∞U

2∞

; (2.24)

the suction coefficient Cq was defined in Eq. (2.21). Key desirable characteristics of HLFCpressure distributions have already been pointed out by Boeing and NASA in their earlyHLFC studies around 1980 (see, e.g., Ref. [124]). They are summarized in Fig. 2.9 for

29Wing and aircraft geometry are herein defined based on a vehicle-fixed Cartesian coordinate system, withx pointing rearwards (along the symmetry plane), z upwards, and y in right-hand (starboard) direction.

30HLFC operations at low speeds or altitudes are mainly complicated by the high probability of undesiredtransition due to insects, ice crystals, or the use of high-lift devices.

31As discussed below, this thesis concentrates on the laminarization of the wing upper side.32Further design measures to prevent ALT were discussed in Sec. 2.2.5. Additionally, a Gaster bump canbe placed at the wing leading edge near the fuselage junction to circumvent leading-edge contamination.

2.3 HLFC design and integration aspects 37

a typical HLFC pressure distribution (similar to that presented in Ref. [162]), togetherwith an HLFC airfoil shape and a typical Cq distribution.

suction shaping

strong4suction

moderate4suction no4suction

(1)

NLF4typical(susceptible4to4CFI)

LFC4typical(susceptible4to4TSI)

(2) (3)(4)

Figure 2.9: Typical characteristics of HLFCpressure and suction distribution(schematic), following Ref. [124]

The leading-edge region with high suscep-tibility to CFI is confined to a small dis-tance by means of a steep initial flow ac-celeration (1). Strong suction is appliedto this region to prevent early transitiondue to CFI. A quite abrupt change ofthe gradient or even a small negative suc-tion peak allows damping cross-flow dis-turbance growth, while the suction inten-sity can be reduced (2). For compari-son, a smoother pressure decrease (as itis typical for NLF on low-swept wings) isshown, which would strongly support CFI,especially at high sweep angles. In themid-chord region (3), a favorable (nega-tive) pressure gradient is required to sup-press TSI, which should be, however, nottoo steep to limit cross-flow amplification.This balancing to find a suitable pressuregradient is additionally influenced by thechord Reynolds number [281]. A zero orpositive pressure gradient in the mid-chordregion—while still keeping TSI under con-trol—can only be established if suctionLFC is extended beyond the front spar (seeupper dashed Cp curve). With a suitable Cp shape in the leading-edge and mid-chord re-gion, the transition point can be delayed up to closely behind the recovery point, i.e.,the point of minimum pressure (4). Correspondingly, shock and pressure recovery regionshould occur late on transonic HLFC airfoils, and shock strengths should be limited bylocal Mach numbers of Msh . 1.2 to prevent shock-induced separation of the laminarboundary layer. A weak shock in combination with decreasing pressure in the mid-chordregion, however, limits the resulting airfoil lift coefficient. This can be compensated byadditional rear loading, or a larger pressure peak in the nose region if allowed by stabil-ity restrictions [316, 281]. Speaking in terms of drag, the viscous drag reduction due todelayed transition has to be balanced with the wave drag that increases with strongershocks, to obtain minimum total airfoil drag for a given lift coefficient Cl.

The overall aircraft design lift coefficient CL,des can be initially estimated from the steadycruise conditions (see Fig. 2.1):

CL,des = L12ρV

2S= (W/S)cr

12ρV

2 . (2.25)

38 Chapter 2. Fundamentals and state of the art

Thus, for a given cruise Mach number Mcr = f (V, h) and altitude (ρ = f (h)), the valueof CL,des is directly connected to the selection of the wing area S = Sref or wing loadingW/S. If TLARs are not yet fixed or allowed to be relaxed, CL,des can also be traded offagainst adaptations of cruise Mach number or altitude, where the change of altitude ismostly more convenient and less critical. During cruise, CL varies within a certain range,dependent on fuel mass reduction and selected steps of cruise altitudes. For this (andother) reasons, the wing should be designed for acceptable off-design performance, i.e.,laminar flow should be maintained over a certain CL range. For subsonic NLF wings, thisis recognized by the typical laminar bucket in the shape of the drag polar CD = f (CL). Fortransonic HLFC wing design, both the balance between TSI and CSI, as well as betweenviscous and wave drag, have to be considered within the desired CL range. For example,on the wing upper side, CFI rather predominate at lower CL and TSI at higher CL dueto corresponding changes in pressure gradients (and vice versa on the lower side) [130].Also, note that increasing CL can lead to a steep increase in wave drag due to strongershocks, which can easily outweigh the frictional drag benefits due to laminar flow.

Though suitable guidelines and measures for HLFC wing design exist, the sensitivity oftransition mechanisms towards wing sweep angle and chord Reynolds numbers impliessome physical boundaries, beyond which HLFC wing design becomes impracticable, or itis always inferior to a similar turbulent design. The realization of the discussed sectionalcharacteristics are further complicated in the context of three-dimensional wing design,especially in wing regions with highly three-dimensional effects and flow interactions (in-board wing, pylon attachments, etc.). Examples for HLFC airfoil and wing design appli-cations can be found in Refs. [220, 281, 307, 321]. The discussed HLFC airfoil design prin-ciples will be revisited and applied for the HLFC wing design method in Sec. 3.3. Further,integrated HLFC wing and aircraft design studies (including variations of wing area, span,sweep, etc.) using the entire proposed method will be presented and discussed in Chap. 4.

2.3.2 HLFC system and structural integration aspects

The opportunity to laminarize the wing beyond the physical limits of natural laminar flowby applying HLFC involves the integration of a suitable suction system into the wing.From the aerodynamic point of view, the boundary-layer suction has been introduced interms of the suction coefficient Cq or the suction velocity ww through a wall. An air flowthrough the wing outer surface can be realized by a pneumatic system inside the wingthat sucks the boundary layer through slots or a porous outer surface, where this thesisonly considers the latter approach for the reasons discussed in Sec. 2.2.6.

The HLFC concept applies suction only ahead of the front spar, which requires replacingthe conventional nose box by a porous leading-edge suction panel. The original HLFCconcept by Gratzer [101] proposed a separated double skin panel construction, with aporous outer and a nonporous inner skin containing a collector chamber (divided intoseveral compartments), through which the air passes to a duct inside the airfoil nose.This classical type of suction system with separately controlled compartments has beenapplied in different flight tests, e.g., with a Dassault Falcon 900, Boeing 757, or Airbus

2.3 HLFC design and integration aspects 39

A320 [317, 219]. Within the European ALTTA33 project, Airbus and the DLR developeda simplified approach with reduced suction system weight and complexity, applying atitanium double sheet structure with a porous outside skin and an inner sheet with orifices.The main advantages of the simplified ALTTA system are a new production technology(guaranteeing higher-quality suction surfaces), a significantly reduced system complexity(with only one large suction chamber), and the avoidance of a control system, i.e., theHLFC system is self-adapting without specifically controlling the suction flow rate [128,264]. This concept is also applied for HLFC system sizing within the proposed method(see Sec. 3.4).

The integration of the suction panel implies severe structural and manufacturing require-ments [137]. The micro-perforated structure has to meet high surface quality standards,because surface imperfections (e.g., steps or gaps, waviness, surface roughness34, isolated3D roughness elements35) or blocked holes can cause premature transition. Manufactur-ing techniques to produce such high-quality surfaces are nowadays available [219]. Theprevention of surface waviness has also to be ensured for the case of deformation throughloads. For the wing, these requirements are much more severe than for tails because ofthe larger span, along which several suction panels have to be arranged while ensuringstructural integrity. A load-bearing substructure underneath the outer skin panels canenhance stiffness and resistance, e.g., against bird strikes. For the fabrication of the per-forated surface, the suction holes can, for example, be drilled using lasers or electronbeams. Bonding and brazing are convenient manufacturing techniques for a smooth at-tachment of the perforated outer skin. Titanium is mostly selected as appropriate ma-terial (favored over aluminum or CFRP36) due to its high strength and stiffness, as wellas resistance against corrosion [183, 264]. More detailed considerations about structural,manufacturing, and materials aspects are beyond the scope of this thesis, as discussedabove. For a deeper insight, the reader may refer to the cited references, or to Joslin [142]for an overview and further literature.

Besides the panel structure and the ducts inside the leading edge, the HLFC system fur-ther comprises components to generate the required suction (mass) flow rate, such ascompressors, pumps, motors, valves, and wires. The compressor, for instance, suppliesthe energy that is required by the suction system to establish the desired pressure insidethe chambers and ducts [233]. The energy of the electrically or hydraulically driven com-pressor is ultimately taken off as shaft power from the engines. This shaft power offtakefrom the engines is significant in the preliminary design context, because it implicitly in-creases the specific fuel consumption (SFC) of the engines. The implementation and in-teraction of the systems and engine model within the proposed method will be describedin Sec. 3.2. The SFC increase and the additional HLFC system mass (i.e., the sum ofall subcomponent masses) reduce the benefit obtained from aerodynamic drag reductionby means of laminarization. The integrated design assessment of these single effects onaircraft level in terms of a net benefit (e.g., block fuel) is a key aspect of the proposedHLFC aircraft design method.

33Application of Hybrid Laminar Flow Technology on Transport Aircraft34Surface roughness can be caused by manufacturing processes or by erosion during operations [111].35Isolated roughness elements can be rivet heads, paint graininess, or—during operations—dirt, insects, orice crystals, and they can cause 3D flow disturbances [316, 111].

36carbon fiber-reinforced plastic (or polymer)

40 Chapter 2. Fundamentals and state of the art

In addition to the suction system, the realization of HLFC includes the integration ofsuitable systems or techniques for high-lift, insect protection, and anti-icing. These arediscussed in the next section along with operational requirements.

2.3.3 HLFC operational aspects

As discussed in Sec. 2.3.1, the simultaneous suppression of different boundary-layer insta-bilities to delay transition requires a carefully balanced aerodynamic wing design. Dur-ing aircraft operations the state of laminar flow is very sensitive towards different influ-ences, which can easily cause premature transition and thus a partial or complete loss oflaminarity. The main causes of a shortfall of laminar flow are a technical failure of thesuction system, a disturbance of the laminar flow by surface imperfections, icing or insectcontamination37, or blocked suction holes.

A partial or total mechanical failure of the HLFC system can lead to insufficient orcompletely lost boundary-layer suction in the wing nose region. On large swept wings,this probably causes transition at the attachment line or in the vicinity of the leading edgedue to strong cross-flow amplification. Hence, the probability of HLFC system failureshave to be analyzed and ensured to stay below an accepted limit, as it is done for otheraircraft systems [326].

The high surface quality requirements to ensure smooth laminar surfaces have to be satis-fied by appropriate and precise manufacturing techniques (see Sec. 2.3.2). Consequently,any damage of the laminar surface, e.g., caused by ground service operations or foreignobject debris, has to be prevented. Apart from structural surface imperfections, transitioncan also be provoked by insects or ice crystals, which can either block the suction holesor, more notably, adhere to the wing surface (usually in the leading-edge region). On thesurface, they act as 3D disturbances and—if exceeding a critical roughness height—leadto undesired transition in the form of turbulent wedges.

The occurrence of insects and their impact on laminar flow depend on atmospheric andclimate conditions, as well as their population density, which usually decreases with alti-tude [141]. Though insect population density above 500 ft is sparse [326], a suitable pro-tection mechanism has to be applied during operations at altitudes up to 5000 ft to avoidinsects from adhering to the wing surface [124]. Different insect protection techniques ex-ist, which can be classified into mechanical (shielding/deflectors, scrapers, wipers, papercovers) and liquid (mostly glycol based solutions) protection techniques [141]. The insectprotection liquids can also be used to prevent ice accretion, as it was demonstrated on theVFW 614 / ATTAS [252] and on a Dornier Do-228 [264] aircraft. When flying throughclouds, ice, or rain, a so-called self-cleaning or natural washing of the wing surface couldalso be observed, but this cannot provide any guaranteed protection [327]. Another pro-posal is a self-cleaning coating, serving both for insect protection and anti-icing [264].

37A good overview of potential contamination sources, their possible effects, and appropriate means ofmitigation or protection is given by Humphreys [133].

2.3 HLFC design and integration aspects 41

A widely accepted and applied solution is the use of a Krueger flap as mechanical shieldingagainst insects [316, 111]. With this multifunctional approach, the Krueger flap fulfillsboth its classical function as leading-edge high-lift device, as well as a protection functionby diverting insects around the wing and thus preventing them from striking and adheringto the surface. The optimal setting of the Krueger flap to successfully deflect the insectsusually differs from the aerodynamic optimum setting, which can slightly reduce low-speedperformance at maximum lift [124], and increase kinematic complexity and thus systemsmass. The Krueger flap is also selected as state-of-the-art solution for the HLFC airfoiland aircraft design applications presented within this thesis, see Chap. 4. A significantdrawback of using the Krueger flap as protection shield is that laminar flow cannot bemaintained on the lower wing side due to the gap between the retracted Krueger flapand the main wing structure. Alternative high-lift solutions, however, mostly involveeven more difficult problems in the context of HLFC aircraft design and integration. Aconventional slat additionally involves a gap on the upper side (at the junction of slatand fixed wing), which makes HLFC effectively impracticable. If a seamless leading-edge device (e.g., a “smart” droop nose) is applied, or even no leading-edge device atall, both upper and lower side could be laminarized, but maximum lift coefficient canreduce significantly, and an insect protection technique would additionally be required,e.g., using liquid solutions. Generally, upper surface suction promises higher savings thanonly lower surface suction [281], and—in combination with the Krueger flap—it also showsadvantages concerning manufacturing and maintenance aspects (see Ref. [173]).

Besides insects, different forms of ice, snow, or rain, as well as other airborne particlescan block the suction holes and lead to partial shortfall of suction mass flow. Morecritically, however, is the accretion of ice crystals in the leading-edge region of the wingsurface, which can lead to a drag increase or a reduction of maximum lift coefficient.For the realization of laminar flow, ice particles have to be prevented from adhering tothe wing, because they act as 3D disturbances, from which turbulent wedges originate.A suitable deicing or anti-icing system can basically be selected and applied similar toconventional operations without laminar flow. However, the combined integration of thesuction system, an anti-icing system, and, for instance, a Krueger flap (as high-lift andinsect protection device) into the wing nose box poses a difficult systems design problem,especially concerning space allocation and functionality during different operation phases.This task is additionally complicated by the small leading-edge radii of HLFC airfoils forthe prevention of ALT and by specific pressure distribution requirements (see Sec. 2.3.1).An integrated approach is, for example, presented by Overbergh [197], with a hot-air fullevaporative anti-icing system installed in the Krueger flap. During high-lift operations,the hot-air anti-icing system prevents ice accretion both on the Krueger flap as wellas on the main wing due to run-back ice. The dual function of the Krueger flap andits integration into the reduced space within an HLFC wing leading edge also requireadvanced kinematics concepts, which have been developed and intensively investigated,e.g., by Boeing [316] and Airbus [111]. To decide for a suitable selection and combinationof the discussed systems solutions, detailed studies have been conducted, in which differentsystems and protection techniques are compared and evaluated towards several criteriasuch as weight, system complexity, or airline operability (see, e.g., Behrens et al. [27]).

42 Chapter 2. Fundamentals and state of the art

An undesired partial or total loss of laminar flow during aircraft operations due to thestated reasons has also to be considered in the context of reserve fuel estimation. Ifplanned for ideal laminar conditions—i.e., no shortfall of laminar flow is expected duringthe whole cruise phase—the amount of loaded reserve fuel can be insufficient to completethe desired route in the adverse case. A reasonable fuel planning approach consideringthis problem will be presented in Sec. 3.2.6, which is incorporated into the proposed HLFCaircraft design method. The impact on aircraft sizing and HLFC overall fuel benefit willbe quantified in connection with the design studies in Chap. 4. Partial loss of laminarflow on only one wing side can also lead to unsymmetrical drag and flight characteristics,associated with increased additional control deflections and trim drag.

In addition to the successful integration and operation of the required systems, the intro-duction of the HLFC technology into real-world airline service also implies requirementstowards maintainability, repair, and overhaul [197]. This influences maintenance costs aspart of the operating costs (see Sec. 3.2.7), and can thus counteract the savings in fuelcosts. More detailed discussions about maintenance and further aspects implied by theapplication of HLFC within airline service are, for instance, given by Meifarth and Hein-rich [182] and Maddalon and Wagner [173].

3 Method for aircraft design withhybrid laminar flow control

This chapter describes the developed method for the design and assessment of air-craft with integrated HLFC systems. As introduced in Chap. 1 and pointed out in

Chap. 2, the preliminary design of HLFC aircraft is a complex multidisciplinary task, thesolution of which requires an integrated software approach including sophisticated designand analysis methods. A computer-based framework has therefore been developed withthe purpose ofMultidisciplinary Integrated ConceptualAircraftDesign and Optimization(MICADO). The software architecture and the overall aircraft design (OAD) philosophyof the MICADO framework are presented in Sec. 3.1. MICADO is conceived to performconceptual designs and optimizations of conventional commercial aircraft, as well as tobeing capable and extensible for preliminary and detailed design investigations. The im-plemented methods for the conceptual design of conventional aircraft components, sys-tems, and engines, as well as for the estimation of aerodynamics, masses and performancecharacteristics, are discussed in Sec. 3.2.

As outlined in Chap. 2, the integration of HLFC affects and changes the classical aircraftdesign approach in different ways. First of all, the aerodynamic design of hybrid laminarflow wings requires methods for the prediction of transition locations and transonic dragcharacteristics. For a practicable and efficient use of such methods on preliminary designlevel, a quasi-three-dimensional HLFC wing design approach is selected. Its implemen-tation and incorporation into the MICADO framework, as well as a demonstration of itsvalidity and relevant design sensitivities are presented in Sec. 3.3. Secondly, the compo-nents of the HLFC system have to be sized and integrated into the wing, in accordancewith the pressure and suction distribution at selected wing design sections. The HLFCsystem sizing methodology, which yields the additional mass and shaft power offtakes dueto the integrated HLFC system components, is described in Sec. 3.4. The incorporation ofthe HLFC aerodynamic and system design methods into MICADO allows for integratedHLFC aircraft sizing for given top-level requirements and design specifications.

3.1 Integrated aircraft design environment MICADO

The acronymMICADO stands forMultidisciplinary Integrated Conceptual Aircraft Designand Optimization and constitutes the central software platform for the proposed HLFCaircraft design method. A comprehensive summary of the MICADO framework alongwith selected design applications is given by the author in Ref. [228].

43

44 Chapter 3. Method for aircraft design with hybrid laminar flow control

The specific software requirements for the development and implementation of MICADObecome evident from the fundamental aircraft design considerations in Sec. 2.1. There,the conceptual and preliminary aircraft design task has been stated as to optimally designan aircraft for a given set of top-level requirements, and with respect to selected keyevaluation criteria, e.g., minimum block fuel or operating costs. Facing the huge numberof design parameters and their possible combinations, the execution of overall aircraftdesign (OAD) studies and optimizations can be very cost and time consuming.

The first requirement is thus to build the MICADO framework upon a smart softwarearchitecture, enabling efficient and flexible program execution and data exchange betweendifferent program modules. The key elements and characteristics of the MICADO softwarearchitecture are presented in Sec. 3.1.1. With the advantage of a homogeneous softwarearchitecture, another important requirement is a reasonable program execution sequenceto ensure an efficient and consistent OAD process. The implemented process flow ofthe MICADO design and analysis programs—also called overall aircraft design logic—isshortly presented in Sec. 3.1.2. The underlying models are discussed in detail in Sec. 3.2.

The realization of HLFC aircraft design through the development and implementationof specific HLFC aerodynamic and system design methods as an integral part of theMICADO framework is summarized in Sec. 3.1.3. The integrated HLFC method under-lines the general applicability of MICADO to technology evaluation tasks, because of itsstrong capability to capture the impact of specific design changes or innovative systemsintegration into key evaluation parameters on overall aircraft level.

The term integrated within MICADO hints at the integrated implementation of compo-nent sizing and performance assessment modules, and their iterative execution yielding afully converged overall aircraft design. This allows for correct coverage of interactions be-tween different disciplines as well as component resizing and mass snowball effects, whichare often neglected in conceptual design applications. The meaning of mass growth andfeedback interactions in the context of overall aircraft design and their realization withinMICADO are explained in Sec. 3.1.4.

The validity of the MICADO framework and its practical utility for preliminary aircraftdesign applications have been demonstrated in various publications and research projects,see, e.g., Refs. [14, 155, 159, 226]. Most recently, MICADO has been used to establish aCentral Reference Aircraft data System (CeRAS) for the European research community1,containing detailed reference aircraft data confirmed by an academic and industrial usergroup [229]. Validity of underlying models are partly discussed in the belonging sectionsbelow, and further evaluated in the context of the aircraft design application in Chap. 4.

Other existing aircraft design programs or frameworks are PrADO developed by Heinze[115], NASA’s FLOPS code [181], PASS [152], CEASIOM [232], as well as the commercialcodes AAA and RDS, originally based on Roskam’s [235] and Raymer’s [213] textbooks,respectively. A comprehensive overview and comparison (including MICADO) with re-spect to selected evaluation criteria is provided by Böhnke [34].

1The CeRAS project can be accessed online via http://ceras.ilr.rwth-aachen.de/.

3.1 Integrated aircraft design environment MICADO 45

3.1.1 Software architecture

For multidisciplinary aircraft design and optimization, a consistent and flexible softwarearchitecture is of particular advantage. The adverse case of software inhomogeneities inprogramming language, program structure or data handling can complicate the enhance-ment by new software modules and possibly lead to misinterpretation of parameters andunits. Further, the efficiency of the overall software system can be reduced in terms ofcomputation time as well as pre- and postprocessing effort by the user.

The MICADO software architecture addresses efficiency in MDO applications by its threemain characteristics that will be explained in the following paragraphs:

• consistent suite of loosely coupled software modules

• full aircraft design parameterization using XML2 storage

• framework for generic execution of parameter studies and optimizations

These software features set the base for the implementation of aircraft design and analysismethods (Sec. 3.2) and their integration into an overall context (Sec. 3.1.2). Further, theyfacilitate the extension by and the interface to more detailed methods for the integrationand assessment of the HLFC technology on aircraft level (Secs. 3.3 and 3.4).

Program structure and data handling

Figure 3.1 schematically illustrates the principle of program execution sequence and in-put/output data handling within MICADO. The control or program flow (vertical dashedarrows) shows that MICADO is composed of several stand-alone programs that are ex-ecuted in a certain order. The execution order (including iteration loops) is determinedby the underlying aircraft design logic (see Sec. 3.1.2).

The dashed line emphasizes the loose (data) coupling3 of the programs, that is, thereis no direct communication or data exchange between them. Instead, all relevant inputor output parameters are read from and stored to data files, where XML is the centrallanguage used within MICADO. Every MICADO module communicates at least with twoXML files (see data flow in Fig. 3.1, represented by horizontal solid arrows):

• Aircraft Exchange (AiX) XML file: central storage for all aircraft design parameters

• configuration XML file: storage for common control and specific program settingsthat influence implemented methods and that can be individually preset by the user

Every module has clearly defined responsibilities within the overall design logic (e.g., “siz-ing of wing planform” or “prediction of drag polars”) and comprises appropriate aircraftdesign or analysis methods. These are applied to the input variables read from the XML

2Extensible Markup Language, as defined and specified by the World Wide Web Consortium (W3C) [322]3Data coupling implies that “output from one software module serves as input to another module” [301].

46 Chapter 3. Method for aircraft design with hybrid laminar flow control

files. For the input parameters from the AiX file, only their existence is relevant but nottheir provenience, i.e., which program has calculated it. This principle supports replace-ability of modules and input data, e.g., in terms of response surfaces derived from moredetailed calculations or experiments. The final results from one MICADO module arewritten as output parameters into the AiX file and can serve as input parameters to an-other module. The availability of all required input variables for every tool is ensured bya reasonable execution sequence determined by the overall design logic.

program #1.XML

config. file #1

.XMLconfig. file #n program #n

inputs

outputs

...

settings

inputs

outputs

settings

program module

.XMLAircraft Exchange

(AiX) file:

aircraft design parameter file

serving as central data repository

.XML data filecontrol flow data flow

Legend

Figure 3.1: Principle of control and data flow of the MICADO environment

The consistency of the MICADO modules is at first guaranteed by a common program-ming language: to support object-orientation, transportability and low computation time,all programs are implemented in C++. Secondly, all software modules are based on a sim-ilar structure and they use, besides individual classes and functions, standardized C++classes and libraries, e.g., for XML parsing, output handling, as well as modeling of at-mosphere, aerodynamics, engine characteristics, or geometries.

The combination of consistency and modularity in terms of stand-alone capability furtherallows for individually specified design studies with flexibly built-up tool sequences.

XML parameterization: Aircraft Exchange (AiX) file

The data coupling approach with independent programs requires common, structured,and unique data storage. The Extensible Markup Language (XML) is chosen as standardwithin the MICADO environment for all parameter and configuration files. XML supportsplatform independence, uniqueness and convenient input and output handling (using opensource XML parsers), as well as it avoids file converting and formatting problems.

Within the MICADO design synthesis, the aircraft constitutes the central object. Conse-quently, all parameters that describe the conceptual aircraft design and its characteristicsare stored in one central XML file, called the Aircraft Exchange (AiX) file. An importantprinciple of the AiX file is the uniqueness and non-redundancy of parameters, that is, no

3.1 Integrated aircraft design environment MICADO 47

parameters are listed that indirectly result from a combination of other parameters. Fewreasonable exceptions occur when a parameter is indeed a composition of other param-eters, but additionally required as key design parameter (such as the operating weightempty). Every parameter within the AiX file is specified by a real or string value and com-plemented by Description and Unit attributes to emphasize human-legibility and clear-ness in data handling and to avoid confusion or misinterpretation of results.

Though “terseness in XML markup is of minimal importance” [322], huge datasets (e.g.,containing engine or aerodynamic characteristics) are stored in separate files and referredto from the AiX file. This supports readability and transportability, as well as it allowsfor easier handling and switching between datasets within design studies, e.g., for in-flightvariation of aerodynamic configurations.

The AiX file is hierarchically structured with the child elements of the root4 representingdifferent aircraft design disciplines, e.g., Geometry, Aerodynamics, orMasses. An overviewof the different disciplines in the AiX file and their sub-contents is given in table A.1.

Geometry modeling

An important precondition for the variation and optimization of aircraft geometries inconceptual and preliminary design is a unique and efficient geometry parameterizationand modeling. Geometry modeling in MICADO makes use of two basic componentsillustrated in Fig. 3.2a: the surface element and the body element.

The surface element is used for wings as well as horizontal and vertical tailplanes. Itstrapezoidal planform is defined by an inner and outer chord, a span width, and a leading-edge sweep angle. The three-dimensional (3D) surface object emerges from the additionaldefinition of an inner and outer airfoil geometry and a linear lofting between them. El-ements for lifting surfaces, i.e., wings and horizontal tailplanes, are further described bytwist and dihedral angles. A whole 3D surface is generated by putting multiple surfaceelements together. In addition to the outer shape, the surface definition is complementedby definitions of inner structure components (e.g., wing front and rear spars) as well asflight controls and high-lift devices.

The body element is applied for the generation of fuselages, nacelles, and landing gearcomponents (e.g., struts and tires). It is built similar to the wing elements, by a linear loft-ing between two circular or elliptical cross sections, which are not necessarily concentric.

The aircraft components are uniquely parameterized within the AiX file. An example forthe parametric XML description of a wing segment is given by the author in Ref. [228] viaXML Schema Definition (XSD). The conversion of the parametric description into a 3Dobject on program level is done by the implemented C++ geometry classes. They join thesingle elements to a full component using 3D reference points and matrix operations (e.g.,rotation of planar wing elements by twist and dihedral angles). The geometry classes areused within the MICADO modules for convenient handling and access of 3D geometries

4The root element in an XML document is the parent of all other elements [322].

48 Chapter 3. Method for aircraft design with hybrid laminar flow control

(e.g., for wing grid generation or space allocation). Various functions are therefore imple-mented that guarantee quick and consistent return of useful geometry values (e.g., wettedsurfaces, or sweep angles or spar heights at given spanwise and chordwise positions).

Body elementSurface element

(a) Basic geometry elements (b) 3D full aircraft configuration model

Figure 3.2: Principle of MICADO geometry modeling: C++ geometry classes create3D model based on parametric description in AiX XML file.

An example of a full 3D geometry model of a MICADO aircraft design5 is shown inFig. 3.2b. The left-hand side is illustrated as wireframe to show the composition of ba-sic surface and body elements to a full aircraft geometry6. For transformation of theMICADO geometry elements into a watertight volume model, an interface to the opensource software platform Open CASCADE [195] has been implemented. It automaticallyexports a 3D computer-aided design (CAD) model for detailed design or postprocessing,e.g., using computational fluid dynamics (CFD) or computational structural mechanics(CSM). Similar approaches for interfaces between conceptual design geometries and “high-fidelity” applications are shown by Haimes and Drela [107] or Rizzi et al. [232].

Framework for parameter studies and optimizations

The modular data coupling approach of MICADO, combined with the aircraft designmethodology described in Sec. 3.1.2, constitutes an integrated and flexible software en-vironment. To exploit its potential to perform extensive aircraft design studies and op-timizations in a large parameter space, a parameter study manager (PSM) program hasbeen implemented into MICADO allowing for generic setups of studies and optimizations.Any parameter from the AiX file or from any other XML file can be selected as one of anarbitrary finite number of n free variables x = (x1, x2, . . . , xn) or m output parametersy = (y1, y2, . . . , ym). For parameter studies, the free variables can be systematically var-ied using different possible combinations, while all output parameters are tracked. Fur-ther, single-objective

{minx∈Rn

(yi)}or bi-objective

{minx∈Rn

(yi, yj)}optimizations can be per-

formed by specifying the desired objective parameters yi (and yj). Additionally, bound-

5The design will be presented as turbulent baseline aircraft in Sec. 4.1.6Note that pylons and landing gear geometries are not displayed, but they are considered by the MICADOprograms, e.g., for prediction of component masses.

3.1 Integrated aircraft design environment MICADO 49

ary conditions of the form bi = f (x1, x2, . . . , xn, y1, y2, . . . , ym) can be specified generi-cally to narrow the design space and thus save calculation time and effort.

Recalling the MICADO program and data flow described above (see Fig. 3.1), the func-tionality of the PSM is illustrated in Fig. 3.3a. The upper box refers to either a param-eter study or an optimization, in both of which multiple MICADO runs are executed.For every run, the actual combination of parameter values x is written to their belong-ing paths in the XML files. For these inputs, an individually selected MICADO programsequence or a full design synthesis is executed, writing outputs to the AiX file. The se-lected output parameters y are then read from the specified XML files and tracked dur-ing the whole study process. The boundary conditions are checked either before or af-ter program execution. To minimize overall computation time the code for execution ofparameter studies has been parallelized using Open Multi-Processing (OpenMP) [52]. Aschematic code example for the parallelization of the above described process using theOpenMP directive #pragma omp is shown in Fig. 3.3b (mirrors are created first as localcopies of the MICADO program sequence).

write inputs

to XML

parameter studyor NOMAD

execute MICADO programs

read outputs

from XML

Check boundary conditions

21, , , nx x x 21, , , myy y

2 21 1, , , ,, ,,i n mb x x y yx y

(a) Execution and data handling sequence:upper block represents either a param-eter study or the NOMAD optimiza-tion algorithm.

#pragma omp parallel for

for (int i = 0; i < N; i++)

{

/**

- create mirrors

- write inputs to XML files

- execute MICADO program sequence

- check boundary conditions

- read outputs from XML files

**/

}

(b) Schematic code sequence for paral-lelized implementation of parameterstudy using OpenMP (loop over to-tal number of N evaluation runs)

Figure 3.3: Principle and implementation of MICADO parameter study manager

For the selection of a suitable optimization algorithm, it has to be noted that due tothe described complex interaction of different program modules—including XML param-eter file handling and the use of lookup tables (see, e.g., Secs. 3.2.2 and 3.2.3)—no self-contained analytical description of the entire MICADO code exists. This practically ex-cludes gradient-based optimization methods from being applied to MICADO, e.g., basedon algorithmic differentiation of the source code. An extensive review of derivative-freealgorithms and software implementations is given by Rios and Sahinidis [225]. The opensource black-box optimization software NOMAD (Nonlinear Optimization by Mesh Adap-tive Direct Search) [4, 166] has been selected and integrated into the MICADO param-eter study manager. It is well suited for the application in MICADO as the algorithmevaluates and optimizes a given combination of free variables only in dependence on se-lected objectives and boundary conditions. The NOMAD code applies a mesh adaptive

50 Chapter 3. Method for aircraft design with hybrid laminar flow control

direct search (MADS) algorithm [3, 5, 25, 164]. NOMAD is a validated optimization soft-ware that has already been applied to numerous multidisciplinary optimization problems(see, e.g., Refs. [10, 110, 177, 185]). For parallelized optimization, the integrated P-MADSalgorithm is applied that uses the Message Passing Interface (MPI) [287] under a mas-ter/slave paradigm [166]. A complete description of the parallel NOMAD versions to-gether with numerical results is given by Le Digabel et al. [165].

Applied to an aircraft design study, the PSM module provides full design sensitivities incase of parameter variations, and global minimum/maximum or Pareto optimal7 solutionsin case of single- or bi-objective optimization, respectively. The MICADO overall aircraftdesign logic and its underlying methods are described in the following sections.

3.1.2 Overall aircraft design approach

To create reasonable and consistent results within an aircraft MDO environment, the dataflow and the execution sequence of design and analysis tools must follow an appropriateorder and design logic. The MICADO overall aircraft design logic and process flow isschematically illustrated in Fig. 3.48. It shows how the different design and analysismodules (white square blocks) are arranged, and how they are interconnected by relevantdesign data (gray blocks). Comparable procedures are basically described in the standardaircraft design books, e.g., by Raymer [213] or Torenbeek [306].

MICADO is capable to initiate and perform a complete aircraft design “from scratch”,where the user only has to specify a minimum set of prescribed requirements and spec-ifications (see start element TLARs in Fig. 3.4). As described in Sec. 2.1, the TLARscomprise design range, payload, and further mission-specific parameters. The latter im-plicitly determine the aircraft performance in the flight phases cruise, climb, take-off, andlanding and thus size the key aircraft design parameters wing loading W/S and thrust-to-weight ratio T/W . After the sizing iteration, the converged aircraft design is checkedfor compliance with the TLARs to prove the validity of the implicit initial design choice.A complete list of the TLARs used in MICADO, complemented by parameter definitionsand boundary conditions, is given in table 4.1. Besides the design mission for overall air-craft sizing, a study mission is defined, on which the converged design is assessed, e.g., interms of block fuel or operating costs.

The automated MICADO design process starts with an initial estimation of W/S andT/W according to the given TLARs. Also, an initial value of the maximum take-offweight MTOW is estimated that is fed back into the subsequent design iteration (seeMTOW iteration loop in Fig. 3.4). At the beginning of every iteration, the structuralaircraft components (fuselage, wing, empennage, nacelles, landing gear) are sized for thegiven key design parameters, i.e., MTOW , reference wing area Sref , and sea-level staticthrust SLST . With varyingMTOW , these parameters change in every iteration run, be-cause W/S and T/W—as key drivers to fulfill the TLARs—are kept constant during de-sign iteration. Accordingly, airframe and engine components are resized in each iteration,

7More precisely, an approximation of the Pareto front is determined (see description by Audet et al. [26]).8The small numbers at the program blocks refer to the sections in which underlying methods are treated.

3.1 Integrated aircraft design environment MICADO 51

until overall design convergence is achieved. As an exception, fuselage geometry is not af-fected by a variation in MTOW , since cross-section and cabin sizing are mainly governedby payload and accommodation specifications. Fuselage and accommodation parametersare therefore commonly fixed before starting the sizing iteration. A description of the im-plemented component sizing methods is given in Sec. 3.2.1.

Component sizing

Mass estimationAerodynamic analysis

Initial sizing

MTOW iteration

Engine sizing

Drag polars

Systems sizing

Engine mapsOWE

Lift distr.Offtakes

Mission analysis

Engine model

W/S, T/W

Design evaluation:- Study mission analysis- Performance analysis - Monetary assessment

- Ecological assessment

Optimization

TLARs

Final design

3.2.1 3.2.5 3.2.2

3.2.6

3.2.3 3.2.4

3.2.7

Legend

MICADO program

Design data

Start/End

GasTurb ©

Figure 3.4: Process overview and design methodology of the MICADO environment

The aircraft geometry resulting from component sizing undergoes detailed aerodynamicand mass analyses (Secs. 3.2.3 and 3.2.4), the results of which are drag polars at differentflight conditions and aerodynamic configurations, and the operating weight empty OWE,including a detailed component mass breakdown. In addition to structural aircraft com-

52 Chapter 3. Method for aircraft design with hybrid laminar flow control

ponents, the engine and its performance characteristics are sized for the thrust require-ments, based on a full thermodynamic engine model (Sec. 3.2.2). Further, the whole con-ventional systems architecture is designed, and the power distribution is determined bya detailed model of energy sources and sinks (Sec. 3.2.5). The different systems massesare also considered for determination of the OWE, and the estimated shaft-power andbleed air offtakes are captured within the engine model during subsequent mission analy-sis. Based on drag polars, OWE, and engine performance maps, the block fuel requiredfor the design mission is calculated using a detailed flight performance model (Sec. 3.2.6).The mission simulation finally results in an updated value of MTOW (as sum of OWE,payload, and fuel mass), which is fed back into the convergence loop.

Consequently, all programs are re-executed, until MTOW and other control parameters(e.g., block fuel, overall center of gravity) reach convergence by falling below a specifiedresidual. The program execution sequence according to the MICADO design logic inFig. 3.4 as well as the convergence control are managed by a separate MICADO programthat can be adjusted and monitored by the user. The result of the design iterationis a completely converged aircraft design that is described in detail by all determinedparameters written into the AiX XML file. On a standard desktop computer, a full designsynthesis is obtained within a time of around 15–20 minutes if started “from scratch”.

For the converged aircraft design, a detailed performance assessment is conducted. Theresulting performance parameters are compared and checked for compliance with theTLARs. Further, different methods have been implemented for technical, monetary, andecological assessment of the converged design (Sec. 3.2.7). Common parameters used forassessment and comparison of different aircraft designs are

• block fuel on study mission: BFsm, kg

• cash operating costs9: COC, $100 ASK

Within this thesis, the primary focus lies on the nonmonetary assessment of aircraft de-signs in terms of BFsm, mainly to reduce unnecessary dependencies on additional uncer-tainties, e.g., fuel price.

Using these evaluation parameters as objectives, and selected aircraft design parametersas free variables, individual parameter studies and optimizations can be performed usingthe PSM module described in Sec. 3.1.1. Every evaluation point of a study or optimizationthen refers to a fully converged aircraft design synthesis. For instance, the key designparameters W/S and T/W , or selected wing design parameters can be varied to find anoverall design optimum with respect to minimum block fuel. Based on the integrated anditerative sizing approach, a characteristic strength of MICADO is the capability to capturethe effect of varying requirements and particular design changes into key overall aircraftdesign parameters, such as MTOW, OWE, BF, or COC. The capturing of local designchanges on aircraft level (including resizing effects) is also of particular importance forthe assessment of innovative systems or technologies, such as HLFC within this thesis (see

9COC are also predicted on the user-defined study mission; ASK denotes available seat kilometers.

3.1 Integrated aircraft design environment MICADO 53

next section). As an outstanding feature of MICADO, the implicit coverage of componentresizing and mass snowball effects is examined in more detail in Sec. 3.1.4.

To summarize, the described MICADO overall aircraft design approach, along with theunderlying flexible software architecture, forms an indispensable basis for reliable design,assessment, and optimization of commercial aircraft with integrated HLFC systems.

3.1.3 Integration of HLFC methods into MICADO

The HLFC aircraft design and assessment methodology is an integral part of the MICADOframework. A summary and application example is given by the author in Ref. [231]. Themain influences of HLFC technology integration have been stated above as the aerody-namic wing design (including influences on structural wing mass), and the additional massand power offtakes of the HLFC system. The implementation of the associated methodsand their incorporation into the MICADO OAD logic is illustrated in Fig. 3.5, which isan extract from Fig. 3.4, complemented with HLFC data flow elements (in blue).

Component sizing

Mass estimationAerodynamic analysis

MTOW iteration

Engine sizing

Drag polars

Systems sizing

Engine mapsOWE

Lift distr.Offtakes

Mission analysis

Engine model

MICADO program

Design data

HLFC power

offtakes

HLFC systems

mass

HLFC airfoil sections

HLFC airfoil drag polars

- Cp and Cq distributions

- HLFC 3D wing geometry

HLFC data

Legend

HLFC 3D wing geometryGasTurb ©

Figure 3.5: Extract of MICADO process with integrated data flow for HLFC aircraftdesign and assessment

The difficult task of covering HLFC aerodynamic wing design on preliminary design levelis solved through the integration of a quasi-three-dimensional wing design approach, com-bined with an interface to a database with specifically optimized HLFC airfoils and theiraerodynamic characteristics. The concept development and implementation of this ap-proach is described in detail in Sec. 3.3. The interconnection of the conventional aero-

54 Chapter 3. Method for aircraft design with hybrid laminar flow control

dynamic analysis program (Sec. 3.2.3) with the HLFC airfoil database allows incorporat-ing transonic HLFC airfoil drag polars (including predicted transition locations) into thefull aircraft configuration drag polars. The lofting of the HLFC airfoil shapes using theMICADO geometry classes (see Sec. 3.1.1) provides the necessary three-dimensional winggeometry, e.g., for wing mass estimation, tank volume integration, or space allocation.

The HLFC system design module, which is described in Sec. 3.4, is integrated into theconventional systems architecture (Sec. 3.2.5). Besides conventional aircraft design dataand HLFC wing geometry, pressure (Cp) and suction (Cq) distributions at selected aerody-namic wing design sections are used as input. With the resulting suction mass flow rates,the required power is estimated and the compressors are sized. Locations and masses forall HLFC system components are determined, including ducting and wiring to the elec-trical generator of the aircraft. The total mass of the HLFC system is added to the con-ventional aircraft mass components (Sec. 3.2.4). The shaft power offtakes are integratedinto the overall power distribution network (Sec. 3.2.5), which is taken into account bythe thermodynamic engine model (Sec. 3.2.2).

The integration of all effects into one evaluation quantity (i.e., block fuel) is provided bythe detailed mission analysis model (Sec. 3.2.6), which also allows simulation of HLFCsystem in-flight failure and its impact on fuel planning and aircraft sizing. Note that theiterative character of the MICADO-HLFC implementation accounts for all relevant designinteractions, including mass snowball effect and component resizing (see next section).

Apart from the detailed implementation of a specific technology integration (as for theproposed HLFC method), MICADO can be used for generic investigations of design sensi-tivities. For example, systematic changes of aerodynamic, mass, or propulsion character-istics for a given baseline aircraft—either as pure off-design analysis, or including full air-craft re-convergence—quickly reveal fuel or costs saving potentials for a virtual systems ortechnology integration. Or, reversely formulated, for a desired reduction of fuel or costs,the sensitivity analyses quantify the amount of required improvement in aerodynamics,structures, or engine technologies. For HLFC, this will be demonstrated in Sec. 4.2.

3.1.4 Design interactions: mass snowball effect and aircraft resizing

Aircraft undergoing a design process—or, being already in service—can encounter subse-quent mass growth, e.g., due to specific design changes, structural modifications, or in-tegration of new technologies or systems. If the aircraft empty mass (OWE) increases,fuel consumption on a given (design) range rises. While increased fuel mass and volumemay even require larger fuel tanks, it primarily results in a higher maximum take-off mass(MTOW ). This can in turn involve further adaptations of structural components (e.g.,wing, tails, landing gear) due to increased flight or ground loads. The thereby increasedcomponent masses again lead to additional fuel mass, and thus higher MTOW , which re-sults in an iterative process. The iterative interaction between take-off mass and massesof structural, systems, or propulsion components is commonly denoted as mass snowballeffect. The so-called mass growth factor quantifies, how much the take-off mass is finallyincreased, provoked by a unit mass increase (e.g., 1kg) of the empty mass due to the orig-

3.1 Integrated aircraft design environment MICADO 55

inal design change (without iteration). Its value strongly varies with aircraft type andrequirements; for subsonic transport aircraft, Fürst [87] states a value of roughly 1.5.

W/S

T/W

cruise req.take-off req.

climb req.

landing req.

⇧ ⇧

(mass growth)MTOW

MTOW

sizing point

valid sizing region

Figure 3.6: Initial sizing diagram: influence ofvariation in MTOW on compli-ance with TLARs

From the overall aircraft design perspec-tive, a significant variation in MTOW canalso involve performance degradations, oreven a violation of requirements, which canin turn be mitigated by a resizing of mainaircraft components (including outer ge-ometries). To demonstrate this, it is mean-ingful to consider a mass growth in com-bination with the key sizing parameterswing loadingW/S and thrust-to-weight ra-tio T/W . Provided that airframe geometryand engines remain unchanged (i.e., S =const, T = const), an increase in MTOWincreases W/S, and reduces T/W . The in-fluence of this relationship is schematicallyillustrated in Fig. 3.6 by a typical initialsizing diagram T/W = f (W/S), as intro-duced in Sec. 2.1. The limiting curves10—representing take-off, climb, cruise, and land-ing requirements—enclose a valid sizing region, inside which an optimum combination ofT/W and W/S has to be chosen. A deviation from this (optimal) sizing point gener-ally reduces overall performance, and can imply noncompliance with TLARs. In Fig. 3.6,where the sizing point is chosen close to the boundary lines, both take-off and climb re-quirements are prone to be violated in case of a mass growth (MTOW ↑). Design adap-tations as described above can be the necessary consequence.

The opposite case of a subsequent mass reduction becomes especially relevant for a retrofitdesign, where a given baseline aircraft is investigated, e.g., for the integration of a fuel-saving technology. If airframe and engine components are again kept constant (“iso-geometry”), the retrofitted design with reduced MTOW exhibits reduced W/S, and in-creased T/W . This is rather uncritical concerning compliance with TLARs (see Fig. 3.6);however, reduced wing loading can also imply performance degradations, and an increasedT/W can involve an “overpowered”, too heavy propulsion system. These effects becomeespecially significant for technologies that promise high fuel and weight savings, e.g.,HLFC or a lighter CFRP wing.

Thus, for maximum exploitation of the benefit due to HLFC integration, a resizing ofaircraft components should be considered, and optionally a re-optimization of W/S andT/W . In MICADO, the preselected combination of W/S and T/W is kept constant dur-ing design iteration (see Sec. 3.1.2). Thus, with varying MTOW , a rescaling of wing area(and thus empennage areas) is performed, i.e., Sref = MTOW

W/S; likewise, the propulsion sys-

tem is rescaled in terms of sea-level static thrust11, i.e., SLST = TW

MTOW gneng

. This prevents

10The shape of the TLAR limiting curves are based on idealized analytical performance equations that arenot explicitly stated here, but, for example, provided by Raymer [213] or Torenbeek [306].

11The sea-level static thrust refers to one engine, i.e., T = nengSLST , where neng is the number of engines.

56 Chapter 3. Method for aircraft design with hybrid laminar flow control

both suboptimal wing performance and an oversized propulsion system, and hence in-creases overall net savings in terms of block fuel or operating costs. The recomputation ofall mass components (see Sec. 3.2.4) during MICADO design iteration allows reliable cap-turing of overall mass growth due to MTOW snowballing, without relying on statisticalapproaches, e.g., based on a mass growth factor. Note that the iterative component sizingwithin MICADO also involves interactions between aerodynamic, structural, and enginecharacteristics. For example, the drag reduction due to laminar flow also reduces block fueland MTOW , which in turn leads to smaller and lighter airframe and engine components.The complex design and discipline interactions require careful design and analysis, comple-mented with systematic parameter variations to find overall design optima. For the HLFCaircraft design and optimization studies in Chap. 4, both the retrofit and component resiz-ing procedures will be applied to quantify the overall net benefit of HLFC on a long rangeaircraft, and the additional saving potential accruing from integrated component resizing.

3.2 Conventional aircraft design and analysis methods

This section describes the implemented MICADO design and analysis methods that un-derlie the program blocks in Fig. 3.4 (with numbers referencing to related subsections).The focus herein lies on the “conventional” aircraft design synthesis, while the enhancedaerodynamic and system design methods as part of the HLFC overall aircraft design (seeFig. 3.5) will be described in detail in Secs. 3.3 and 3.4, respectively. However, let usinitially concentrate on some general principles that have to be considered for the imple-mentation of aircraft design methods and their integration into an overall framework.

The key characteristics of MICADO are its flexible software architecture (Sec. 3.1.1) andits consistent overall aircraft design (OAD) logic (Sec. 3.1.2), which are now complementedby several program modules containing specific design and analysis methods. Hence, themodule implementation first of all conforms with, and benefits from the described softwarestandards, i.e., input/output handling via XML files (see Fig. 3.1), usage of commonclasses and libraries (e.g., geometry, aerodynamics, engine, atmosphere), and stand-alonecapability. If required or beneficial, “external” program modules are incorporated byappropriate wrapper functions12 (see examples in Secs. 3.2.3, 3.3.4, and 3.3.5).

Second, all implemented methods have to serve the central purpose of the overall frame-work, that is, to generate consistent preliminary aircraft designs for given TLARs and op-timize them for given objectives (e.g., block fuel). Since this requires automated and it-erative execution of program sequences within large design spaces, and within an accept-able amount of time, key desired features for the included methods are robustness andmoderate computational costs. Two other important guidelines are introduced as follows:

1. Model types, complexity, and prediction accuracy should be balanced between allmethods in the OAD framework, in agreement with the specific intended application.

12The wrapper approach is used to call an external program module by (1) writing its input file using appro-priately converted MICADO parameters, (2) executing it by creating a child process, and (3) retrievingrequired parameters from generated output files and feeding them back into the MICADO main module.

3.2 Conventional aircraft design and analysis methods 57

2. For a reasonable balance, model complexity and desired accuracy should be mea-sured by the impact of the predicted parameter on the overall aircraft design.

This principle of proportionality has been consistently applied for a balanced method de-velopment within MICADO and will be referred to throughout the following sections. Themethod types (see 1.) implemented in MICADO comprise analytical, empirical, semiem-pirical, and numerical equations and approaches. All MICADO methods are preferablyphysics-based, where the level of detail is tried to be maximized as far as compliant withthe required low computation time. This time limitation and the required robustness andreproducibility also narrow the scope concerning model complexity. For example, highlycomplex models with high pre- or postprocessing effort, or with uncertainties concern-ing numerical stability, are not applicable within the automated process. However, if ahigher model complexity is required or justified by the specific application, appropriatesurrogate models can be applied as interface to the OAD framework (see, e.g., the enginemodel approach in Sec. 3.2.2, or the HLFC airfoil database in Sec. 3.3.8).

The required balance in model complexity and accuracy means that across the disciplines,data and parameters predicted by a module should serve as input for another module, oroffer an added value in understanding and assessing the overall design. If, for example,very detailed aerodynamic characteristics are computed, but structural or performancemodels lack complexity to exploit these data for load or mission analysis, the aerodynamicmodel complexity can be considered as disproportionately high. An imbalance also occurs,if a key influence of a certain parameter is captured (e.g., lower structural weight dueto increased wing thickness), but key adverse sensitivities are not correctly modeled (inthis example, increased wave drag). This can lead to wrong locations of global optima inmultidisciplinary design studies. Facing the large number of conflicting requirements inaircraft design, the completeness of design sensitivities is thus crucial for the consistencyof the overall framework.

Apart from this proper OAD balance, a more detailed resolution of a certain design as-pect can indeed be necessitated by the specific intended application, which can be theimprovement or integration of an aircraft component, system, or technology; neverthe-less, the method balance has to be (re)established. The successful incorporation of suchdetailed design elements into an automated OAD process has been pointed out as unre-solved research topic, in particular for the herein covered HLFC technology. For the pro-posed approach, the complex interconnections in Fig. 3.5 showed how the modeling andintegration of detailed HLFC tasks (e.g., transition prediction, transonic airfoil design,HLFC system design) also requires profound level of detail for the “conventional” designmethods (e.g., considering power offtakes, engine modeling, or mission simulation).

The second guideline above proposes to measure model complexity and prediction accu-racy with respect to the OAD impact of a parameter. This can be quantified in termsof its influence on fuel efficiency, which was expressed by the specific air range SAR inEq. (2.1). Like the Breguet range equation, it contains the key “levers” to improve aircraftfuel efficiency. Consequently, similar accuracy and level of detail are required for predic-tion of overall aircraft aerodynamics (in terms of L/D at given Mcr), overall engine per-

58 Chapter 3. Method for aircraft design with hybrid laminar flow control

formance (in terms of SFC), and aircraft weight (in terms of OWE)13. Likewise, mod-eling effort and accuracy should be balanced within the more detailed parameter groups(e.g., drag items, mass components, or systems power requirements). If this importantbalancing is not ensured, the OAD framework is susceptible to biases or false conclusionsduring discussion and evaluation of results. One bias is here denoted as pretended accu-racy or the elimination of inaccuracies, that is, if two (or more) parameters of similarOAD impact (e.g., L/D and SFC, or two comparable mass items) contain large predic-tion errors, but with an eliminating effect. Certainly, the required accuracy of “interme-diate” results also implies correct sensitivities towards parameter change (e.g., change ofwing mass and wave drag due to reduced sweep angle). This is crucial for a consistent de-sign, and in particular to guarantee reliability in multidisciplinary design studies, whereinaccurate sensitivities can mislead the designer towards nonoptimal solutions.

Complementary to the bias above, an elimination of accuracies can ensue for parameterswith very low OAD impact. For instance, consider a mass item that amounts to 1 % of theOWE; here, the prediction accuracy is of marginal importance, because even apparentlylarge relative errors (of, e.g., 20 %) can virtually be neglected from the OAD perspective.Generally, if the influence of a parameter is negligible compared to other parameters, itmay be excluded from consideration to limit model complexity and development effort.

The above examples pointed out the guidelines and possible pitfalls during developmentof an OAD framework, but still in a general and qualitative way. Since the quantitativeinfluences and dependencies are unknown a priori (apart from experience), the definitionof adequate levels of model complexity, accuracy, and parameter sensitivities requires atedious and iterative process, including testing of implemented models and analysis of re-sults. This has been strictly pursued during the development of the proposed MICADO-HLFC method. Generally, the procedure contains elements of the classical software ver-ification and validation (V&V) process, where verification means to confirm compliancewith specified requirements (i.e., “solving the problem right”), and validation to confirmcompliance with the specific indented use (i.e., “solving the right problem”), which alsoincludes correct modeling of physical laws [302]. In this definition, validation is gener-ally applicable to some MICADO analysis methods, e.g., for aerodynamic drag prediction(see Sec. 3.3.3) or mission simulation (see Sec. 3.2.6). On the other hand, many imple-mented simple analytical or (semi)empirical equations and models “only” allow verifica-tion or plausibility checks by comparison against “real” aircraft data or parameters. Gen-erally, these comparisons can involve uncertainties due to unknown boundary conditionsof available data or due to limited complexity of the preliminary design model.

Even higher ambiguity in evaluating the “right solution” is implied by the component de-sign methods and by the OAD method itself, which have to solve the design problem posedby given TLARs and specifications (see Sec. 2.1). As already indicated by the term “de-sign”, the interpretation of these requirements allows a certain degree of freedom, which isreflected in different design philosophies and strategies (e.g., Airbus versus Boeing), cur-rent and future market scenarios (e.g., fuel price), or other economical or ecological bound-ary conditions. The OAD process itself hence always comprises and combines explicit

13Though the influence of OWE on block fuel is smaller than that of L/D or SFC, the similar magnitudeand its importance regarding mass snowball effects (see Sec. 3.1.4) requires a similar prediction accuracy.

3.2 Conventional aircraft design and analysis methods 59

knowledge (implemented in the physical models) with implicit knowledge (based on em-pirical evidence or experience about realized aircraft types). Thus, according to the abovedefinition, validity of the OAD framework can still be achieved if it contains valid physicalmodels and reasonable strategies to solve the design problem for given TLARs. It is fur-ther suggested to include the above introduced guidelines into the definition of a quality-assured and valid OAD framework, which means to demonstrate OAD consistency, com-pleteness and accuracy of sensitivities, and balance in model complexity and accuracy. Forthe proposed MICADO-HLFC approach, these properties will be shown by the methodicalinsight given within this chapter, and the long range aircraft design application in Chap. 4.

Though the presented guidelines and discussions might appear self-evident for the devel-opment of a simple aircraft design tool, they are regarded as prerequisite for the solution ofthe central task within this thesis, that is, to integrate detailed HLFC design aspects intoan automated preliminary design environment. Prior to elaborating on the HLFC-specificmethods, the following sections will give compact descriptions of the “conventional” de-sign and analysis methods, with specific focus on their implementation and significancewithin MICADO. For more detailed or fundamental descriptions, the reader may refer tothe cited references or to the standard aircraft design books, e.g., by Raymer [213], Toren-beek [306], Roskam [235], Nicolai [190], or Howe [132].

3.2.1 Component sizing

The component sizing block in Fig. 3.4 comprises different program modules that deter-mine location, layout, and geometrical shape of the aircraft main structural components,i.e., wing, empennage, nacelles and pylons, as well as landing gear. The main input pa-rameters are the TLARs and the key sizing parameters MTOW, Sref , and SLST . Thegeometry is determined in terms of the parameterized description presented in Sec. 3.1.1and written into the AiX XML file. Already sized components can be used and accessedby other modules via the MICADO geometry classes (e.g., the empennage module re-quires wing and fuselage geometry). The result is a full general arrangement and 3Daircraft geometry as exemplified in Fig. 3.2. The geometry components are resized andadapted during MICADO process iteration, until overall design convergence is obtained.Several strategies and design rules for the placement of, as well as the interaction and pri-ority between different components are implemented and applied during design iteration(e.g., for propulsion and landing gear integration into the wing). Besides implicit sizingbased on experience or semiempirical approaches, the full parameterization allows for lo-cal or global (i.e., overall-aircraft) design adaptations, iterations, and optimizations withrespect to selected objectives. The sizing methods implemented for the single componentsare shortly discussed below.

The fuselage design program determines the optimum cross section, the layout of cabinand cargo decks, as well as the outer fuselage geometry, according to given payload, accom-modation, and cargo specifications. Further accommodation data such as cabin or cargovolumes are calculated for later systems design and power distribution (see Sec. 3.2.5).Since the fuselage design is mainly determined by payload and accommodation specifica-

60 Chapter 3. Method for aircraft design with hybrid laminar flow control

tions, it is initially fixed and kept constant during MTOW iteration. Consequently, fuse-lage and cabin are only redesigned if payload requirements change.

The wing design program sizes planform parameters and airfoil shapes, and places high-lift devices and spar positions. Detailed considerations will be given in Sec. 3.3 in connec-tion with the proposed HLFC transonic wing design method. The sizing module for hori-zontal tailplane (HTP), vertical tailplane (VTP), and control surfaces applies semiempir-ical approaches, including volume coefficients; optionally, an implicit and iterative solu-tion of flight-mechanics equations with respect to certification specifications can be used(see Ref. [82]), where stability and control characteristics14 are obtained by a wrappedversion of the Digital Datcom program [314].

For wing-mounted engines (as considered within this thesis), nacelles and pylons are sizedwith respect to the installed engines and placed according to experience-based designstrategies. Sizing and placement of main and nose landing gear are conducted accordingto critical clearances and stability criteria (for details, see, e.g., Refs. [48, 51]). Specificdesign aspects of nacelles, pylons, and landing gears, however, are of minor importancein the context of this thesis.

3.2.2 Engine modeling

The MICADO engine model is based on a full thermodynamic gas-turbine cycle analysisconducted with the commercial software GasTurb15 [153]. GasTurb has already been usedin several aircraft design applications or performance analyses, see, e.g., Refs. [54, 108, 280,312]. A validation is, for example, presented by Vera-Morales and Hall [312] who comparedata from GasTurb models with flight data recorded from commercial aircraft operations.

GasTurb thermodynamic engine model

Exported engine maps

MICADO engine model· interpolation in engine maps

· consideration of offtakes and operational limits

· rubber-engine scaling

Operational limits

Power offtakesSca

led e

ngi

ne

chara

cter

istics

GasTurb ©

, ,NF f M h N1

1, ,fm f M h N

Figure 3.7: Principle of MICADO engine model

Figure 3.7 illustrates how GasTurb is applied within MICADO. From designed GasTurbthermodynamic models, engine maps are exported as CSV16 data sheets containing severalengine parameters—e.g., net thrust FN , fuel flow mf , exhaust gas temperature EGT—asa function of Mach number M , flight altitude h, and the rotational speed of the low-pressure shaft N1, i.e., FN = f (M, h, N1) , mf = f (M, h, N1), etc.

14Dynamic flying qualities (including handling qualities) can also be assessed with a module developed bythe author [227], which incorporates the 6-degree-of-freedom flight dynamic model JSBSim [29].

15A listing of GasTurb references can be accessed online at http://www.gasturb.de/publications.html.16comma-separated values

3.2 Conventional aircraft design and analysis methods 61

The unscaled engine maps are used as basis for the MICADO engine model, inside whichthe low-pressure spool speed N1 is the connecting variable between all engine parameters.The MICADO engine model also determines and considers operational limits of the en-gine—e.g., EGT , N1, acceleration/deceleration17, or fuel-air-ratio in the combustor—forthe actual flight condition (i.e.,M and h). Available thrust, fuel flow, and other engine pa-rameters are then computed according to operational limits, selected engine rating (e.g.,Maximum Continuous, Climb), as well as bleed air (mbleed) and shaft power (Pshaft) off-takes. As an important aircraft design parameter, the specific fuel consumption

SFC = mf

FN= f (M, h, N1, Pshaft, mbleed) (3.1)

thus shows the relevant sensitivities to flight condition (M, h), engine setting (N1), andofftakes (Pshaft, mbleed).

To summarize, a detailed engine model is integrated in MICADO that allows for correctcapturing of the impact of altitude, Mach number, and offtakes on engine performance andefficiency, while also respecting operational limitations. These dependencies are also con-sidered for the mission simulation by the detailed MICADO in-flight performance analysiscode, see Sec. 3.2.6. As the thrust-to-weight ratio is sized to match the specific thrust re-quirements, the sea-level static thrust SLST scales withMTOW during MICADO designiteration. Accordingly, the engine model including its performance parameters is scaledwith respect to the actual SLST value. For the influence of bleed air and power offtakes,specific correction functions are implemented based on detailed analyses of available en-gine installation manuals. For the integration of the propulsion system (including nacellesand pylons), engine core geometry parameters are scaled according to engine “rubberizing”principles. Scaling of engine characteristics is assumed to be valid for small deviations ofthe SLST from its reference value, which is usually the case for specific parameter varia-tions around a baseline aircraft configuration, see Chap. 4. Various baseline engine modelsin different thrust classes have therefore been built and integrated into MICADO, whichcan automatically be selected for the thrust requirements of the actual aircraft design.

3.2.3 Full-configuration aerodynamic analysis

For overall aircraft design applications, the aerodynamic characteristics of the full aircraftconfiguration have to be taken into account. Most importantly, this includes the predictionof aircraft drag polars, which are a crucial input for the mission simulation (see Fig. 3.4).To provide input for all mission phases, the prediction methods have to cover subsonic andtransonic flight regime, and should further include trim capabilities to balance forces andmoments, especially during cruise. Consequently, the trimmed aircraft drag polars showsensitivities towards flight condition, aircraft geometry, and aerodynamic configuration,i.e., CD,total = f (CL, M, Re, geometry, configuration).

17The acceleration or deceleration can be measured by the maximum or minimum ratio of the fuel flow mf

to the burner inlet pressure p3 (as denoted for the respective thermodynamic station within GasTurb).

62 Chapter 3. Method for aircraft design with hybrid laminar flow control

Since the full-configuration aerodynamic analysis including the large number of functionalrelationships has to be executed automatically and multiple times during MICADO overalldesign iteration, highly complex or computation-intensive methods are not applicable. Onthe other hand, most conceptual design approaches lack some of the capabilities describedabove, and are especially insufficient for the difficult requirements implied by HLFC wingdesign (see Sec. 2.3.1). Therefore, the MICADO aerodynamic analysis program combinesdifferent methods with varying fidelity levels, which are chosen according to the aerody-namic impact of the different drag and aircraft components and the specific application.For example, viscous and wave drag estimation for HLFC wings requires a sophisticatedmethod, which is described in detail in Sec. 3.3 and connected to the MICADO full-configuration aerodynamic module by an airfoil database approach. On the other hand,aerodynamic properties with reduced significance in the present preliminary design con-text (e.g., influence of fuselage and nacelles on induced drag) are rather covered by semiem-pirical correction functions. An overview of the applied methods and corrections to predictlift (CL), pitching moment (CM), and different drag (CD) coefficients is given in table 3.1.

Table 3.1: Method overview for prediction of aerodynamic coefficients in MICADO

Aerodyn. Considered Prediction Comments andcoefficient components methods referencesCL wing, HTP, (fuselage) LIFTING_LINE incl. compressibility corr. *CM wing, HTP LIFTING_LINE incl. compressibility corr. *

fuselage, nacelles semiempirical Eqs. in Torenbeek [306]CD,ind wing, HTP LIFTING_LINE incl. compressibility corr. *

fuselage, nacelles semiempirical Eqs. in Roskam [235]CD,visc wing MSES via database interface †

tails, fuselage, nacelles component buildup Eqs. (3.3)–(3.4)CD,wave wing MSES via database interface †

HTP Korn–Mason ‡ Eqs. (3.5)–(3.7)* The Göthert–Prandtl–Glauert compressibility correction included in LIFTING_LINE is used [126].† The transonic flow solver MSES is described in Sec. 3.3.4; for the database interface, see Fig. 3.10.‡ CD,wave,htp is mostly negligible; the Korn–Mason Eq. is optionally applicable to turbulent wings.

The table concentrates on the clean aircraft configuration during cruise, which is of pre-dominant importance for HLFC long range aircraft design. The total drag coefficientCD,total is composed of the following components, named after their physical origins:

CD,total = CD,ind + CD,visc + CD,wave. (3.2)

This breakdown into induced drag (CD,ind), viscous drag (CD,visc), and wave drag (CD,wave)components will be used throughout this thesis, but is only one out of many possibledrag composition definitions18. The drag component terminology will also be revisited in

18As noted in Chap. 1, the comma-separated, extended subscript notation is preferred over commonly usedshorter notations (e.g., CDi, CDv, CDw) to avoid misunderstandings in light of various drag definitionsand breakdowns used throughout this thesis (e.g., subscript w could denote either wave or wing).

3.2 Conventional aircraft design and analysis methods 63

connection with the wing design method in Sec. 3.3. The single summands in Eq. (3.2)include contributions of the aircraft components listed in table 3.1 (see second column).The methods listed in table 3.1 and their underlying equations are described in more detailin the following paragraphs. The coverage of low-speed aerodynamic configurations isdiscussed at the end of this section. All aerodynamic data are exported into a specific XMLpolar data format (similar to Ref. [117]), which is accessed during mission simulation viaMICADO aerodynamic C++ classes providing appropriate data interrogation functions.

A description of the initial implementation of the MICADO aerodynamic module (withoutairfoil database interface), along with a comparison and validation against existing aircraftmodels is given by Lammering et al. [157]19. A similar approach and validation of full-configuration drag estimation can be found in Ref. [106]. Boppe [37] comprehensivelysummarizes aircraft drag analysis methods; a recent review of drag prediction methodsin aircraft design is given by Takahashi et al. [299]. Mason further provides an extensiveoverview of available software for aerodynamic design and analysis on his website [178].

Induced drag, pitching moment, and (total and spanwise) lift coefficients

As core program of the MICADO aerodynamic analysis module, the multiple lifting-linecode LIFTING_LINE20 (LILI) is incorporated using the aforementioned wrapper ap-proach. It is used to compute (total and spanwise) lift, pitching moment, as well as in-duced drag for the wing-HTP configuration. LILI is based on potential theory and appli-cable to nonplanar wing configurations with multiple lifting surfaces, where each surface issegmented into spanwise and chordwise panels. On each panel, a vortex system is placedand solved under consideration of transitional and kinematic flow conditions. A quadraticcirculation distribution is defined on each spanwise panel, which is a key advantage com-pared to conventional vortex-lattice methods (VLM) and provides accuracies comparableto lifting-surface or panel methods. The integration of the circulation over the wing yieldsthe lift coefficients, while CD,ind is obtained via a projection of the circulation into theTrefftz plane [126]. The applicability of LILI is extended to compressible subsonic flows,where Göthert’s 3D extension [98] of the Prandtl–Glauert rule [251] is used for compress-ibility correction, including appropriate geometry modifications [126]. At given total liftcoefficients CL, spanwise Cl distributions computed with LILI even show acceptable agree-ment at transonic conditions compared with RANS (Reynolds-averaged Navier–Stokes)computations (see, e.g., Ref. [169], or the validation example in Sec. 3.3.3). Capabilitiessimilar to LILI are, e.g., provided by the AVL code [67], which employs an extended VLM.

The prediction of drag polars CD = f (CL) at different flight conditions requires multipleLILI runs. Though execution at one evaluation point only takes few seconds, the largenumber of required (M | CL) combinations make LILI a critical element for the requiredcomputation time of the MICADO OAD iteration. As a compromise, LILI is executedover a wide range of selected angles of attack α, but only once without and once with com-pressibility correction (using the design cruise Mach number Mcr). The relations CL (α)

19The presented modifications of semiempirical methods have been revised for use within this thesis.20The LIFTING_LINE procedure and software have been developed by Horstmann [125] at the GermanAerospace Center (DLR). For the studies presented in this thesis, release version 2.3 is used [126].

64 Chapter 3. Method for aircraft design with hybrid laminar flow control

and CM (α) from the LILI sample points are then approximated by a linear function, andthe relation CD,ind (CL) by a quadratic function, both using least-squares fitting via QRdecomposition. The resulting analytical expressions allow evaluation at any CL and witharbitrarily small increments ∆CL, which is crucial for proper assignment of CD,ind withCD,visc and CD,wave according to Eq. (3.2). The total coefficients CD,ind, CM , and CL, aswell as wing spanwise Cl distributions at all off-design Mach numbers21 are obtained viainterpolation. This is not performed linearly, but following the Prandtl–Glauert factorβ =√

1−M2, which has been proven to provide much more realistic results.

Further, influences of fuselage and nacelles on CM and CD,ind are considered using semiem-pirical correction terms proposed by Torenbeek [306] and Roskam [235], while more spe-cific influences (e.g., pitch-up influence of engine thrust on CM) are neglected. Fuselage im-pact on spanwise lift distribution is considered via heuristically “untwisting” (i.e., reducinglocal twist angle) of the most inner “wing” segment that virtually lies inside the fuselage.

Since interactions between wing and HTP are captured within LILI, trim drag sensitivitiesare automatically included in the proposed approach. For cruise conditions, the overallaircraft configuration is trimmed by adapting the incidence angle ihtp of the (all-movable)horizontal tailplane22 such that CM (CL) = 0. This is performed iteratively during OADconvergence using the lift coefficient CL,opt, where L/D reaches its maximum. Apart fromihtp, no additional trim deflections are used.

Viscous drag

In the drag terminology used within this thesis, total aircraft viscous drag includes frictiondrag, form drag, as well as interference and miscellaneous drag components. The formdrag includes that part of the (lift-dependent) pressure drag, which is not generated byshock waves. The latter is herein denoted as wave drag (see next paragraph). If no wavedrag is present, the viscous drag is sometimes also referred to as parasite drag [11].

For the estimation of total aircraft viscous drag, a component buildup method is used,as proposed, e.g., by Raymer [213]23. It combines flat-plate skin friction drag coefficientCD,fric, form factor FF , and interference factor Q for every aircraft component (c), wherethe respective product is weighted by the ratio of components’ wetted surface Swet to wingreference area Sref . Further, a miscellaneous drag coefficient CD,misc is added that coversextra parasite drag due to specific component shapes (e.g., aft fuselage upsweep angle),as well as leakages or protuberances. The viscous drag coefficient can thus be written as

CD,visc =

∑c

(CD,fric,c FFc Qc Swet,c)

Sref+ CD,misc. (3.3)

21Distribution of off-design Mach numbers around Mcr and selection of altitudes is explained in Sec. 3.3.8.22The all-movable (or adjustable) horizontal tail is also called trimmable horizontal stabilizer (THS).23Similar component buildup approaches are, e.g., presented in Refs. [139, 190, 306]. Raymer’s method,however, provided most convincing results in a comparison of results with available transport aircraft data.

3.2 Conventional aircraft design and analysis methods 65

For full turbulent flow, CD,fric,c can be approximated by the following expression [308]

CD,fric,c = 0.455(log10Rec)2.58 (1 + 0.144 M2)0.65 , (3.4)

which provides additional sensitivity towards Mach number M (cf. simplified relation inSec. 2.2.1). The component Reynolds number Rec is obtained for the respective combi-nation of M and altitude h, and a characteristic length l, either defined as total length offuselage and nacelles, or as mean aerodynamic chord (MAC) of wing or tails.

The form factors FFc are derived using semiempirical relations depending on differentaircraft design parameters. For wings, tails, and pylons, these are thickness-to-chord ratiot/c, Mach number M , as well as sweep angle and relative chord position of maximum-thickness line. Form factors for fuselage and nacelles are described by specific functionsof their fineness ratios24 f = l/d. Interference factors Qc consider additional drag due tocomponent integration and interaction effects, where they range between 1.0 and 1.05 forfuselage, wings, and tails, and between 1.3 and 1.5 for nacelles. CD,misc is also predictedusing semiempirical relations (see Ref. [213]). The required geometry input parametersare obtained by the MICADO geometry classes, which ensures reasonable capturing ofsensitivities during aircraft design studies.

Due to the significance of wing viscous drag (in particular for HLFC aircraft design),CD,visc,w is herein predicted using the more sophisticated quasi-three-dimensional wingdrag prediction method (see Sec. 3.3), which includes the flow solver MSES (Sec. 3.3.4).

Wave drag

Wave drag arises at speeds above the critical Mach number Mcrit, and is mainly governedby the strength of shock waves on the wing. Like CD,visc,w, the wing wave drag coeffi-cient CD,wave,w is herein predicted by using the coupled Euler/boundary-layer code MSES(Sec. 3.3.4). However, for comparison and to expose the key influences on transonic dragrise, let us briefly address a semiempirical method that is commonly used in conceptualaircraft design applications (see, e.g., Ref. [106, 176]). It is based on Lock’s approxima-tion of Cd,wave as a fourth-order function of critical Mach number exceedance [120, 134]:

Cd,wave = 20 (M −Mcrit)4 , ifM > Mcrit. (3.5)

For M ≤Mcrit, the wave drag is assumed to be zero. With the common definition of thedrag divergence Mach number MDD via the respective slope of the wave drag coefficient(i.e., dCd,wave

dM

∣∣∣MDD

= 0.1), Mcrit can be derived from Eq. (3.5) as follows:

Mcrit = MDD −(0.1

80

)1/3≈MDD − 0.108. (3.6)

24The fineness ratio of a slender body is defined as the ratio of its length l to its maximum diameter d.

66 Chapter 3. Method for aircraft design with hybrid laminar flow control

MDD can be estimated using Korn’s relation [36], which has been extended by Mason withsimple sweep theory (see Sec. 3.3.2) to make it applicable to swept wing sections [179]:

MDD cosϕ+ Cl10 cos2 ϕ

+ t/c

cosϕ = kA. (3.7)

Combining Eqs. (3.5) through (3.7), a relation for CD,wave is obtained that includes the im-portant wing design trade-off between (local) lift coefficient Cl, wing/airfoil thickness ratiot/c, and wing sweep angle25 ϕ. Further, the airfoil technology factor kA represents specificairfoil transonic characteristics; it can be derived from experiments or CFD calculations.For conventional airfoil technologies, kA has a value of 0.87, while it takes values near0.95 for supercritical airfoils with severe pitching moments [36]. In MICADO, the Korn-Mason equation can (optionally) be applied to predict the wave drag for turbulent wings,if no transonic airfoil drag polars are available. The MICADO implementation accountsfor spanwise variations of t/c, ϕ, and Cl, as it predicts CD,wave by a strip-wise summationof local coefficients Cd,wave, weighted by the ratio of local strip area to Sref (cf. Ref. [100]).This method is herein also applied to predict CD,wave,htp, which is, however, mostly neg-ligibly small due to low lift coefficients on the HTP at trimmed cruise conditions.

Semiempirical wave drag prediction methods generally allow quick trade-offs between keydesign parameters. However, since they are not sensitive to specific airfoil shapes, theirapplicability is mostly restricted to certain airfoil “families” (e.g., in terms of kA or othercalibration terms). Thus, they are in particular not sufficient for HLFC wing design, whereshaping of airfoil geometry and Cp distribution is crucial to delay transition, while stilllimiting transonic drag rise (see Sec. 2.3.1). This discussion will be reconsidered in Sec. 3.3.

Drag polars for low-speed configurations

For appropriate consideration of different flight phases during mission simulation (seeSec. 3.2.6), the MICADO aerodynamic module predicts drag polars for different aerody-namic configurations. In addition to the discussed cruise (clean) configuration, take-offand climb, as well as approach (with retracted and deployed landing gear) and landing con-figurations are covered. The low-speed configurations all include partially or fully deployedleading- and trailing-edge high-lift devices. The belonging aerodynamic polars are derivedfrom the clean polar at M = 0.2 and h = 0 ft, by applying semiempirical predictions fordifferences in local (∆CL) and maximum lift coefficients (∆CL,max). Prediction methodsare based on Refs. [213, 306] and include sensitivities towards relevant geometrical param-eters, such as spanwise and chordwise extension of high-lift devices, as well as local sweepangle. Nonlinear effects, e.g., due to flow separation or reattachment, are neglected.

25The wing sweep angle has to be chosen at a fixed local chord, e.g., at the leading edge, quarter- or mid-chord, where the latter is proposed by Gur et al. [106]. This topic will be revisited in Sec. 3.3.2.

3.2 Conventional aircraft design and analysis methods 67

3.2.4 Mass estimation

To predict the masses and center of gravity positions of all aircraft components, differ-ent methods have been implemented into the MICADO mass estimation program. Themanufacturing weight empty (MWE) and the operating weight empty (OWE) are de-termined as sum of the following mass groups26:

MWE = mstructures +mpower unit +msystems +mfurnishings, (3.8)OWE = MWE +moperator items. (3.9)

The mass groups are further broken down into mass chapters as summarized in table A.2.For every listed mass chapter, a method is implemented that predicts the component massas well as a center of gravity (CG) position (x, y, z)CG, assuming the whole mass of onecomponent to be concentrated in the CG point. A weight and balance analysis by means ofcomputing different combinations of masses and loadings yields forward and aft CG limits.

The implemented mass prediction methods incorporate physical, semiempirical and em-pirical approaches, or combinations of them. According to the discussion at the begin-ning of Sec. 3.2, model complexity and desired accuracy of the methods are oriented to-wards the OAD impact of the single component. Correspondingly, masses of wing andfuselage as main contributors to the structures group are predicted based on analyticalstructural models, while masses of large systems (e.g., hydraulic or electric system) arerather predicted by semiempirical methods, and masses of small systems (e.g., ice andrain or fire protection) by statistical correlations. The developed wing structural model isdescribed in more detail below. The fuselage mass estimation method has been adoptedfrom Ref. [16]. For the majority of other mass components, methods available in litera-ture (see, e.g., Refs. [132, 151, 213, 283, 303, 306]) have been soundly reviewed and com-pared with regard to their prediction accuracy for different MICADO models of exist-ing commercial aircraft [28, 291]. Those methods showing best agreement of the resultswith public available validation data, e.g., provided by the German “LuftfahrttechnischesHandbuch (LTH)” [283], have been incorporated into the MICADO mass estimation pro-gram. If regarded necessary or beneficial, additional correction terms or own regressionfunctions derived from correlations against data from LTH have been implemented. Anoverview of implemented methods and belonging references for the different mass chap-ters is given in table A.2.

Most significantly, all mass prediction methods are sensitive to the relevant aircraft de-sign parameters. Important design characteristics influencing the different mass groupsare summarized in table 3.2. Masses of structural components are mainly determined bytheir geometrical shapes, design masses (e.g., MTOW , MWE, MLW 27), and maneuverloads. The other mass group components are also governed by group-specific quantitiessuch as available thrust (propulsion group), systems parameters (systems group), or pay-load and accommodation specifications (furnishings and operator items groups). Thus,

26Note that the unit ofMTOW, OWE, etc. is kg, in spite of theW (=weight) in the used standard notations.27maximum landing weight

68 Chapter 3. Method for aircraft design with hybrid laminar flow control

during MICADO overall design iteration, all mass values change with component size andbelonging design parameters, according to the implemented equations and relationships.

Table 3.2: Sensitivities of MICADO mass estimation methods

Mass group Design sensitivities (list not exhaustive)Structures geometrical shapes, design masses, maneuver loadsPower unit thrust, fuel volume, aircraft dimensions (→ ducting)Systems design masses, aircraft dimensions (→ wiring and ducting),

passengers and flight crew, power requirements and efficienciesFurnishings design masses, passengers and flight crew, pressure altitude,

dimensions and volumes of cabin and cargo decksOperator items number of passengers and flight crew, total fuel volume

Wing structural model and mass prediction

For wing mass prediction in conceptual or preliminary aircraft design applications, semiem-pirical (see, e.g., Ref. [132, 213, 306]) or physics-based approaches (see, e.g., Ref. [16, 144,145]) are commonly applied. A good state-of-the-art review of mass estimation methodsfor primary and secondary wing structures is, for example, given by Dorbath [57].

For the considered design and optimization of aircraft with laminar wings, a physics-basedmodel is necessary to capture variations in wing geometry parameters, flight conditionsand aerodynamic loads. Reliable interactions between aerodynamic and structural char-acteristics are, e.g., required to trade airfoil thickness, wing sweep angle and Mach num-ber, or to find well-balanced spanwise load distributions, both in order to optimize over-all HLFC aircraft design.

An enhanced structural wing beam model is therefore implemented into the MICADOmass estimation program [300]. Based on an approach presented by Gallman et al. [89],the primary structure is modeled by a trapezoidal box, fitted inside front and rear sparand local airfoil geometry at selected wing design sections. To be able to apply this modelalso to nonplanar lifting surfaces (such as strut-braced or box wings), an equivalent fi-nite element equation system is formulated and solved for the given external loads. Theseinclude spanwise aerodynamic loads predicted by LILI (see Sec. 3.2.3), point loads ofpropulsion and landing gear (if integrated into the wing), as well as relieving distributedinertia and fuel loads. As dimensioning load case, a quasi-static 2.5 g pull-up maneuveris selected, performed at MTOW (with maximum payload and corresponding fuel capac-ity), sea level, and maximum operating speed VMO. Certainly, for detailed wing designapplications, multiple load cases (for maneuvers and gusts) within the whole flight enve-lope have to be considered, under static and dynamic aeroelastic deformations28. How-ever, the 2.5 g load case is considered to be sufficient for the proposed wing mass pre-

28Though the static deformations of the wing under the given loads are determined by the proposed method,it does not account for aeroelastic effects due to missing aero-structural feedback iteration.

3.2 Conventional aircraft design and analysis methods 69

diction method and for capturing of relevant design sensitivities, which is a common andreasonable assumption within preliminary design applications (see, e.g., Refs. [16, 309]).

An iteration of minimum wing box material thickness required to withstand calculatedinternal forces at distinct wing sections yields the overall mass of primary structuralwing elements, including skins, spars, and ribs. For mass prediction of secondary wingstructure (fixed and movable leading- and trailing-edge devices), semiempirical equationsare derived, which include sensitivities to key geometrical parameters of the high-liftsystem, and which are correlated against data from Ref. [283]. Further wing mass elementssuch as pylon attachments and landing gear supports are predicted based on empiricalrelations, with sensitivities to structural pylon and main landing gear mass, respectively.

3.2.5 Systems sizing and power distribution

A detailed systems model has been integrated into MICADO by Lammering [155] thatsizes the entire aircraft systems architecture during overall design synthesis. Apart fromthe determination of systems masses and center of gravity positions (see Sec. 3.2.4), thecentral task of the model is the determination of the power distribution within the air-craft systems architecture. The systems architecture is therefore considered as coheringnetwork of energy sources, conductors, and sinks, as illustrated in Fig. 3.8. The enginesand the auxiliary power unit (APU) represent the power sources, from which shaft poweror bleed air is taken off to drive the other systems. The conductor systems (electric, hy-draulic, and bleed air) feed energy or circulate air to the sinks or consumer systems. Keysystems of the different consumer types are listed in the lower boxes in Fig. 3.8.

Propulsion and APU

Bleed air consumers:· Air conditioning & pressurization system· Deicing system

Bleed air system

Bleed air offtakes Shaft power offtakes

Electric system Hydraulic system

Hydraulic consumers:· Flight controls· Landing gear

Electric consumers:· Environmental Control System (ECS)· Furnishing systems· Fuel system, etc.

Sin

ks

Con

duct

ors

Sou

rces

Energy losses

Figure 3.8: Schematic model of MICADO conventional systems architecture based onnetwork of sources, sinks, and conductors

For all energy sinks, specific methods are implemented that determine the maximumpower requirements (used for systems sizing), as well as mission-dependent power require-ments, according to varying specifications and boundary conditions with different flightphases. The implemented methods show sensitivities towards aircraft design parameters

70 Chapter 3. Method for aircraft design with hybrid laminar flow control

(e.g., component dimensions, payload specifications), flight conditions (e.g., Mach num-ber, altitude, pressure, temperature), as well as systems parameters (e.g., efficiency fac-tors or specific quantities of subcomponents). A detailed listing of input parameters to-gether with quantitative sensitivity analyses is provided by Lammering [155].

According to the mass chapter terminology29 listed in table A.2, the MICADO powerdistribution network comprises all chapters of power unit, systems, and furnishings group,as well as the landing gear as important hydraulic consumer. The accumulated powerrequirements of all sinks plus the determined energy losses of the conductor systems equalthe total shaft power and bleed air that is taken off from the power sources.

The implemented methods to estimate power consumptions and air flows range betweenstatistical and physical approaches suitable for conceptual and preliminary design appli-cations. The level of detail is again oriented to the OAD impact of the respective system,e.g., by means of an implicit SFC increase through power or bleed air offtakes. Conse-quently, the environmental control system (ECS) and the deicing system as main bleedair consumers are modeled based on physical relations, including balances of energy, massflow and heat loads. In contrast, small electrical consumers such as fuel or lighting sys-tems are modeled based on statistical estimations. The systems methods can generallycomprise several uncertainties due to systems specific input parameters. Nevertheless, thesignificance of possible inaccuracies on sub-system level is low due to the moderate OADimpact of maximum offtakes (∼ 3–5 % relative SFC increase during cruise [79, 158]), andcompared with the advantage of additionally gained level of detail and design sensitivities.

The impact of shaft-power and bleed air offtakes on engine specific fuel consumption iscaptured through the thermodynamic engine model (Sec. 3.2.2), which is continuouslyaccessed during mission simulation (Sec. 3.2.6). Quantitative assessment of offtakes onaircraft fuel efficiency using MICADO is presented in Refs. [156, 158].

The modular network structure of the systems module allows for flexible and efficientimplementation and integration of innovative systems or technologies (such as HLFC)into the conventional systems architecture. Still, sizing and integration of HLFC systemcomponents require individual methods, the underlying equations and implementation ofwhich will be described in Sec. 3.4. The incorporation into the described coherent systemsnetwork, and further into the MICADO OAD framework automatically ensures correctcapturing of the impact of additional HLFC system mass and shaft power offtakes onOWE and SFC, respectively. The sensitivities of the mass prediction methods to systemsspecific parameters (see table 3.2) also covers relevant systems interdependencies, e.g., ahigher generator mass due to increased maximum power requirements.

29The MICADO systems module applies the ATA 100 chapter classification [7] for a consistent and struc-tured definition of system boundaries. Despite a different numbering, the ATA classification is similar tothe presented mass chapter nomenclature, in terms of level of detail and system boundaries. For consis-tency, the mass chapter numbering as listed in table A.2 will be used throughout this thesis.

3.2 Conventional aircraft design and analysis methods 71

3.2.6 Mission analysis and fuel planning

The MICADO mission analysis program determines required block and reserve fuel bysimulating a specific mission, e.g., design or study mission. The cruise altitude profile canbe optimized for minimum fuel burn during simulation if desired. The program comprisesa detailed flight performance model described by Anton et al. [13] who present a detailedapplication study including different operational procedures (standard versus multi-stopmissions, and air-to-air refueling), which cannot be covered by more simplified models.

Flight performance model

The basic mission parameters (e.g., range, payload, climb speed schedule) are derived fromthe TLARs or can be specified manually. Input for the mission simulation are the aircraftmass ma/c (considered as point mass), the drag polars (as function of Mach number andaircraft configuration), as well as the full thermodynamic engine model (see Fig. 3.4).The flight path is discretized into sufficiently small mission increments, on each of whichNewton’s second law is analyzed. This is done by iteratively solving the flight-mechanicsequations of motion applicable to the respective flight phase. For the general case of anaircraft in accelerated climb, the equations of motion are30 [192]:

T −D −W sin γ = ma/cdV

dt, (3.10)

L−G cos γ = ma/c Vdγ

dt≈ 0. (3.11)

Aircraft weight(W = ma/c g

), as well as aerodynamic (L, D) and thrust (T ) forces have

been introduced for cruise in Fig. 2.1. The velocity V denotes the current true airspeed(TAS) of the aircraft. γ is the flight path angle, which is measured between geodetic xgand aerodynamic xa axes, and assumed to be steady during climb

(dγdt≈ 0

). Introducing

the kinematic condition between the rate of climb (ROC) and flight velocity, i.e., ROC =dhdt

= V sin γ, Eq. (3.10) can be rewritten as power equilibrium between the excess powerof thrust and drag and the sum of the growth rates of potential and kinetic energy:

(T −D) V︸ ︷︷ ︸excess power

= ma/c gdh

dt︸ ︷︷ ︸growth rate of potential energy

+ ma/c VdV

dt︸ ︷︷ ︸growth rate of kinetic energy

(3.12)

⇔ (T −D) Vma/c g

= dh

dt

1 + V

g

dV

dh︸ ︷︷ ︸acceleration factor

. (3.13)

Equations (3.12) and (3.13) are, for example, given by Oates [192], and also used by Eu-rocontrol under the term “total-energy model” for the implementation of the Base of Air-

30The equations are given for the Cartesian aerodynamic coordinate system (xa, za), with xa pointing inthe direction of the flight path, and za pointing downwards (perpendicular to xa).

72 Chapter 3. Method for aircraft design with hybrid laminar flow control

craft Data (BADA) software [77]. In Eq. (3.13), the acceleration factor is introduced; itbecomes zero for unaccelerated (constant speed) climb, leading to the well-known simpli-fied expression ROC = (T−D)V

W. It is obvious that the power (or energy) balance is shifted

during flight by the exchange or variation of thrust, velocity, and rate of climb. The abovedifferential equation, which states an initial value problem, can thus be solved for eachmission increment by presetting two of the three variables31 T, V , and ROC, and itera-tively resolving for the remainder third parameter. Basic types of flight phases used in theMICADO performance model, along with belonging parameter specifications32, are sum-marized in table 3.3. For parameter transformations (e.g., between calibrated and trueairspeed), the implemented equations of the ISA model [136] are applied (see Sec. 2.1).

Table 3.3: Basic flight segment types of MICADO flight performance model

Flight phases/segments Specified parameters Resulting parameterAccelerated climb or descent ROC, thrust rating speed (TAS or M)Constant speed climb CAS or M , thrust rating ROC, γLevel flight (cruise) M , γ = 0 (ROC = 0) thrust TConstant speed descent CAS or M , γ thrust T

Thrust and drag are modeled in MICADO as functions of flight conditions (M and h), andtotal aircraft mass reduces with increasing flight time according to dma/c

dt= −mf . These

interdependencies require iterative solving of Eq. (3.13) for every mission increment. Dur-ing iteration, drag and thrust are obtained for current flight condition and aerodynamicconfiguration or thrust setting from the described C++ aerodynamic and engine classes.Besides interpolation functions, several routines are implemented that constantly check ifoperational limits (e.g., CL,max, ROCmin) are exceeded, and mitigate if appropriate.

The solution of the power equilibrium also yields the fuel flow mf for every mission incre-ment. Its successive summation over all time increments gives the trip fuel. During missionsimulation, the total shaft power and bleed air offtakes—determined by the MICADO sys-tems module (Sec. 3.2.5) for each mission segment—are taken into account via the includedengine model (Sec. 3.2.2). Also, performance limitations (e.g., minimum climb gradients),aerodynamic boundaries (e.g., maximum lift coefficients, buffet limits), and engine oper-ational limits are checked “on the fly”, i.e., during iteration on every mission increment.

Fuel planning and fuel quantities

Since the MICADO mission analysis module performs a forward simulation of the spec-ified mission, the total loaded fuel including reserve fuel is determined beforehand, anditeratively adapted during overall design convergence. The fuel planning method used

31For thrust control, the following thrust ratings are used within MICADO: take-off, maximum continuous,climb, cruise, idle. The velocity is specified in terms of a constant calibrated airspeed CAS or Machnumber M . For descent segments, a constant flight path angle γ is specified, or a rate of descent (ROD).

32The performance conditions are specified in the MICADO mission XML file that is automatically gener-ated based on TLARs and on standard climb and descent procedures derived from Ref. [76].

3.2 Conventional aircraft design and analysis methods 73

within MICADO and throughout this thesis follows the “Fuel Policy” prescribed by theEuropean Union (EU) Regulation (EU) No. 965/2012 (CAT.OP.MPA.150)33 [75], andthe additional explanations given in Ref. [8]. The minimum required total fuel quantityto complete the specified mission is denoted as loaded fuel or mission fuel (mMF ). It isdefined as sum of block fuel mBF = BF and reserve fuel mRF , where the block fuel is thesum of trip fuel mTF and taxi fuel at take-off (mTXF, out) and landing (mTXF, in)34:

mMF = mBF +mRF

= mTF +mTXF, out +mTXF, in +mRF . (3.14)

Reserve fuelmRF consists of contingency fuelmCF (assumed as 3 % of calculated trip fuel),alternate fuel mAF (for diversion distance of 200NM after missed approach at destinationairport), and final reserve fuelmFRF (for 30-minute holding at 1500ft at alternate airport):

mRF = mCF +mAF +mFRF . (3.15)

Maximum take-off weight (MTOW ) results from mission analysis35 as

MTOW = OWE +mSPP +mMF,dm −mTXF, out, (3.16)

with mMF,dm denoting the calculated mission fuel on the design mission, and mSPP thestandard passenger (design) payload. Since MTOW is thus both input and result of theaircraft sizing process, it is determined iteratively during OAD convergence (see Fig. 3.4).

Fuel planning for laminar flow operations

Aircraft design including laminar flow technology poses important questions for appropri-ate fuel planning procedures with regard to certification requirements. As most optimisticapproach, fuel planning and mission simulation can be performed for “ideal” laminar con-ditions; for HLFC, this means to assume the predicted aerodynamic drag reduction and aproperly operating suction system during the whole flight. However, premature transitioncaused by contamination, flying through clouds, or other outer disturbances, or by fail-ure or malfunction of the HLFC system can lead to sudden (partial or full) degradationof laminar flow during flight, which can or cannot be restored before reaching the desti-nation airport. These occurrences involve many uncertainties and probability-theoreticalinvestigations, and thus a variety of possible scenarios. These may here be generalized bythe following consistent procedure:

1. Simulate design mission by assuming predicted laminar flow only to a certain pointX, as from which full turbulent flow is assumed up to the destination airport.

2. After OAD convergence, simulate study mission with laminar flow over whole flight.

33also known as IR-OPS (see Refs. [75, 78] for details about regulation nomenclature and history)34Additional fuel and extra fuel (being at the captain’s discretion [8]) are optional and not included here.35Note that this relation holds only if the design mission is constrained byMTOW , and not by tank volume.

74 Chapter 3. Method for aircraft design with hybrid laminar flow control

The point X is here specified in terms of relative share of range or flight time; by default,the middle point of the design mission range is selected, i.e., X = 0.5Rdes. The describedprocedure thus sizes the aircraft for a probable degradation of laminar flow during flight(including mass snowball effect and component resizing), and then fairly evaluates theconverged design on the study mission under “ideal” conditions. The mission analysisprogram also automatically detects if increased drag due to laminar flow shortfall leads toinsufficient engine thrust for minimum climb performance. To allow convenient switchingbetween laminar and turbulent polars during mission simulation, drag coefficients com-puted for both laminar and full turbulent flow (see Sec. 3.3) are stored together in thepolar XML file (see Sec. 3.2.3) for every data point.

Optimization of cruise altitude profile

While climb and descent mission profiles are strongly determined by the specified climb ordescent speed schedules as well as thrust ratings or glide path angles, the cruise phase offersimportant optimization potential by variation of speed and altitude. Though cruise MachnumberMcr is sometimes slightly varied for cost-index or long range cruise considerations,it is herein kept constant during cruise as specified with TLARs. Hence, the remainingfree variable is the cruise altitude. As argued in Sec. 2.1, fuel burn during cruise can beminimized by continuously maximizing specific air range SAR as defined in Eq. (2.1) [8].

Consequently, the altitude profile is optimized “on the fly” during MICADO mission anal-ysis by continuously selecting the altitude that yields maximum SAR for Mcr = constand the actual aircraft gross weight (W = ma/c g) at the respective mission increment.By trend, the weight decrease during cruise implies higher optimum (pressure) altitude,mainly to compensate for reduced aerodynamic performance in terms of L/D = f (CL).To account for operational ATC requirements, which do not permit continuous alti-tude changes, the allowed cruise climb steps are specified in terms of a fixed ∆h, e.g.,1000 ft, 2000 ft, or 4000 ft. At every mission increment with the actual altitude h, it isthus checked whether SAR (h+ ∆h) > SAR (h), and if so, a step climb is performed.For the climb segment from h to h + ∆h, a constant rate of climb of ROC = 300 ft/minis preset. The required fuel for the climb segment is also considered for the altitude op-timization: if climbing to h+ ∆h and continuing cruise on this flight level would requiremore fuel than directly continuing cruise on flight level h, the step climb is not performed.This prevents inefficient short step climbs, especially at the end of the cruise phase.

With the only boundary condition of constant climb steps ∆h, the mission simulationmodule thus yields a cruise altitude profile optimized for minimum fuel burn. Notethat the SAR maximization also implies an optimum compromise between aerodynam-ics (M L

D), engine efficiency (SFC), and aircraft mass (ma/c), see Eq. (2.1). From the

aerodynamic point of view, which is usually most critical, the selected optimum altitudeshould correspond to flying at the lift coefficient CL that yields maximum L/D at Mcr.Since CL decreases with aircraft weight (CL ∼ W ) for steady cruise at constant altitude,the resulting CL cruise profile typically exhibits a sawtooth shape, as it will be demon-strated in the aircraft design studies in Chap. 4.

3.2 Conventional aircraft design and analysis methods 75

The cruise altitude optimization is a very important feature for consistent and reliableaircraft design and assessment, because it treats all aircraft designs equally, that is, itprevents over- or underrating of aircraft designs due to their specific aerodynamic orengine characteristics. For example, an aircraft design that has its maximum cruise L/Dat lower lift coefficients can benefit from this feature by automatically flying at lower cruisealtitudes. If it had otherwise to perform a given reference mission at higher altitudes, thisspecific aircraft design would be disadvantaged compared to other designs with highervalues of CL,opt. This would effectively constitute an “unfair” comparison and could leadto wrong design selections or conclusions.

Discussion and validation

0

100

200

300

400

0

750

1500

2250

3000

altit

ude

h, 1

00 ft

cons

umed

fuel

(fro

m B

R),

kg

altitude

fuel

TOW = 62 t (Airbus) TOW = 62 t (MICADO) TOW = 74 t (Airbus) TOW = 74 t (MICADO)

0 10 20 30

0 50 100 150

time

t, m

in

range R, NM

Figure 3.9: Climb profile for A320 type aircraftcompared with data from Ref. [8]

The detailed flight performance model un-derlying the MICADO mission analysis al-lows reliable prediction of trip, block, andmission fuel. This has been demonstratedin different applications, see, e.g., the op-erational studies in Ref. [13], or the shortrange reference aircraft design in Ref. [229].Compared to simpler methods, which areoften based on Breguet range equationand empirical mass fractions, the presentedmethod has significant advantages. First,the detailed resolution of the flight pathand the consideration of different types offlight phases realistically cover climb andacceleration segments and the respectiveincreased fuel consumption. If these effectsare neglected, the deviation of predictedblock fuel can be large, especially on short haul flight with high percentage of climb anddescent phases. Second, only the fine granularity and sensitivity towards aerodynamic andengine performance input data allows for the discussed in-flight optimization of the cruisealtitude profile. This is an outstanding feature for HLFC long range aircraft design, be-cause it considers different shapes of aerodynamic drag polars during mission simulation,importantly linking these disciplines. Furthermore, the iterative approach (of the OADsynthesis and the mission simulation itself) allows for forward simulation, whereas othermission analysis modules mostly apply backward prediction (from the landing weight tothe take-off weight).

To demonstrate the validity of the model, the (most critical) climb flight phase—frombrake release before take-off to initial cruise altitude—is analyzed for an Airbus A320 typeaircraft. The MICADO design of this aircraft type is presented under the name CSR-01 in Ref. [229]. For comparison, data from climb tables published by Airbus are used(see, e.g., Refs. [8, 248]). These include time, distance flown, and consumed fuel frombrake release (BR) to a certain flight altitude, in dependence on aircraft weight at BR. Asfar as provided, equal boundary conditions have been chosen, e.g., concerning the climb

76 Chapter 3. Method for aircraft design with hybrid laminar flow control

speed schedule or atmospheric conditions. In Fig. 3.9, the resulting parameters from theMICADO simulation (dashed lines) are plotted as a function of range R for two differenttake-off masses (62t and 74t), and compared against Airbus climb table data (data points).The comparison shows good agreement for preliminary design applications. It may benoted that this kind of comparison always underlies uncertainties, especially with respectto selected thrust rating as well as aerodynamic and engine performance input data.

3.2.7 Design evaluation: performance and cost analysis

As indicated in the design evaluation block in Fig. 3.4, MICADO comprises differentmodules for aircraft assessment after design convergence. Of primary importance withinthis thesis is the analysis of aircraft performance, and secondly of operating costs, asdescribed below. Furthermore, MICADO includes a prediction model for nonrecurring andrecurring costs, as well as list price and unit costs [160]. Franz et al. [83, 85] have expandedthe focus towards the whole life cycle to allow for sustainability-driven aircraft design.This includes models for monetary, social, and ecological assessment, where the lattercomprises prediction of emissions [85] and noise characteristics [238]. Basically, differentevaluation parameters can always be combined by appropriate weighting functions forthe purpose of multi-criteria decision analyses. This thesis, however, concentrates onaircraft design with respect to minimum fuel by means of systematic parameter studiesand optimizations.

Performance characteristics

After convergence of the overall aircraft design, a detailed performance assessment isconducted within MICADO, the key elements of which are:

• block fuel on the specified study mission BFsm (see Sec. 3.2.6)

• performance parameters as specified in the TLAR list (see table C.1)

• payload-range diagram

The study mission is defined with a fixed range36 to compare block fuel and operatingcosts between different aircraft designs with possibly different design ranges. The abovedescribed flight performance model is used to simulate the study mission; to optimizethe cruise altitude profile, a “small” iteration is conducted including the systems moduleto ensure convergence of flight-condition-dependent systems offtakes and block fuel. Forthe HLFC long range aircraft design studies in Chap. 4, the block fuel BFsm on a studymission of 4000 NM will be the key evaluation parameter.

The specified top-level aircraft requirements (TLARs) lead to an initial and implicit sizingof the key parameters W/S and T/W at the very beginning of the design. For the final(converged) design, the belonging parameters have to be determined and compared to the

36Common study mission ranges are 4000 NM for long range, and 500 or 800 NM for short range aircraft.

3.2 Conventional aircraft design and analysis methods 77

required values. Only if all TLARs are fulfilled, the aircraft design is valid; otherwise it hasto be revised, e.g., by changing W/S or T/W . All parameters are not roughly estimated,but explicitly simulated using the flight performance model with the respective boundaryconditions (e.g., atmosphere ISA+10). Also for the prediction of required take-off andlanding field lengths, the related forms of the equations of motions are solved. Still, theseparameters always comprise some uncertainties, e.g., due to ground friction or brakingcoefficients37. Besides the TLARs, relevant parameters according to the certificationspecifications are determined and checked, e.g., minimum required climb gradients indifferent take-off segments.

The payload-range diagram is a central evaluation element providing quick insight intodesign limitations with respect to payload,MTOW , and fuel storage. It is produced basedon multiple mission simulation runs with different combinations of payload and range.

Furthermore, various kind of classical performance diagrams and representations are pro-vided, e.g., flight envelope, SAR performance, or take-off and landing field length asfunctions of aircraft weight and airport altitude. These are here not described in detail,because they are basically all derived by suitable application of the flight performancemodel, and the underlying arrays of aerodynamic polars and engine performance maps.

Operating costs

The MICADO operating cost model described in Ref. [84] determines cash operating costs(COC) and direct operating costs (DOC) according to the following breakdown:

COC = Cfuel + Cmaintenance + Ccrew + Cfees, (3.17)DOC = COC + Cinsurance, depreciation. (3.18)

The fuel costs are calculated using the fuel mass determined for the study mission andthe kerosene price of the considered year (here: 2010). The other cost components are es-timated based on existing models that have been widely used (also by airline operators),see, e.g., Refs. [23, 24, 71, 73, 113, 253]. The underlying equations are updated to theyear 2010 by multiplying with the corresponding consumer price index to ensure consis-tent evaluation. The combined MICADO COC/DOC model shows relevant sensitivitiestowards aircraft design characteristics, operating company, as well as scenario parame-ters (e.g., fuel price or emission fees). Within this thesis, COC is preferred as evaluationparameter over DOC (see Chap. 4), because it does not depend on insurance and depre-ciation, which excludes additional uncertainties, e.g., considering aircraft list price.

37Applied values for (dry runway) braking and rolling coefficients are µbrake = 0.5 and µroll = 0.03.

78 Chapter 3. Method for aircraft design with hybrid laminar flow control

3.3 HLFC aerodynamic wing design method

The methodical approach for HLFC aircraft design using MICADO has been outlinedin Sec. 3.1.3. In Sec. 3.2, the basic OAD components for integrated HLFC sizing andevaluation have been presented, i.e., aircraft drag polars, component masses, systems andengine models, as well as capabilities for performance and monetary assessment. Thecurrent and the following section describe the elaborated HLFC wing aerodynamic andsystem design methods, respectively. Their implementation into the MICADO softwarearchitecture and their inherent connection to the belonging OAD modules follow thecentral motivation of this thesis to develop an integrated HLFC aircraft design framework.

A summary of the HLFC aerodynamic wing design methodology discussed within thissection is given by the author in Ref. [230]. Related literature concerning methods andapplications of laminar flow wing design has been given in Sec. 2.3.1.

Considering the required amount of effort and level of detail for aerodynamic and systemdesign methods, the second guideline stated in the introductory remarks of Sec. 3.2 appliesagain. Consequently, on aerodynamic wing sizing—as key element and driver of HLFCaircraft design—much more elaboration is spend than on HLFC system integration. Thelatter has significant smaller impact on OAD, as it will be shown in the design studies inChap. 4.

Based on the theoretical considerations about HLFC aerodynamic wing design in Sec. 2.3.1,the herein proposed method covers the following capabilities and requirements:

1. prediction of transition locations and drag polars of HLFC wings

2. design and shaping of HLFC airfoils for given wing planform and flight conditions

3. efficient integration of HLFC wing design and drag prediction into OAD framework

The first two points classically involve a detailed single-point 3D (inverse) wing designincluding aerodynamic models of high complexity. However, within the present context,this task has to be considered and solved on conceptual to preliminary design level. Raj-narayan and Sturdza [212] take the same line by claiming “the ability to predict transitionat the conceptual design stage, and ideally to perform aerodynamic shape optimizationand multidisciplinary optimization while including transition prediction.” Still, the combi-nation of all three stated requirements in an integrated OAD approach remains unsolved.

To find a suitable approach to address the first requirement, let us initially recall the pre-liminary aerodynamic analysis methods presented in Sec. 3.2.3. To predict the viscousdrag coefficient CD,visc,w of a laminar wing, Eq. (3.3) can basically be applied by separat-ing laminar and turbulent wetted surfaces and respectively estimating skin friction dragcoefficient CD,fric,w (see, e.g., Eq. (3.4) and Sec. 2.2.1) and form factor FFw. Besidesrarely available form factor estimates distinguishing laminar and turbulent flow, the keymissing part in this procedure is evidently the location of the transition line on the wing.Unverified assumptions (e.g., fixed chord transition) or the use of purely empirical transi-tion prediction methods, however, would not do justice to the complex physics of transi-

3.3 HLFC aerodynamic wing design method 79

tion phenomena on swept wings as discussed in Sec. 2.2.5; these at least require the use ofsemiempirical methods like the eN method (see Sec. 2.2.4). The herein considered tran-sonic HLFC wing design involves the additional difficulty of finding suitable suction dis-tributions (in agreement with feasible system integration), and of balancing viscous dragreduction with acceptable transonic drag characteristics, especially for long range aircraftwith preferably high cruise Mach numbers.

In the latter context, further consider the semiempirical prediction of the wing wave dragcoefficient CD,wave,w according to Eqs. (3.5) to (3.7). If calibrated for a specific airfoil“family”, these equations can provide good wave drag estimates. However, since suchcalibration should be repeated for every new aircraft type or airfoil technology, a profoundvalidation database would be required, which is specifically not available for HLFC airfoils.The mentioned possible interval for the airfoil technology factor kA (between 0.87 and0.95) already implies an uncertainty of nearly 10 %, which is on the order of obtainabledrag benefits due to HLFC. For a well-performing HLFC wing, however, the requiredcompromise between reduced viscous drag and acceptable wave drag has to be achievedon a much more precise basis. Further, the strong susceptibility of typical HLFC pressuredistributions (see Fig. 2.9) to exhibit strong shocks and thus wave drag has to be takeninto account, which is also not provided by semiempirical methods.

Bringing together the uncertainty in viscous and wave drag prediction via semiempiricalmethods, the crux becomes obvious that already on preliminary design level, a reliabletreatment of HLFC wing aerodynamics is not possible without immersing into specificcharacteristics of airfoil shapes and pressure distributions. These have further to becombined with suitable methods to predict transition locations, under consideration ofproper suction distributions.

Above all, however, the dilemma between required complexity (3D HLFC wing design)and limited feasibility in preliminary aircraft design has to be solved. Since a full 3D in-verse HLFC wing design is not feasible in preliminary design for many reasons—e.g., toohigh modeling and computational effort, too low automation capabilities and robustnesstowards large design changes—a suitable reduced order approach has to be found accord-ing to the paradigm as less time consuming as possible, but as accurate as necessary. Here,a quasi-three-dimensional (Q3D) method combined with conical wing geometry and flowassumptions is proposed. The term quasi implies that no real 3D flow calculation is con-ducted, but 2D calculations at different wing sections are performed trying to approximatethe local 3D solutions by appropriate transformations. This applies to local aerodynamiccoefficients, but in the first instance also to local (streamwise) pressure distributions, forwhich accurate shape representations are severely required in the context of laminar wingdesign. The applied transformations, which combine equations underlying simple sweeptheory (SST) with assumptions of conical geometry and flow to account for tapered wingeffects, will be described in Sec. 3.3.2. As usual in Q3D or 2.5D methods, wing transonicprofile drag is determined by summarizing local drag at selected wing sections, weightedby belonging section areas. According to the underlying assumptions and the segment-or strip-wise approach, the method is herein also called conical 2.5D (2.5Dc) method. Avalidation case for the 2.5Dc method comparing predicted transonic wing lift and dragcharacteristics with results from RANS computations will be presented in Sec 3.3.3.

80 Chapter 3. Method for aircraft design with hybrid laminar flow control

Summarizing these thoughts under consideration of the above stated first requirement, anautomated, robust, and reproducible process is required that is capable to predict dragpolars of HLFC airfoils within a tapered segment of a 3D wing. This implies a reasonableinterconnection of a flow solver that includes both viscous and transonic effects with amethod to predict transition locations under consideration of both Tollmien–Schlichtingand cross-flow instabilities on swept wings (see Sec. 2.2.5). Appropriate methods selectedfor this purpose will be addressed in Secs. 3.3.4 and 3.3.5, respectively. The completeHLFC airfoil analysis process along with details about its implementation and an examplevalidation case will be discussed in Sec. 3.3.6.

With this—already intricate—process, no design capabilities are provided yet, but alreadythe opportunity to predict full arrays of laminar drag polars for a given wing geometryin a fast and robust way. However, in preliminary overall aircraft design, it is the centralgoal to assess different aircraft configurations, with larger changes in geometry parameters(e.g., wing sweep angle) and design flight conditions (e.g., cruise Mach number). Theherein contained additional level of difficulty is expressed in the second requirement listedabove, that is, to provide the capability for HLFC airfoil inverse design and optimizationfor a given tapered wing geometry segment, as well as given flight conditions (Machnumber, Reynolds number, lift coefficient). The approach and implementation to realizethese design capabilities will be presented in Sec. 3.3.7, including an application exampleto demonstrate relevant design sensitivities.

The proposed HLFC wing/airfoil design and analysis approach provides significantly re-duced computing and modeling effort compared to conventional 3D approaches. Never-theless, the very high number of evaluation runs to provide full arrays of drag polars (re-quired for mission simulation) prohibits fully automated execution during MICADO over-all aircraft design synthesis. Also, the automated application of numerical aerodynamicprediction methods over such large parameter spaces always implies a general suscepti-bility towards numerical imponderabilities (e.g., outliers, not converged cases). This andthe specific requirements for HLFC airfoils at varying design conditions (with respect topressure and suction distributions) requires the engineer to “stay in the loop” to a cer-tain amount. To maintain the powerful automated design capabilities of MICADO andcombine them with the HLFC airfoil design procedure, a database approach is selected.The developed database contains several HLFC airfoils that are designed and multi-pointoptimized at different selected flight conditions, as well as the belonging transition loca-tions and drag polars at design and various off-design conditions. Implementation, archi-tecture, and exemplary cases of the HLFC airfoil database will be treated in Sec. 3.3.8.

This leads us to the third requirement, that is, an integrated treatment of HLFC wingaerodynamics within conceptual aircraft design. The fulfillment of this requirement hasremained unsolved and is an outstanding feature of the proposed method. The followingsection therefore explicitly illustrates how the different involved design levels (aircraft,wing, airfoil), and the corresponding interconnection of methods and aerodynamic datais implemented and processed within the MICADO framework. Initially highlightingthis overall aircraft context in Sec. 3.3.1 also supports a connective understanding of thedetailed methods and tools discussed in the subsequent sections 3.3.2 through 3.3.8.

3.3 HLFC aerodynamic wing design method 81

3.3.1 Design approach and integration into MICADO

The above stated third requirement has claimed an efficient integration of HLFC wing de-sign and drag prediction into the OAD framework. How this is realized within MICADOis schematically illustrated by the matrix-type flow chart in Fig. 3.10. It has been empha-sized that the difficulty lies in the incorporation of the detailed and partly manual HLFCairfoil design approach into the fully automated OAD synthesis. The herein involvedthree levels of design and fidelity are represented by the three main vertical columns ofblocks: the aircraft level, the wing level, and the airfoil level, considering overall configu-ration, wing planform geometry, and sectional shapes, respectively. The horizontal rowsof blocks represent the corresponding geometries, methods, and aerodynamic data.

Aircraft level Wing level Airfoil level

Geo

met

ryM

etho

dsA

erod

ynam

ic d

ata

MICADOHfull-configurationHaerodyn.Hmodule LIFTING_LINE

HLFCHairfoilHanalysisHprocessH

LFC

Hairf

oilHd

atab

ase

Q3D

Happ

roac

h→ Sec. 3.2.3 → Sec. 3.3.6

→Sec.

3.3.2

→Sec.

3.3.8

drag polar (overall configuration)

totala/clift

coeff

.C

L

total a/c drag coeff. CD,total

distr. of wing lift coeff. Cl

lift

coeff

.C

l(y

)

spanwise coordinate y

airfoil drag polarand transition location

local(airfoil)lift

coeff

.C

l

(x/c)trans drag coeff. Cd

Cd,viscCd,waveCd,airf

Figure 3.10: Process of HLFC airfoil aerodynamics integration into MICADO, withinterconnection of geometry, methods, and aerodynamic data

On aircraft level, the MICADO aerodynamic program estimates total aircraft drag polarsfor different Mach numbers and aerodynamic configurations, as described in Sec. 3.2.3.To explain the integration of HLFC airfoil drag polars, let us here concentrate on onlyone drag polar CL = f (CD,total) at a transonic cruise Mach number, as sketched in thelower left diagram block. For every total aircraft lift coefficient CL, the total aircraftdrag coefficient is predicted as the sum of drag coefficients of all aircraft components (i.e.,CD,total = ∑

cCD,c), which are in turn composed of drag terms due to different physical

origins (see table 3.1). The total wing drag coefficient can be written as

CD,w = CD,ind,w + CD,visc,w + CD,wave,w = CD,ind,w + CD,prof,w. (3.19)

82 Chapter 3. Method for aircraft design with hybrid laminar flow control

While the wing induced drag coefficient CD,ind,w is herein predicted by LIFTING_LINE(LILI), the wing transonic profile38 (i.e., viscous plus wave) drag coefficient CD,prof,w iscalculated by the proposed Q3D segment-wise approach, including properly transformedHLFC airfoil drag polars. Recall that for every aircraft lift coefficient CL, the sub-moduleLILI is executed for the actual arrangement of wing and HTP, where the following liftcoefficient relation holds: CL = CL,w+CL,htp ShtpSref

. Thus, every total aircraft CL is assignedwith a wing lift coefficient CL,w, and a belonging distribution of local lift coefficientsCl (y) along the wing spanwise coordinate y. The predicted spanwise distribution (asexemplified in the lower middle diagram block) depends on wing planform parameters, aswell as spanwise distribution of wing twist angles ε (y) and airfoil shapes.

The geometric connection between wing and airfoil level (see upper middle and rightdiagram) works via segment-wise treatment at selected design sections39. For a givenHLFC airfoil geometry, the automated and robust HLFC airfoil analysis process describedin Sec. 3.3.6 is applied to produce large sets of airfoil drag polars and other aerodynamiccoefficients. These arrays of airfoil characteristics include predicted transition locations(x/c)trans and coefficients of viscous drag (Cd,visc) and wave drag (Cd,wave) as illustratedin the lower right diagram, and are systematically stored in an HLFC airfoil aerodynamicdatabase (see Sec. 3.3.8). The database allows closing the aerodynamic “gap” betweenairfoil and wing level, using the segment-wise approach to predict CD,prof,w: at all spanwisestations i of the LIFTING_LINE paneling, the local lift coefficient Cl,i (yi) is sent as queryto the database, which returns the corresponding local laminar drag coefficients Cd,visc,iand Cd,wave,i. The total wing transonic profile drag is finally obtained by

CD,prof,w =

∑i

(Cd,visc,i + Cd,wave,i) SiSref

, (3.20)

where the local drag coefficients are summed over all spanwise stations i, weighted by therespective local wing segment area Si. The weighted sum is divided by the wing referencearea Sref , which is herein used as reference value for all aircraft drag coefficients. Thetotal wing drag (including CD,ind,w) is added up with the drag of other aircraft componentsto get one point in the overall aircraft drag polar (see bottom left figure). For the cleanaircraft configuration, this procedure is repeated for the whole range of lift coefficients(with sufficiently small increments), as well as for Mcr and all specified off-design Machnumbers. The low-speed drag polars with different aerodynamic configurations are derivedfrom the clean polar at M = 0.2 as described in Sec. 3.2.3.

Through this “on-the-fly” incorporation of HLFC airfoil coefficients into aircraft dragpolars via rapid multiple database queries, the complex laminar flow and transition physicsare transported and made accessible on overall aircraft level. This also means that dragreduction due to partly laminarized wings and the specific shape of the laminar drag

38While some classical definitions of profile drag do not include wave drag [11], the herein used terminologytransonic profile drag coefficient CD,prof,w does include CD,wave,w; this is in line with the terminology “ide-alized profile drag” (i.e., CD,total− C2

L

πΛ ), which is being used in the AIAA drag prediction workshops [168].39The MICADO 3D wing geometry is lofted over the (streamwise directed) airfoils at specified spanwisestations, see Fig. 3.2. Apart from that, conical geometry transformation is applied for airfoil drag pre-diction within the Q3D approach, see Sec. 3.3.2.

3.3 HLFC aerodynamic wing design method 83

polars are captured during mission simulation; hence, the impact of HLFC aerodynamicson overall aircraft efficiency can be quantitatively measured, e.g., in terms of block fuel.The interconnection of optimum cruise and aerodynamic design conditions for HLFC wingand airfoil design will be revisited in Sec. 3.3.7 and demonstrated in Chap. 4.

To reveal further advanced capabilities of this integrated approach, return to Fig. 3.5.The aero-structural assessment of the full aircraft geometry and the connection of aero-dynamic and mass prediction modules via wing lift distribution open up opportunity formultidisciplinary HLFC wing design and optimization through variation of wing planformparameters (e.g., sweep angle) and/or twist distribution. Further, the integration into theentire MICADO process flow (see Fig. 3.4) allows performing these wing optimizations notonly locally—which might lead to suboptimal solutions—but within an iterative overallaircraft design. This includes effects and interconnections of all aircraft components anddisciplines, as well as resizing and snowball effects as argued in Sec. 3.1.4. This also meansthat a variation of cruise Mach number—as one key driver of HLFC technology integra-tion—is considered as a top-level requirement change, which does consequently not onlyimpact wing design, but the full aircraft sizing process. With this integrated OAD strat-egy, global aircraft design optima can be predicted on a more efficient and reliable basis.

After these reflections within the OAD context, the next sections elaborate on the im-plemented conical 2.5D approach and the HLFC airfoil analysis and design process (seeright-hand blocks in Fig. 3.10). Its development has been in line with the requirementsfor a well-working, i.e., consistent, efficient, and robust framework on airfoil level, includ-ing a smart interface to the methods and software elements on wing and aircraft level.

3.3.2 Assumptions and relations for conical 2.5D approach

It has been argued in the introductory part of this section, that full 3D flow solutions aretoo expensive in terms of required computation time and modeling effort for being ap-plied within the proposed conceptual to preliminary design method. On the other hand,simple 2D transformations based on (infinite yawed) swept wings neglect significant flowphenomena occurring on tapered wing geometries. The context of laminar wing designadditionally imposes severe requirements, e.g., to the shape of HLFC pressure distribu-tions (see Fig. 2.9) and to transition prediction considering Tollmien–Schlichting instabil-ities (TSI) as well as cross-flow instabilities (CFI). While streamwise transition predictionwith respect to TSI is often found in airfoil or low-swept wing design applications, a si-multaneous and reliable coverage of CFI for highly swept and tapered wing applicationsis rarely included within preliminary aircraft design.

The herein proposed method uses a conical 2.5D (2.5Dc) approach. It combines equa-tions of sweep-taper theory (i.e., an enhancement of simple sweep theory for tapered winggeometries) with conical-flow assumptions. The latter are used for relating 2D and 3Dpressure distributions, and are also the basis for formulation and solution of the compress-ible conical boundary-layer equations, see Sec. 3.3.5. The governing relations of the 2.5Dcmethod are discussed below, followed by a validation example. Incorporated methods forprediction of viscous and wave drag as well as transition location are presented thereafter.

84 Chapter 3. Method for aircraft design with hybrid laminar flow control

Sweep-taper theory: relations between 3D and 2D flow characteristics

To apply a segment-wise 2.5D approach to a swept wing, aerodynamic characteristicsof the 3D wing can be replaced by equivalent characteristics of 2D airfoil sections. Foran infinite swept wing, the so-called simple sweep theory (SST), which is based on earlyswept-wing investigations by Busemann [42], provides transformation rules for geometryand flow conditions. The SST defines the equivalent 2D freestream Mach number M∞,2Das the wing-normal component of the 3D freestream Mach number:

M∞,2D = M∞,3D cosϕref . (3.21)

For the lift coefficient Cl, the following transformation relation holds:

Cl,2D = Cl,3Dcos2 ϕref

. (3.22)

Accordingly, the angle of attack transformation writes as α2D = α3D/ cosϕref , which is,however, of minor relevance in the present context. Further relations to translate geometryas well as pressure and drag coefficients will be given in the following paragraphs.

isobars assumed along iso-chord lines Ovirtual wing apex

Figure 3.11: Conical-flow assumption on a ta-pered wing segment

For the infinite swept wing, the choiceof the transformation sweep angle ϕref isunique. For the more realistic case of afinite tapered wing segment, sweep anglevaries with local chord position x/c, thusa suitable choice of ϕref has to be made.At subsonic speeds, the sweep angle at thequarter-chord line ϕ25 can reasonably beselected; instead, for transonic flow condi-tions over swept tapered wings, the localsweep angle of the shock position has beenshown to serve well as transformation ref-erence [37]. To achieve good 2D/3D agree-ments, a precise knowledge of the shock lo-cation is crucial, because the corresponding value of ϕref governs the transformed (2D)freestream conditions. Shock location and strength (and thus wave drag) in turn stronglydepend on freestream conditions and also vary along the span on transonic tapered wings,so that simplified or generalized assumptions (e.g., using the mid-chord sweep angle ϕ50)mostly lead to insufficient results [37]. So, if no 3D flow solution already exists, the shocklocation is unknown a priori. The herein proposed method therefore applies an iterativeapproach to properly determine ϕref , including an automatic detection algorithm for theshock location (x/c)sh = (x/c)ref . This procedure will be discussed in detail in Sec. 3.3.6.

The extension of SST for application to finite tapered wings is commonly called sweep-taper theory. It is based on the formulations by Lock [170], and has been proposedby Boppe [35] in the scope of the aerodynamic design of the X-29A aircraft. Applicationsto turbulent wings can, for example, be found in Refs. [150, 309]. Figure 3.11 shows the

3.3 HLFC aerodynamic wing design method 85

planform view of a tapered wing segment with the sweep angles ϕLE at the leading edge,ϕTE at the trailing edge, and ϕ at an arbitrary local chord station x/c. Further, conicalgeometry and flow assumptions are indicated by the virtual wing apex O, from which raysof constant relative chord originate. The conical-flow concept will be revisited below fortransformation of geometry and pressure distributions. The cylindrical polar coordinatesystem (θ, r, z) and its belonging velocity components (uθ, − vr, w) are used to formulatethe compressible conical boundary-layer equations, see Sec. 3.3.5 and App. B.

Conical geometry transformation for tapered wing sections

In the context of SST (i.e., for an infinite swept wing), the airfoil geometry for the equiv-alent 2D flow solution has to be considered in direction normal to the wing leading edge.Accordingly, airfoil thickness has to be adapted by applying the relation

(z

c

)2D

=(z

c

)3D

1cosϕ (3.23)

to the relative local coordinates(zc

)3D

of the 3D (streamwise directed) wing airfoil. Forthe tapered wing segment in Fig. 3.11, local sweep angle ϕ is a function of relative chord x

c

as well as of leading- and trailing-edge sweep angle according to the following expression:

tanϕ = tanϕLE(

1− x

c

)+ tanϕTE

x

c. (3.24)

Combining Eqs. (3.23) and (3.24) yields the following relation:

(z

c

)2Dc

=(z

c

)3D

√1 +

[tanϕLE

(1− x

c

)+ tanϕTE

x

c

]2. (3.25)

It transforms the coordinates of a streamwise-directed airfoil section within a taperedwing segment into an equivalent airfoil geometry, which virtually develops along a conicalarc chord (indicated by the subscript 2Dc, i.e., conical 2D). The origin of this arc lies inthe mentioned virtual wing apex O, from which all generator lines of constant percentagechord originate. The terminology of the conical wing geometry concept has been intro-duced by Kaups and Cebeci [143], and is also being intensively studied at DLR [295].

Relations between 3D and 2D pressure distributions

With the transformed values of M2D and Cl,2D, a 2D flow solver can be applied to thetransformed conical airfoil geometry. To use the pressure distribution from the (2Dc) flowsolution within 3D wing design considerations, the equivalence law formulated by Lock[170] is used within the proposed method. Most importantly, the 3D pressure distribu-tion (in streamwise direction) is required as input for the conical laminar boundary-layercalculation in the applied transition prediction procedure, see Sec. 3.3.5.

86 Chapter 3. Method for aircraft design with hybrid laminar flow control

To shortly summarize the relevant equations and assumptions, again first consider thesimple case of an infinite swept wing, for which the pressure coefficients relate as follows:

Cp,3D = Cp,2D cos2 ϕ. (3.26)

For the tapered finite wing in Fig. 3.11, the conical-flow assumption is postulated, that is,the isobars (lines of constant pressure) are aligned with the constant-percent-chord gen-erators originating from the virtual conical wing apex O. This assumption is reasonable,especially if the distance of the apex from the conical wing element is sufficiently large,which is the case for moderate taper ratios [259].

The 3D flow with the freestream Mach number M∞,3D =: M∞ over the tapered wingat a spanwise station y can then be considered equivalent to the flow over a 2D airfoilat a reduced freestream Mach number M∞ cosϕ if the following condition holds: Thecomponent of the local Mach number at relative chord x/c on the 3D wing section, whichis normal to the isobar with local sweep angle ϕ, is equal to the local Mach number at thesame percent-chord x/c of the 2D airfoil. Likewise, the isentropic flow relations betweenMach number and local pressure coefficient Cp have to be the same. Lock formulates therespective relations for two cases (i.e., for the 2D freestream Mach numbersM∞ cosϕ andM∞ cosϕref ), which leads to the following equivalence law between 3D and 2D pressuredistribution [170]:

Cp,3D = f − 1γ2M

2∞

+ f Cp,2Dc cos2 ϕref ,

with f =[

1 + γ−12 M2

∞ cos2 ϕ

1 + γ−12 M2

∞ cos2 ϕref

] γγ−1

, (3.27)

and with γ denoting the ratio of specific heats40. A derivation of these equations is givenin App. B. Besides the freestream Mach numberM∞ and a reference sweep angle ϕref , theequivalence law to translate pressure coefficients Cp,2Dc uses local sweep angles ϕ (x/c) ofthe respective isobars, which implies consideration of wing taper according to Eq. (3.24).Although a 2D flow solver is applied within the proposed method (see Sec. 3.3.4), the 2Dpressure coefficient Cp,2Dc is denoted with the conical subscript c, because it is determinedfor the conical airfoil geometry, see Eq. (3.25).

An extension of Lock’s equivalence law that additionally includes three-dimensional in-duced velocities is presented by van Der Velden and Kroo [310], applied to the design ofa supersonic oblique flying wing. The implications of conical flow in laminar wing designhave also been studied by Streit et al. [295] at DLR and NASA. Good agreement of 3Dwing pressure distributions from wind tunnel measurements with 2D flow solver resultstransformed according to the discussed sweep-taper relations is, e.g., shown by Boppe [37].He underlines that agreement can only be achieved if the variation of the shock (reference)sweep angle ϕref with flow conditions is taken into account. In the proposed method, thisis covered by an automated detection and iteration of the shock location as described in

40For ideal or perfect gases, the ratio of specific heats (also called heat capacity ratio) equals the isentropicexponent. For air at standard atmospheric conditions, γ = 1.4 [11].

3.3 HLFC aerodynamic wing design method 87

Sec. 3.3.6. The procedure further includes an iteration of the transition location (x/c)transpredicted based on boundary-layer calculation and a two N -factor method, see Sec. 3.3.5.The quality of the pressure distributions obtained with the proposed approach in the con-text of HLFC wing design is discussed in the validation example in Sec. 3.3.6.

Transformation of drag coefficients

As a result of the iterative HLFC airfoil analysis process (Sec. 3.3.6), laminar drag coef-ficients are obtained with respect to the converged values of (x/c)ref and (x/c)trans. Ac-cording to the conical sweep-taper transformation, the resulting drag coefficients are ini-tially available in the conical (2Dc) plane; this is also how they are stored in the HLFCairfoil database, see Fig. 3.10 and Sec. 3.3.8. However, for the summation of wing tran-sonic profile drag according to Eq. (3.20), drag coefficients are required in streamwise(3D) direction. To present adequate transformation rules between Cd,2Dc and Cd,3D, firstconsider the breakdown of the airfoil drag coefficient (Cd,airf = Cd)

Cd,airf ==Cd,visc︷ ︸︸ ︷

Cd,fric + Cd,visc -p + Cd,wave︸ ︷︷ ︸=Cd,pres

, (3.28)

with its main components friction drag Cd,fric, viscous drag due to pressure forces Cd,visc -p(also called form drag), and wave drag Cd,wave. Several applications and 2D solvers (e.g.,MSES [65], see Sec. 3.3.4) alternatively follow a terminology with only two drag com-ponents, as indicated by the upper and lower braces, i.e., Cd,airf = Cd,fric + Cd,pres =Cd,visc + Cd,wave. For the first sum, the following transformation rule can be applied:

Cd,3D = Cd,fric,2Dc + Cd,pres,2Dc cos3 ϕref , (3.29)

which has originally been formulated by Busemann [42] for infinite swept wings. Whilethe (lift-independent) friction term Cd,fric,2Dc remains unchanged, the pressure term istransformed by considering both the changed orientation (cosϕref ), as well as the nor-mal direction of the dynamic pressure (cos2 ϕref ). Within the context of preliminary air-craft design, the transformation rule (3.29) has, e.g., been used by Greitzer et al. [105].However, since the alternative terminology based on Cd,visc and Cd,wave as introduced inSec. 3.2.3 is more common in conceptual and preliminary design applications, an equiva-lent transformation is required. The relation

C ′d,3D = Cd,visc,2Dc cosϕref + Cd,wave,2Dc cos3 ϕref , (3.30)

which is, e.g., used by Büscher [41] and Wunderlich [324], can be applied with sufficientsmall deviations compared to Eq. (3.29), and is therefore selected for the proposed method.

To demonstrate the small deviations between both transformations, the difference Cd,3D−C ′d,3D may be quantified. Since the physical uncertainty lies in the differently transformedviscous drag components (Cd,fric,2Dc and Cd,visc -p,2Dc, see Eq. (3.28)), the result is related

88 Chapter 3. Method for aircraft design with hybrid laminar flow control

to the untransformed coefficient Cd,visc,2Dc. This yields the following deviation function

Cd,3D − C ′d,3DCd,visc,2Dc

= rf + (1− rf ) cos3 ϕref − cosϕref

=: ∆Cd,err,rel (rf , ϕref ) with rf = Cd,fric,2DcCd,visc,2Dc

, (3.31)

-10-8-6-4-202468

10

15 20 25 30 35

∆Cd,e

rr,r

el (

r f, ϕ

ref),

%

reference sweep angle ϕref, deg

Cl ↑

sample points for HLFC airfoilvalidation example (see Sec. )

rf = 0.5 rf = 0.6 rf = 0.7

3.3.6

Figure 3.12: Deviation in drag transformationas a function of ϕref and rf , seeEq. (3.31); sample points com-puted at M = 0.85, Cl = 0.3 – 0.7

which only depends on the reference trans-formation sweep angle ϕref and on the ra-tio rf of friction to (total) viscous drag.The function is plotted in Fig. 3.12 forthree different values of rf , together withsample points calculated at M = 0.85 forthe HLFC airfoil that will be used as val-idation example in Sec. 3.3.6. The exam-ple shows that the relative (viscous drag)deviation |∆Cd,err,rel| stays well below 5%over a wide range of lift coefficients be-tween Cl = 0.3 and 0.7. For the airfoilsconsidered within this thesis, rf has beenobserved to take values mainly between 0.6and 0.65 in the relevant cruise lift regionaround Cl ≈ 0.5. This ensures negligible differences between the two transformation ap-proaches, nearly independently of the selected reference sweep angle ϕref , see Fig. 3.12.

3.3.3 Validation case for conical 2.5D wing drag prediction method

Table 3.4: Reference wing parameters for vali-dation of drag prediction method

Symbol Unit Values m 40λ = ctip/croot − 0.25c (η = 0.5) m 8ϕLE

◦ 35.0ϕTE

◦ 24.7M∞,3D − 0.80Rec (η = 0.5) − 53.4 · 106

Before the details of the laminar flow wingdesign method are described in detail,a turbulent validation case is presentedfor the 2.5D conical wing drag predictionmethod. Basically, the principle for lami-nar drag prediction is the same, except forthe different transition location. The qual-ity of pressure distribution shapes, whichare crucial within laminar wing design, willbe discussed in the HLFC airfoil validationexample in Sec. 3.3.6. For the turbulentvalidation case, a single-tapered wing ge-ometry with the parameters in table 3.4 isdefined; a transonic turbulent airfoil shapeprovided by DLR [234] is used and kept constant over the span. The reference wing isuntwisted and has no dihedral. For validation, a 3D flow calculation is performed withthe unstructured RANS solver TAU of the DLR [92, 279], using the one-equation Spalart-

3.3 HLFC aerodynamic wing design method 89

Allmaras turbulence model, and an unstructured hybrid grid created with the mesh gen-eration software Centaur™ [47]. The proposed wing drag prediction method is also ap-plied to the reference wing according to the principle illustrated in Fig. 3.10. For the 3Dairfoils at different stations of the tapered wing segment, the iterative airfoil analysis pro-cess (Sec. 3.3.6) is used, with the integrated 2D transonic flow solver MSES (Sec. 3.3.4).The results are written into the database using the procedure explained in Sec. 3.3.8. TheMICADO aerodynamic program (including the module LILI, see Sec. 3.2.3) is then ap-plied to predict the total wing drag polar at M = 0.80. As described above, for every liftcoefficient CL = CL,w, the spanwise distribution of lift coefficients are obtained from LILI.At every panel station y, drag coefficients are retrieved from the database for the respec-tive local value of Cl (y). The weighted sum of transformed drag coefficients accordingto Eqs. (3.29) or (3.30) yields CD,prof,w (see Eq. (3.20)), which is added up with CD,ind,wfrom LILI to obtain CD,w (see Eq. (3.19)).

The results are presented in Fig. 3.13, where the Cl distributions are compared in Fig. 3.13a,and the drag polars in Fig. 3.13b. The Cl distributions are compared at equal CL,w, whichgenerally shows very good agreement. The slight tendency towards higher outboard load-ing for the 3D Navier–Stokes results is reasonable due to 3D (cross-)flow effects on theswept wing. Since LILI does not consider viscous effects, specific nonlinear trends as ob-served at CL = 0.63 on the outboard wing are not captured. Further, angle of attacks αfor the same CL differ noticeably. This can be crucial in some applications (e.g., in thelow-speed regime), but is considered of minor importance in the present high-speed wingdesign context, which throughout uses constant lift coefficients as connecting parameters.Generally, qualitative sensitivities and quantitative spanwise Cl distributions provided byLILI for the transonic speed regime are considered as fully sufficient for the herein con-sidered preliminary design applications.

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

1.10

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

loca

l lift

coe

ffici

ent

Cl (

y)

relative spanwise coordinate η = 2y/b

TAU: α = 0°, CL = 0.27

TAU: α = 1°, CL = 0.39

TAU: α = 2°, CL = 0.50

TAU: α = 3°, CL = 0.63

LILI: CL = 0.27 (α = −0.9°)

LILI: CL = 0.39 (α = 0.2°)

LILI: CL = 0.50 (α = 1.3°)

LILI: CL = 0.63 (α = 2.6°)

(a) Spanwise Cl distributions atM = 0.80and equal values of CL = CL,w

-0.20

-0.10

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

0.000 0.005 0.010 0.015 0.020 0.025 0.030

win

g lif

t co

effic

ient

CL

,w

wing drag coefficient CD,w

2.5Dc+LILI: CD,fric,w

2.5Dc+LILI: CD,w [transf. Eq. ] 2.5Dc+LILI: CD,w [transf. Eq. ] 3D TAU: CD,fric,w

3D TAU: CD,w

(3.30)(3.29)

(b) Drag polars at M = 0.80; comparisonof different transformation equations

Figure 3.13: Validation of conical 2.5D drag prediction method for wing data in ta-ble 3.4; 3D Navier–Stokes solutions computed with DLR TAU code [92]

90 Chapter 3. Method for aircraft design with hybrid laminar flow control

The comparison of drag coefficients in Fig 3.13b also shows good agreement. While frictiondrag coefficients CD,fric,w nearly coincide over the whole considered CL range, total dragcoefficients41 CD,w are slightly underpredicted by the proposed Q3D method at low CL.More importantly for the considered cruise applications, deviations are small at higherCL, which also underlines physically reasonable capturing of transonic drag rise. The solidblack and dotted dark gray curve differ in the applied (2.5Dc to 3D) drag transformationsaccording to Eqs. (3.30) and (3.29), respectively. Only very small deviations can beobserved here, and the trends abstractly presented in Fig. 3.12 are well confirmed.

This validation case shows consistency and functionality of the proposed method, butdoes not claim at all general validity. Quite the opposite, it is underlined that the pro-posed method is very much recommended for preliminary design studies, but does not re-place subsequent 3D flow computations with a Navier–Stokes solver, for instance. Onlysuch approaches can reliably predict and quantify “real” 3D flow effects and specific flowphenomena (e.g., severe separation, shock/boundary-layer interaction, double shocks). Inturn, since detection and elimination of these phenomena is a key task of detailed wingdesign, they can reasonably be excluded from preliminary design investigations.

3.3.4 2D transonic flow solver (MSES)

As reflected at the beginning of this section, a reasonable consideration of HLFC wingaerodynamics requires immersing into airfoil characteristics, also on preliminary designlevel. Therefore, a flow solver has to be integrated into the proposed method, which isrequired to allow for the following characteristics or capabilities:

• prediction of pressure distribution → Eq. (3.27)

• prediction of viscous/wave drag coefficients (with fixed transition) → Eq. (3.30)

• airfoil shape design and optimization

• low preprocessing effort and low computation time

• robustness within automated process

A 3D flow solver has been excluded, mainly due to insufficient compliance with the last tworequirements. Instead, the conical quasi-3D approach discussed in Sec. 3.3.2 is proposed,for which a 2D flow solver is adequate. Generally, the CFD methods and governingequations summarized in Fig. 3.14 are applicable, with the Navier–Stokes equations42as the most general formulation; this implies, however, higher model complexity andcomputation time. A short, certainly not exhaustive overview of existing 2D flow solvers isgiven below. A comprehensive summary of airfoil design and analysis software is providedby Mason on his website [178]; selected airfoil analysis codes are compared in Ref. [180].

41The other drag subcomponents, i.e., CD,ind,w (from LILI), CD,visc -p,w, and CD,wave,w are not comparedseparately, because they can not be extracted distinctly from the 3D RANS solution obtained with TAU.

42For a description of the different approaches to model or solve the Navier–Stokes equations, e.g., RANS,LES/DES (large/detached eddy simulation), or DNS (direct numerical simulation), see, e.g., Ref. [163].

3.3 HLFC aerodynamic wing design method 91

DNS

Euler Eq.

RANS

LES/DES

Nonlinear Potential Eq.

inviscid, irrotational, linear

Linear Potential Eq.

+ nonlinear

+ rotation

+ viscous

1970

s19

60s

1980

s19

90s

- to

day

applica

ble

to

conce

ptu

al

or p

relim

inar

y d

esig

n

incr

easi

ng

mod

el c

omple

xit

y &

com

puta

tion

al c

osts

Navier–Stokes Eq.

Figure 3.14: Governing equations of CFDmethods, after Schröder [275]

One of the first transonic airfoil codes isTSFOIL developed by Murman et al. [188]that solves the transonic small disturbanceequations. Another method capable to pre-dict transonic drag characteristics is Jame-son’s FLO 36 [138] code, which incorpo-rates a multiple grid solution of the po-tential equations. Both are valuable pro-grams, but not capable to predict viscousdrag characteristics. This capability is,for example, provided by Drela’s XFOILcode [68], which couples the potentialflow solution (obtained from a vorticity-based panel formulation) with an integralboundary-layer method. However, XFOILcannot be applied to transonic flows. Dueto the close interactions between reduced viscous drag and acceptable wave drag charac-teristics in the context of transonic HLFC airfoil design, prediction of both viscous andwave drag is required for the proposed method. One opportunity would be to apply a 2DNavier–Stokes flow solver (e.g., TAU [92]), which would, however, involve increased mod-eling and computational effort, especially concerning the required design and optimiza-tion capabilities. Also, robustness of grid generation and numerical convergence withinan automated process over a wide range of flight conditions can be critical. Especially,for the—herein most relevant—transonic viscous flow cases, grid convergence can, e.g., becomplicated by varying shock locations or shock-induced separations.

A good compromise for preliminary design applications is provided by the fully-coupledviscous/inviscid interaction method developed by Drela [58] and Giles [94]. Theoretically,this approach is based on the introduction of Prandtl’s assumption of two separated flowregions into the Navier–Stokes equations, as discussed in the fundamentals section 2.2.1.This allows interpreting the complete Navier–Stokes solution as being composed of an“outer” solution (e.g., of the Euler equations) and an “inner” solution of the boundary-layer equations. The coupling of the two solutions in the boundary region yields the(simplified) complete solution [250]. The code MSES [65] (former ISES) incorporatesthis principle, being superior to XFOIL due to the included Euler equation solver, whichmakes it applicable to transonic flows. Since it best fulfills all above stated requirements,MSES is included into the proposed HLFC airfoil suite, and shortly introduced below.

In MSES, the inviscid flow field is numerically formulated by a conservative finite-volumediscretization of the steady 2D Euler equations on an intrinsic streamline grid [58]. Theviscous flow regions (i.e., boundary layers and trailing wakes) are described by a two-equation compressible integral boundary-layer formulation, and are fully coupled withthe inviscid streamlines via the displacement thickness δ∗ (see Eq. (2.4)). The Euler andboundary-layer equations are simultaneously solved applying a global Newton solutionscheme [94]. Drag coefficients are obtained from a momentum balance over a control vol-ume around the airfoil, where Cd,visc and Cd,wave are computed by integrating the momen-tum defects in the viscous and the inviscid (shock) wakes of the flow field, respectively [58,

92 Chapter 3. Method for aircraft design with hybrid laminar flow control

65]. The coupled formulation and solution of Euler and boundary-layer equations allowsboth (direct) airfoil analysis by specifying airfoil geometries, as well as (inverse) airfoildesign by imposing target pressure distributions [95]. The inverse design and optimiza-tion capabilities are also applied within this thesis, and will be revisited in Sec. 3.3.7.

Due to the streamline coordinate system, MSES allows automated grid generation andadaptation with the flow field. It can thus be operated over a wide range of flight con-ditions, for which it provides pressure distributions and drag coefficients, optionally withfixed transition. It can predict flows with transitional separation bubbles, shock waves,and trailing-edge as well as shock-induced separation [62]. Further characteristics and ca-pabilities, e.g., to handle multielement airfoils, along with appropriate validation cases,are presented in Refs. [59, 60, 66].

MSES has been applied in many airfoil and wing design applications. For example, Fu-jino et al. [86] present an NLF airfoil design for a lightweight business jet, along witha comparison of MSES results against wind-tunnel and flight test data. The validationshows good agreement, especially for drag rise and shock location characteristics. Furtherairfoil design applications can be found in Refs. [184, 328]. Application of MSES withinconceptual wing or overall aircraft design are, for example, given in Refs. [88, 93, 147].

MSES also includes a simplified eN based database approach (envelope-fitting method)for transition prediction. This is, however, not applicable within the context of this thesis,mainly because it is not capable to cover cross-flow instabilities, but only streamwise (TS)instabilities. How TSI and CFI are simultaneously covered by the more sophisticatedSTABTOOL code is described in the following section.

3.3.5 Transition prediction modules (STABTOOL)

A physics-based transition prediction has been reasoned to be inevitable for a reliablerealization of the proposed preliminary HLFC wing design method. Different methodsfor transition prediction have been discussed in Sec. 2.2.4, and the eN method has beenselected as best suitable within the present context. Recapitulating the laminar flowfundamental section 2.2, transition prediction with the eN method (for given freestreamconditions and wing geometry) requires conducting the following steps [17]:

1. prediction of Cp distribution (see Sec. 3.3.4)

2. boundary-layer analysis to calculate laminar velocity and temperature profiles

3. linear stability analysis for each boundary-layer profile

4. integration of growth rates to determine N -factor envelopes

5. correlation of envelopes with limiting N -factor curve to obtain transition location

Within the proposed approach, steps 2–5 are performed using the STABTOOL suite de-veloped by Schrauf [259, 265] at Airbus Bremen, which constitutes the standard transition

3.3 HLFC aerodynamic wing design method 93

prediction module at Airbus and DLR for NLF and HLFC wing design. STABTOOL alsocomplies well with the last two requirements stated in the context of the flow solver se-lection, i.e., low preprocessing effort and computation time, as well as convenient integra-tion into an automated and robust process. Further, a key advantage of STABTOOL isthat it requires as input only a streamwise 3D pressure distribution Cp,3D, the freestreamconditions (Mach and chord Reynolds number), and the tapered wing geometry in termsof leading- and trailing-edge sweep angles (ϕLE, ϕTE). Further, a suction distributionCq (x/c) can be included for LFC or HLFC airfoil analysis. Though only using the Cp dis-tribution at a specific wing section (without information about the 3D flow field), the so-lution of the compressible boundary-layer equations in combination with the conical-flowassumption (see Sec. 3.3.2) yields quasi-3D results. These include N -factors for both TSand cross-flow, which are correlated to predict the transition location for the given wingsegment. This approach perfectly suites into the proposed method, where the Cp,3D dis-tribution is provided from applying the equivalence law in Eq. (3.27).

STABTOOL consists of different modules, which are summarized in table 3.5 togetherwith the belonging tasks and relevant output parameters. The first module PrepCPCQpreprocesses the Cp,3D distribution, which is especially significant in the region aroundthe stagnation point, since the pressure at the stagnation point (Cp,3D,stag) initializes thesubsequent boundary-layer calculation. Cp,3D,stag also strongly influences the effective(leading-edge) sweep angle ϕeff and the attachment-line momentum-thickness Reynoldsnumber Reθ,AL, which are the governing parameters for attachment-line transition (ALT)criteria, see Eqs. (2.20) and (2.22). A closer look at these parameters will be taken inthe HLFC airfoil validation example in Sec. 3.3.6. The other modules COCO, LILO, andNCFNTS are shortly discussed in the following paragraphs, while results and level of de-tail will also be exemplified in the course of Sec. 3.3.6.

Table 3.5: Overview of STABTOOL modules

Module name Incorporated task Output parametersPrepCPCQ Analysis and preparation Reθ,AL, ReAL (→ ALT criterion),

of Cp (and Cq) distribution effective sweep angle ϕeffCOCO [259] Boundary-layer analysis temperature profiles T (x, z),

velocity profiles u (x, z) , v (x, z);derivatives ∂

∂zand ∂2

∂z2 of T, u, vLILO [265] Linear stability analysis N -factors: NTS and NCF

NCFNTS N -factor correlation transition location (x/c)trans

The STABTOOL suite has already been applied and validated in many different industrialapplications, including evaluation of flight tests, see Refs. [260, 271, 272]. It is also inte-grated into the Navier–Stokes solver TAU [148] of the DLR, where it is used for automatictransition prediction for 3D aircraft configurations [149]. Other codes including laminarboundary-layer stability methods for transition prediction are, for example, COSAL [175],SALLY [290, 289], and LASTRAC [49] by NASA, or CASTET by ONERA [154]. Moresimplified or advanced methods for transition prediction have been mentioned in Sec. 2.2.4.

94 Chapter 3. Method for aircraft design with hybrid laminar flow control

Boundary-layer analysis (COCO)

For transition prediction using the eN method, temperature and velocity profiles of thelaminar boundary layer are required as input for the linear stability calculations (seeSec. 2.2.3). For detailed design applications, these profiles can be extracted from 3DNavier–Stokes or boundary-layer solutions. For preliminary design purposes, however,calculation of the profiles by applying quasi-3D boundary-layer methods is a reasonableand mostly sufficient alternative [131]. Kaups and Cebeci [143] first presented such an ap-proach for swept, tapered wings with suction by applying the conical wing flow approxima-tion introduced in Sec. 3.3.2. A similar approach is implemented in the compressible lami-nar boundary-layer code COCO [259], originally developed under the name COAST [255].

COCO is based on the numerical formulation of the conical compressible boundary-layerequations. The compressible boundary-layer equations, which were given for a 2D Carte-sian coordinate system in Eqs. (2.7) to (2.10), are therefore reformulated based on theconical-flow assumptions with the cylindrical polar coordinates defined in Fig. 3.11. Theresulting equations are given in App. B; for a derivation and formulation of the com-plete nonlinear differential equation system, refer to Schrauf [259]. The equation sys-tem, which also includes suction velocity if specified, is numerically solved using Newton’smethod with a second-order backward finite-difference scheme [263]. The solution yieldsthe boundary-layer profiles for temperature T (x, z) and velocities u (x, z) , v (x, z), aswell as their first and second derivatives with respect to the wall-normal43 coordinate z.

High numerical accuracy of the boundary-layer profiles is important due to their stronginfluence on linear stability results [17]. Profiles and derivatives computed with COCOare compared with results from wind tunnel experiments in Ref. [259]. Conical-flowboundary-layer solutions generally agree well with 3D flow solutions (see, e.g., comparisonsby Sturdza [296] with 3D Navier–Stokes results at supersonic speeds). Certainly, this islimited to wing regions that are not highly governed by 3D flow effects, like in the vicinityof root, tip, or nacelles. The conical-flow concept is especially meaningful if straightisobars (or minimum spanwise pressure gradients) are desired for other design reasons,e.g., for optimum suction system layout on full-chord LFC wings [143].

Linear stability analysis (LILO)

The LILO program applies linear local (or nonlocal) stability theory to determine N -factors, which have been defined in Eq. (2.19) as maximum value of the natural logarithmsof the amplification rates. Input for the calculation are the boundary-layer profiles and therespective derivatives provided by COCO. Amplification rates andN -factors are computedfor the boundary layer at different chordwise stations x/c. The twoN -factor method (classC) is used by computing two separate values in streamwise (NTS) and cross-flow (NCF )direction, with envelope-of-envelopes (class B) methods as sub-strategies, see Sec. 2.2.4.

43Additional derivatives are required for nonlocal stability theory, i.e., PSE methods, which are not con-sidered within this thesis.

3.3 HLFC aerodynamic wing design method 95

Besides the frequency ω, the propagation direction in terms of the wave angle ψ is fixed44for calculation of NTS, and the wavelength λ (optionally the spanwise wave number β)is fixed for calculation of NCF . The numerical formulation of the linear local stabilitytheory for compressible flow as implemented in LILO was given by the system of lineardifferential equations (2.15). In LILO, this generalized eigenvalue problem is transformedinto a standard eigenvalue problem for efficient numerical solution. The eigenvalues aredetermined using QR decomposition or a generalized inverse Rayleigh iteration [265].

The calculation algorithm to find amplification rates and N -factors at given chord stationsand frequencies can be simply illustrated by recalling the correspondence with the stabilitydiagram in Fig. 2.5. After a quick pre-check of the boundaries of the stability diagram,an initial station is placed in the unstable (inner) region of the stability diagram at agiven frequency (for the TS case). Starting with this amplified mode, calculations atupstream and downstream stations are performed to identify existence and location ofstations at which waves are first amplified (neutral point), or damped again. Consequently,systematic variations of stations and frequencies within the boundaries yield the completeneutral curve, from which the corresponding amplification rates and N -factor envelopesare derived and plotted [265]. Similarly, the relevant wave lengths are estimated at whichCFI occur.

Correlation of transition location

The NCFNTS module is used for transition prediction using the two N -factor strategy.As illustrated in Fig. 2.6, the distinct transition location (x/c)trans is obtained by the in-tersection of the NCF/NTS envelope pairs (at different x/c stations) with an experimen-tally correlated limiting curve. Within this thesis, the axes interception values of thiscritical curve are selected as [268]:

• NCF,crit = 7.5

• NTS,crit = 9.5

These limiting values thus determine the transition location if only one of the instabilitymechanisms is present. For the combined cases, a convex-shaped HLFC correlation curveis used, which will be shown in the validation example in the next section. Accordingto Redeker et al. [214], the convex shape represents a weak interaction between TSI andCFI. The applied correlation curve is proposed by Schrauf [268] based on results and con-clusions from different wind tunnel and flight tests (e.g., the A320 HLF fin tests) [261].The correlation curve is implemented into the NCFNTS code for HLFC in free flight. Itexhibits lower values than another implemented correlation curve, which is validated forNLF in free flight. This is plausible, because the additional (distributed) roughness of thesuction panel in HLFC applications generally causes larger initial amplitudes for the sta-tionary cross-flow vortices. Another uncertainty in HLFC tests is the influence of noisegenerated by the suction system on the amplification of TS waves [261]. The used corre-

44Though strongest growth rates of TS waves occur at higher angles in compressible flow (see Sec. 2.2.5),the wave angle is here fixed at ψ = 0◦, since differences in results have been shown to be small [272].

96 Chapter 3. Method for aircraft design with hybrid laminar flow control

lation curve is the state of the art at Airbus and the DLR; however, it needs to be vali-dated in further flight tests [268]. It is evident that choosing different values of limitingN -factors has significant influence on the predicted transition location, viscous drag, andthus overall aircraft performance. However, the consistent choice made herein ensurescomparability between all presented design applications. Also, the N -factor limiting val-ues are assumed to be chosen rather conservative than optimistic [268].

3.3.6 HLFC airfoil analysis process

This section summarizes the automated HLFC airfoil analysis process, using the equationsand modules presented in the previous sections. The process has been implemented intoa robust program, which includes basic software elements already introduced for theMICADO software architecture, i.e., C++ programming language, XML data interface(see Fig. 3.1), and the wrapper approach for incorporation of MSES and STABTOOLmodules. Hidden behind the term robust, a variety of knowledge based error and exceptioncase handling is implemented. These are not described in detail, but they are a crucialfeature making the process a valuable and efficient tool for fast and automated predictionof laminar drag polars. The latter is especially difficult for HLFC wings, implying suction,highly transonic viscous flow cases, as well as strong cross-flow susceptibility. Accordingto its functionality, the developed program, which also includes design and optimizationcapabilities (see Sec. 3.3.7), is named HYbrid Laminar Flow Airfoil Suite (HYLFAS).

Recall that the term airfoil in the section title does not imply a pure 2D approach, becausethe considered airfoils are always obtained as line-in-flight cuts from a 3D wing geometryspecified in the AiX file. The conical 2.5D approach then implicitly incorporates theinfluences of the tapered wing geometry, as well as instabilities in streamwise and cross-flow direction. The reintegration of airfoil geometry and drag polars onto MICADO wingand aircraft level works via the airfoil database approach, as illustrated in the matrix-type overview in Fig. 3.10. Let us thus now concentrate on the right (airfoil level) columnof that figure, which is shown as an expanded process flow diagram in Fig. 3.15.

The main HYLFAS analysis process is represented by the center flow diagram. For givenwing planform and airfoil geometry, freestream conditions (M∞,Rec), lift coefficient Cl,3D,and suction distribution Cq, it calculates the 3D pressure distribution Cp,3D, as well ascoefficients of viscous drag Cd,visc and wave drag Cd,wave. The process comprises twonested iterations, the outer with respect to the transition location (x/c)trans, and theinner with respect to the relative chord location (x/c)ref , which is used for sweep-tapertransformation, and which equals the shock location (x/c)sh at transonic flow conditions.The latter (MSES) iteration process is displayed in enlarged form in the left part ofFig. 3.15. In the right part the STABTOOL process introduced in Sec. 3.3.5 is magnified.

When the given geometry and flow conditions first enter the inner (left) MSES iterationprocess, start values of (x/c)ref = 0.5 and (x/c)trans = 0 (i.e., full turbulent flow) arespecified45. With these values, conical transformation of the airfoil geometry is applied

45For subsonic Mach numbers, a start value of (x/c)ref = 0.25 is specified (see Sec. 3.3.2). Though successof convergence does not generally depend on the start value, its proper choice can accelerate convergence.

3.3 HLFC aerodynamic wing design method 97

Lock equivalence law

convergence?

STABTOOL process

sweep-tapertransf.

flow field

Shock detection

convergence?

sweep transf.

ref sh

x c x c

ref PrepCPCQ:input preparation

COCO: boundary layer calculation

NTSNCF: correlationof transition location

LILO: linear stability analysis

,3,, l DcM CRe

tapered wing

,2p DcC

,3p DC

trans

x c

yes

no

no yes

ref

x c

transx c

, / ,2d visc wave DcC

,,2 2,D l DM C

2D airfoil

trans

x c

,3, l DM C

tapered wing ,3p DC qC

temp. & velocity profiles,and derivatives

TSNCFN

trans

x c

algorithm

module

data

decision

Legend

MSES iteration

,2p DcC

MSES:flow solver

(3.25) (3.21)–(3.22)

(3.27)

Figure 3.15: HYLFAS flow chart for HLFC conical 2.5D airfoil analysis, includingMSES, STABTOOL, and nested iteration for (x/c)ref and (x/c)trans

according to Eq. (3.25). The sweep angle ϕref at the local chord position (x/c)ref of thetapered wing element is used for transformation of Mach number and lift coefficient, seeEqs. (3.21) and (3.22). For the transformed input data, MSES is executed with fixedtransition at (x/c)trans, which yields the flow field in terms of p (x) , ρ (x) ,M (x), etc., forthe conical 2D wing section.

For a proper transformation of 3D and 2D aerodynamic characteristics at transonic con-ditions, the actual shock location of the flow field is required. Since this is unknown apriori, an automated shock detection algorithm has been implemented that scans the flowfield for locations x/c, where the density gradient46 ∂ρ

∂xexhibits local maximum values.

As control conditions, changes of signs in the vicinity of the detected shock location arechecked, i.e., ∂2ρ

∂x2 = 0. To exclude very weak density gradients from automated shock de-tection, a minimum constant threshold can be preset by the user, which is set by defaultto the experience-based value

(∂ρ∂x

)th

= 2.5. If no shock is detected (e.g., at low Machnumbers or lift coefficients), the center-of-pressure location is selected, or optionally thequarter-chord position. If multiple shocks are detected, the most aft position is selected.

The determined shock location (x/c)sh is fed back as reference position (x/c)ref into theMSES and shock detection iteration process (see Fig. 3.15), which is re-executed untilconvergence. Convergence is achieved if the residual εref = (x/c)ref,n− (x/c)ref,n−1 in thenth run falls below a specified threshold, which is set by default to εref,th = 0.003.

46Other parameters have also been investigated as shock detection measure, e.g., enthalpy H or entropyS, which are derived using classical isentropic gas dynamics equations. However, the density gradientperformed best within a robust detection algorithm due to exhibiting most distinct local peaks.

98 Chapter 3. Method for aircraft design with hybrid laminar flow control

After convergence, the pressure distribution Cp, 2Dc for the conical airfoil section is trans-formed back into 3D (streamwise) direction using Lock’s equivalence law (3.27), see centerprocess flow in Fig. 3.15. Together with a user-specified suction distribution47 Cq (x), 3Dflow conditions and tapered wing geometry, the 3D pressure distribution Cp, 3D is then usedas input for the STABTOOL process, as illustrated in the right-hand process in Fig. 3.15.The transition location (x/c)trans predicted by STABTOOL is also fed back into the overallHYLFAS analysis process, which results in the nested iteration. For the transition locationresidual in the mth run of the outer iteration, i.e., εtrans = (x/c)trans,m− (x/c)trans,m−1, athreshold value of εtrans,th = 0.005 is preset. Thus, convergence of the nested iteration isachieved, as soon as εref < εref,th ∧ εtrans < εtrans,th. The overall process then includes n×mMSES andm STABTOOL executions, and it takes between 1 and 5 minutes48 on a stan-dard desktop computer. The nested (double) iteration is superior to the procedure “MSESiteration – STABTOOL – MSES with fixed transition”, because it additionally capturesthe interaction between transition location and pressure distribution via the viscous flowfield, and it ensures consistency, e.g., in terms of independence of selected start values.

The finally obtained viscous and wave drag coefficients Cd,visc,2Dc and Cd,wave,2Dc are theoutputs from the last MSES run with fixed transition at the converged values of (x/c)refand (x/c)trans. They are thus the laminar drag coefficients for the conical 2D section.The transformation into streamwise 3D direction according to Eq. (3.30) is performedduring strip-wise summation on wing level in combination with the database approach,see Fig. 3.10 and Sec. 3.3.8. Note that since the first iteration run was started with(x/c)trans = 0, the turbulent drag coefficients are obtained meanwhile, and stored to thedatabase together with the laminar aerodynamic coefficients. This becomes important forreserve fuel estimation and aircraft sizing for in-flight failure cases of the HLFC system,see Sec. 3.2.6 and design studies in Chap. 4.

Validation example

Table 3.6: Geometry and design conditions forHLFC airfoil validation case [114]

Parameter Symbol ValueMach number M∞,3D 0.85Reynolds number Rec 49.4 · 106

Lift coefficient Cl,3D 0.645LE sweep angle ϕLE 33.8◦TE sweep angle ϕTE 23.9◦

Results and validity of the HYLFAS analy-sis process are examined using an exampleHLFC airfoil that has been designed by Ro-dax [234] at DLR for the flow conditionsand tapered wing geometry49 summarizedin table 3.6. For this airfoil, the above de-scribed iterative procedure is illustrated bythe results in Fig. 3.16, where the 3D airfoilgeometry (streamwise wing cut) and thespecified suction distribution Cq are shownin the lower diagrams of Fig. 3.16a. Theupper part of this figure shows the trans-formed 3D pressure distribution Cp,3D for three different runs of the nested iteration, i.e.,

47The suction distribution Cq (x) is parameterized in a separate XML file, which allows for convenient userspecification and systematic studies and optimization of required suction strengths.

48Computation time depends, e.g., on the required number of iterations and the complexity of the flow case.49The design conditions are in agreement with the long range reference aircraft presented in Chap. 4.

3.3 HLFC aerodynamic wing design method 99

the start run with (x/c)ref = 0.5 and (x/c)trans = 0, an intermediate run, and the finalrun with (x/c)ref = 0.68 and converged transition location (x/c)trans = 0.48. For com-parison, a streamwise pressure distribution is shown that was computed by DLR with theconical (“2.75D”) method of the structured RANS solver FLOWer50 [211]. The convergedHYLFAS solution agrees well with the FLOWer result; this especially holds for the localgradients in the front part, as well as for location and strength of the shock, which is impor-tant, because they inherently influence laminar boundary-layer stability (thus transitionand viscous drag) and the amount of wave drag, respectively. Also, the visible “smearing”of the shock pressure rise demonstrates capabilities of MSES to capture shock/boundary-layer interactions. Slight deviations in the Cp shapes can be observed at the upper rearpart behind the shock, as well as for the small suction peak at the airfoil nose, which are,however, not significant within the present context. To recapitulate how the presented Cpand Cq distributions suppress TSI and CFI, compare with the HLFC pressure distributioncharacteristics introduced in Fig. 2.9. It is further obvious that the different transforma-tion locations of the other iteration runs yield inadequate pressure distribution character-istics (e.g., local gradients), which is especially unfavorable for laminar wing design dueto the stated reasons. This also holds for the mid-chord location (x/c)ref = 0.5, which isoften used as constant default value in preliminary design applications.

-1.0

-0.5

0.0

0.5

1.0

Cp,

3D

HYLFAS, (x/c)ref = 0.50, (x/c)trans = 0.00 (it. 0-0) HYLFAS, (x/c)ref = 0.63, (x/c)trans = 0.00 (it. 1-3) HYLFAS, (x/c)ref = 0.68, (x/c)trans = 0.48 (it. 5-2, final) FLOWer (DLR RANS solver)

-10

-5

0Cq ,

10-4 suction distribution (upper side)

-0.1

0.0

0.1

0 0.2 0.4 0.6 0.8 1

z/c

x/c

3D airfoil geometry

(a) Variation of Cp distribution during it-eration of (x/c)ref ; comparison withresult from RANS solver FLOWer

0.4

0.6

0.8

1.0

1.2

1.40.0 0.2 0.4 0.6 0.8 1.0

-10

-5

0

5

10

15

ρ

dρ/

dx

x/c

ρdρ/dx

(b) Principle of automated shock detectionalgorithm by scanning local peaks ofdensity gradient ∂ρ

∂x

0.0

0.2

0.4

0.6

0.8

0-0 1-1 1-2 1-3 2-1 2-2 2-3 3-1 3-2 4-1 4-2 5-1 5-2 16

20

24

28

32

x/c

ϕ ref

iteration run (transition it. − shock/ref. it.)

(x/c)trans

(x/c)ref

ϕref

(c) History of nested iteration for transitionlocation (x/c)trans and transformationvariables (x/c)ref and ϕref

Figure 3.16: Results of iterative HYLFAS analysis process for HLFC airfoil exampleand comparison of pressure distribution with Navier–Stokes solution

50Comparisons of the FLOWer “2.75D” method with 3D RANS solutions are presented in Refs. [294, 295].

100 Chapter 3. Method for aircraft design with hybrid laminar flow control

Figure 3.16b illustrates the automated shock detection algorithm by scanning the flowfield for local peaks of density gradient ∂ρ

∂x. While 3D flow applications may require more

sophisticated shock detection procedures (cf. Refs. [198, 323]), the implemented algorithmhas been proven to be completely sufficient for a robust shock detection within HYLFAS.

The history of the nested iteration is presented in Fig. 3.16c, where the first number onthe x axis refers to the (outer) transition iteration, and the second number refers to the(inner) iteration of (x/c)ref . It can be observed that (x/c)trans converges after 5 iterations,and 13 iteration runs are required in total. Note that after initial convergence of the flowsolution within MSES (i.e., in run 0-0), this converged flow case is used as start solutionfor the subsequent iterations, which significantly accelerates overall process time.

The final iteration results of the STABTOOL process (right side in Fig. 3.15) are nowshortly discussed to present the level of detail of the incorporated methods. Figure 3.17shows results of the laminar boundary-layer calculation performed with COCO for theairfoil upper side. For different relative stations s/c along the conical airfoil arc contour,Fig. 3.17a shows computed profiles of the velocity components in streamwise (uθ) andcross-flow (vr) direction (see Fig. 3.11); the wall-normal coordinate z on the ordinate isrelated to the displacement thickness δ∗. While the streamwise profiles do not changesignificantly with s/c, the cross-flow velocity develops rapidly in the leading-edge regiondue to the strong negative pressure gradients. Where positive pressure gradients prevail,e.g., behind the leading-edge suction peak (s/c = 0.1), or where laminar separation wouldoccur (s/c = 0.67), S-shaped or reversed cross-flow velocity profiles can be observed.While cross-flow profiles are inherently inflectional, the streamwise profiles only showan inflection point near the wall at the (theoretical) laminar separation point (s/c =0.67). These qualitative characteristics are fully consistent with the 3D boundary-layerfundamentals discussed in Sec. 2.2.5, or in more detail by Arnal [17].

0

2

4

6

8

0 0.5 1

z/δ

*

streamwise velocity uθ/ue

displacementthickness δ *

s/c

0.000.010.050.100.200.400.67

-0.05 0cross-flow velocity vr/ue

(a) Velocity profiles uθ and vr as functionof relative airfoil arc length s/c

0

2

4

6

8

0 0.2 0.4 0.6 0.8 12.0

2.5

3.0

3.5

4.0

c f·

103 ;

δ c*,

mm

H12

s/c

end of suction transition shock

skin friction coeff. cf·103 (COCO, lam., ref.) skin friction coeff. cf·103 (COCO, lam., no suction) skin friction coeff. cf·103 (MSES, lam./turb., ref.) skin friction coeff. cf·103 (MSES, lam./turb., no suc.) compr. displacement thickness δc* (COCO, lam., ref.) shape factor H12 (COCO, lam., ref.)

(b) Characteristic boundary-layer param-eters as function of s/c

Figure 3.17: Results of conical compressible boundary-layer analysis with COCO

Figure 3.17b shows characteristic boundary-layer parameters as a function of relative arclength s/c, namely skin friction coefficient cf , compressible displacement thickness δ∗c , and

3.3 HLFC aerodynamic wing design method 101

shape factor H12, see definitions in Sec. 2.2.1. Note the gradient changes of the parametersat s/c ≈ 0.14, where the suction velocity is decreased to zero, and at the transition point(s/c)trans ≈ 0.5. The influence of suction on skin friction in the laminar boundary layer(cf,lam) is also illustrated by a comparative computation with COCO without suction(Cq = 0), see dashed gray curve. The blue curves represent the converged MSES solutions(with and without suction); note the significant cf increase in the turbulent boundarylayer behind the transition point, which jumps to the leading edge if Cq = 0. Goodagreement is observed between COCO and (2.5Dc) MSES results for cf,lam. Though theinfluence of Cq on cf,lam is not captured within MSES, it can be considered as negligible inview of the much larger impact of the transition position on cf (and thus on Cd,fric/visc).

0

2

4

6

8

10

12

14

16

18

NT

S

NTS envelope(for Cq,ref)

frequency, Hz (for Cq,ref)

5500507646864325399236843401313928972674

2468227821031941179116531526140913001200

-10-5 0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Cq·

104

x/c

variation of suction distribution Cq,ref

weaker (−50 %) stronger (+50 %) extended chord

(a) N -factors for TSI analysis

0

2

4

6

8

10

12

14

16

18

NC

F

NCF envelope (for Cq,ref)

additional envelopes refer tovaried suction distributions(see bottom figure)

wave length, mm (for Cq,ref)

0.8300.9691.1301.319

1.5391.7972.0972.447

2.8553.3323.8884.538

5.2966.1807.2128.416

9.822

-10-5 0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Cq·

104

x/c

variation of suction distribution Cq,ref

weaker (−50 %) stronger (+50 %) extended chord

(b) N -factors for CFI analysis

Figure 3.18: Tollmien–Schlichting and cross-flowN -factors calculated with local linearstability solver LILO, including variation of suction distribution Cq (x)

Results of the local linear stability analysis with LILO are plotted in Fig. 3.18 in termsof the natural logarithms of the computed amplification rates (N -factors51) as functionof relative chord position x/c. Figure 3.18a illustrates amplified TS waves at differentfrequencies, and Fig. 3.18b shows the NCF -factors for cross-flow instabilities at differentwave lengths. The bottom diagrams show the reference suction distribution Cq,ref (blackcurve), along with three variations (blue curves). If suction is strong enough, TSI ampli-fication starts not before the end of the suction panel; its chord-wise extension is, how-ever, restricted by the position of the front spar (see Sec. 3.3.7). The influence of Cq onCFI is even more critical, since too weak suction leads to transition at the leading edge,which is supported by the high leading-edge sweep angle (ϕLE = 33.8◦) in this example.Stronger suction may further suppress CFI, but also implies additional laminar frictiondrag (see Fig. 3.17b) and increased HLFC system power requirements (see Sec. 3.4). The

51Note that for convenience, the N -factor here denotes the natural logarithm of the amplification rates ingeneral, though it was defined in Eq. (2.19) more precisely as their maximum (envelope) value.

102 Chapter 3. Method for aircraft design with hybrid laminar flow control

effect of different suction distribution shapes on transition location is further discussed inSec. 3.3.7, as well as by Schültke in Ref. [277].

0

1

2

3

4

5

6

7

8

9

10

0 1 2 3 4 5 6 7 8 9 10

NT

S

NCF

HLFC correlation curve

x/c

0.10

0.20

0.30

0.40

0.48

Figure 3.19: Correlated transition location us-ing HLFC limiting curve

Relating the values of the NTS and NCF

envelopes (dark black curves) at differentchord stations x/c, the two N -factor dia-gram shown in Fig. 3.19 is obtained. Asintroduced in Fig. 2.6, transition occurswhere the computed NCF/NTS curve in-tersects the correlated HLFC curve, whichhere yields (x/c)trans ≈ 0.48. The axesintersections of this curve are the criticalvalues NTS,crit = 9.5 and NCF,crit = 7.5as introduced in Sec. 3.3.5; for consistencythis HLFC correlation curve [268] will beused as transition criterion throughout thisthesis. In cases, where no intersectionpoint (and thus no transition) is found52,the transition point is set to the laminarseparation point predicted by COCO, i.e.,(x/c)trans = (x/c)lam,sep.

While this example of the HYLFAS analy-sis process only included transition predic-tion for the airfoil upper side, transition prediction for the lower side can be applied simi-larly. The nested iteration process in Fig. 3.15 then comprises one inner iteration variable(x/c)ref (always on upper side), and two instead of one outer transition iteration variables((x/c)trans,upp and (x/c)trans,low) for the upper and lower side, respectively. Still, the pro-cess remains twofold nested, but all three variables have to converge for overall processconvergence. Though this process has been implemented and tested within HYLFAS, it isnot further considered within this thesis, which focuses on application of HLFC to the wingupper side, mainly due to Krueger flap integration on the wing lower side, see Sec. 2.3.2.

Effective sweep angle and attachment-line transition

On laminar swept wings, the flow conditions at the wing leading edge—or, more precisely,in the vicinity of the attachment line—are crucial, since they highly influence the stabilityof the laminar boundary layer, especially in terms of CFI and ALT (see Sec. 2.2.5). As animportant parameter to characterize the leading-edge flow, Redeker and Wichmann [215]introduced the effective leading-edge sweep angle ϕeff during evaluation of flight testswith the DLR VFW-614 / ATTAS aircraft; ϕeff is related to the geometrical leading-

52This may either be physically due to favorable laminar characteristics or, more seldom, due to numericalproblems in the frequency or wave length estimators of LILO.

3.3 HLFC aerodynamic wing design method 103

edge sweep angle ϕLE by the following expression:

ϕeff = ϕLE + ∆ϕeff = arcsin(vr,stagU∞

), (3.32)

where ∆ϕeff characterizes the displacements effects caused by the 3D flow around theleading edge. For backward-swept wings, the effective sweep angle is larger than thegeometric leading-edge sweep angle (∆ϕeff > 0), and vice versa for forward-swept wings(∆ϕeff < 0) [215]. The velocities vr and U∞ have been defined in Fig. 3.11, where thenormal velocity component at the stagnation point is zero.

-1.0

-0.5

0.0

0.5

1.0-0.020 -0.015 -0.010 -0.005 0.000 0.005 0.010

pres

sure

coe

ffici

ent

Cp,

3D

z/c

Cp,3D,stag,orig = 0.82

Cp,3D,stag,cstr = 0.77

analysis of Cp,3D at leading edge

Cp,3D computed (MSES) Cp,3D interpolated (PREPCPCQ) Cp,3D constructed for ϕeff,spec

Figure 3.20: Construction of adapted Cp,3Ddistribution around stagnationpoint for specified ϕeff

Table 3.7: Comparison of results for effectivesweep angle ϕeff and Cp,3D,stag

Method Cp,3D,stag ϕeff ,◦

HYLFAS:ϕeff from Cp 0.82 31.93HYLFAS:ϕeff Eq. (3.33) 0.77 34.45DLR FLOWer [234] 0.77 34.54

From a 3D flow solution, the effectivesweep angle can thus be determined fromthe velocity or the pressure coefficientCp,3,D,stag at the stagnation line (e.g., byusing the LEA routine implemented inthe PREPCPCQ module [257, 266]). Inthe present context, however, where thestreamwise Cp distribution is not extractedfrom a 3D solution, but transformed ac-cording to Eq. (3.27), it can be shownthat ϕeff theoretically always equals ϕLE,i.e., ∆ϕeff = 0. The practically ob-tained values can still vary with the gridfineness used within MSES. However, forbackward-swept wings, this aspect leads inmost cases to an underprediction of cross-flow amplification. To bring the miss-ing 3D information into the proposed con-ical 2.5D HYLFAS method, the effectivesweep angle can be specified as input tothe PREPCPCQ module, which then re-spectively adapts the pressure distributionaround the stagnation point. As a simple and consistent approach to specify ϕeff , thefollowing equation proposed by Streit et al. [295] is used, which estimates the displace-ment effect from the difference of absolute thicknesses at the root (tr) and the tip (tt) ofa tapered wing segment with the span sseg:

∆ϕeff = tr − tt2sseg

. (3.33)

This approach is perfectly in line with the conical 2.5D assumptions introduced inSec. 3.3.2. For the validation example discussed above, Fig. 3.20 and table 3.7 show re-sults of the STABTOOL module PREPCPCQ. The black squares in Fig. 3.20 representthe “original” Cp points as predicted with MSES and transformed via Lock’s law53. Thecomputed Cp,3D,stag value results in an effective sweep angle of ϕeff = 31.93◦, which is even

53Note that the 2D/3D Cp transformation can generally result in Cp,3D,stag values that are smaller than 1.

104 Chapter 3. Method for aircraft design with hybrid laminar flow control

smaller than ϕLE = 33.8◦, and could only slightly be increased by a finer MSES grid54. Ifthe effective sweep angle is specified using Eq. (3.33), however, a reasonable value of ϕeff =34.45◦ > ϕLE is obtained, which also shows very good agreement compared to the DLRFLOWer results in table 3.7. Figure 3.20 shows how PREPCPCQ constructs an adaptedCp distribution around the stagnation point according to the specified value of ϕeff .

As discussed in Sec. 2.2.5, the 3D flow along the wing leading edge is also crucial forthe evaluation and prevention of attachment-line transition. As key parameter, theattachment-line Reynolds number Reθ,AL (or ReAL) has been introduced in Eq. (2.20).The mentioned LEA routine [266] is also used to predict Reθ,AL within HYLFAS. Theapplication of the corresponding ALT criteria (see Sec. 2.2.5) will be demonstrated in thelong range aircraft application studies in Sec. 4.3.

Automated prediction of HLFC drag polars

The automated iterative procedure exemplified above yields transition location and dragcoefficients of only one evaluation point at fixed geometry and flight conditions. HYLFAShas further been developed to enable rapid and robust prediction of drag polars for taperedwing geometries at design and various off-design conditions. Drag polar prediction is hereshown for the above used validation case at the design cruise Mach number M = 0.85.Further design parameters and off-design sensitivities will be discussed in the next section.

To predict a laminar drag polar (Cd = f (Cl,3D)) at given Mach and Reynolds number, theHYLFAS analysis has to be executed at different lift coefficients Cl,3D. For most efficienthandling of this task including parallelized computation, the MICADO parameter studymanager (PSM) is applied, see Fig. 3.3. Input and output parameters are communicatedvia HYLFAS-specific XML files, and evaluation results are summarized in a CSV filecontaining all relevant aerodynamic parameters as function of the study variables (e.g.,M, Cl). The PSM-HYLFAS process can take full advantage of the MSES characteristic toconverge much faster if starting with solutions converged on the same streamline grid atsimilar flow cases (here: at different Cl). The benefit is especially significant for difficultviscous transonic flow cases as faced for the presented HLFC airfoil.

For four selected lift coefficients, Fig. 3.21a shows the Cp,3D distributions of the convergedHYLFAS evaluations. Reasonable qualitative physical sensitivities can be observed, e.g.,the upstream shift of shock location with decreasing Cl. The table in Fig. 3.21b summa-rizes the predicted shock and transition locations for the four lift coefficients, and com-pares them with results computed by DLR [234] with the FLOWer solver [211] and theSTABTOOL suite for transition prediction. The shock locations are predicted very ac-curately by HYLFAS in all cases. Transition locations also show good sensitivities andagreement; the deviations at the two upper Cl values are due to an additional cross-flowamplification behind the suction panel detected by DLR using LILO manual mode [234],which leads to premature transition. It may be repeated, however, that consistency, ro-bustness, and correctness of physical sensitivities of HYLFAS outweigh small deviations

54Systematic grid studies with MSES to find a good compromise in terms of computation time and accuracyhave been conducted by Schültke [277]. An MSES grid domain size study is also presented by Drela [64].

3.3 HLFC aerodynamic wing design method 105

in single aerodynamic parameters. Also, note that relative deviations detected in transi-tion location become smaller considering airfoil viscous drag, and even more consideringoverall aircraft drag coefficients.

-0.8

-0.4

0.0

0.4

0 0.2 0.4 0.6 0.8 1

Cp

x/c

Cl[]=[]0.40Cl[]=[]0.50Cl[]=[]0.59Cl[]=[]0.65

(a) Variation of Cp distribution with Cl

Cl,3D 0.40 0.50 0.59 0.65HYLFAS 0.44 0.54 0.64 0.68(

xc

)sh FLOWer 0.43 0.54 0.63 0.67

HYLFAS 0.32 0.34 0.46 0.48(xc

)trans FLOWer 0.31 0.32 0.35 0.40

(b) Comparison of shock and transition lo-cation with DLR FLOWer results [234]

0.0

0.2

0.4

0.6

0.8

0 0.25 0.5 0.75 1

airfo

il lif

t co

effic

ient

Cl,3

D

relative chord x/c

(x/c)ref

(x/c)trans

0 0.005 0.01 0.015 0.02 0.025airfoil drag coefficient Cd

Cd,wave,lam

Cd,visc,lam

Cd,airf,lam

Cd,wave,turb

Cd,visc,turb

Cd,airf,turb

(c) Shock and transition location as func-tion of lift coefficient Cl,3D; lami-nar (and turbulent) drag polars, withCd,airf = Cd,visc + Cd,wave

Figure 3.21: Results of automated HYLFAS drag polar prediction process for valida-tion case (see design parameters in table 3.6)

In Fig. 3.21c, laminar airfoil drag polars (gray curves) predicted with the PSM-HYLFASprocedure are plotted, along with upper side transition and shock locations. The auto-mated shock detection algorithm captures the upstream shift of shock location with de-creasing Cl, which is significant for the transformation between 3D and 2D aerodynamicparameters, see Sec. 3.3.2. Below Cl = 0.3, no shock is detected, thus the default value of(x/c)ref = 0.25 is selected. Note that this assumption is reasonable, as it does not producesignificant step changes of the transformation location. The transition location (x/c)transalso reaches its maximum values at high Cl, producing a small laminar bucket around thedesign lift coefficient Cl = 0.645, which can be recognized in the polar of the laminar vis-cous drag coefficient Cd,visc,lam in the right diagram. It is very important to see that thehighly transonic design conditions imply strong increase of wave drag coefficient Cd,wavewith increasing Cl, which requires careful trading between reduced viscous drag and ac-ceptable wave drag characteristics. For further comparison, drag polars for full turbulentflow, i.e., (x/c)trans = 0, are shown (blue curves), which are automatically obtained fromthe first iteration run. As expected, main differences are observed in the viscous dragcoefficients; however, an additional increase in wave drag is also captured through theEuler/boundary-layer coupling within MSES. Note that all drag coefficients in Fig. 3.21crefer to the conical 2.5D plane; the transformation into 3D coefficients is done during

106 Chapter 3. Method for aircraft design with hybrid laminar flow control

“on-the-fly” database access, using Eq. (3.30). In this way, predicted differences betweenCd,airf,lam and Cd,airf,turb are also transported into overall aircraft drag polars and can, e.g.,be used for analysis of HLFC system failures during mission simulation (see Sec. 4.3.1).

3.3.7 HLFC airfoil design and optimization procedure

The presented HYLFAS analysis process allows automatically computing laminar dragpolars for a given airfoil within a tapered wing geometry. However, design requirementsand thus optimal airfoil shape change with different wing planform and flight conditions.For example, reducing cruise Mach number or increasing wing sweep angle can mitigatetransonic drag penalties, and would thus allow thicker airfoils in favor of reduced struc-tural weight. Variations in Mach number, sweep angle, or chord Reynolds number alsotrigger instability mechanisms on transonic swept wings (see Sec. 2.2.5), and thus stronglyinfluence the design of HLFC airfoils (see Sec. 2.3.1).

Though “high-resolution” airfoil shaping is of reduced significance in conceptual and pre-liminary design applications, the mentioned trade-offs and dependencies should be cov-ered if HLFC aircraft design studies with varying wing planforms and cruise require-ments are performed. HYLFAS has therefore been enhanced by inverse-design and airfoil-optimization capabilities. For semi-inverse design, the MSES subprogram MEDP is used.Starting with a previously-converged MSES solution, this module allows imposing targetpressure distributions and modifying airfoil geometry by an inverse calculation. More de-tailed theoretical and methodical background is given by Drela [65]. The inverse redesignoption is used to obtain larger geometry changes (e.g., airfoil thickness adaptation) due tochanged design conditions. For “fine-tuning” of the airfoil shape at the selected design con-ditions, the airfoil optimization module LINDOP [63] is also incorporated into HYLFAS.For optimization with LINDOP, geometry deformation and element position modes aredistributed over the airfoil contour, which allows modifying and optimizing the shape withrespect to selected optimization objectives, e.g., minimum drag. As mode shape functions,Chebyshev polynomials are used by default for the proposed method, which provide higherresolution at the leading and trailing edge compared to the simpler sine waves. LINDOPprovides capabilities for constraint as well as multi-point optimization, which are both ap-plied within this thesis as discussed below. Available procedures to minimize the selectedobjective functions are the steepest descent, conjugate-gradient, or quasi-Newton method,the formulation of which is given in Ref. [61]. Other airfoil optimization applications us-ing the MSES-LINDOP program suite are, for example, given in Refs. [88, 147, 184, 328].

The MEDP and LINDOP modules have been integrated into HYLFAS using the describedwrapper approach with a fixed execution sequence. Via the HYLFAS XML configurationfile, the user has the opportunity to set and change selected parameters. Generally,default values are preset for all parameters according to the rules and guidelines givenin the MSES [65] and LINDOP [63] user manuals, and based on additionally conductedsensitivity studies of specific tool settings, see Ref. [32].

Before the HYLFAS inverse design and optimization option is applied for the creation ofthe HLFC airfoil database (see Sec. 3.3.8), the general procedure is explained below and

3.3 HLFC aerodynamic wing design method 107

exemplified for the validation case discussed above. The central objective of the HYLFASdesign mode is to optimally adapt a given airfoil geometry for a variation in designparameters. These design parameters primarily result from the freestream conditions, thelocal lift coefficient, and the tapered wing geometry, i.e.,

• freestream Mach number M∞,3D

• (chord) Reynolds number Rec

• lift coefficient Cl,3D

• wing leading- and trailing-edge sweep angles ϕLE, ϕTE

From these 3D design parameters, equivalent 2D design parameters are derived accordingto the sweep-taper transformation rules given in Sec. 3.3.2. How a convenient combinationof corresponding flow cases can reduce the number of parameters is shown in the databaseconcept in Sec. 3.3.8. To design and optimize the airfoil geometry for the target conditions,the HYLFAS airfoil design process runs through the following steps:

1. off-design calculation of reference airfoil at target flow conditions

2. inverse calculation at target conditions with imposed reference Cp distribution

3. multi-point optimization for minimum total airfoil drag

+0.03

-0.03

-0.01 +0.01

design point

off-design points

,3l DC

,3DM

Figure 3.22: Off-design points for HLFC air-foil multi-point optimization

The multi-point optimization procedurehas been chosen to guarantee a design thatcan be operated robustly during the wholecruise phase in terms of stable laminarflow characteristics. Since a deviation fromthe favorable HLFC pressure distributioncan lead to undesired premature transition,and Mach number and lift coefficient havethe most significant impact on the Cp dis-tribution, the 5-point scheme illustrated inFig. 3.22 is applied. It includes the designpoint and four off-design points. The dif-ference between upper and lower lift coeffi-cient (∆Cl = 0.06) corresponds well to theband, inside which total aircraft CL com-monly ranges during cruise, see Chap. 4. Since the Mach number is usually kept constantduring cruise, only a small variation of ∆M = ±0.01 has been chosen; this also reducesrisk of undesired convergence problems of MSES at severely changed flow conditions.

For the inverse design (step 2), 5 deformation modes are placed on the wing upper side,where larger geometry changes are intended within the present context. For the optimiza-tion procedure (step 3), 10 deformation modes are placed on the wing upper and lowerside, respectively. During optimization, thickness constraints are additionally specified atmaximum thickness position as well as selected stations in the airfoil front region. These

108 Chapter 3. Method for aircraft design with hybrid laminar flow control

are designated to maintain the HLFC favorable pressure gradients, which could be sacri-ficed by the optimizer for weakened shocks in the airfoil rear part to reduce wave drag.

Application case

The described HYLFAS design and optimization procedure is now exemplified for theHLFC airfoil validation case discussed in Sec. 3.3.6. The design conditions of the referencecase are therefore changed such that both Mach number and leading-edge sweep angleare reduced at fixed lift coefficient. The resulting target conditions are compared withthe reference design conditions in table 3.8.

Table 3.8: Reference and target conditions forHLFC airfoil design example

Parameter Ref. TargetϕLE 34◦ 28◦ϕTE 24◦ 17◦

M∞,3D 0.85 0.80Re 49.4 · 106 46.5 · 106

Cl,3D 0.645 0.645

The results of the optimized HLFC air-foil design are presented in Fig. 3.23. InFig. 3.23a, the evolution of the Cp distribu-tion is shown according to the three designsteps listed above. The reference design atM = 0.85, ϕLE = 34◦ (see Fig. 3.16a) isrepresented by the dotted blue line. Com-puting the reference airfoil at off-designflow conditions and with target wing sweepangles (i.e., M=0.80, ϕLE = 28◦), the lightgray curve is obtained, which exhibits aslightly degenerated pressure distributionwith the shock further upstream (step 1). The inverse calculation (step 2)—using the pre-scribed reference Cp distribution as target—yields the dark gray curve, now again show-ing a similar distribution compared to the reference. The solid black line represents theresult after several multi-point optimization steps, where total airfoil drag is minimizedat constant lift coefficient (step 3). The final (solid black) airfoil geometry obtained withthe HYLFAS design procedure is compared in the lower diagram with an airfoil shape de-signed by DLR [234] for the same design conditions using the inverse design capabilities ofthe FLOWer code [293]. The very good agreement of the shapes proves the functionality ofthe HYLFAS design procedure for this validation example, note well without imposing thepressure distribution of the target case, but only starting with the reference airfoil design.

The advantage of the multi-point-optimized airfoil compared to the inverse design case isnot evident from the pressure distributions, but becomes clearer when looking at the dragpolars in Fig. 3.23b, where the airfoil drag is significantly reduced in the relevant upperCl region. The figure reveals the two already mentioned design trades between reducedviscous and acceptable wave drag characteristics, as well as between suppressing TSI andCFI. Concerning the latter, the right diagram shows the NCF - and NTS-factors at theintersection with the HLFC correlation curve (see Fig. 3.19) as a function of Cl. WhileCFI dominates at lower Cl, TSI becomes dominant at higher Cl, as expected due to thevarying pressure gradients (cf. Ref. [130]). The reduction in Cd,airf is mainly achieved dueto an improved wave drag behavior; for 0.5 < Cl < 0.6, this even outweighs the earliertransition. Through the multi-point optimization, the selected off-design conditions (seeFig. 3.22) are implicitly considered, so that favorable drag characteristics are obtained

3.3 HLFC aerodynamic wing design method 109

-1.0

-0.5

0.0

0.5

Cp,3

D

HYLFAS airfoil design process Reference (Ma = 0.85, ϕLE = 34°) 1.) Ref. airfoil @ Ma = 0.80, ϕLE = 28° 2.) Ma = 0.80, ϕLE = 28° (inverse design) 3.) Ma = 0.80, ϕLE = 28° (multi-pt. opt.)

-0.1

0.0

0.1

0 0.2 0.4 0.6 0.8 1

z/c

x/c

Ma = 0.80, ϕLE = 28°

HYLFAS design DLR design

(a) Evolution of Cp,3D distributions andcomparison of final airfoil contourwith DLR design for same design con-ditions [234]

−0.2

0.0

0.2

0.4

0.6

0.8

0.2 0.4

airfo

il lif

t co

effic

ient

Cl,3

D

(x/c)trans

0.005 0.01 0.015 0.02airfoil drag coeff. Cd,airf

∆Cl = 0.06

Ma = 0.80, ϕLE = 28°

inverse design multi−pt. opt.

0 5 10N−factor

NCF

NTS

(b) Comparison of drag polars and up-per side transition characteristics be-tween inverse design and multi-point-optimized case

Figure 3.23: Results of HYLFAS inverse design and multi-point optimization processfor example case with target design conditions listed in table 3.8

over a larger range of M and Cl (see shaded design Cl region). This robustness becomesparticularly important for the integration of airfoil drag polars into overall aircraft polars,and their consideration during mission analysis. In Ref. [230], a similar airfoil design caseincluding drag polars at off-design conditions is presented by the author.

0.000

0.004

0.008

0.012

0.016

0.020

1 2 3 4 5 6 7 8 9 10 110.0

0.1

0.2

0.3

0.4

0.5

Cd

(x/c)

tran

s

design runoff-designanalysis

inversedesign

optimization runs selecteddesign

Cd,airf Cd,visc Cd,wave (x/c)trans

Figure 3.24: History of HYLFAS airfoil designand optimization procedure

The required balance between viscous andwave drag is further illustrated by theHYLFAS design and optimization historyin Fig. 3.24, showing drag coefficients andtransition location for all subsequent evalu-ation runs. After the off-design (1) and theinverse design run with MEDP (2), severalLINDOPmulti-point optimization runs areperformed, until convergence fails in oneof the 5 flow condition points, or until thetotal drag residual falls below a specifiedlimit. The LINDOP optimization proce-dure tries to continuously weaken the shockto lower wave drag; this is impeded by local thickness constraints, because it can in turnimply earlier transition and thus increased viscous drag. Consequently, as final design, anevaluation run with possibly lowest total drag, but concurrently favorable HLFC charac-teristics in terms of late transition is manually selected (i.e., run 8 in the present example).

110 Chapter 3. Method for aircraft design with hybrid laminar flow control

Note that the off-design calculation in step 1 already shows good drag characteristics,which could mislead into assuming that selecting the off-design case would suffice. How-ever, firstly this is rather an exception than the standard case, because the off-design cal-culation mostly implies a much more pronounced pressure peak near the leading edge,leading to early transition on the airfoil [316]. For the present example, the final designalso exhibits larger thickness ratio compared to the reference design, which will be favor-able with respect to reduced structural wing weight in overall aircraft design studies. Notleast, the design procedure has to be maintained and applied in a consistent way, whichis especially important for the buildup of the HLFC airfoil database (see Sec. 3.3.8), andto guarantee consistent aerodynamic behavior within OAD studies.

Sensitivities towards Reynolds number and suction distribution

Two other important parameters, which have been kept constant so far, are the suctiondistribution Cq (x/c) and the flight Reynolds number Re. While Re is determined by localchord lengths as well as cruise altitude and Mach number, the suction distribution has tobe designed such that transition mechanisms are suppressed sufficiently. Too high suction,however, increases HLFC system mass and costs, and imposes undesired disturbances tothe boundary-layer flow. How the influences of Re and Cq are considered in the HYLFASdesign procedure is illustrated in Fig. 3.25. For the HLFC airfoil design example discussedin the preceding paragraph, it shows results of a parameter variation in flight altitude hand suction strength, while maintaining the design conditions M = 0.80 and Cl = 0.645.

0.0020.0030.0040.0050.0060.0070.0080.009

00.10.20.30.40.50.60.7

Cd,v

isc

(x/c

) tran

s

Cd,visc@high Cq

Cd,visc@mid Cq

Cd,visc@low Cq

(x/c)trans@high Cq

(x/c)trans@mid Cq

(x/c)trans@low Cq

0

2

4

6

8

10

10000 15000 20000 25000 30000 35000 40000

N−f

acto

rat

tra

nsiti

on

altitude h, ft

NCF @high Cq

NTS @high Cq

NCF @mid Cq

NTS @mid Cq

NCF @low Cq

NTS @low Cq

(a) Cd,visc, (x/c)trans, and correlated TSand CF N -factors as a function offlight altitude and suction intensity

0

1

2

3

4

5

6

7

8

9

10

11

0 1 2 3 4 5 6 7 8 9 10 11

NT

S

NCF

x/c

increasing suction

Cq,max= -0.0008

0.10

0.20

0.30

0.35 Cq,max= -0.0006

0.10

0.20

0.30

0.35

Cq,max= -0.0004

0.10

0.15

(b) Influence of suction intensity Cq,maxon correlated N -factor curves inNTS/NCF diagram (h = 35000 ft)

Figure 3.25: Influence of altitude and suction intensity Cq,max on transition and dragcharacteristics at constant design conditions (M = 0.80, Cl = 0.645)

3.3 HLFC aerodynamic wing design method 111

In the upper part of Fig. 3.25a the predicted transition locations and viscous drag coeffi-cients are plotted as a function of varied flight altitude h, where the reference case (highCq) is represented by the black curves. The underlying shape of the reference suction dis-tribution was shown in Fig. 3.16a. It can be observed that the transition location reduceswith altitude, which is due to progressively growing TS waves with increasing Reynoldsnumber Re. In this case, the reduction of (x/c)trans counterbalances the reduction of fric-tion drag with increasing Re, so that Cd,visc stays nearly constant with altitude. Thelower diagram, in which the critical correlated N -factors at transition are plotted, provesthat the suction rate is sufficient to provide stable laminar flow characteristics also at lowaltitudes. However, susceptibility towards CFI increases with decreasing altitude (due tohigher Re), which explains earlier transition in the upper diagram. For the design alti-tude of h = 35000, Fig. 3.25b shows the belonging correlation trajectory in the NCF/NTS

diagram, which resides close to the NTS axis as desired.

If suction intensity is reduced by 25 % (i.e., Cq,max = −0.0006), the trend of Cd,visc and(x/c)trans in Fig. 3.25a remains similar at high altitudes, but experiences a sharp changebelow h ≈ 25000 ft. In the lower diagram, it can be observed that this is due to a sud-den cross-flow dominance, which leads to transition directly at the leading edge. In theNCF/NTS diagram, this corresponds to a horizontal exceedance of the HLFC correlationcurve at low x/c. The displayed gray curve for h = 35000 ft—where CFI can be con-trolled—is aligned vertically at higher x/c, but shifted to the right due to reduced Cq. Ifsuction is further reduced (Cq,max = −0.0004), the (blue) trajectory exhibits critical cross-flow amplification already at the design point. Only at higher altitudes, a reduced transi-tion location of (x/c)trans ≈ 0.15 can be maintained. The suction distribution is thus in-sufficient in this case, which would lead to undesired shortfall of laminar flow during cruise.

From the above observations, the following design guidelines for a suitable selection ofsuction strength are derived:

• At design Reynolds number (or altitude), apply suction such that NCF/NTS trajec-tory develops nearly vertically and stays close to the NTS axis (cf. Ref. [316]).

• For the selected Cq distribution, perform variations in flight altitude (or Reynoldsnumber) to check whether sudden cross-flow dominance occurs at lower altitudes.

Since CFI often entails transition in close vicinity of the leading edge, the appearance ofsudden CFI dominance should at least be precluded at all altitudes higher than the initialcruise altitude, above which the HLFC system is usually switched on. The specified designprinciples are consistently applied within the proposed method, as further discussed for theHLFC airfoil database creation in the next section. How the requirements are fulfilled—interms of specific shaping of the Cq (x/c) distribution—can in practice indeed imply manyadditional degrees of freedom. However, though a complex optimized Cq shape (e.g.,including several step changes as well as discontinuities) may have advantages in someapplications, the benefit is small compared to the required effort, especially in the presentpreliminary design context. Also, too complicated Cq designs may imply high HLFCsystem complexity, and thus increased system mass or difficulties in manufacturing [128].

112 Chapter 3. Method for aircraft design with hybrid laminar flow control

Hence, to apply an efficient and consistent approach, the herein used method is primar-ily oriented towards the key requirements for a suitable Cq distribution introduced inSec. 2.3.1. These are to provide a sufficiently high suction peak (Cq,max) at the leadingedge to suppress CFI and ALT, as well as to maintain a reduced amount of suction to keepTSI under control. The Cq distribution is therefore parameterized (via XML) by a com-position of piecewise linear segments, which has already been shown for the HLFC air-foil validation example in Fig. 3.16a. By default, three suction segments are used, wherethe first is automatically initiated at the stagnation point55 for suppression of ALT andCFI, and held on a strong level for a short distance. The reduced Cq intensity after thelinear decrease is maintained, maximum up to the front spar position; here, a maximumvalue of (x/c)front spar = 0.16 is assumed (see, e.g., Ref. [114]). If a further chordwise ex-tension of suction would delay critical TS amplification (see Fig. 3.18a), this limitationmay sacrifice additional viscous drag reduction. However, the additional saving potentialis mostly small, especially with regard to the limited opportunity to shift the front sparfurther rearwards due to structural or fuel capacity constraints. However, most impor-tantly, the assumed maximum front spar position removes this parameter from the designspace for the creation of the HLFC airfoil database.

3.3.8 HLFC airfoil aerodynamic database

With the detailed airfoil-specific topics discussed above, the OAD focus presented inSec. 3.2 has literally receded into distance. However, it has been illustrated in Fig. 3.10how the HLFC airfoil characteristics are integrated into the MICADO overall aircraftdrag polars; the only missing element in this interacting process is now the HLFC airfoildatabase. The database approach has mainly been chosen due to the huge number of re-quired airfoil evaluation points in every OAD iteration step. These result from the speci-fication of aircraft drag polars at different Mach numbersM and with small increments inCL (for smooth interpolation during mission simulation), combined with the section-wisewing drag prediction approach. Further considering robustness requirements and numer-ical unpredictabilities, this practically excludes an “on-the-fly” procedure. The proposedHLFC airfoil database approach makes full use of the HYLFAS analysis and design capa-bilities described in the previous sections. For the use within MICADO, different HLFCairfoils are designed and optimized at different design conditions. Before the selectionof these design points is described, the database architecture and creation process areshortly examined.

Database architecture and processing of aerodynamic data tables

For structured storage and rapid database access from the C++ MICADO aerodynamicmodule (Sec. 3.2.3), the SQLite56 software library is chosen. The HLFC airfoil databaseis composed of two tables:

55Adjusting suction to the (moving) stagnation point prevents undesired transition at off-design conditions.56SQLite is written in C and implements an SQL (Structured Query Language) database engine [121].

3.3 HLFC aerodynamic wing design method 113

• airfoil table: contains all airfoils with their design conditions (M,Cl,Re,ϕLE,ϕTE)

• aerodynamic data table: contains laminar and turbulent aerodynamic charac-teristics (drag coefficients, shock and transition location) as a function of M and Cl

The interconnection between the airfoils and their aerodynamic data tables is establishedvia specific identifiers (airfoil IDs). Every airfoil designed for the database undergoes adeterminate process to calculate its aerodynamic data and import it into the database.This process is roughly sketched in Fig. 3.26a. First, the automated HLFC drag po-lar prediction process using the PSM-HYLFAS interface (see Sec. 3.3.6) is applied to thestreamwise (3D) airfoil geometry in a tapered wing segment. Using parallel computing viaOpenMP [52], the process is repeated by running through the whole predefined (M × Cl)matrix, the definition of which is explained below. On a desktop computer with 8 cores57,the execution of all evaluation points (364 in total) takes approximately 2 hours, where ev-ery evaluation run includes the above described nested iteration of (x/c)ref and (x/c)trans.

All results are written into a CSV file, which contains all relevant parameters for bothturbulent and laminar flow, e.g., Cd,visc,Cd,wave, (x/c)ref , (x/c)trans. If a single evaluationrun fails, all output values are set to invalid (NaN) numbers. If this occurs beyond therange of valid evaluation runs, the respectiveM -Cl combination is interpreted as to exceedthe physical limitations of the incorporated modules (mainly MSES). Invalidity is herereasonable, since the considered flow cases (e.g., excessive drag rise or flow separation)should anyway be precluded within the relevant mission phases. On the contrary, if asingle failed evaluation run (or an outlier) lies inside a range of valid runs, it is attributed tonumerical problems (e.g., convergence issues of HYLFAS process or MSES). These missingpoints have to be filled with reasonable values, because a dense database matrix within thephysical boundaries is required to enable linear database interpolation by the MICADOaerodynamic module. A cubic spline interpolation algorithm is therefore applied to theCSV file; this is implemented into a semi-automated tool that also allows the user toquickly identify and expunge outliers. The updated CSV file contains the (physically)complete data matrix. Another program has been implemented, which can finally be usedto import the airfoil and aerodynamic data tables into the SQLite database format.

The selected off-design combinations of Mach numberM and lift coefficient Cl,3D are tab-ulated in the upper right diagram 3.26b. Their definition is oriented towards coverage ofthe whole flight regime of a typical mission profile. The low Mach numbers (0.2 and 0.5)are assigned with low altitudes at sea level and 10000 ft, respectively, and are computedup to Cl = 1.5, with a step width of ∆Cl = 0.05. Further, six higher Mach numbersare defined by a fixed distribution around the design cruise Mach number Mcr, where atypical average cruise altitude of h = 35000 ft is selected for the upper five values. Thestep width is half as large (∆Cl = 0.025) to capture nonsmooth polar shapes due to lam-inar and transonic flow effects. The Cl range is limited at Cl = 1.0, because in nearly alltransonic flow cases, convergence limits within MSES are already reached at lower Cl val-ues. Physically, the maximum valid Cl value is interpreted as buffet onset limit. For thehigher Mach numbers, both laminar and turbulent aerodynamic characteristics are pre-dicted, while only turbulent flow data are produced for the three lowest Mach numbers.

57In this case, the 8 cores are virtually achieved on a quad-core CPU with hyper-threading technology.

114 Chapter 3. Method for aircraft design with hybrid laminar flow control

PSM with matrix of

ref. wing segment

HYLFAS analysis process

airfoil geometry

,3, l DM C

repea

ted for

whole

matr

ix

.csv file with aerodyn. parameters:

.csv file with full splined data matrix

cubic splining of aerodyn. data

SQLite database import program

.sqlite database containingHLFC airfoil aerodynamic data

, ,, , / , / ,d visc d wave trans shC C x c x c

(→ Fig. 3.3)

(→ Fig. 3.15)

(a) Process chain for creation of aerody-namic data tables for a given airfoil

low speed @ Cl ∈ [−0.2, 1.5]; ∆Cl = 0.050M h, ft flow type0.2 0 turb.0.5 10000 turb.

high speed @ Cl ∈ [−0.2, 1.0]; ∆Cl = 0.025∆M = M −Mcr h, ft flow type−0.20 20000 turb.−0.10, − 0.05−0.02, ± 0, + 0.01 35000 lam.+turb.

(b) Parameter combinations for off-designpoints in aerodynamic data tables

0

5

10

15

20

25

30

35

40

0 10 20 30 40

long

itudi

nal x

coo

rdin

ate,

m

spanwise y coordinate, m

cr

cdes

ct

A−A

Reference wing planforms:s=20 m, λ= 0.25, cdes=8 m

(cr= 12.8 m, ct=3.2 m)

Ref. wing 1: ϕLE = 30 deg Ref. wing 2: ϕLE = 40 deg

−0.1

0.0

0.1

0.0 0.5 1.0

z/c

x/c

A−A

(c) Tapered reference wings

Figure 3.26: Principle of HLFC airfoil and aerodynamic database

The latter is because the HLFC system is assumed to be switched on only above initialcruise altitude, i.e., roughly between 25000 and 35000 ft. Further, the degeneration ofHLFC Cp distributions at off-design Mach numbers much lower than Mcr would anywayincrease the susceptibility to early transition, which would also reduce numerical robust-ness of the iterative HYLFAS process.

The combined definition of Mach number and altitude pairs is beneficial, as it savesan additional parameter dimension in the aerodynamic off-design tables, which wouldsignificantly increase effort of computation, splining, and data handling. The missionoriented M -h assignment also ensures that reasonable flight Reynolds numbers Rec,DB =f (M,h, cDB) are stored in the database (DB), where cDB denotes the chord length ofthe reference wing (see discussion below). However, the selected approach neglects theinfluence of Re due to variations in altitude and chord at constant Mach number. Theinfluence on viscous drag due to altitude variation during cruise is comparably small atconstant transition location (see, e.g., Fig. 3.25a). The influence of chord length c can bemore significant, especially in preliminary design applications with larger wing planformvariations. To additionally account for this effect, a simple (but efficient) Reynolds numbercorrection is applied. It makes use of earlier introduced flat-plat solutions of the friction

3.3 HLFC aerodynamic wing design method 115

drag coefficient Cd,fric,FP [274], which can be expressed as follows for partly laminar flow:

Cd,fric,FP (Rec, (x/c)trans) = 1.328Re−12

c (x/c)trans︸ ︷︷ ︸laminar flow

+ 0.074Re−15

c [1− (x/c)trans]︸ ︷︷ ︸turbulent flow

. (3.34)

Now recall that within the MICADO aerodynamic module the drag coefficients are re-trieved from the database at different spanwise wing sections with the local chord cloc (y)and lift coefficient Cl (y), which influence local Reynolds number Rec,loc and transitionlocation (x/c)trans, respectively. For every database query during “on-the-fly” strip-wisedrag prediction, the following correction term is applied to the viscous drag coefficient:

Cd,visc,loc = Cd,visc,DB ·Cd,fric,FP

(Rec,loc, (x/c)trans,DB

)Cd,fric,FP

(Rec,DB, (x/c)trans,DB

) . (3.35)

Note that this flat-plat approach is not used for quantitative drag prediction in thiscontext, but only for adaptation of the computed Cd,visc,DB values to the actual localwing chords. This correction has been studied and proven to yield good and physicallyreasonable results; its application will be revisited for the long range aircraft design studiesin Chap. 4. The usage of the same airfoil or Cp distribution at different chord lengthis further justified by the above discussed robustness of HLFC airfoil design against Revariations, which prevents sudden change of transition location.

All drag coefficients are stored in the database as obtained from the final laminar (or tur-bulent) MSES calculation within the HYLFAS iteration, i.e., in the conical (2Dc) plane.The transformation into streamwise (3D) direction is performed within the MICADOaerodynamic module using Eq. (3.30). It is important to notice that the local transfor-mation sweep angle ϕref is derived from the respective value of (x/c)ref , but within thetapered wing segment of the actual aircraft design. This ensures correct capturing ofsweep-taper effects, independent of the reference wing geometry used for computation ofdatabase coefficients. Since (x/c)ref , which mostly equals (x/c)sh, varies with local Cl(see Fig. 3.21), curved shock lines on the wing can basically be represented. The specifichandling of drag transformation and aerodynamic characteristics for inboard segments of(real aircraft) kinked wing planforms is discussed for the design application in Chap. 4.

Furthermore, for every wing lift coefficient CL,w, the transition line on the wing is obtainedas polyline, i.e., as piecewise linear connection of predicted local transition locations.Since (x/c)trans varies with Cl and is retrieved at all spanwise panel stations of the LILIcomputation, nonlinear transition lines are also well mirrored by the proposed method.

Reduction of parameter space for HLFC airfoil design points

Having discussed the concept of the aerodynamic data table, let us now focus on the setupof the airfoil table, which contains the design conditions of the HLFC airfoils. The keyparameters that govern HLFC airfoil design within the scope of this thesis have beenlisted in Sec. 3.3.7 (M, Cl, Rec, ϕLE, ϕTE). It is immediately evident that, if using a full

116 Chapter 3. Method for aircraft design with hybrid laminar flow control

factorial design matrix, the database becomes unfeasibly huge, e.g., with a total numberof 1024 airfoils in case of 4 values per parameter. One central task of the herein proposedapproach is therefore a significant reduction of the parameter space.

For now disregarding the Reynolds number, it is promising that the other four parametersare closely linked via the sweep-taper approach introduced in Sec. 3.3.2. Consequently,the central idea of the parameter reduction is the concentration on only two key designparameters, which are the Mach number M∞,2Dc and the lift coefficient Cl,2Dc for theconical 2D (2Dc) section according to Eqs. (3.21) and (3.22). The transformation sweepangle ϕref in these equations depends on ϕLE and ϕTE (see Eq. (3.24)), so it alreadyincludes sweep and taper effects. Hence, the airfoil designs can be stored in the databaseand accessed according to the respective (M∞,2Dc | Cl,2Dc) parameter combinations, whiletheir characteristics are transformed to 3D data during interpolation in the MICADOaerodynamic module. This approach is basically self-contained for a turbulent airfoildatabase. For laminar airfoil design, however, explicit values of sweep angles as wellas streamwise (3D) Cp distributions are crucial for conical boundary-layer analysis andtransition prediction. HLFC even requires adaptation of Cq distribution with varyingsweep angle to control CFI. To include these effects, while still keeping the number ofdatabase design points within reasonable limits, the key principle of corresponding flowcases is introduced (see Gödert [96] for detailed discussions). It simply states that for twowings A and B with different sweep angles, corresponding pairs of 3D freestream conditions(M∞,3D | Cl,3D) can be found such that equal 2Dc freestream conditions are obtained if:

M∞,2Dc,des = M∞,3D,A cosϕref,A = M∞,3D,B cosϕref,B

∧ Cl,2Dc,des = Cl,3D,Acos2 ϕref,A

= Cl,3D,Bcos2 ϕref,B

. (3.36)

Taking full advantage of this principle, only two tapered reference wing geometries withdifferent sweep angles but otherwise similar planform parameters are defined, which arecompared in Fig. 3.26c. For a selected number of database parameter combinations(M∞,2Dc | Cl,2Dc), table 3.9 shows the resulting corresponding 3D flow cases for the ref-erence wings with ϕLE = 30◦ and ϕLE = 40◦. Note that finding corresponding 3D flowcases is not always trivial and may require iterative adjustment due to a priori unknownshock locations (x/c)sh = (x/c)ref [96].

Table 3.9: 2D design points for HLFC airfoil database with corresponding 3D cases

M∞,2Dc (I) 0.67 (II) 0.71 (III) 0.75ϕLE 30◦ 40◦ 30◦ 40◦ 30◦ 40◦

M∞,3D 0.7366 0.8262 0.7813 0.8755 0.8254 0.9238(a) Cl,2Dc = 0.6 Cl,3D 0.4965 0.3946 0.4954 0.3950 0.4954 0.3955

M∞,3D 0.7373 0.8262 0.7810 0.8745 0.8125 0.9042(b) Cl,2Dc = 0.8 Cl,3D 0.6606 0.5261 0.6611 0.5273 0.6816 0.5504

The design process is initiated at critical design conditions (III-b), which are close to thatof the validation case in Sec. 3.3.6 (according to the 3D flow correspondence in Eq. (3.36)).

3.3 HLFC aerodynamic wing design method 117

For the considered long range aircraft design application, a physically reasonable rangeof 0.73 < M∞,3D,des < 0.92 and 0.39 < Cl,3D,des < 0.68 is covered, while ϕLE = 30◦ is cer-tainly assigned with lower M∞,3D and higher Cl,3D values, and vice versa for ϕLE = 40◦.A key advantage is that corresponding 3D flow cases with equal 2Dc design conditions willalso lead to the same airfoil geometry and Cp distribution in the 2Dc plane. The HLFCairfoil design thus has only to be performed on one reference wing geometry, which leadsto the following design procedure:

1. HLFC airfoil design and multi-point optimization on reference wing 2 (ϕLE = 40◦)

2. adjustment of Cq distribution and re-iteration on reference wing 1 (ϕLE = 30◦)

3. on both reference wings, computation of aerodynamic data tables (see Fig. 3.26a)

-1.0

-0.5

0.0

0.5

1.0 0

5

10

15

20C

p,3

D

N-fa

ctor

(up

per

side)

NTS

NCF

III-b (ϕLE = 30 deg) III-b (ϕLE = 40 deg) III-a (ϕLE = 30 deg) II-a (ϕLE = 30 deg)

-10-50C

q , 1

0-4

-0.1

0.0

0.1

0 0.2 0.4 0.6 0.8 1

(z/c)

2Dc

x/c

Figure 3.27: Comparison of selected HLFCairfoil database designs

Airfoil design and multi-point optimiza-tion consistently follows the procedure de-scribed in Sec. 3.3.7. Wing 2 is chosen asdesign reference since its higher sweep an-gle is more critical with respect to CFI.Shaping and adjustment of Cq and Cpdistributions follow the design guidelinesstated at the end of Sec. 3.3.7, as well asthe fundamental principles introduced inSec. 2.3.1. For airfoil thickness, the prin-ciple as thick as possible in favor of lighterwing structure is followed. As shown inSec. 3.3.7, semi-inverse design by impos-ing a reference Cp distribution at reducedMach number or increased sweep angle au-tomatically considers this principle. Fur-ther, a well-balanced relation between vis-cous drag reduction due to laminar flowand acceptable wave drag characteristics ispursued, where the amount of wave drag isstrongly connected to the shock strength, which is governed by the Mach number at therecovery point (shock location).

Figure 3.27 exemplifies the realization of these principles by showing the HLFC airfoildesigns for the database points III-b, III-a, and II-a, see table 3.9. The influence ofM∞,2Dc,des and Cl,2Dc,des on upper side airfoil geometry and Cp,3D distribution is illustratedin the lower and upper diagram, respectively. The upper diagram also shows how thedatabase includes reasonable sensitivities of TS and CF N -factors towards ϕLE. The morecritical NCF -factor history for ϕLE = 40◦ can still be damped by means of an adapted Cqintensity and distribution (see middle diagram).

The influence of taper is already covered by the principle of corresponding flow cases, andis further considered for geometry and Cp transformation, as well as for the enhancedpolar interpolation (see next paragraph). The Reynolds number Re, which has been

118 Chapter 3. Method for aircraft design with hybrid laminar flow control

excluded from the above considerations, has certainly significant influence on laminarairfoil design, as it strongly triggers TSI and CFI. However, it is refrained from introducingRe as additional design parameter, as this would increase parameter space and numberof required airfoil designs, with a comparably poor cost-benefit-ratio. Still, Re is alreadyincluded as indirect design parameter through the influence of M∞,des, and it is adaptedwith M and h for all off-design computations. Further, the used reference design chordcdes = 8 m (see Fig. 3.26c) is larger than mean aerodynamic chord (MAC) values ofclassical long range aircraft, which basically allows application of designed airfoils tosmaller chords, e.g., on the outer wing or on smaller planforms. For the inboard wingregion, additional conservative assumptions for limited laminarity are applied anyway (seeSec. 4.3.1). Another argument justifying to omit Re as design parameter is the robustnessof HLFC airfoil designs with respect to lower altitudes (and thus higher Re) by supplyingsufficient suction (see Fig. 3.25).

HLFC airfoil selection and validation of database interpolation concept

Within the MICADO aerodynamic module, designed HLFC airfoils are selected as follows:From the spanwise wing design Cl distribution, which is obtained at Mcr, des and CL, des58,local values of Cl,3D,des are obtained at selected design sections. For the tapered winggeometry and a default shock location59 of (x/c) = 0.6, the 2Dc design conditionsM∞,2Dcand Cl,2Dc are derived. An automated search algorithm locates the 4 (M∞,2Dc | Cl,2Dc)base points with closest distance to the design (search) point. For each of the 4 basepoints, all off-design aerodynamic tables are loaded (both for ϕLE = 30◦ and ϕLE = 40◦),followed by a bilinear interpolation of all aerodynamic characteristics (in both datasets)with respect toM∞,2Dc and Cl,2Dc. Next, a sweep interpolation is applied to all data usingthe local wing leading-edge sweep angle. Since linear interpolation has been evaluated asinsufficient, an enhanced sweep interpolation60 is applied. It takes full advantage of theabove introduced principle of corresponding flow cases, by transforming all Cl,3D valueswith respect to database and local wing reference transformation sweep angles:

Cl,3D,transf = Cl,3Dcos2 ϕref,loccos2 ϕref,DB

; (3.37)

ϕref,loc is obtained at the computed reference location (x/c)ref,DB within the local taperedwing segment. The base drag polars at ϕLE = 30◦ and ϕLE = 40◦ are thus “mapped” tothe target sweep angle and virtually approach each other, which allows more precise in-terpolation, including the influence of taper. Sweep-taper geometry is further consideredfor transformation of 2Dc drag coefficients into streamwise (3D) direction according toEq. (3.30). To validate the interpolation approach—and with it the grid fineness of theselected database points—an intermediate (IM) HLFC airfoil design has been conductedat M∞,2Dc = 0.74, Cl,2Dc = 0.75, ϕLE = 35◦ (see table 3.9). Drag polars at different Machnumbers obtained from bilinear (M,Cl) interpolation are compared with the IM design po-

58The design lift coefficient is initially selected according to Eq. (2.25).59The (reasonable average) default shock location is only used for initial base point selection; the enhancedinterpolation approach is based on the specific computed shock locations.

60A more detailed description of this concept, including selected validation cases, is given by Gödert [96].

3.3 HLFC aerodynamic wing design method 119

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 0.01 0.02 0.03 0.04

airfo

il lif

t co

effic

ient

Cl,3D

airfoil total drag coefficient Cd,2Dc

10% error bars

ϕ = 30°, Mades (IM-Design)ϕ = 30°, Mades (DB-Interpol.)ϕ = 30°, Ma = 0.5 (IM-Design)ϕ = 30°, Ma = 0.5 (DB-Interpol.)ϕ = 40°, Mades (IM-Design)ϕ = 40°, Mades (DB-Interpol.)ϕ = 40°, Mades+0.01 (IM-Design)ϕ = 40°, Mades+0.01 (DB-Interpol.)

(a) Comparison of drag polars obtainedfrom bilinear (M, Cl) interpolationwith intermediate (IM) design point

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 0.01 0.02 0.03 0.04

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il lif

t co

effic

ient

Cl,3D

airfoil total drag coefficient Cd,2Dc

ϕ = 30°, Mades (BiLin. DB-Interpol.)ϕ = 40°, Mades (BiLin. DB-Interpol.)ϕ = 35°, Mades (IM-Design)ϕ = 35°, Mades (Lin. DB-Interpol.)ϕ = 35°, Mades (Transf. DB-Interpol.)

(b) Comparison of drag polars obtainedfrom enhanced sweep interpolationwith intermediate (IM) design point

Figure 3.28: Validation of drag polar interpolation in HLFC airfoil database

lars in Fig. 3.28a. Relative deviations lie well within the marked error range of 10 %. Notethat reasonable interpolation at all off-design Mach numbers is only guaranteed, since allaerodynamic data have been calculated for the specific distribution tabulated in Fig. 3.26b(i.e., fixed low-speed Mach numbers and fixed spacings ∆M around Mcr). The same dis-tribution is also applied around Mcr,des in the MICADO aerodynamic module, which en-sures reasonable integration of HLFC airfoil polars into overall aircraft drag polars.

The enhanced sweep interpolation approach is demonstrated in Fig. 3.28b, in which themost outer black and blue drag polars show the (bilinearly interpolated) base polars atϕLE = 30◦ and ϕLE = 40◦, respectively. It can be observed that with the enhancedinterpolation according to the transformation in Eq. (3.37), much better agreement withthe (gray) IM design polar is achieved than if using linear interpolation (light blue polar).Additionally, the maximum lift coefficient takes higher values corresponding to the IMdesign, and is not limited by the more critical polar at ϕLE = 40◦. More detailed validationstudies and investigations of design and off-design influences are conducted by Gödert [96].

Apart from drag polars, interpolation is also applied to the stored 2Dc airfoil geometries,as well as to Cp,2Dc and Cq distributions. Finally, airfoil geometries and Cp,2Dc distribu-tions are transformed into streamwise (3D) direction by inversely applying Eqs. (3.25)and (3.27), respectively. Cp,3D and Cq distributions are passed as input to the HLFCsystem design module described in the next section. In this context, possible numericalinterpolation artifacts have been proven to have negligible influence on predicted HLFCsystem mass and power consumption.

120 Chapter 3. Method for aircraft design with hybrid laminar flow control

3.4 HLFC system design method

With the Q3D HLFC aerodynamic wing design method elaborated in the preceding sec-tion, the drag reduction due to laminar flow and the wing outer shape are predicted.Within MICADO, the impact is mirrored in key design parameters, e.g., OWE, MTOW ,or block fuel. For a thorough net benefit assessment of HLFC technology on aircraft level,the impact of the suction system yet needs to be estimated and incorporated into the over-all sizing approach. This section describes the implemented HLFC system sizing method,while the principle of its integration into the MICADO OAD logic and its interconnectionwith other modules was already introduced in Fig. 3.5. The effort and level of detail putinto the development of the HLFC system sizing method (and with it the extent of thissection) is considerably smaller than for the HLFC aerodynamics method. This propor-tion is deliberately selected as it follows the second guideline of the proportionality prin-ciple stated in the introductory remarks of Sec. 3.2, that is, to measure model complex-ity according to the OAD impact of the predicted parameters, e.g., in terms of block fuel.The main output parameters of the HLFC system sizing are the total HLFC system mass(mhlfc,tot) and the total electrical power required to drive the suction system (Phlfc,tot).The impact of these parameters on block fuel is comparably small. For example, considera typical long range aircraft (such as Airbus A330 or Boeing 777), for which even 1000 kgadditional mass would only amount to less than 1 % of the OWE. Further, impact of en-ergy requirements of all aircraft systems on engine SFC during cruise roughly amounts toan increase in 3–5 %, where the majority mostly attributes to bleed air extraction, and onlya smaller share to secondary shaft power offtakes61. This also implies small influence of ad-ditional shaft power offtakes due to suction system integration. These relations and state-ments will be underpinned in the course of the HLFC aircraft design studies in Chap. 4.

The implemented HLFC system design module follows the simplified suction concept de-veloped during the ALTTA project for the A320 fin [128, 129], as well as the supplementarymethods and equations proposed by Pe and Thielecke [200]. The principle of the ALTTAconcept has been described in Sec. 2.3.2 and a schematic illustration is shown in Fig. 3.29.It is shortly described below, how the concept is implemented in line with the parame-terized MICADO aircraft geometry and HLFC aerodynamic input data, and how powerconsumption and masses of the HLFC system components are determined. For more de-tailed descriptions and additional equations, the reader may refer to the cited references.

Suction system sizing and underlying flow equations

The HLFC system sizing module is an integral part of MICADO and thus follows the soft-ware principle in Fig. 3.1. Initially, the program reads the aircraft geometry and designflight conditions from the AiX parameter file and loads methodical parameters from theconfiguration XML file. The latter contains parameters describing specific characteristicsof HLFC system components, e.g., duct material density or motor efficiency. Further cru-cial input are the HLFC aerodynamic design data, i.e., Cp and Cq distributions obtainedfrom the HLFC airfoil database (see Sec. 3.3.8) at selected wing design sections. Gen-

61The relative shares vary with flight phase, as well as aircraft and engine type, see, e.g., Refs. [56, 79].

3.4 HLFC system design method 121

erally, the systems architecture can be sized for application of HLFC to wings and tails,where the compressor sizing procedure explained below focuses on the wing. The imple-mentation further includes different topology options, e.g., decentralized (along the wingspan) versus centralized compressor placement, or a ducting system with either separate(one per compressor) or collective pipes.

space for Krueger flap kinematics

compressor

space for Krueger flap actuating system

duct

front

spa

r

to duct:

chamber:

outside sheet (porous surface)

inner sheet (titanium)

wall/surface:

Figure 3.29: Principle of simplified suctionsystem inside wing leading edge,after Ref. [129]

The wing compressors have to supply thesuction power to establish laminar flowover a certain spanwise interval. The shaftpower of a compressor can generally bewritten as Pcmp = mY/ηcmp, with the massflow m, the specific energy transfer Y , andthe compressor efficiency ηcmp [297]. Topredict the mass flow m that is suckedthrough the porous surface, consider awing section as sketched in Fig. 3.29. Thefreestream conditions (Mach number M∞and altitude h) are given at the designpoint according to the TLARs; the belong-ing state variables p∞, ρ∞, T∞, U∞ derivefrom the ISA equations implemented in theMICADO atmosphere class. With the sec-tional streamwise Cp distribution, the wallsurface pressure pw along the arc coordi-nate s is obtained via the definition of Cp in Eq. (2.24), i.e., pw (s) = p∞ + ρ∞U2

∞2 Cp (s).

Likewise, the suction velocity through the porous surface writes as ww (s) = U∞Cq (s),see Eq. (2.21). The boundary-layer wall temperature Tw is calculated as a function of theso-called recovery factor r [129, 250]:

Tw = T∞(1 + 0.169 r M2

∞

), with r = 0.95. (3.38)

The mass flow can now be obtained by numerical calculation of the double integral

mw =∫∫

Sρw (s, y)ww (s, y) ds dy, (3.39)

where S is the (developed) wing surface area within the spanwise (y) and chordwise (s)suction boundaries of the respective compressor. The Cp and Cq distributions at therequired y positions are obtained via interpolation between the given design sections.

The estimation of specific energy transfer Y requires knowledge about the compressorinlet and outlet conditions [33]. According to the ALTTA concept sketched in Fig. 3.29,the flow conditions are therefore described along all relevant stations, i.e., from the surfacethrough the double sheet structure and the suction duct to the compressor inlet, andfrom the compressor outlet to the outflow valve. From the surface wall to the compressorinlet (cmp,in), isothermal change of states is assumed, i.e., Tw = Tc = Td = Tcmp,in. The

122 Chapter 3. Method for aircraft design with hybrid laminar flow control

pressure drop through the outside (porous surface) sheet is modeled by the equation [129]

∆pwc = Aµwµ0ww +B

ρwρ0w2w, with A = 13553 N s

m3 , B = 56845 N s2

m4 , (3.40)

and with the reference values ρ0 and µ0 according to ISA [136] and Sutherland’s viscositymodel [298], respectively. The constants A and B are measures for the porosity of thesuction surface and derived from experiments [129]. The pressure loss ∆pcd through themetering orifices in the inner sheet strongly depends on parameters such as hole size, whichare not known at the considered preliminary design stage. Therefore, a constant value of∆pcd = 3000 Pa is adopted from the ALTTA project. The pressure of the suction ductinside the wing leading edge can then be set to pd = min (pc)−∆pcd, using the minimumvalue of the variable chamber pressure pc [262]. Further considering pressure losses dueto the flow passing through the ribs inside the wing leading edge, the compressor inletconditions are obtained. The compressor outlet conditions are iteratively determined suchthat on the one hand, relations for isentropic compression between compressor inlet andoutlet are fulfilled, and on the other hand, the desired conditions at the outflow valve (ov)are reached. The outflow conditions are here assumed as Mov = 0.2 and pov = p∞. Thepressure loss between compressor outlet and outflow valve is predicted with equations forcompressible pipe flows, see, e.g., Ref. [297]. For the decentralized compressor architecturewith collective ducting, which is the favored concept within this thesis, additional couplingconditions between different compressor outlets and pipe inlets are considered.

The electrical power Phlfc,tot, which is ultimately taken off as secondary shaft power fromthe engines, is related to Pcmp via the efficiencies η of the electrical motor (mot) and avariable-frequency drive (VFD), i.e., Phlfc,tot = Pel,vfd = Pcmp/ (ηmot ηvfd) [199].

Mass prediction of HLFC system components

The overall mass of the HLFC system is predicted as sum of its single mass components:

mhlfc,tot = mcmp +mduc +mel, (3.41)

where mcmp includes compressors, motors, and VFDs, mduc refers to the pipes of theducting system, and mel to the electric wiring. The mass prediction methods proposed byPe and Thielecke [199, 200] are implemented, since they provide a suitable level of detailfor preliminary design applications. To estimate mcmp, linear regressions as a function ofPcmp are used. For the prediction of mduc and mel, the ducting and wiring architecture isfirst placed within the MICADO overall aircraft geometry. The ducting connects wing andtail compressors with the outflow valves, while the wiring system connects the electronicand equipment (E/E) bay in the front body of the aircraft with the electric motors thatdrive the compressors. With the resulting overall lengths l, both masses can be estimatedaccording to m = ρA l, with constant material densities ρ. For the ducting, the cross-sectional area Aduc depends on the wall thickness of the pipes, which is set to 3 mm bydefault. Ael is predicted based on cable properties such as electrical resistivity, voltage,

3.4 HLFC system design method 123

and maximum power. Further, correction factors are applied to mduc and mel to accountfor supplementary production material [199].

Impact on overall aircraft design

The influences of HLFC system integration on overall aircraft design are captured withinthe automated MICADO sizing process. The mass prediction module (Sec. 3.2.4) addsmhlfc,tot to the OWE, and considers the HLFC system center of gravity (CG) position,which, however, negligibly influences overall aircraft CG due to close vicinity to the wingCG. The integration into the MICADO overall aircraft systems and power distributionarchitecture (Sec. 3.2.5) also accounts for relevant system interdependencies, e.g., an in-creased mass of the electrical generation system due to higher maximum peaks in sec-ondary shaft power offtakes. Together with other systems offtakes, Phlfc,tot is written tothe MICADO mission XML file, and so respected for fuel estimation during mission sim-ulation (Sec. 3.2.6) via the integrated engine model (Sec. 3.2.2).

It is important to notice that the HLFC system is herein assumed to be switched on onlyduring cruise. The first reason is that the initial cruise altitude (∼ 27000–35000 ft) canbe selected as design condition, while lower design altitudes would significantly increasecompressor power and size due to higher air densities. Sizing for hICA also implies conser-vative layout regarding operations at higher cruise altitudes. Secondly, the reduced Machnumbers in climb and descent phases lead to degenerated HLFC pressure distributionswith pronounced peaks at the leading edge, which is expected to degrade laminar flow,and thus makes lower design altitudes less worthwhile [316]. In this context, sensitivitiesof block fuel towards HLFC mass and power requirements, as well as their sensitivitiestowards system design conditions will be revisited in Chap. 4.

The certification-relevant aspects of system reliability and redundancy are herein alsocaptured from an operational point of view. This is done by considering additional reservefuel and its impact on aircraft resizing due to laminar flow degradation during flight (seeSec. 3.2.6), which can certainly also be provoked by an HLFC system failure.

It may be concluded that though the HLFC system sizing method includes many assump-tions and uncertainties, e.g., in terms of porosity factors, efficiencies, or correction factors,it incorporates the relevant sensitivities towards aircraft size, flight conditions, and aero-dynamic input data. Together with the HLFC aerodynamic wing design method, it thusenables integrated and consistent HLFC overall aircraft sizing, as demonstrated in the nextchapter. More detailed system-specific investigations as well as architectural and topologystudies have to be elaborated by the systems engineer, as demonstrated, e.g., by Pe [199].

4 Application of developed method toHLFC overall aircraft design

One objective of this chapter is the application and validation of the developed HLFCaircraft design method as proposed in Chap. 3. The reliability and validity of an

overall aircraft design (OAD) method strongly depends on the following aspects:

• consistency of overall aircraft design

• accuracy of aircraft design parameters

• accuracy of aircraft design sensitivities

These aspects have been treated in detail in Secs. 3.1 and 3.2. The OAD consistency prin-ciple is an immanent feature of MICADO. It includes uniform implementation of meth-ods with a balanced level of detail, correct interrelations of aircraft design parameters,and the capability to quantitatively assess different disciplines by key evaluation param-eters. The prediction accuracy of aircraft design parameters and sensitivities inhere tothe implemented aircraft design and analysis methods. Especially the design sensitivi-ties (e.g., influence of varying wing parameters such as span or sweep on aerodynamics orstructural mass) are crucial for reliable trade studies and determination of global aircraftdesign optima. Still, they are difficult to validate against real-world applications due tolack of realized geometrical variants.

A systematic procedure is followed in this chapter to prove the above-listed criteria forMICADO and the incorporated HLFC methods. First, a MICADO design for a longrange passenger aircraft is presented in Sec. 4.1, which serves as baseline for assessment ofsubsequent HLFC designs. For validation, design results are compared against availablekey reference data from Airbus. Further, the potential for optimum HLFC integration isinvestigated in Sec. 4.2 by appropriate sensitivity analyses and parameter variations.

Based on the consistent reference aircraft design as well as validated aircraft design meth-ods, the main objective of this chapter and of the overall thesis is addressed in Sec 4.3,that is, the optimum overall design of HLFC aircraft. This task is solved by means of de-tailed aircraft design studies (primarily to minimize block fuel), which clearly go beyondthe state of the art by simultaneously considering the following aspects:

• HLFC airfoil transonic drag characteristics and transition locations, incorporatedinto overall aircraft drag polars via Q3D database approach (Sec. 3.3)

125

126 Chapter 4. Application of developed method to HLFC overall aircraft design

• HLFC system mass and power consumption (Sec. 3.4), incorporated into aircraftmass estimation (Sec. 3.2.4), systems design (Sec. 3.2.5), and engine model (Sec. 3.2.2)

• detailed mission simulation, including cruise altitude optimization for consistentblock fuel prediction, and reserve fuel planning for HLFC system failures (Sec. 3.2.6)

• interactions of disciplines within overall design convergence, including resizing ofmain aircraft components and mass snowball effects (see Sec. 3.1.4)

It has been extensively justified within this thesis that the full potential of HLFC canonly be reliably exploited by the proposed integrated design and assessment approach.

4.1 Design and validation of long range reference aircraft

For any quantitative assessment of innovative technologies or design approaches, a refer-ence aircraft is required. Since hybrid laminar flow control (HLFC) shows its full poten-tial on long distance flights, a conventional (turbulent) long range aircraft configuration isselected as reference. Specifications for a suitable long range baseline configuration weregiven by Airbus within the scope of the German research project HIGHER-LE1 [114].The document contains a set of top-level aircraft requirements, key aircraft characteris-tics, a general arrangement, and few selected aerodynamic and propulsion system param-eters. Though it provides no detailed design data such as airfoil geometries, drag polars,or a mass breakdown, it is considered as suitable source for comparison and validation ofMICADO design data. The MICADO design of the long range reference aircraft is dis-cussed in detail in this section. Besides the validation of results, this serves the purposeto give insight into, and reveal level of detail of the implemented methods as described inSec. 3.2. Further, a profound dataset is created that is used for quantitative comparisonsin all subsequent design studies. With the sensitivity studies and parameter variations inSec. 4.2, the fuel saving and HLFC integration potential is analyzed, and sensitivities areagain compared with available reference data. The knowledge of the expectable predic-tion accuracy for design interactions and sensitivities is a crucial precondition for reliableinterpretation and evaluation of HLFC aircraft design studies in Sec. 4.3.

Overall aircraft design considerations

The following paragraphs present the results of the MICADO design of the turbulentbaseline configuration. Where available, results are compared against Airbus data speci-fied in Ref. [114], which will consistently be denoted by the term “Airbus reference (ref.)value”. The reasons for the choice of this conventional long range configuration as turbu-lent reference aircraft have been justified above. A different configuration without reliablereference data for comparison and validation would have reduced the credibility of quan-titative predictions for the HLFC fuel saving potential in Sec. 4.3. This holds even more

1The project was carried out in the framework of the German Aeronautical Research Program (LuFo).

4.1 Design and validation of long range reference aircraft 127

for the possible selection of any unconventional reference configuration, which would haveadded many undesired uncertainties to the (already) preliminary design considerations.

The configuration of the reference aircraft includes a conventional arrangement of wing,fuselage, and empennage, and two wing-mounted turbofan engines. It has a design ca-pacity of 470 passengers (PAX) in a two-class seat arrangement, which corresponds to astandard passenger payload (SPP) mass2 of mSPP = 44650 kg. The SPP design rangeamounts to Rdes = 8150 NM. A selection of other sizing-relevant top-level aircraft re-quirements (TLARs) is given in table 4.1. A detailed listing of TLARs can be found intable C.1, which also contains the conditions under which the requirements apply. Someof these details will be revisited during the performance assessment later in this section.

Table 4.1: Selected TLARs forMICADO design of longrange reference aircraft

TLAR Unit ValueDesign range NM 8150Std. PAX number − 470Std. passenger payload kg 44650Maximum payload kg 71600Cruise Mach number − 0.85Initial cruise altitude ft ≥ 33000Time to climb min ≤ 25Take-off field length ft < 10700Landing distance limit ft < 6800Maximum wing span m 80

0.05

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0.15

0.20

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0.30

0.35

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0.45

0.50

300 400 500 600 700 800 900

T/W

W/S, kg/m2

Cruise req.(Macr = 0.85)

Climb req.(TTC ≤ 25 min,ICA ≥ 33000 ft)

Take-off req.(TOFL < 10700 ft)

CL,max, T/O 2.0 2.2 2.4

Landing req.(LDL < 6800 ft)

CL,max, LDG 2.4 2.6 2.8

Airbusref. value

Figure 4.1: MICADO initial siz-ing diagram for TLARsgiven in table 4.1

Preliminary insight how the given TLARs drive the aircraft design can be gained by thetypical initial sizing chart introduced in Sec. 3.1.4. Figure 4.1 shows the dependenciesof thrust-to-weight ratio T/W and wing loading W/S as computed by the MICADOinitial sizing program. The solid limiting lines represent the different requirements, wherethe valid combinations of T/W and W/S reside above the cruise, climb, and take-offcurves, and left of the landing distance limit curve. The enclosed sizing region agreeswell with the Airbus reference value, which lies in the lower left part close to the cruiseand climb boundary lines. The sizing point could basically also be selected farther right(i.e., at higher W/S) in favor of a smaller, lighter (clean) wing; this would, however,imply higher cruise lift coefficients CL (see Eq. (2.25)), and possibly require an improved,heavier high-lift system. Around the initial estimates of maximum lift coefficients3 attake-off (CL,max,T/O = 2.2) and landing (CL,max,LDG = 2.6), which presumably complywith requirements, a variation of ∆CL,max = ±0.2 is conducted to show the influence onthe limiting curves. With the landing distance requirement supposed to be slightly less

2The SPP results from an assumed average mass of 95 kg per PAX (including luggage). On off-designmissions, additional passengers and/or cargo can be carried, up to a maximum payload of 71600 kg.

3For full-configuration CL,max values of existing commercial aircraft, refer, e.g., to Obert [193].

128 Chapter 4. Application of developed method to HLFC overall aircraft design

critical, both reductions in CL,max,T/O or CL,max,LDG further constrict the optimum sizingplateau, and possibly require lower W/S and/or higher T/W values. Thus, as initiallyconfirmed by the diagram, the key sizing parameters

• W/S = MTOWSref

= 717 kg/m2

• T/W = 2 SLSTMTOW g

= 0.26

are used for the MICADO design, with g = 9.80665 m/s2, and the sea-level static thrustSLST referring to one engine. The sizing point has additionally been confirmed by aparameter study of W/S and T/W , including OAD convergence and TLAR compliancechecks, where it agrees well with the computed block fuel minimum (see Fig. C.2a).

According to the procedure illustrated in Fig. 3.4, the developed MICADO platform isused to design the long range reference aircraft with respect to the specified TLARs.Before the design iteration, fuselage geometry and cabin layout are sized according to thepassenger and cargo accommodation specifications in table 4.2, with 400 PAX seated ineconomy class (EC), and 70 in business class (BC). Key aircraft characteristics specifiedin Ref. [114] are used as target parameters to ensure a consistent basis for comparisonsand validation in the following paragraphs. The most important overall aircraft designparameters are given in table 4.3, and a more detailed listing is given in table C.2.

Table 4.2: Accommodation specifica-tions for reference design

Passenger accommodationEC seats (seating) 400 (3− 4− 3)BC seats (seating) 70 (2− 3− 2)Flight + cabin crew 4 + 13Lavatories 14Galleys 7

Cargo accommodationLD3 containers 24 (12× 2)Pallets (96 in× 125 in) 9 (9× 1)

Table 4.3: Key aircraft characteris-tics of reference design

Parameter Unit ValueW/S kg/m2 717T/W − 0.26MTOW t 405MLW t 300OWE t 212Sref m2 565b m 80SLST kN (klbf) 511 (115)

Figure 4.2: 3D view of MICADO design oflong range reference configuration

The MICADO overall aircraft iteration isexecuted for the 8150 NM design mission,where the initial sizing parameters T/Wand W/S are kept constant as describedin Sec. 3.1.2. The general arrangement re-sulting after overall design convergence isillustrated in the 3D view4 in Fig. 4.2, in-cluding all main aircraft components. Inthe following paragraphs, a more detailed

4The watertight CAD geometry model is automatically generated by MICADO, see Sec. 3.1.1.

4.1 Design and validation of long range reference aircraft 129

description of the aircraft design characteristics and results from the MICADO modelsand analysis programs are discussed and compared with available reference data. All pro-gram settings or design decisions made for the reference design will be maintained for allsubsequent HLFC aircraft designs5; this allows quantifying even very small design influ-ences by means of changes in key evaluation parameters (e.g., block fuel).

Engine model and performance characteristics

The propulsion system of the reference aircraft includes two turbofan engines with a sea-level static thrust of SLST = 115 klbf (≈ 511 kN) per engine. According to the prin-ciple of the MICADO engine model described in Sec. 3.2.2, a thermodynamic model fora generic turbofan engine6 has been built with GasTurb7 [153]. The GasTurb cycle hasbeen designed to meet thrust and fuel flow specifications given in Ref. [114]. As additionalsource, the type certificate data sheet of the General Electric GE90-115B engine [69],which exhibits the same thrust class, has been used to derive additional parameters re-quired for the MICADO engine model, e.g., the operational exhaust gas temperature lim-its for take-off (EGTT/O) and maximum continuous (EGTmax ct) rating.

0

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st (

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Mach number M

sea levelISA+15

20000 ftISA+10

35000 ft {

equivalent thrust, SL, ISA+15

max. T/O, SL, ISA+15

max. climb, 35000 ft, ISA+10

max. cruise, 35000 ft, ISA

[ Airbus ref. values ]

max. take-off, w/o OT

max. take-off, with OT

max. cont, with OT

ISA+10, N1max cont, w OT

ISA+10, 0.9N1max ct, w OT

ISA, 0.9N1max ct, w OT

(a) Net thrust FN as a function of Machnumber, flight altitude, atmosphericconditions, and engine thrust ratings

13 14 15 16 17 18 19 20 21 22 23

20 40 60 80 100 1200.45

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/s)/

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lb/h

r)/l

bfnet thrust (per engine) FN, kN

109%N1

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. con

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1 max

. con

t.

flam

eout

lim

it

bucket curve (without offtakes) bucket curve (with avg. offtakes) Airbus reference value

(b) SFC bucket curves at cruise designconditions (M = 0.85, 35000 ft, ISA),with influence of average offtakes

Figure 4.3: Performance characteristics of MICADO baseline engine model

For the converged reference aircraft design, performance characteristics and sensitivitiesof the MICADO engine model are shown in Fig. 4.3 and compared to specified referencevalues. Figure 4.3a presents curves of net thrust FN with varying Mach number and fordifferent operating conditions. The thrust curves at maximum take-off rating, which is

5This corresponds to unchanged configuration files (see Fig. 3.1) and can include system-specific parameters(e.g., switch-off altitude for wing anti-icing) or a mass scaling factor to achieve agreement in OWE.

6The designated turbofan engine offers a bypass ratio of 9.6 and a technology level of the year 2012.7The selected engine type in GasTurb is a “Geared Unmixed Flow Turbofan”. Thrust and fuel flow contoursof the created engine model (unscaled, and without limitations or offtakes) are shown in Fig. C.1.

130 Chapter 4. Application of developed method to HLFC overall aircraft design

limited by EGTT/O, show the typical strong decrease with increasing Mach number. Thedifference between the solid black and the dashed dark gray curve shows the influence oftypical bleed air and power offtakes (OT). The gradient of thrust decrease complies wellwith the two specified reference points, where the Airbus equivalence thrust is definedindirectly as 1.25 times the reference take-off thrust at M = 0.25. The SLST determinedwith MICADO agrees very well with this equivalence value, where the value withoutofftakes (w/o OT) is used as reference for thrust scaling and adaptation to T/W duringMICADO sizing iteration (see Secs. 3.2.2 and 3.1.4).

The strong thrust decrease with altitude also shows the expected behavior. At the cruisedesign point (M = 0.85, h = 35000 ft), the MICADO thrust curves again show goodagreement with the reference values. Here, it has to be noted that the actual thrustsetting in terms of low-pressure spool speed N1 strongly influences the net thrust FN .Since the actual settings of the reference ratings maximum cruise and maximum climbare unknown, the interval between FN at maximum continuous rating8 (N1,max ct) and FNat 0.9 N1,max ct is displayed by the two upper green curves. The maximum climb ratingis expected to reside within this interval, which is confirmed by the reference value. Thethrust at maximum cruise rating is less significant, since during cruise, N1 is always setaccording to the thrust required for steady flight, i.e., to balance drag (T = 2FN = D).

In Fig. 4.3b, the (thrust-)specific fuel consumption SFC is plotted versus FN for the cruisedesign point, which represents the so-called bucket curve according to its characteristicshape. The two bucket curves show the engine behavior without and with average cruiseofftakes9 (Pshaft,avg-cr = 324 kW, mbleed,avg-cr = 2.45 kg/s), where the relative differenceat the distinctive minima of the curves amounts to ∼ 5%. This minimum point is calledbucket point, which nearly coincides with the reference values of SFCbkt = 0.0147 kg/s

kNand FN,bkt = 79.3 kN. The figure further shows the corresponding percentage N1 valuesat characteristic points, as well as relevant operational limits.

During the iterative MICADO sizing process, engine performance characteristics arescaled according to the actual thrust requirements, where the sea-level static thrust is usedas reference scaling value (see Sec. 3.2.2). The core engine model will be maintained forall subsequent design studies, since scaling of performance characteristics is assumed tobe valid for the herein presented parameter variations around the reference configuration.

Wing characteristics

The technology standard of the reference aircraft includes a CFRP wing and fuselage [114].Though MICADO methods for structural sizing and mass estimation (Sec. 3.2.4) have notspecifically been adapted with respect to CFRP-optimized manufacturing, the materialproperties offer potential—besides weight reduction—for more efficient shaping. Thismainly concerns the wing of the reference aircraft, which has increased aspect ratio andtaper compared to conventional aluminum wings. The wing planform geometry of theMICADO reference design is shown in the upper diagram of Fig. 4.4a, including front and

8The maximum continuous rating is limited by EGTmax ct, which can imply values higher than 100 %N1.9The values represent total systems power and bleed air requirements averaged over cruise (see Fig. 4.7).

4.1 Design and validation of long range reference aircraft 131

rear spar positions10. As described in Sec. 3.1.1, the MICADO 3D wing is composed by thegeometry classes via linear lofting over different spanwise airfoil sections; in this case, fivesections are used, as depicted by the blue numbers and dash-dotted lines. The turbulentreference airfoils at kink and tip sections have been designed by the DLR during the projectHIGHER-LE [234]; at the wing-fuselage junction, an available airfoil with typical rootcharacteristics (cf. Ref. [193]) is used. All airfoils have been selected or designed accordingto the specified thickness-to-chord (t/c) distribution as shown in the lower diagram ofFig. 4.4a, which is well approximated regarding the few number of design sections.

30

35

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60 0 10 20 30 40

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spanwise y coordinate, m

1 2 3

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5

wing planform shape front and rear spar

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c

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le ε

, deg

relative spanwise coordinate η=y/(2b)

root

kink

tip

tickness ratio t/c

t/c (Airbus ref. values) twist angle ε

(a) Upper diagram: wing planform, air-foil sections, spar locations; lower dia-gram: spanwise distribution of thick-ness ratio and twist angle

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

01234567

0 10 20 30 40

lift

coef

fient

Cl

Cl ⋅

c, m

spanwise y coordinate, m

M0.85, CL=0.51, 35000 ft,

∗ Airbus reference, untrimmed

Cl(y), LILI Cl(y), AI ref.∗ Cl(y) ⋅ c(y), LILI

0

1000

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3000

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0.00 0.25 0.50 0.75 1.00 0

10

20

30

40

shea

r fo

rce

Fz,

kN

bend

ing

mom

ent

Mx, 1

06 N m

relative spanwise coordinate η=y/(2b)

2.5g maneuver@MTOW, SL, VMO

win

g ro

otm

ain

gear

engi

ne

Fz(y) Mx(y)

(b) Spanwise distributions of Cl and Cl cat cruise conditions (upper figure),and of shear force and bending mo-ment at 2.5 g maneuver (lower figure)

Figure 4.4: Geometrical, aerodynamic, and structural wing characteristics

The lower diagram also shows the distribution of local twist angles ε of the MICADOreference design. Basically, thickness and twist distributions resemble those publishedfor comparable long range aircraft, e.g., by Obert [193]. The local twist angles havebeen determined within MICADO with respect to aero-structural considerations, i.e., inagreement with acceptable lift and load distributions. The upper diagram of Fig. 4.4bshows the trimmed distribution of local lift coefficients Cl (y) at cruise conditions. Thecomparison with the (untrimmed) reference distribution shows good agreement, where thedeviations are mainly due to differences in root airfoil geometry and local twist angles.A validation case for the incorporated LIFTING_LINE program has been presented inFig. 3.13. The lift distribution, which is here represented by the product of local chordand lift coefficient Cl (y) c (y), exhibits a slightly “under-elliptic” shape. This allows a

10A detailed listing of wing planform and sectional geometry parameters is given in table C.3.

132 Chapter 4. Application of developed method to HLFC overall aircraft design

good compromise between inboard and outboard spanwise loading, which are beneficialin terms of structural and aerodynamic considerations, respectively.

The results of the MICADO wing structural sizing program (see Sec. 3.2.4) for the selected2.5g pull-up maneuver are shown in the lower diagram of Fig. 4.4b, where the local shearforces Fz and bending momentsMx are displayed on the left and right y axes, respectively.All relevant influences (e.g., Cl distribution, stored fuel, wing own structural weight, pointloads) are considered. The relieving influence of wing-mounted engines and main landinggear can be noticed by the local jumps in Fz. Though local deflections of the wingstructure are determined by the MICADO beam model, no aero-structural iteration isperformed with the deformed geometry. Differences between jig and flight shapes, whichwould become relevant for more detailed wing design including aeroelastic analyses, arethus neglected. The 3D MICADO wing geometry including dihedral and twist, whichundergoes the more detailed aerodynamic analysis, can, however, be regarded as targetflight shape in this context.

The high-lift system of the reference aircraft includes two inboard droop-nose devices(η = 0.10–0.29) and six outboard slats (η = 0.34–0.93) at the leading edge. At thetrailing edge, two advanced dropped hinge flaps (η = 0.09–0.64) are arranged next to twooutboard ailerons (η = 0.64–0.93). Further, eight spoilers are integrated on the inboardand outboard wing [114].

The wing fuel tank system includes one center tank and two wing tanks, offering a max-imum fuel weight capacity of MFW = 208 t. The value is determined by volume inte-gration using the MICADO geometry classes and agrees well with the specification givenin Ref. [114]. The maximum fuel storage capacity is calculated and continuously updatedduring MICADO sizing iteration and can constrain the design, e.g., in case of a too smallwing area. However, note that the herein presented long range reference design is notclose to be tank-limited, as it will become evident in the payload-range diagram below.

Full-aircraft-configuration aerodynamics

Aerodynamic characteristics of the full reference aircraft configuration are determined bythe MICADO aerodynamic module, including the component and drag buildup approachdescribed in Sec. 3.2.3. The turbulent wing transonic profile drag is determined using theenhanced Q3D method proposed in Sec. 3.3, and integrated into overall aircraft polarsaccording to Fig. 3.10. Hence, turbulent drag polars (i.e., without transition prediction)have been predicted for the reference airfoils and imported to the SQLite database (seeprocedure in Fig. 3.26a). More detailed investigations for drag prediction on the inboardwing showed that—due to strong change in airfoil shape and thickness in the vicinity ofthe wing root—the usage of a surrogate aerodynamic dataset for the root airfoil providesreasonable results; here, the drag polars are therefore predicted for an airfoil with slightlyreduced thickness11 and the reference wing planform used in Sec. 3.3.3. The turbulent root

11The geometry is based on the NASA supercritical airfoil family [112] and has a (scaled) thickness ratioof t/c ≈ 0.135 (see Fig. 4.4a). The off-design polars are computed for different reference Mach numbersto allow for database interpolation as discussed in Sec. 3.3.8.

4.1 Design and validation of long range reference aircraft 133

airfoil with its specific shape and aerodynamic characteristics will also be retained for thesubsequent HLFC aircraft designs, assuming that laminar flow is not obtainable at thewing-fuselage junction due to strong 3D flow and very high chord Reynolds numbers (cf.Ref. [247]). Since the real wing planform shown in Fig. 4.4a has an unswept trailing edgeinboard of the kink, the back-transformation (2Dc→ 3D) of drag coefficients according toEq. (3.30) leads to higher drag coefficients in streamwise direction (Cd,3D). This implicitlyaccounts for the reduced sweep of shock location and isobars, which can be observed in3D flows on transport aircraft wings in the vicinity of the wing-fuselage junction (see,e.g., Ref. [193]). An alternative approach is presented by Greitzer et al. [105] who use a“heuristic unsweep function” to handle drag transformation on the inboard wing.

-0.2

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0.01 0.02 0.03 0.04

tota

l airc

raft

lift

coef

ficie

nt C

L

total aircraft drag coefficient CD, total

M 0.20, SL M 0.50, 10000 ft M 0.80, 35000 ft M 0.85, 35000 ft M 0.85, 35000 ft (AI ref. value) M 0.86, 35000 ft

(a) Predicted drag polars at differentMach numbers and flight altitudes

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0.002

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lift-

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L/D

wav

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ag c

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D,w

ave

total aircraft lift coefficient CL

opt.

CL r

ange

: CL

,opt

± 0

.03

L/D = CL/CD,total

L/Dinc = CL/(CD,ind + CD,visc) L/D (Airbus ref. value) CD,wave

(b) Cruise lift-to-drag ratio as a functionof CL; influence of wave drag charac-teristics on location of CL,opt

Figure 4.5: Aerodynamic characteristics of full aircraft (clean) configuration

For the converged MICADO reference design, Fig. 4.5a shows the predicted drag polars forthe full aircraft (clean) configuration at different Mach numbers and flight altitudes. Forsubsonic conditions, the typical parabolic polar shape can be observed, while drag increasebecomes stronger with higher Mach numbers and lift coefficients due to increasing impactof viscous pressure and, in particular, wave drag. The Airbus reference value atM = 0.85is well approximated by the cruise drag polar. Figure 4.5b, however, reveals that theoptimum CL range, where the cruise lift-to-drag ratio L/D reaches maximum values (solidblack curve), lies a little left of the specified reference value. In this context, it is interestingto take the “incompressible” L/D curve into consideration, i.e., without the influence ofCD,wave (dashed dark gray curve). Here, CL,opt,inc resides at higher values around 0.55.The CL,opt value of the total L/D curve is thus a result of CL,opt,inc and the compressibledrag rise, which is represented by the CD,wave = f (CL) curve plotted on the second yaxis. The wing drag rise characteristics in turn mainly depend on wing sweep, thicknessratio, and airfoil technology. The existing differences in these parameters thus explainthe deviation, and the CL,opt could be shifted to the right by an improved airfoil design interms of reduced wave drag. This is, however, beyond the present scope and could on the

134 Chapter 4. Application of developed method to HLFC overall aircraft design

other hand involve structural drawbacks. In this aircraft design context, it is importantto summarize, that the CL,opt value is a result from the transonic wing characteristics, andfurther, a shift in CL,opt is automatically compensated during mission simulation by anadaptation of optimum cruise altitude. The automated consideration of this interrelationis an outstanding feature of the proposed method and will be elaborated below.

At cruise conditions, the incidence angle of the (all-movable) horizontal stabilizer is au-tomatically set to trim the overall aircraft configuration for the actual cruise design point(i.e., CM = 0 at CL,opt). This procedure automatically considers additional trim drag,e.g., if changed airfoil geometries or spanwise loadings require increased trim deflections.

Aerodynamic coefficients for lift, drag, and pitching moment are determined for differentflight conditions and configurations (cruise, take-off, climb, approach without and withlanding gear, and landing), and exported to the polar XML file that is used for missionsimulation. Though here not discussed in detail, all relevant characteristics are thus deter-mined and captured during MICADO design iteration. For the leading- and trailing-edgearrangement mentioned above, the semiempirical prediction of total aircraft maximum liftcoefficient (see Sec. 3.2.3) yields the following reference values for take-off and landing:

• CL,max,T/O = 2.30

• CL,max,LDG = 2.62

Though no reference data exist for comparison, the determined values correspond wellwith published aircraft data (see, e.g., Ref. [193]). Further, they lie in the acceptable rangeto fulfill the required take-off and landing field lengths, as initially predicted in Fig. 4.1.

A summary of the predicted aerodynamic coefficients, including a drag component break-down at cruise conditions, is given in table C.4.

Mass estimation

The masses of all primary components and systems of the reference aircraft are deter-mined using the physical and semiempirical methods described in Sec. 3.2.4. The pre-dicted masses of the superordinate groups (structures, power unit, systems, furnishings,and operator items), as well as the resulting MWE and OWE are summarized in ta-ble 4.4. A detailed breakdown of all considered mass chapters is given in table C.5. Fig-ure 4.6 illustrates the mass breakdown and shows the main mass groups as percentageof OWE. Though no detailed mass breakdown is available for comparison, the share ofmass components in OWE or MTOW agrees well with published data for similar longrange aircraft [283]. Note that masses belonging to furnishings group and operator itemsstrongly depend on configuration and comfort of the passenger classes, e.g., in terms ofseat masses, which is, however, not the focus of the presented study. As discussed in theintroductory paragraph of Sec. 3.2, it may be repeated that not merely the accuracy ofevery single mass component value has priority, but rather a complete and correct captur-ing of sensitivities towards relevant aircraft design parameters. Certainly, large deviationsin mass reference values also have falsifying influence on design sensitivities. Of central

4.1 Design and validation of long range reference aircraft 135

importance in the present context are wing mass sensitivities due to geometrical changesas well as component interactions and mass snowball effects (see Secs. 4.2 and 4.3).

Table 4.4: Mass breakdown forreference design

Mass group/component mass, tStructures group 123.0·wing 55.3· fuselage 41.8· landing gear 17.6· others (HTP, VTP, pylons) 8.3Power unit group 28.4Systems group 16.1Furnishings group 19.8MWE 187.3Operator items 24.9OWE 212.2

0 20 40 60 80

100 120 140 160 180 200

OWE Struct.group

Prop.group

Systemsgroup

Furn.group

OperatorItems

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s, t

mas

s fra

ctio

n, %

OW

E

WingFuselage

HTPVTP

Landing gearPylon

Structures groupPropulsion group

Systems groupFurnishings group

Operator items

Figure 4.6: Breakdown of mass groupsand relative share in OWE

Besides masses, center of gravity (CG) positions are predicted for every mass chapter. Forthe converged reference design, the predicted overall aircraft CG position during cruise12is located at xCG = 39.96 m (measured from the nose), which corresponds to 28.2 %of wing mean aerodynamic chord (MAC). This CG location is continuously updatedduring MICADO design iteration, and used as reference point by the automatic trimalgorithm. This ensures trim drag sensitivity with respect to variations in CG location.The MICADO weight and balance module is further used to verify satisfying stability andcontrol characteristics for the reference aircraft. For all subsequent design variations, thereference static stability margin is kept constant to minimize undesired design interactions.

Systems offtakes

The MICADO systems design module presented in Sec. 3.2.5 sizes the conventional sys-tems architecture. Apart from the above discussed masses and center of gravity loca-tions, the power distribution is determined according to the applied network model ofsinks, sources, and conductors. The systems are sized according to maximum energy re-quirements on the design mission. Further, mission-dependent shaft-power offtakes andbleed air requirements are determined at distinct points of the determined mission profileaccording to the prevailing flight conditions. The mission simulation program (see nextparagraph) establishes the connection to engine model parameters and consumed fuel.For the reference 8150 NM design mission, Fig. 4.7 shows total systems power offtakesand bleed air requirements (accumulated for all energy consumers).

12The mass configuration for this CG point includes OWE, mSPP , and fuel mass at the mid-cruise point.

136 Chapter 4. Application of developed method to HLFC overall aircraft design

0200400600800

100012001400

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t po

wer

offt

akes

, kW

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distance covered, 1000 NM

cruise

2.0 4.0 6.0

power offtakes bleed air

8.05 8.10 8.150.01.02.03.04.05.06.07.0

blee

d ai

r, kg

/s

descent/approach

Figure 4.7: Total systems power and bleed airrequirements (8150 NM mission)

The different scaling of covered distance onthe x axis is used to accentuate peaks andsignificant power changes in the climb andapproach phases. The peaks in the shaft-power profile are due to retraction and de-ployment of landing gear and high-lift de-vices. Galley and in-flight entertainmentsystems are assumed to be continuouslyoperated, which implicates the constantlyhigh background power level during cruise.The bleed air offtakes are higher duringearly climb and late descent due to activewing anti-icing, where the flight altitude above which wing anti-icing is switched off is setto 12000 ft. The bleed air offtakes during cruise are mainly used for cabin pressurization,and a small share is due to active engine anti-icing.

Mission simulation

During MICADO design iteration, the mission analysis program (Sec. 3.2.6) simulatesthe 8150 NM sizing mission, which is MTOW -restricted in this case. Aircraft mass, dragpolars, and engine maps are used as input to iteratively solve the total-energy modelequations. As boundary conditions, mission parameters included in the TLAR list suchas Mcr are considered, as well as additional mission specifications, e.g., the climb speedschedule, which is here set to “250 kt/300 kt/M 0.83” (see Sec. 2.1). Further, an alternatedistance of 200NM is used for reserve fuel planning according to the procedure described inSec. 3.2.6. A summary of relevant mission specifications for the design and study missionincluding parameter definitions is given in table C.6. The table also includes simulationresults in terms of take-off mass as well as required amounts of fuel and time.

For the converged reference design, the results of the 8150NM sizing mission are illustratedin Fig. 4.8. In the upper diagram of Fig. 4.8a, the mission altitude profile is shown. Thecruise steps (ranging from FL13≈ 300 to 380) result from in-flight maximization of specificair range (SAR), with a specified step increment of ∆h = 1000 ft (see Sec. 3.2.6). Theresulting profile of the lift coefficient CL exhibits the typical sawtooth-like contour andis well-arranged around the optimum lift coefficient CL,opt = 0.472. It is important tonote that the marked light blue interval (with ∆CL = CL,opt ± 0.03) is equivalent to thathighlighted for the L/D curve in Fig. 4.5b.

The total (required) thrust T and the consumed fuel are plotted versus covered distance inthe lower diagram. The thrust peaks in take-off or climb segments and the increased fuelconsumption on segments with higher thrust ratings indicate the realistic incorporationof the engine model. The gradient of the fuel curve slightly decreases with increasingdistance, implied by the interaction between reduced aircraft mass, drag, thrust, and fuel.

13FL denotes flight level, i.e., the (indicated) flight altitude in feet divided by 100 [8].

4.1 Design and validation of long range reference aircraft 137

The impact of systems offtakes (as displayed in Fig. 4.7), which implicitly increase enginespecific fuel consumption (SFC), is already included in the plotted fuel curve.

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d) t

hrus

t T, k

N

fuel

con

sum

ed, 1

000

kg

distance covered, NM

thrust FN block fuel

(a) Altitude profile, lift coefficient,thrust, and consumed fuel as a func-tion of covered distance

110

120

130

140

300 310 320 330 340 350 360 370 380altitude (flight level) h, 100 ft

260

280

300

320

340

360

380

tota

l airc

raft

mas

s m

a/c,

t

70

80

90

100

110

120

130

140

150

SAR, mkg

(b) Specific air range contours and progres-sion of altitude and mass during cruise

0.00.20.40.60.81.0

0.0 0.1 0.2 0.3

Mac

h nu

mbe

r M

2.0 4.0 6.0distance covered, 1000 NM

M TAS

CAS

7.9 8.0 8.1 8.20100200300400500

airs

peed

, kt

(c) Mach number and velocity profiles

Figure 4.8: Mission simulation results for 8150 NM SPP design mission

Figure 4.8b shows the SAR contours forMcr = 0.85 as function of total aircraft mass andflight altitude. The black step contour represents the progression of mass and altitudeduring cruise, corresponding to the cruise altitude step profile in Fig. 4.8a. It is evidentthat the step contour approximates well the connection between all local SAR maxima,which would exactly be reached in the limiting case of continuous cruise climb. Machnumber as well as true (TAS) and calibrated airspeed (CAS) are plotted over the entiremission in Fig. 4.8c. A zoom is again applied to climb and descent phases to highlight thespeed schedules, i.e., 300 kt above, and 250 kt below 10000 ft, respectively. Note that theSAR-optimized cruise profile leads to a top-of-climb altitude lower than the cross-overaltitude, which requires stronger acceleration at the transition from climb to cruise phase.The initial cruise altitude capability, however, is always checked independently of the(SAR-)optimal cruise altitude profile on the sizing mission (see TLAR discussion below).

After overall design convergence, the MICADO reference aircraft is assessed on the4000 NM SPP study mission; simulation results are summarized in table C.6 and dis-played in Fig. 4.9. Here, the SAR maximization results in a cruise altitude profile withonly one step climb, where the step increment is specified to ∆h = 2000 ft. The ini-tial cruise altitude is significantly higher than on the design mission due to lower take-offweight. Further, note that the second flight level (FL 370) is maintained until top of de-scent (TOD) in favor of minimum overall fuel burn, because the additional fuel to climbto FL 390 would overbalance the benefits from better SAR at this higher altitude.

138 Chapter 4. Application of developed method to HLFC overall aircraft design

0

100

200

300

400

0 1000 2000 3000 4000 0

20

40

60

80

altit

ude

h, 1

00 ft

fuel

, 100

0 kg

; 100

⋅ C

L

distance covered, NM

opt. CL range: CL,opt ± 0.03

altitudeCL

fuel consumed

Figure 4.9: Altitude, CL, and block fuel pro-files for 4000 NM study mission

Again, the range of the resulting (saw-tooth) CL profile during cruise correspondswell with the optimum L/D interval high-lighted in Fig. 4.5b. Hence, it can be con-cluded that independently of range andmission specifications, optimization withrespect to SAR automatically implies fa-vorable CL cruise profiles, which is of sig-nificant importance for an equitable assess-ment of different aircraft designs.

The block fuel—i.e., the sum of trip fueland taxi fuel (see Eq. (3.14))—computedon the 4000 NM study mission amounts to BFsm = 63.3 t. This value will be used asreference to quantify relative fuel savings in all subsequent aircraft design studies.

Performance assessment and requirement checks

For the converged MICADO reference design, a detailed evaluation is conducted, includingperformance assessment and compliance checks with TLARs (see Sec. 3.2.7).

In Fig. 4.10, take-off and landing performance characteristics are shown, where requiredtake-off (TOFL) and landing field lengths (LFL) are plotted as function of operationaltake-off or landing weight as well as airport altitude.

1000

2000

3000

4000

5000

200 250 300 350 400

take

-off

field

leng

th, m

operational take-off weight, 1000 kg

max

imum

tak

e-of

f wei

ght

required TOFL valuecomputed TOFL value

altitude, ft0 ft

2000 ft4000 ft6000 ft8000 ft

10000 ft

(a) Take-off field length as function oftake-off weight and airport altitude(ISA+15 conditions)

1400

1600

1800

2000

2200

200 220 240 260 280 300

land

ing

field

leng

th, m

operational landing weight, 1000 kg

max

imum

land

ing

wei

ght

required LFL valuecomputed LFL value

altitude, ft0 ft

2000 ft4000 ft6000 ft8000 ft

10000 ft

(b) Landing field length as function oflanding weight and airport altitude(ISA conditions, dry runway)

Figure 4.10: Take-off and landing performance characteristics

The TOFL curves in Fig. 4.10a are computed at ISA+15 atmosphere conditions accordingto the TOFL requirement (see table C.1). The plot does not indicate a tire speed limit,which is, however, not expected to be restrictive for take-off distance at sea level. It

4.1 Design and validation of long range reference aircraft 139

can be observed that the requirement (at MTOW and sea level) can only be fulfilledvery closely. An improvement could, for example, be achieved by reduced high-lift dragor increased take-off thrust. The predicted landing characteristics (ISA conditions, dryrunway) in Fig. 4.10b show that the LFL value (at MLW and sea level) stays well belowthe required landing distance limit.

All TLAR parameters listed in table C.1 (e.g., approach speed, time to climb, OEI netceiling), are individually computed applying the detailed MICADO performance modelwith the belonging boundary conditions. For the reference design, all top-level require-ments are proven to be fulfilled; a comparison of computed values with required limits isgiven in table C.7. The fulfillment of all TLARs approves a balanced and realistic refer-ence aircraft design, as well as it sets a reasonable basis for the following parameter stud-ies. The automated TLAR check reveals, which parameter changes lead to a violation ofone or more TLARs, and which design adaptations are required to reestablish full TLARcompliance. Also, trades to challenge TLARs in favor of further improving key evalua-tion parameters such as block fuel are possible with this procedure.

0

10

20

30

40

50

60

70

80

0.0 2.0 4.0 6.0 8.0 10.0 12.0

payl

oad

(mas

s) m

PL, 1

000

kg

mission range R, 1000 NM

max. structural payload mPL,max

MTO

W = 405 to

MICADO, FL 340/360/380 MICADO, FL opt., 1000 ft step incr. Airbus ref. values SPP study mission point

Figure 4.11: Comparison of payload-range di-agram with Airbus reference data

Another important performance measure isthe payload-range diagram. It may herealso serve to validate block fuel predictionof the MICADO mission simulation pro-gram at different combinations of payloadand range against Airbus reference val-ues. To thoroughly compute the payload-range diagram, the mission simulation pro-gram is used in its inverted mode, that is,for a given payload, the range at whichgiven limits are reached (e.g., MTOW orfull tanks in terms of MFW ) is itera-tively determined. Since the specific cruisealtitudes underlying Airbus reference val-ues are not explicitly known, two differentprocedures are chosen for cruise altitudeselection: one uses a fixed altitude pro-file with three equidistant cruise phases atFL 340/360/380 (solid black line), and the other applies SAR-optimized cruise altitudeswith ∆h = 1000 ft as discussed above (dashed gray line). For the reference aircraft, theresulting payload-range diagrams of both procedures are presented in Fig. 4.11, where avery good agreement with Airbus reference values can be observed. While the maximum-payload boundary (mPL,max) is used as specified, the payload-range combinations formPL,max and MTOW (see upper right kink) virtually coincide, i.e., the selected fixed-altitude profile is nearly optimal on short mission ranges. A simplified approach based onthe Breguet range equation has also been applied for comparison, which could not achievethis desired accuracy. Due to the different simulated intermediate points, the (more re-alistic) nonlinear curve shape is revealed, where concavity increases with improved cruiseprocedures, so that the benefit of altitude optimization over the fixed-mission approachincreases with longer ranges. It is finally important to note that even at ferry range

140 Chapter 4. Application of developed method to HLFC overall aircraft design

(mPL = 0 kg), the fuel tank limit is not yet reached, thus no second kink appears in thediagram. The study mission point is marked for completeness and due to its significancein the following parameter studies and design evaluations.

4.2 Design sensitivities and HLFC integration potential

In the previous section, a consistent and satisfactorily validated design of the long rangereference aircraft has been presented. This section presents design studies conductedaround the reference configuration to serve two main purposes: First, the potential ofHLFC technology integration is analyzed by quantifying the change in block fuel forappropriate variations of drag, mass, and power offtakes. Second, the design sensitivitiesare approved by comparison with available reference data [114], which is an importantprerequisite for the reliability of further overall aircraft design studies presented in Sec. 4.3.

Approaches to assess impact of design changes on aircraft level

If the impact of a design change or parameter variation on aircraft efficiency (e.g., interms of block fuel) is to be quantified, different approaches can be applied, which areimportant to be explicitly distinguished for a clear interpretation of results. First ofall, recall that block fuel (BF ) or COC analysis for the assessment of design changes isconducted on the SPP study mission, here with a range of 4000 NM; this holds for allsubsequent design studies. Further, the term design change generally refers to any changeor parameter variation applied to the reference aircraft. This may be either a variationof a specific design parameter (such as wing sweep angle), a variation of a TLAR (suchas cruise Mach number), or the integration of a new technology such as HLFC, with allits design implications. The specific procedure for integration and assessment of HLFCtechnology within MICADO was discussed in Sec. 3.1.3.

The simplest assessment approach is a pure off-design analysis, that is, the design change isapplied to the converged reference aircraft and its primary effect is analyzed on the studymission. However, no MICADO iteration is applied to account for reciprocal design effects.This approach is useful to separate and quantify unaffected design impacts, e.g., the pureimpact of a (generic) drag reduction on fuel consumption without mass snowball effect.

For a meaningful overall aircraft assessment of design changes, however, (re-)convergenceof all MICADO programs within the sizing loop is required before BFsm is predicted (seeFig. 3.4). As discussed in Sec. 3.1.4, design interactions during convergence include masssnowball effect and resizing of main aircraft components. To quantify and separate thebelonging influences, two different design approaches (D1 and D2 ) are defined, which willbe referred to throughout all following design studies. Their principle and implementa-tion regarding block fuel assessment within MICADO are sketched and summarized inFig. 4.12. Recall that the depicted MICADO analysis programs also include specific siz-ing routines, e.g., structural wing sizing for maneuver loads inside the mass estimationmodule (Sec. 3.2.4). Thus, interaction between mission analysis and structural compo-

4.2 Design sensitivities and HLFC integration potential 141

nent masses (due to changes in MTOW ) is already captured in design approach D1.However, the MTOW snowball effect—and thus impact of design changes on the over-all aircraft—is much stronger in D2 due to component resizing (mainly wing and propul-sion system). This further implies changes in engine, power distribution, and—most no-tably—aerodynamic characteristics, which can slightly counteract the mass growth. Thedistinction between D1 and D2 also serves the purpose of comparison and validation, sinceall Airbus reference values are based on design approach D1 (see next paragraph).

while no convergence

Mission analysis(design mission)

Mission analysis(study mission)

(D1)

MT

OW

snow

bal

là

ret

rofit

des

ign

(D2)

full c

ompon

ent

resi

zing

Ref. design

Design change

BFsmBFsm,ref

MICADO sizing programscomponents, systems, propulsion

MICADO analysis programsaerodynamics, masses

assessment ofdesign change

(D1) Retrofit design (blue):Snowball effect due to MTOW vari-ation is captured by adaptationsof systems and component masses.MICADO programs for main compo-nent sizing are excluded from itera-tion loop, i.e., outer geometries andpropulsion system remain unchanged(Sref = const, SLST = const).

(D2) Component resizing (green):MTOW variation implies full resizingof aircraft components, where key pa-rameters Sref and SLST are adaptedwith respect to constant wing loadingW/S and thrust-to-weight ratio T/W .

Figure 4.12: Retrofit and resizing approach for design change evaluation in MICADO

In the context of HLFC technology integration, application of D1 means to apply theHLFC system to the aircraft as add-on solution, which is also denoted as retrofit design.Only approach D2, however, allows for full exploitation of HLFC fuel saving potential,because continuous resizing of all aircraft components for the actual design point allowslocating global optima, while maintaining compliance with TLARs.

For quantitative assessment in the following studies, results of block fuel—or of any otherarbitrary design parameter X—will be specified by its absolute value x, or as relative orpercentage change with respect to the reference value xref . For the relative or percentagechange, the following short notation

∆refX := ∆xxref

= x− xrefxref

(4.1)

is introduced, which will be used either dimensionless or in %. The difference of twopercentages will be indicated in percentage point (pp).

142 Chapter 4. Application of developed method to HLFC overall aircraft design

Analysis and validation of design sensitivities for HLFC integration

Before the developed HLFC overall aircraft design method is applied in Sec. 4.3—in-cluding the enhanced methods for HLFC aerodynamics (Sec. 3.3) and system design(Sec. 3.4)—this paragraph provides generic sensitivities to roughly explore and quantifythe HLFC fuel saving potential. The primary implications of HLFC technology integra-tion, i.e., viscous drag reduction due to laminar flow as well as increased mass and shaftpower offtakes due to the integrated HLFC system, are therefore generically applied tothe turbulent reference aircraft. The influences on the 4000 NM study mission block fuelBFsm and on other relevant design parameters are explored with MICADO, using thedifferent assessment approaches discussed in the preceding paragraph. The results of theconducted sensitivity studies are compiled in Fig. 4.13.

-25

-20

-15

-10

-5

0

5

10

-35-30-25-20-15-10-5 0

∆ ref (

BF

sm

); ∆ r

ef (

CD);

−∆re

f (

L/D

), %

drag reduction ∆CD, drag counts

roughly estimated drag saving potentialdue to (50% chord) laminar flow onwing and tails (upper and lower side) {

wing (upper side) + HTP + VTPwingwing + HTPwing + HTP + VTP

∆ref (CD): w.r.t. CD @ CL,ref −∆ref (L/D) @ CL,ref = const ∆ref (BFsm): primary effect ∆ref (BFsm): D1: MTOW snowb. ∆ref (BFsm): D2: comp. resizing

Airbusref. value:∆ref (BFsm) @∆ref (CD) = 1% (D1)-4

-2

0

-6-4-2 0

(a) Influence of drag count reduction onL/D and block fuel BFsm

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 500 1000 1500 2000 2500 3000

0 0.2 0.4 0.6 0.8 1 1.2 1.4

∆ ref

(B

Fsm

), %

mass increase ∆m, kg

∆ref (OWE), % (not resized)

expected range of totalHLFC system mass (wing+tails)

primary effect (4000 NM ) D1: MTOW snowball AI ref. value @ ∆m=1t (D1) D2: full component resizing

(b) Influence of mass increase on OWEand block fuel BFsm

0.0

0.5

1.0

1.5

2.0

2.5

3.0∆ r

ef (

BF

sm),

%

primary effect, cruise primary effect, whole mission D1: MTOW snowball, cruise AI ref. value @ ∆ref (SFC) = 1% (D1) D2: full component resizing, cruise

-0.5

0.0

0.5

1.0

1.5

0 50 100 150 200 250 300 350 400 450 500 550 600

∆ ref

(S

FC

bkt),

%

additional (electr.) shaft power offtake ∆ Pshaft, kW

* computed at cruise design conditions: M 0.85, FL 350, ISA, 90%N1

expected range of total HLFC system power offtakes (wing+tails)

MICADO engine model GasTurb * Airbus ref. value

(c) Influence of additional shaft power off-takes on SFC and block fuel BFsm

-4

-2

0

2

4

-8 -6 -4 -2 0 2 4 6 8

∆ ref

(O

WE

), %

∆ref (MTOW), %

MICADO D1: MTOW snowball Airbus ref. values (D1)

(d) Reciprocal influence of MTOW varia-tion on OWE (snowball effect), D1

Figure 4.13: Generic analysis and validation of HLFC integration impact on block fuel

The expected purely aerodynamic benefit due to laminar flow is depicted in the upperleft figure 4.13a. It presents results of a generic drag reduction sensitivity study, where∆CD has been constantly added to the overall aircraft drag polars, and one drag count

4.2 Design sensitivities and HLFC integration potential 143

(dc) equals 0.0001 CD. The vertical green lines roughly represent the idealized14 savingpotential if 50 % chord laminar flow is achieved on both upper and lower sides of wingand tails. The corresponding values of ∆CD are approximately estimated based on thesemiempirical viscous drag prediction method discussed in Sec. 3.2.3, using different fric-tion coefficients for laminar and turbulent flow. The predicted drag saving for laminariza-tion of wing and tails (∆ref (CD) ≈ −15 %) corresponds well to values indicated in litera-ture15: for example, reductions of 14 – 15 % in total drag are stated in Refs. [128, 141, 233]for laminarization of wing, tails, and nacelles, where the latter contribute only small ad-ditional benefit. For the wing, this thesis primarily focuses on applying HLFC only tothe upper side due to the Krueger flap integration against contamination (see Sec. 2.3.2).Assuming that laminarization of the upper side contributes to roughly 2/3 of total wingviscous drag reduction [281], the drag savings for laminar flow on upper wing and tailscan approximately be estimated to ∆CD ≈ −25 dc and ∆ref (CD) ≈ −12 % (see verticaldashed line in Fig. 4.13a). At CL = const, the corresponding relative change |∆ref (L/D)|shows increasingly greater values due to the asymptotic behavior. The relative block fuelchange ∆ref (BFsm) has nearly the same slope than ∆ref (CD) if only the primary effectis considered. Taking into account mass snowball effect (D1), or even full component re-sizing (D2), block fuel savings increase significantly, e.g., by ∼ 3 pp at ∆CD = −25 dcin case of D2. The small zoom figure shows that the MICADO D1 curve proceeds wellthrough the Airbus reference point of ∆ref (BFsm) for ∆ref (CD) = 1 %.

The mass snowball effect, which is incorporated in the D1 and D2 curves, is quantifiedmore explicitly in the bottom right figure 4.13d. It shows the reciprocal influence ofa generic percentage change of MTOW on ∆ref (OWE) for the iterative MICADO D1approach. Predominant contributors are the structural components that are resized withrespect to changed flight and ground loads due to changedMTOW . This mainly concernswing and landing gear, and, less significantly, tailplanes and flight control systems. Thethree available Airbus reference points are quite well approached by the MICADO curve.Sref and SLST are here kept constant according to D1; MTOW snowball effect would befurther amplified if outer component geometries and propulsion system are resized (D2).

Returning to the specific integration impact of HLFC, Fig. 4.13b shows the percentageblock fuel change ∆ref (BFsm) as a function of a generic absolute mass increase ∆m, whichis here intended to represent the total mass of all HLFC system components. For the con-sidered long range aircraft, the expected total HLFC system mass roughly lies in the inter-val between 0.5 and 1.5t (cf. Ref. [199]). The average value of ∆m = 1000kg correspondsto a percentage change in OWE of ∼ 0.5 %, and results in a block fuel increase between0.3 and 0.7 %, depending on the evaluation approach. The reference point lies slightlyabove the MICADO D1 curve; here, note that a clear separation and indication of themass snowball effect (see Figs. 4.13b and 4.13d) can still contain ambiguities concerningthe specific design procedure (see Fig. 4.12). Generally, a mass variation can also resultfrom geometrical or structural changes of aircraft components. The integration of HLFCmay, e.g., require adaptations of wing sweep or airfoil thickness, where only moderatechanges can imply a mass increase higher than the total HLFC system mass, see Sec. 4.3.

14The study does not consider 3D flow conditions at root or tip, or the occurrence of turbulent wedges.15Note that for equal (L/D)opt, the relative drag saving ∆ref (CD) can still vary in dependence on CL,opt.

144 Chapter 4. Application of developed method to HLFC overall aircraft design

Figure 4.13c summarizes the influence of additional electrical shaft power offtakes ∆Pshaft(as required by the HLFC system) on engine SFCbkt (see Fig. 4.3b) and BFsm. In thelower diagram, the values of ∆ref (SFCbkt) from the MICADO engine model are comparedwith those from the original GasTurb model at selected evaluation points16, confirmingthe validity of the offtake correlation within MICADO (see Sec. 3.2.2). Results of similarquality have also been obtained in studies conducted for analyzing the influence of bleedair, which are, however, not discussed within this context. The two Airbus (AI) referencevalues also confirm the SFC sensitivity towards ∆Pshaft, and further, the impact of∆ref (SFC) = 1 % on BFsm in the upper diagram. Here, the curves for the primaryeffect on BFsm show a similar slope than the SFC curve, and only a small difference isdetected between virtually activating the HLFC system during the entire mission, or onlyduring cruise. Though the influence is again strongly amplified in case of D1 and D2,∆ref (BFsm) stays below 1 % at an average expected value of ∆Pshaft = 250 kW.

To summarize, the fuel saving potential by viscous drag reduction due to laminar flowis much more significant than the fuel increasing effects of additional mass and energyconsumption of the HLFC system. For HLFC on upper wing and tails, a net benefit in∆ref (BFsm) of more than 10 % can thus still be expected combining the effects presentedin Fig. 4.13. Certainly, these rough and idealized assumptions will be worked out preciselyin Sec. 4.3. In the presented sensitivity studies, the different effects have been separateddeliberately to focus on the reciprocal sizing effects within design approaches D1 andD2. Here, it could be observed that the curves for D1 and D2 significantly deviatefrom the primary effect curves, with slightly nonlinear trends; a quantitative estimationof these effects is only enabled by the integrated MICADO sizing procedure. If thedesign changes are considered simultaneously, however, additional reciprocal influences arecaptured during iteration. The incorporation of the enhanced HLFC methods (Secs. 3.3and 3.4) into the HLFC overall aircraft design studies presented in the next section furtherallows elaborating on more detailed aspects, e.g., HLFC aerodynamic airfoil design andimpact on wing mass, realistic shaping of transition line on the wing, feasibility of HLFCsystem design, and reserve fuel estimation for laminar flow degradation during cruise.

4.3 HLFC aircraft design and optimization

In the previous sections of this chapter, the foundation for subsequent HLFC aircraft de-signs has been laid in terms of a consistent turbulent baseline aircraft design and sensi-tivity studies to indicate the HLFC integration potential. This section returns to specif-ically answer the central questions of this thesis raised in the introductory chapter 1.These questions can be reformulated as two design tasks with different level of difficulty,which can both be solved by the presented MICADO-HLFC methodology. The first taskcomprises HLFC integration and assessment for a given aircraft configuration; it will bepresented in Sec. 4.3.1 for the baseline configuration as well as further two design points.The second, more difficult task addresses the question which overall aircraft configurationis most beneficial for the integration of HLFC. As thoroughly discussed throughout this

16The constant value of 90%N1 used in the GasTurb evaluation does not necessarily correspond to thebucket point, which, however, has involved only small discrepancies.

4.3 HLFC aircraft design and optimization 145

thesis, the high difficulty of this task results from the combined requirements to quicklyinvestigate different parameter combinations on overall aircraft level, and to simultane-ously perform new HLFC aerodynamic wing design and HLFC system sizing for everynew aircraft design parameter combination. Solution and results of this task using theproposed methodology are presented in Secs. 4.3.2 and 4.3.3, including HLFC overall air-craft design and optimizations.

4.3.1 HLFC aircraft design: single point evaluation

The turbulent baseline aircraft discussed in Sec. 4.1 has been designed using the developed“conventional” MICADO methods presented in Sec. 3.2, including the Q3D enhanced draganalysis (Sec. 3.3) for turbulent airfoils. For HLFC aircraft design and assessment, the de-tailed HLFC-specific methods presented in Secs. 3.3 and 3.4 are now applied additionally.

Table 4.5: Selected HLF design points [247]

HLFD-0 HLFD-1 HLFD-2Mcr 0.85 0.80 0.80ϕLE,OB 34◦ 34◦ 28◦

To elaborate on the incorporated level ofdetail, selected single design points mayfirst be investigated, before full OAD pa-rameter variations and optimizations willbe performed in Secs. 4.3.2 and 4.3.3. Thefirst hybrid laminar flow design (HLFD)point is apparently given by the baselineconfiguration and therefore referred to asHLFD-0. Two further design points are derived by a variation of the parameters cruiseMach number Mcr and (outboard) leading-edge sweep angle ϕLE,OB, both being keydrivers for realizing HLFC on the wing. The parameter combinations for the HLF designpoints 0, 1, and 2 are summarized in table 4.517. The integrated MICADO-HLFC siz-ing methodology is applied to the three design points, where both the retrofit design ap-proach (D1) as well as the component resizing approach (D2) are applied, as opposed inFig. 4.12. Before focusing on overall aircraft design evaluation, results of the HLFC aero-dynamic wing design and system sizing methods are discussed and compared below.

HLFC aerodynamic wing design

Important results of the HLFC aerodynamic wing design approach (Sec. 3.3) are illus-trated in Fig. 4.14. The upper diagram of Fig. 4.14a shows the wing planform geometry ofHLFD-1 after D1 convergence (i.e., not resized and thus equivalent with the baseline), aswell as the HLFD-2 planform with reduced sweep angle on the outboard wing. For a clearinterpretation of further results, recall the proposed integrated wing and airfoil design pro-cedure (Sec. 3.3.8), after which HLFC airfoils are selected from the database according tolocal values of M2D,des and Cl,2D,des. These are derived from Mcr and the spanwise distri-bution of lift coefficients at CL,des (see Eq. (2.25)) via local sweep angle transformation;the location of HLFC airfoil design sections inside the wing planform are indicated in the

17For comparability, the specific values of the HLFD points are chosen corresponding to those investigatedwithin the LuFo project HIGHER-LE [226, 247].

146 Chapter 4. Application of developed method to HLFC overall aircraft design

upper diagram. For design section 1, a validation of this implicit airfoil design procedureis presented in Fig. 4.14c, where the dashed black contours show the airfoil geometriesinterpolated from the database for Mcr and a constant value of CL,des = 0.51. The differ-ent thickness ratios t/c mirror the design influence of Mach number and sweep angle: forHLFD-1, the reduction ofMcr to 0.80 leads to an increased t/c; for HLFD-2, this is in turnpartly compensated due to the reduced sweep angle. The obtained shapes are comparedto airfoils manually designed by Rodax [234] at DLR for the same design conditions (bluecontours). For HLFD-0, the almost identical contours can virtually be regarded as self-evident, since the database creation process has been initiated from this baseline point (seeSec. 3.3.8). Yet, the very good agreement of HLFC airfoil designs for HLFD-1 and -2 is im-posing, especially because neither geometry nor Cp distribution of the given airfoils havebeen used as input to the database. Though the small local contour deviations can still im-ply differences in Cp distributions, this figure demonstrates both quality and consistencyof the presented approach, especially within the intended preliminary design context.

30

35

40

45

50

55

60 0 10 20 30 40

x, m

y, m

root

HLFC airfoildesign section 1

HLFC airfoildesign section 2

HLFD−1: laminar area HLFD−1: front spar HLFD−1: wing planform HLFD−2: wing planform

0.2

0.4

0.6

0.8

0.10

0.12

0.14

0.16

Cl (

y)

t/c

(y)

t/c

Cl

HLFD−0 HLFD−1 HLFD−2(twist distributions optimized)

0

40

80

120

0.00 0.25 0.50 0.75 1.000.00

0.04

0.08

0.12

Cd (

y), d

rag

coun

ts

Cd·

c (y

), m

η=y/(2b)

Cd,visc

Cd,visc,corr

Cd,visc,corr·c

Cd,wave

Cd,wave·c

(all HLFD−1)

(a) Top diagram: wing planform geome-tries and predicted laminar area; mid-dle and bottom diagram: spanwise dis-tribution of thickness ratio t/c and liftand drag coefficients at CL,des

200

300

400

500

600

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Re−

AL

η=y/(2b)

Re−

AL,crit = 250 (without suction)

[ with CQ = 2 CQ,ref ]

AL is contaminated (turbulent)above Re

−AL,crit limit lines

HLFD−0 (Cl var.) HLFD−1 (Cl var.) HLFD−2 (Cl var.)

Re−

AL,crit (HLFD−0)

Re−

AL,crit (HLFD−1) Re−

AL,crit (HLFD−2) Re−

AL,crit (HLFD−0)

(b) Evaluation of attachment-line transi-tion including suction (see Eq. (2.22))at Mcr and 0 < Cl < 0.9

-0.050.000.05

z/c

MICADO HLFC DB DLR design

HLFD-0t/c = 0.103

-0.050.000.05

z/c

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(c) Comparison of HLFC database airfoilgeometries (CL,des = 0.51 = const, de-sign section 1) with DLR airfoils [234]

Figure 4.14: HLFC aerodynamic wing design results for design points in table 4.5

The spanwise t/c distributions for the converged D1 designs (see middle diagram inFig. 4.14a) also show the discussed design trends, while differences compared to Fig. 4.14care due to the variable design CL. Here, it is important to note that the selection of

4.3 HLFC aircraft design and optimization 147

database airfoils strongly influences local drag coefficients, pitching moment, and wingstructural characteristics, and thus the overall aircraft design. In turn, some OAD limita-tions are considered for proper airfoil selection: for example, if a database airfoil designedfor too low Cl implies unfavorable wave drag characteristics for the cruise point of theoverall aircraft drag polar, the design lift coefficient Cl,des is increased. Besides selectedairfoil shapes, wing characteristics are strongly influenced by the spanwise distribution oflocal Cl. In this example, the twist distributions are optimized for all three designs withrespect to minimum block fuel BFsm. This yields a balanced Cl distribution and thus agood compromise between aerodynamically and structurally favorable characteristics, in-dependent of varying planform geometries (e.g., reduced sweep angle for HLFD-2). In ad-dition to higher wing mass, the adverse case of excessive outboard loading can also implypoor stall behavior or high wave drag on the outer wing.

For HLFD-1, the bottom diagram of Fig. 4.14a shows the viscous and wave drag charac-teristics in terms of spanwise distributions of Cd and Cd c. Due to the balanced Cl dis-tribution, the wave drag is kept on an acceptable level over the whole span. Cd,visc andCd,visc,corr (dashed dark and light gray curves) represent the viscous drag coefficients di-rectly obtained from the database, and those corrected with local Reynolds number (seeEqs. (3.34) and (3.35)), respectively. The spanwise distribution of Cd,visc is strongly con-nected to the predicted extent of laminar flow on the wing, as depicted by the gray area inthe upper diagram. Generally, the achievable laminar flow area can be even higher; how-ever, note that the presented designs already include the important compromise betweenreduced viscous drag and acceptable wave drag characteristics. The shape of the transi-tion line further includes the assumption that HLFC cannot be obtained in close vicinityto the wing-fuselage junction, due to very high Reynolds numbers and since local flow ishighly governed by 3D effects (the latter are also expected to cause full turbulent flow inthe wing tip region). Transition at the wing root section is therefore assumed to occur di-rectly at the leading edge; the constantly increasing transition location on the inner wingreflects the cross-interpolation between the turbulent root airfoil18 and the HLFC airfoilcharacteristics at the kink section. The slight nonlinear shape of the transition line showscorrect capturing of the dependency of (x/c)trans on local Cl via the database approach(see Cl distribution in middle diagram and the airfoil polar example in Fig. 3.21c).

As explained in Sec. 3.3.8, the HLFC database airfoils have been designed with individu-ally adapted suction distributions, primarily to suppress both TSI and CFI. Another sig-nificant aspect for the realization of HLFC on swept wings is to avoid leading-edge contam-ination (LEC), and thus transition at the attachment line (see Sec. 2.2.5). For the threeHLF designs, ALT is evaluated using the K-criterion (2.22), which includes the effect ofsuction. At the respective cruise Mach numbers Mcr, a Cl variation is conducted at twospanwise stations (η = 0.4 and η = 0.85). The computed attachment-line Reynolds num-bers ReAL (see Sec. 3.3.5) are represented by the black, gray, and blue evaluation pointsin Fig. 4.14b, with higher values of ReAL at η = 0.4, as expected. According to Eq. (2.22),the critical limit ReAL,crit = 250 is raised to 250 − 150 K if suction is considered. Thesuction parameter K = Cq

sinϕeff ReAL is also computed at both spanwise stations, yieldingthe—linearly connected—ReAL,crit limits, above which the attachment line is expected to

18As discussed in Sec. 4.1, turbulent root airfoil aerodynamics are retained for the HLFC aircraft designs.

148 Chapter 4. Application of developed method to HLFC overall aircraft design

be contaminated (i.e., turbulent). At η = 0.85, the attachment line is thus laminar forall considered points as they reside below the respective limits. Yet, at η = 0.4, LEC islikely to occur for HLFD-0 and HLFD-1, mainly due to high sweep angles and the largerleading-edge radius for HLFD-1; the sweep reduction for HLFD-2 allows to shift all pointsbelow ReAL,crit (except for one outlier). Note that the applied criterion holds for an ini-tially turbulent attachment line; if it is initially laminar or relaminarized by a suitable de-vice on the inboard wing (e.g., a Gaster bump), the ReAL,crit limits will be further raised(see Sec. 2.2.5), so that ALT should usually be avoidable during flight [219]. Hence, fromthe preliminary design perspective, the presented level of detail is considered as fully suf-ficient. If a design still shows ALT-critical conditions, the proposed method quickly re-veals adequate design measures, as exemplified by the dotted black curve in Fig. 4.14b,where an increased suction strength (Cq = 2 Cq,ref ) raises ReAL,crit, so that all HLFD-0points become noncritical. Generally, a well-balanced suction compromise has to considerboth aerodynamics (as much suction as necessary to suppress CFI and ALT), as well asHLFC system sizing (as little as possible to keep power requirements low). In addition tothe provided aerodynamic sensitivities, the cost of increasing suction in terms of HLFCsystem mass and power consumption will be quantified in the following paragraph.

HLFC system design

According to the methodology described in Sec. 3.4, the HLFC system is sized to establishrequired suction on wing and tails. The layout of the resulting systems architecture isschematically illustrated for the baseline configuration (HLFD-0) in Fig. 4.1519. For thewing, a decentralized layout is chosen with three compressors per wing side, which is seenas reasonable number concerning mass and power requirements on the one hand, andsystems reliability and redundancy aspects on the other hand (cf. Ref. [199]). HLFCon the horizontal and vertical tailplane is established by respectively one compressor.Compressors and outflow valves are connected via a collective ducting system. Further,electric wiring from the electronic and equipment (E/E) bay to wing and tails to drivethe compressors is considered. Resulting total electric power requirements (Phlfc,tot) andmasses for the HLFC system components (see Eq. (3.41)) are summarized in table 4.6.

In the upper part of the table, results for HLFD points 0, 1, and 2 are compared with ref-erence data given by Pe [199] for the same configurations (see small italic numbers). Theresults agree well both in trend and in absolute values, where the relative errors, whichmostly lie below 10 %, can virtually be neglected within the OAD context. For better com-parability, Cq distributions of the DLR reference airfoils [234] have been used. Using theautomated HLFC airfoil database interpolation (“db-ip”) method leads to higher power re-quirements, because suction has not specifically been attenuated for tip airfoils during thedatabase creation process, see Sec. 3.3.8. The effect of this conservative assumption, how-ever, is again very small within the OAD context. It can generally be observed that duct-ing massmduc is a key contributor, amounting to more than half ofmhlfc,tot, while the mass

19Note that symbol dimensions are not to scale, and wing compressor chordwise positions are only approxi-mately, as they are certainly integrated in the leading-edge box ahead of the front spar in practice. Rout-ing of wires and ducts are not drawn for production purpose, but rather from an automated preliminarysizing perspective to measure overall lengths, which scale with varying aircraft dimensions.

4.3 HLFC aircraft design and optimization 149

for electric cable wiring mel is small with a share less than 5 % of mhlfc,tot. The differencesin power consumption Phlfc,tot and thus compressor mass20 mcmp between HLFD-0, -1, and-2 are mainly due to different Cq requirements. These sensitivities will be discussed below.

compressoroutflow valve

ductingwiringE/E bay

front spar

Figure 4.15: Schematic layout ofHLFC systems architec-ture for retrofitted base-line design (HLFD-0)

Table 4.6: Comparison of HLFC sys-tem design results

Ptot mtot mcmp mduc mel

kW kg kg kg kgHLFD results (compared with Ref. [199])0 248 733 255 455 23(db-ip) 278 760 272 462 26

215 703 233 458 281 323 807 299 479 29

249 822 251 531 402 223 713 240 452 21

231 801 295 484 22HLFD-0: architectural layout study

central 296 589 223 346 20indiv. 252 955 257 675 23no tails 192 544 185 344 15

The lower part of table 4.6 shows results of a short architectural layout study conducted forHLFD-0 with the MICADO HLFC system design tool. A central architecture (“central”),i.e., with only one big compressor per wing side, yields stronger power requirements, butreduced mass, mainly due to shorter ducts. An individual (opposed to a collective) ductingsystem significantly increases ducting mass (see “indiv.” in second row). The variationsunderline the above mentioned compromise decision for the herein used reference layout.The last line shows the results if HLFC is only applied to the wing (“no tails”). Moredetailed HLFC system design specific questions and layout variations are not consideredwithin this context, but, e.g., further investigated by Pe and Thielecke [199, 200].

In Fig. 4.16, sensitivity study results of the HLFC system sizing method with respect toflight conditions and suction distribution are shown, which are relevant for HLFC systemintegration trade-offs on aircraft level. Figures 4.16a and 4.16b show relative and absolutechanges of total HLFC system power Phlfc,tot and mass mhlfc,tot for variations in designcruise Mach number and altitude around the reference valuesMcr = 0.85 and h = 33000ft,with suction and pressure distributions assumed to be constant. Power requirementsincrease with increasing M and decreasing h, which is mainly triggered by the suctionmass flow rate through the surface mw, which is in turn proportional to freestream velocityU∞, surface wall density ρw, and Cq (see Eq. (3.39)). The underlying equations of theMICADO atmosphere model are mirrored by the slight bending of the curves in Fig. 4.16babove the ISA tropopause at 11 km ≈ FL 360. The relative impact of M and h on totalmass mhlfc,tot is much lower, because changed power requirements mainly size masses ofcompressors (and belonging components), while wiring and especially ducting keep nearly

20The compressor mass also includes belonging masses of motor and variable-frequency drive (see Sec. 3.4).

150 Chapter 4. Application of developed method to HLFC overall aircraft design

unaffected by changes in design cruise conditions. The high relative changes are againstrongly attenuated within the OAD context, which becomes evident when regarding theblock fuel sensitivities towards masses and power requirements in Fig. 4.13c. The highpower requirements at low altitudes, however, underline to select the initial cruise altitudeas design altitude (see Sec. 3.4) to ensure power reserves at higher cruise altitudes.

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(d) Selected Cq (x/c) distributions—withbelonging Cp (x/c)—to demonstratevariation in Fig. 4.16c

Figure 4.16: HLFC system mass and power requirements as function of design Machnumber M , altitude h, and suction distribution Cq (x/c)

Figure 4.16c shows, how (too) strong suction requirements can significantly increase powerrequirements. The second (upper) x axis shows the belonging maximum suction coeffi-cients Cq,max at the wing kink section, with Cq,max,ref = −0.0008; suction distributionvariation and its relatively small influence on Cp is exemplified in Fig. 4.16d. As discussedabove, the suction strength has to be carefully balanced between aerodynamic needs tosuppress CFI and ALT, and limiting system integration and feasibility aspects, e.g., interms of compressor size and space allocation. From the preliminary design perspective,Figs. 4.16 and 4.14 provide the relevant information for this decision, which has, however,to be specifically investigated within the detailed design and integration process.

4.3 HLFC aircraft design and optimization 151

Overall aircraft design evaluation

Having discussed the HLFC specific aerodynamic and systems design aspects, the 3 HLFCdesign points 0, 1, and 2 (see table 4.5) are now investigated in the overall aircraft con-text. The aircraft designs are conducted using the integrated MICADO-HLFC sizingprocedure (see Fig. 3.5). Since the iterative design process including all reciprocal influ-ences complicates clear separation of design influences, a step-wise design investigation isperformed. The results for the three HLF design points are shown by means of the de-sign evolution in Fig. 4.17a; the relevant design influences on the x axis are “measured”in terms of the corresponding relative change in study mission block fuel ∆ref (BFsm)with respect to the turbulent baseline design. The separated design influences left of thedashed vertical line are evaluated with respect to their primary effect, that is, the designchanges are successively applied to the aircraft design, and the resulting block fuel BFsmis respectively computed, without sizing iteration (see Sec. 4.2).

First, HLFC is applied to the upper wing by the automated database interpolation ap-proach and the integration of transformed HLFC airfoil polars into total aircraft drag po-lars. A trim iteration by adjusting ihtp is performed to ensure consistent comparison be-tween different designs. The highest fuel savings are obtained for HLFD-1, mainly dueto the reduced Mach number, which allows less wave drag-critical HLFC airfoil designs.Further, HLFC is applied to the HTP (upper and lower side) and the VTP. Due to thesmaller impact of HTP and VTP airfoils on OAD as well as less complex HLFC airfoil de-sign requirements compared to the wing, no specific HLFC airfoil design or database ac-cess is performed for the tails. Instead, drag savings due to laminar flow on the tails areestimated based on the semiempirical viscous drag equation (3.3), with separated frictiondrag prediction for turbulent and laminar flow, and assuming a constant transition posi-tion of (x/c)trans = 0.4 over the whole span (outside the fuselage). Pure aerodynamic ben-efit due to HLFC thus yields a primary effect of ∆ref (BFsm) ≈ −8 to −9 %. Next, influ-ence of changed airfoil geometries, sweep angle, and load distribution on wing structuralmass is analyzed. Here, an optimization of wing twist angles at kink and tip is performedto guarantee a well-balanced loading between favorable aerodynamic and structural char-acteristics, and thus a fair design comparison. The negative impact on BFsm for HLFD-0is mainly due to the mass increase implied by the thinner HLFC airfoils21. Though theairfoils selected for HLFD-1 are thicker due to the reduced Mach number, they imply un-favorable spanwise loadings and trim characteristics, which can only partly be compen-sated by the twist optimization, resulting in a net wing mass increase. The mass andblock fuel reduction for HLFD-2 is mainly triggered by the reduced wing sweep angle.

As argued above, for all HLFC aircraft designs a Krueger flap is applied to the wing,both as leading-edge high-lift device and as shielding device against contamination (seeSec. 2.3.3). Based on the semiempirical prediction methods implemented in MICADO,the replacement of the conventional droop nose (inboard) and slat (outboard) system by afull-span Krueger solution leads to a slight overall wing mass decrease, but also to slight de-crease in maximum lift coefficient CL,max. The latter leads to an increase of Vapp by approx-imately 1 kt, which still complies with TLARs. It is remarked that especially the Krueger

21Sensitivity of wing mass towards airfoil thickness agreed well with available Airbus reference data [247].

152 Chapter 4. Application of developed method to HLFC overall aircraft design

mass prediction contains high uncertainty, since it strongly depends on the Krueger kine-matics concept and belonging systems complexity and integration issues [236]. For ex-ample, an upward shift of the Krueger flap in favor of insect shielding—but away fromthe aerodynamic optimum—may imply significant installation effort, and thus increasein high-lift system mass. However, though mass prediction based on detailed kinematicsis beyond the scope of this thesis, it is presumed that the very small OAD impact (seeFig. 4.17a) can be maintained by a sophisticated and well-balanced Krueger design.

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Figure 4.17: Overall aircraft design evaluation of HLFD points in table 4.5, includingreserve fuel estimation and resizing for in-flight loss of laminarity

The HLFC system integration in terms of additional mass and power offtakes results inan increase of ∆ref (BFsm) by roughly 1 pp, which underlines the small OAD impact dis-cussed in the context of Fig. 4.13. Right of the vertical dashed line, the integrated and it-erative MICADO sizing procedure is applied to analyze the potentials of both retrofit de-sign (D1) as well as component resizing including all reciprocal influences (D2). Note thesignificant resizing potential between 1 and 2pp, where the amount depends on the under-lying changes in OWE andMTOW . Next, a twist optimization is performed again—nowfor the full OAD loop—which takes around 2.5 h on a standard desktop PC if parallelizedon 8 cores (see Sec. 3.1.1). Though twist has already been “pre-optimized” before, a smallblock fuel reduction can still be achieved. This shows that a “local” optimization (onlyon wing level) often yields suboptimal results, compared to an overall aircraft optimiza-tion based on an integrated sizing approach. The best net reduction in block fuel can beachieved for HLFD-2 and amounts to about 11 %. However, for a fair evaluation, notethat some improvements included in this number could also be achieved by a turbulentdesign for the same conditions; for HLFD-2, these are mainly the lower wing mass due toreduced sweep angle, and the slightly improved wave drag characteristics. Design studiescomparing both turbulent and HLFC aircraft will be presented in Secs. 4.3.2 and 4.3.3.

Fig. 4.17a finally shows how a conservative fuel planning with regard to a sudden completeloss of laminarity during cruise affects the overall design. The implemented fuel planningprocedure (Sec. 3.2.6) switches between laminar and full turbulent drag polars at a certainfraction of mission range R. Two scenarios are analyzed, one with a loss of laminarity at0.5 R (i.e., halfway between origin and destination airport), and the other assuming loss

4.3 HLFC aircraft design and optimization 153

of laminarity over the whole sizing mission. According to the additional fuel reserves andthe respective range fractions, the scenarios are called AFR-50 and AFR-100. Certainly,the AFR-50 is more realistic than the rather pessimistic AFR-100 scenario consideringpossible operational mitigation procedures (e.g., rerouting or reclearance); also, in-flightfailures of the HLFC system could be handled by a redundant systems concept. Theassessment on the study mission is conducted without loss of laminarity, which leads toblock fuel penalties of roughly 1 and 2pp for the AFR-50 and -100 scenarios, respectively.

In Fig. 4.17, the relative percentage changes of key design parameters are compared forHLFD-0 (D1 and D2) and HLFD-2 (D2 and AFR-50). It can be observed how propulsionsystem (in terms of SLST ) and geometry (Sref and b) are kept constant for the retrofitdesign (D1), and rescaled with MTOW and constant W/S and T/W for D2. The L/Dbenefit is slightly reduced for HLFD-0 D2 (compared to D1) due to the resized smaller wingarea. While HLFD-0 (D1) shows an increase in wing mass mw and OWE (due to thinnerairfoils and the integrated HLFC system), a net reduction is obtained for the D2 design,which shows the strong reciprocal impact of reduced MTOW on component masses. Theresizing potential (i.e., the difference between D1 and D2) generally increases with higherMTOW reduction. It is further important to note that relative changes in block fuel arealways higher on longer distances, which underlines the significance of a clear indicationof the used evaluation mission. For HLFD-2 (AFR-50), fuel saving is strongly reduced onthe sizing mission leading to increasedMTOW , while the penalty on the study mission iscomparatively small. Finally, a net COC reduction of ∼ 5 % with respect to the baselinedesign is achieved for both HLFD-0 and HLFD-2, where the improved fuel efficiency forHLFD-2 is compensated by the reduced Mach number. A possible increase in maintenancecosts due to the integrated HLFC system is herein not considered.

A more detailed insight into the differences between and interactions within the differentdesigns is given by Fig. 4.18, showing selected overall aircraft aerodynamics as well as mis-sion simulation results. Figure 4.18a compares the computed overall aircraft L/D curvesand wave drag characteristics for HLFD-0 and -2 (both D2) with those of the turbulentbaseline (Turb. BL) design, where all curves are shown for the respective cruise MachnumberMcr. The L/D benefit for HLFD-0 compared to the turbulent baseline can clearlybe observed, while the thinner airfoils allow more favorable wave drag characteristics, withCD,wave ≈ 3.9 %CD,total. For HLFD-2, only a slight further increase of (L/D)opt by approx-imately 3 % is achieved, but at higher CL,opt due to the reduction ofMcr from 0.85 to 0.80.At CL,opt, a reasonable amount of wave drag is obtained again (CD,wave/CD,total ≈ 3.2 %).This proves reliable trading of the governing parameters Mcr, sweep angle, and airfoilthickness, where the latter is implicitly designed by the HLFC airfoil database access.

To evaluate overall aircraft aerodynamic performance, the characteristics at off-designMach numbers are further significant, with the parameter M (L/D)opt as key measure.In Fig. 4.18b, the resulting values of (L/D)opt and M (L/D)opt for HLFD-2 (D2) areplotted versusM and compared with the turbulent baseline characteristics. The turbulentbaseline design reaches its optimum value of M (L/D)opt at Mcr,ref = 0.85 (as desired).The maximum value for HLFD-2 is reached at slightly lower Mach numbers than its designcruise point Mcr = 0.80, however, with only a slight relative difference in M (L/D)opt of

154 Chapter 4. Application of developed method to HLFC overall aircraft design

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Figure 4.18: HLFC overall aircraft aerodynamics and mission simulation results

roughly 1 %. This figure demonstrates that also the off-design characteristics are neatlycaptured by the implicit airfoil and wing design based on the integrated database concept.

Fig. 4.18c shows mission simulation results for selected designs on the 8150 NM sizingmission. In the upper diagram, the optimized altitude profiles and the resulting sawtoothCL profiles are shown, which stay well within a narrow band around the optimum cruise CLcorresponding to Fig. 4.18a. Generally, higher CL,opt, higher Mcr, or lower aircraft weightlead to flying at higher altitudes by means of SAR optimization. The weight effect isslightly observable for HLFD-0; for HLFD-2, the increased CL,opt value is compensated bythe reduced cruise Mach number, which results in similar cruise altitudes. Independentlyof the optimum top-of-climb altitude computed for the design mission, the required hICAcapability (see TLAR table 4.1) is separately checked and could be fulfilled for all designs.Further, observe that at the end of the cruise phase, no additional climb step is performedif the extra fuel required for the climb segment makes it unfavorable (see Sec. 3.2.6).

In the middle diagram, fuel and thrust curves are shown, where the nonlinear gradientsand thrust peaks for the step climbs with ROC = 300ft/min reveal the underlying detailedflight performance model. Observe that the gradient of the green fuel curve (HLFD-2AFR-50) increases as soon as the mission simulation module switches from laminar to

4.3 HLFC aircraft design and optimization 155

turbulent drag polars at the mid-range point (0.5Rdes) of full laminarity loss22. Also, thethrust curve exhibits an immediate jump due to increased drag. Note that these detailedsimulation results are only obtainable since all HLFC airfoil drag polars are calculatedboth with predicted transition location as well as for full turbulent flow (see Sec. 3.3.6).

The total shaft power offtakes (of all systems) are plotted in the lower diagram. TheHLFC system is switched on and stays active during the whole cruise phase23, whichleads to the significant increase in Pshaft. The lower HLFC system power requirementsfor HLFD-2 are mainly due to the reduced Mach number (see table 4.6).

4.3.2 HLFC overall aircraft design studies

Conduction and discussion of HLFC aircraft designs at selected sizing points conveyedinsight into level of detail, specific influences, and complex design interactions underlyingthe integrated MICADO-HLFC sizing procedure. In this section, overall HLFC aircraftdesign studies are investigated. This constitutes an outstanding feature of the presentedintegrated sizing methodology, and would not be realizable without it. It allows solvingthe central task raised in the introductory chapter 1, that is, to directly find HLFC optimalaircraft designs, without optimizing turbulent aircraft and successively retro-fitting themwith HLFC. Selected key design parameters and HLFC drivers will be varied first, tostudy their fuel reduction potential and their OAD influence including compliance withtop-level requirements. Finally, integrated HLFC wing and OAD optimizations will beconducted to fully exploit the HLFC saving potential on aircraft level.

As key sizing parameter, the wing loading W/S is varied in a first set of parameterstudies. W/S variations are performed for the turbulent baseline design, as well as forthe HLFD-0 and -2 configurations presented above, while applying design mode D2 (i.e.,W/S is constant in each MICADO design iteration, see Fig. 4.12). Results are presentedin Fig. 4.19a, where the study mission block fuel BFsm is plotted againstW/S, and whereevery point represents a fully converged aircraft design. This is illustrated by the two topviews that show CAD geometries resulting from MICADO turbulent design iteration atW/S = 600 and 800 kg/m2, where the latter clearly exhibits smaller wing and tail areas.All curves reflect common OAD trends, that is, designs are limited towards low wingloadings due to increased component areas and thus higher MTOW , and towards highW/S due to constraints at high-speed (high cruise CL) and low-speed (violation of TOFL,LDL, and/or Vapp requirement). Optimization of W/S thus requires finding designswith minimum fuel or cost, but still fulfilling all requirements (see initial sizing chart inFig. 4.1). This is the case for the turbulent baseline design (green curve), where bothTOFL and Vapp requirements are violated (diamond symbols) just right of the reference(Ref.) point.

22The loss of laminarity is here (conservatively) assumed to be provoked by outer disturbances (e.g., cloudsor insects), and not by a system failure, so that the HLFC system power requirements are maintained.

23The switch-on and -off points do not exactly coincide with the TOC and TOD points, since the MICADOsystems module (Sec. 3.2.5) divides the mission into longer segments for the assignment of offtakes values.This discrepancy has, however, negligible impact on consumed fuel.

156 Chapter 4. Application of developed method to HLFC overall aircraft design

The black curve represents the HLFD-0 aircraft, where the TOFL and Vapp requirementsare already violated at lower W/S due to worse low-speed (off-design) aerodynamics aswell as the integrated Krueger flap. Two main drivers to “re-fulfill” these requirementsare an increased take-off thrust (besides reduced low-speed drag), and a higher maxi-mum lift coefficient CL,max, respectively. Assuming the Krueger flap to be already at itsmaximum lift capability limits, CL,max can still slightly be increased by a chord exten-sion of the trailing-edge flap system. For example, an increase in T/W by 3 % and inrelative flap chord by ∆ (x/c)flap = 0.025 allows shifting the valid design region up toW/S > 720kg/m2, which, however, implies a block fuel penalty of roughly 1.2 % (see darkand light gray curves). A more efficient high-lift system can also be achieved on wingswith reduced sweep angles, which is given for HLFD-2 (blue curve). Without increasedthrust or flap extension, TLAR violation here occurs at values already higher than the ref-erence wing loading, above which no significant block fuel reduction can be expected any-way. Too high wing loadings (in combination with reduced MTOW , and thus small wingarea) are limited by the fuel tank capacity, as indicated at the bottom right of Fig. 4.19a.

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fuel tanklimit

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(a) Influence of W/S variation on BFsmand TLAR compliance; trade-off withT/W and flap chord (x/c)flap

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Figure 4.19: HLFC aircraft designs for variations in wing loading and wing span

Figure 4.19b shows the results of variations in wing span at constant wing reference areaSref , which effectively corresponds to the nonlinear scaling of the aspect ratio Λ on theupper x axis. In the upper diagram, the study mission block fuel BFsm is plotted, andsymbols for requirement violation equal those in Fig. 4.19a. The block fuel sensitivity ap-pears less strong than for W/S, because L/D improvement with increasing wing span bis compensated by higher structural wing mass (due to increased root bending moment);the respective curves for OWE and L/D are plotted in the lower diagram for HLFD-0.However, no twist re-optimization is performed, which can lead to suboptimal designs interms of block fuel or a violation of TLARs. A combined optimization will be presentedbelow. Still, it can already be observed that at higher spans, the adverse effect for the tur-bulent design is stronger than for the laminar designs, so that HLFD-0 and -2 reach their

4.3 HLFC aircraft design and optimization 157

block fuel minima at higher spans. This is reasonable, since the reduced friction drag ofthe laminar aircraft designs makes it worthwhile to reduce induced drag as well (e.g., bya span increase) to maintain a balanced drag share in the region of (L/D)opt [39]. Due toreduced MTOW and constant Sref , favorable laminar designs reside at increased spansand slightly reduced wing loading W/S, which is finally limited by insufficient climb ca-pability. A larger wing area (or reduced wing loading) can generally be beneficial for lam-inar designs, as the additional increase in friction drag is smaller compared to turbulentdesigns [39]. Fig. 4.19b also indicates that the saving potential of higher wing spans canbe further exploited in combination with reduced sweep angles (see blue HLFD-2 curve).Note that airport limitations by maximum wing spans of 80 m are relaxed within thisstudy, which can be mitigated by a resizing of wing area for reduced MTOW . These im-portant considerations to find optimum wing planforms for maximum HLFC benefit andunder certain constraints will be revisited in the optimization studies below.

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Figure 4.20: HLFC aircraft designs for variations in Mach number and wing sweep

Fig. 4.20a shows the results of a conducted Mach number variation at constant wingsweep, as already discussed in more detail for HLFD-0 and -1. For the turbulent design,no automated airfoil shape adaptation (e.g., thicker airfoils at reduced Mach number) isperformed, so that the optimum lies slightly below the reference cruise Mach number.Due to the automated HLFC airfoil design selection from the database, the optimum forHLFD-2 can be shifted to lower Mach numbers. The influence of reduced design Machnumber on increasing airfoil thickness is depicted in the lower diagram for the design sec-tion close to the wing kink (see Fig. 4.14a). Likewise, the optimum lift coefficient CL,optincreases with decreasing Mach number due to more favorable drag rise characteristics(see Fig. 4.18a). The average cruise lift coefficient CL,avg increases in close agreement withCL,opt, which again underlines the important interaction between (laminar) aerodynamicsand mission simulation. The sharp decrease of CL,avg at Mach numbers below 0.74 is dueto a detected buffet (or maximum-lift-coefficient) limit, at which the aircraft is forced toleave its climb schedule and to enter cruise at lower altitudes (thus decreased lift coeffi-cients). An adaptation of the climb-speed schedule to the reduced cruise Mach numberwould compensate this problem. However, note that too low Mach numbers are unfavor-

158 Chapter 4. Application of developed method to HLFC overall aircraft design

able for the desired long range aircraft. Also, they can be subject to uncertainty in thiscontext if they exceed the limits of the HLFC airfoil database (see table 3.9); here, no ex-trapolation is allowed, which leads to constant airfoil thickness for Mcr . 0.73.

The combined influence of Mach number Mcr and wing sweep angle variation ϕLE,OB onblock fuel is shown in Fig. 4.20b for a matrix of HLFC aircraft designs using the D2 pro-cedure. The inboard sweep angle is herein not varied to concentrate on the HLFC air-foil impact, and to minimize the above discussed uncertainties concerning drag predic-tion on the (partly turbulent) inboard wing. The HLFD-0 block fuel curve in Fig. 4.20athus effectively represents a slice through the surface in Fig. 4.20b at constant sweep an-gle. Slightly unsmooth trends in the surface or the contour lines are due to interpolationof HLFC airfoils and its characteristics from the database (see Sec. 3.3.8). Generally, aMach number reduction is beneficial, as it allows more favorable HLFC airfoil designs interms of wave drag characteristics and instability mechanisms (due to reduced Reynoldsnumber). For every Mach number, a certain sweep angle optimum can be identified, witha trend towards smaller ϕLE,OB (compared to the reference) due to improved cross-flowcharacteristics and reduced wing mass. However, optimum locations might still be shifted,if further parameters (e.g., twist angles) are additionally varied. For the turbulent air-craft, Fig. C.2b shows results of a similar design study for the turbulent aircraft, includ-ing inboard wing sweep, but without adaptation of airfoil thickness or shape at each de-sign point, which shifts the overall optimum to higher Mach numbers.

4.3.3 HLFC overall aircraft design optimization

The presented HLFC aircraft design studies revealed the influence and fuel saving poten-tial of different design parameters, as well as differences compared to turbulent designs.It is important to perform these studies to quantify and separate different design impacts.Since specific constraints are mostly included in single parameter variations (e.g., varia-tion of W/S at constant aspect ratio, or variation of wing span at constant Sref ), it isnow investigated how a combination of indicated favorable design changes (e.g., increasedspan, or reduced sweep angle and Mach number) can further increase HLFC benefits onaircraft level. This task of finding the global optimum for given TLARs is highly complex,because it requires the evaluation of a large number of parameter combinations, whichcan only be solved by an integrated and automated approach. Also, for every evaluationpoint, the discussed reciprocal influences (e.g., mass snowball effect, component resizing)and cross-influences between the disciplines (e.g., aerodynamics and structures) have tobe considered, which is ensured by the proposed MICADO-HLFC design approach.

Besides allowing to exploit the full HLFC potential on aircraft level, the overall design opti-mization also demonstrates full capabilities of the integrated MICADO-HLFC frameworkby using the parameter study manager introduced in Sec. 3.1.1. For optimization, the in-tegrated NOMAD algorithm is used, as already shown for the wing twist optimization inSec. 4.3.1. The free design variables should be able to cover the improvements indicatedin the preceding design studies, while not being dependent on each other. The selected9 design variables are listed in table 4.7, containing the design cruise Mach number Mcr

and several wing geometry parameters. The wing planform is parameterized by ϕLE,OB,

4.3 HLFC aircraft design and optimization 159

the spanwise segment widths inboard and outboard of the kink (sIB, sOB), and the threechord lengths at root, kink, and tip (croot, ckink, ctip). Here, sIB includes the wing segmentvirtually lying inside the fuselage, and sOB excludes the tip segment, which is scaled ac-cording to the actual value of its inner chord ctip (see reference planform in Fig. 4.14a).Wing loading or wing area are not added as free variables, because Sref is implicitly de-fined by the combination of spans and chords, and W/S follows based on the convergedvalue of MTOW 24. Further, twist angles at kink and tip (εkink, εtip) are varied to ensurea well-balanced compromise between favorable aerodynamics and low wing weight.

Table 4.7: Design variables for HLFC overall aircraft optimization

Mcr ϕLE,OB sIB sOB croot ckink ctip εkink εtip

Table 4.8: HLFC overall aircraft de-sign optimization results

Par. Unit Ref. Turb. HLFC

opt. objective → BF BF COC

BFsm t 63.3 61.7 55.4 55.7COCsm

$ASK 3.32 3.29 3.11 3.07

Mcr − 0.85 0.81 0.80 0.836ϕLE,OB

◦ 33.8 30.0 25.8 28.0b m 80.0 78.5 83.1 83.1Λ − 11.3 11.5 12.7 13.0Sref m2 565 537 546 529W/S − 717 734 695 705MTOW t 405 394 380 373OWE t 212 205 208 201

Figure 4.21: Fuel-optimized aircraftgeometries (gray: tur-bulent; blue: HLFC)

To constrain the overall design space for the optimizer, lower and upper boundaries arespecified for each design variable, which are summarized in table C.8. The lower bound-ary of 0.80 for Mcr is set to obtain more realistic designs in terms of long range opera-tions. Further, to ensure a feasible landing gear integration into the wing, the inboardtrailing-edge sweep angle is constrained to −0.5◦ < ϕTE,OB < 2◦. This boundary con-dition is passed to the optimizer dependent on the inboard wing segment geometry andchecked “a priori” of each evaluation (see Fig. 3.3a), which significantly accelerates the op-timization process. The overall computation time of the full HLFC aircraft optimizationtakes ∼ 11 h if parallelized on 8 cores, with roughly 1000 OAD evaluation points (includ-ing parameter combinations that violate TLARs or boundary conditions). Optimizationsare also conducted for the turbulent aircraft to allow fair evaluation and comparison ofresults. Here, the local thickness-to-chord ratios at kink and tip are additionally definedas free variables, since no turbulent database airfoil design is used, and the semiempiri-cal drag prediction methods described in Sec. 3.2.3 are applied, which have initially beencalibrated to the aerodynamic characteristics of the baseline aircraft (see Fig. 4.5). TheOAD optimizations are further conducted for different objectives (i.e., block fuel BFsm

24Also, additional variation of T/W and (x/c)flap has not been required within the optimum design region.

160 Chapter 4. Application of developed method to HLFC overall aircraft design

and cash operating costs COCsm for the study mission). The optimization results (in-cluding optimum values of all design variables) are presented in table C.8.

Let us here focus on the selected key design parameters summarized in table 4.8, whichcompares reference values (see Sec. 4.1) with optimization results of the turbulent aircraft(for BFsm) and of the HLFC aircraft (for BFsm and COCsm). The turbulent optimumis found at reduced Mach number, but similar wing planform parameters, offering addi-tional savings of ∆ref (BFsm) ≈ −2.5 % and ∆ref (COCsm) ≈ −1 %. The HLFC aircraftoptimized for minimum BFsm confirms the designs trends discussed in Sec. 4.3.2, exhibit-ing an optimum combination of increased span (and aspect ratio), reduced Mach numberand sweep angle, and reduced W/S. This results in a block fuel benefit of ∼ 12.5 % and10%, compared to the turbulent reference and optimum design, respectively. Fig. 4.21shows the difference in optimum wing planforms between HLFC (blue) and turbulent(gray) designs. The optimization towards minimum COC sacrifices some of the fuel sav-ing by higher values of Mcr, ϕLE, and W/S for being more efficient in terms of long rangeoperations, and offers a reduction potential in COC of ∼ 7 %.

Recall that every HLFC design comprises all discussed details of the proposed method(e.g., transition characteristics, HLFC system layout). The optimization thus finds thebest compromise between favorable laminar flow characteristics and low wave drag, aero-dynamics and structural wing characteristics, and low-speed and high-speed performance(via compliance with TLARs). Also, if further (stricter) boundary conditions arise duringthe more detailed design (e.g., local chord constraints), they can easily be included for re-optimizing wing planform and the overall aircraft design. Concerning the wing span limitof bmax = 80 m (see table C.1), the sum of sIB and sOB interestingly stays below 40 m forboth optimized HLFC aircraft designs; thus, airport capability could be maintained by aslight resizing of the wing or the use of a folding wing tip. The highest uncertainty for thepresented designs lies in the high aspect ratio HLFC wing, which would have to be fur-ther investigated with respect to structural deformations during cruise (also concerningthe stiffness of the HLFC panels). The predicted COC benefit will also be further reducedif maintenance costs for the HLFC system are additionally considered. Other operationalaspects (e.g., disturbance of laminar flow causing turbulent-flow wedges) have partly beencovered by the conservative assumption of transition on the inboard wing (see Fig. 4.14a,and by the fuel planning procedure for in-flight loss of laminarity (see Sec. 4.3.1). Theimpact of different conservative fuel planning procedures (including resizing) has beenquantified in Sec. 4.3.1, and can additionally be included for the aircraft optimization.

It is concluded that the HLFC saving potential could be further exploited by the integratedOAD optimization. However, the additional savings compared to the HLFD-1 to -2designs in Sec. 4.3.1 are moderate, since these configurations already showed favorabledesign parameters and wing planforms. It could thus be demonstrated how the proposedmethod rapidly reveals optimum designs for maximum HLFC benefit on aircraft levelfor given TLARs and objectives, which has been formulated as central task in Chap. 1.Though the predicted fuel and cost saving potentials are expected to be lowered duringthe detailed design process, they are still significant enough to make HLFC a promisingtechnology for the application to the wings of upcoming commercial aircraft programs.

5 Conclusions and outlook

The objective of this thesis was the development and application of a preliminary over-all design method for aircraft with hybrid laminar flow control on wings and tails. In

the introductory chapter 1, this objective was derived from the problem statement thatmethods for conceptual aircraft design on the one hand, and detailed HLFC aerodynamicand system design methods on the other hand, only exist decoupled from each other, po-tentially leading to inconsistent and unreliable results. The underlying crux is that anyvariation of key conceptual design parameters (e.g., cruise Mach number, wing sweep an-gle) inherently implies reconsideration of complex tasks, such as transition and laminardrag prediction on swept tapered wings, or suction system layout and integration, succes-sively followed by an integrated assessment on aircraft level. The manifest need to closethis gap between conceptual overall aircraft design and detailed hybrid laminar flow inves-tigations has been answered by the proposed HLFC aircraft design method and software.

HLFC integration and assessment on aircraft level requires from the overall designerprofound understanding of laminar flow physics and of critical challenges in HLFC design,integration, and operations. Underlying theory and fundamental aspects were elaboratedin Chap. 2, including comprehensive supplementing literature for further reading.

The proposed HLFC overall aircraft design method was presented and discussed in detailin Chap. 3. A key challenge in its development has been to provide both width in all rele-vant disciplines, as well as depth by means of interconnecting detailed methods for HLFCaerodynamic and system design. As solid ground to solve this both multidisciplinary and“multi-fidelity” task, an integrated aircraft design framework called MICADO has beendeveloped (Sec. 3.1). It is based on a flexible software architecture, including full param-eterization in XML files, object-orientation using C++ class structures, and modularityby means of loosely coupled programs. This allows generically setting up individual pro-gram sequences, parameter studies, and optimizations, including parallelization for mostefficient exploration of design spaces and identification of overall aircraft optima.

MICADO follows a requirement-driven design approach that allows initiating an auto-mated sizing process by specifying only a minimum set of top-level aircraft requirements.Iterative execution of incorporated sizing and analysis methods according to a certainoverall design logic produces converged and consistent aircraft design data. The imple-mentation of the different MICADO models (Sec. 3.2) followed the introduced principleof proportionality, which ensures balanced level of detail and orients development effort,complexity, and desired accuracy for the implemented prediction methods towards theirrespective impact on overall aircraft design. The capability of a reliable integration ofHLFC design methods could be ensured by the following MICADO key elements:

161

162 Chapter 5. Conclusions and outlook

• parametric geometry modeling with CAD interface for detailed design postprocessing

• prediction of full-configuration aerodynamics, including trim and transonic effects

• comprehensive mass prediction methods, including sophisticated wing beam model

• sizing of full systems architecture, based on source-sink power distribution network

• thermodynamic engine model with secondary power offtakes and operating limits

• detailed mission simulation program, capturing all above disciplines into block fuel

This broad aircraft design basis has been extended and interconnected with the HLFCconceptual aerodynamic wing design method proposed in Sec. 3.3, which constitutes akey achievement of this work. It combines a quasi-3D wing drag prediction method withrapid queries to a SQLite database containing pre-optimized HLFC airfoils. This allowsintegrating computed HLFC airfoil characteristics into full aircraft configuration dragpolars, and thus into overall aircraft considerations including mission simulation.

For efficient and robust prediction of transonic (laminar) drag polars for airfoils within3D tapered wing segments, the Hybrid Laminar Flow Airfoil Suite (HYLFAS) has beendeveloped, containing the Euler/boundary-layer flow solver MSES and the STABTOOLsuite for transition prediction via the eN method. The HYLFAS analysis process appliesappropriate transformations of geometry, pressure distribution, and aerodynamic coeffi-cients between (3D) streamwise and (2Dc) conical wing sections. The automated shockdetection algorithm and the nested iteration of transformation (shock) sweep angle andtransition location, combined with the parallelized computation approach, allows rapidand consistent prediction of large sets of drag polars, including physical breakdown ofdrag coefficients. HYLFAS thus enables quick trades between viscous drag savings andwave drag penalties, as well as it provides survey of dominance regions of either Tollmien–Schlichting or cross-flow instabilities. The above mentioned crux could finally be solvedby semi-inverse design and multi-point optimization of HLFC airfoils at different designpoints, which were consistently stored in the database including wide range of off-designcharacteristics. For every design, additional robustness was achieved by systematic off-design sensitivity studies (e.g., with respect to altitude variations) to reveal critical flightconditions and take appropriate mitigation measures (e.g., individual adaptation of suc-tion intensity and shape). The density of the HLFC airfoil database could be minimized byreasonably applying sweep-taper theory, and by an enhanced sweep interpolation, whichwas demonstrated to minimize deviations in drag polars compared to target design points.

The HLFC overall aircraft design method is rounded off by the integration of the HLFCsystem sizing module presented in Sec. 3.4. According to the ALTTA simplified suctionconcept, it analyses relevant flow stations and sizes all relevant suction system compo-nents for the given parametric aircraft model, flight conditions, as well as sectional pres-sure and suction characteristics from the designed HLFC airfoils. Final outputs are HLFCsystem component masses and locations, as well as required power consumption. TheHLFC system design module becomes even more powerful as being an integral part ofthe MICADO conventional systems design program, and thus being inherently connected

163

to engine modeling and the overall aircraft. Detrimental effects of HLFC system integra-tion—in terms of additional mass and power requirements—on operating empty weight,engine fuel flow, and finally block fuel can thus properly be quantified. Further, systemsinterdependencies are captured, such as increasing total generator mass in case of highermaximum power offtakes.

The MICADO design of the turbulent baseline aircraft in Sec. 4.1 demonstrated overalldesign consistency, as well as granularity and validity of underlying models by good agree-ment with Airbus reference values. Outstanding features were highlighted, for example,the automated specific air range optimization of cruise altitude profiles, which ensuresproper capturing of optimum lift-to-drag ratio regions at transonic cruise conditions, andthus equitable evaluation of different (laminar and turbulent) aircraft designs.

The high level of detail obtained by the integration of laminar drag and transition predic-tion capabilities into preliminary aircraft design was revealed by HLFC aircraft designsat different design conditions. Variation in key HLFC drivers Mach number and sweepangle were mirrored in airfoil contour and thickness, spanwise lift and drag characteris-tics, location of transition polyline, as well as compliance with attachment-line transitioncriteria. Likewise, the sensitivities of the HLFC system sizing module against flight con-ditions, suction intensity, and different architectural layouts were demonstrated.

Distinct investigation of different design impacts on study mission block fuel showed thatthe detrimental effects due to the additional HLFC system mass and power offtakes arecomparably small, each ranging between 0.5 and 1 %. As expected, the achieved dragbenefit due to laminarization on wing and tails strongly governs the design, with savingsaround 8 %, excluding wing lower side and the inboard wing. The overall aircraft impactof HLFC airfoil thickness and shape via wing structural mass, spanwise wing loading,and trim characteristics is comparable or even larger than the impact of the completeHLFC system integration, which requires a carefully balanced aero-structural wing design.Further, the influence of overall design iteration including MTOW snowball as well ascomponent resizing effects is significant (∼ 1− 2 %), where the achievable resizing benefitincreases with the obtained reduction in MTOW . A net benefit of more than 10 % inblock fuel (and ∼ 5 % in COC) could be achieved by the converged and resized HLFCaircraft designs. In view of probable certification requirements, additional reserve fuelplanning for sudden loss of laminar flow at the halfway point of the design mission hasbeen considered, including full aircraft resizing. This procedure is expected to reduce theachieved net benefit by ∼ 1 %, which certainly also depends on mission range and relativeMTOW reduction.

The HLFC overall aircraft design studies and optimizations in Sec. 4.3 showed the fullpotential of the presented methodology to investigate:

• local and overall design optima, including optimized HLFC wing design conditions

• influence of design variations on compliance with top-level requirements

• trade-offs between block fuel improvements and violation of requirements

164 Chapter 5. Conclusions and outlook

Through the integrated sizing studies, the saving potential could be further increased to∼ 12 %. Further, important overall design trends for laminar aircraft could be revealed,which were also confirmed by the integrated aircraft optimization. Most efficient andrealistic HLFC aircraft designs were enabled by combinations of smaller Mach numbersand/or reduced wing sweep angles, mainly due to less critical laminar wing design condi-tions in terms of wave drag, cross-flow instabilities, and attachment-line transition. Dueto the reduced friction drag, optimum HLFC aircraft also tend towards larger wing spansand reduced wing loadings compared to turbulent aircraft designs. However, too largevariations can always lead to violation of top-level requirements, or the benefits may becompensated by stronger adverse overall aircraft design penalties, such as an increase inMTOW . Exactly these considerations again underline the significance of the proposedmethod in finding well-balanced HLFC aircraft designs for maximum fuel or cost bene-fits, and in close interaction with detailed design investigations. The integrated softwareframework further helps to clearly accelerate the design process in case of initiating acomplete new HLFC aircraft design for a different set of top-level requirements.

Due to its multidisciplinary and “multi-fidelity” approach, the proposed HLFC aircraftdesign method opens up wide opportunities for additional research. The following aspectsare considered as most important to spend further investigation and research effort on:

• The integration of the 2.5Dc HYLFAS method offers opportunity to be coupled to a3D inverse laminar wing design process, which is likely to produce mutual benefitsin terms of accuracy, low computation time, and physical interpretability.

• Due to the large wetted areas, increased laminarity on the inboard wing wouldpromise significant further drag reduction potential, compared to the (conservative)assumptions used within this thesis. A combined approach including 3D flow com-putations, HLFC airfoil design at high chord Reynolds numbers, and the presentedHLFC overall aircraft design method is recommended to exploit this potential.

• Laminarization of the lower wing side has been sacrificed within this thesis in favor ofrealistic contamination shielding via a Krueger flap. Alternative anti-contaminationdevices (such as liquid solutions) should be investigated to enable a different high-liftconcept (e.g., sealed droop nose or no leading-edge device). Overall aircraft designstudies should be conducted to trade off possible penalties in low-speed performancewith additionally achieved drag benefits due to laminarization of the wing lower side.For the Krueger solution, the impact of suboptimal positioning for shielding couldbe quantified by more sophisticated mass prediction methods including kinematics.

• The presented HLFC aircraft designs—especially those with high wing spans—couldbe further investigated with respect to structural deformations during cruise, whichshould also consider the stiffness of the HLFC panels.

• More detailed monetary assessment studies for different scenarios could be con-ducted for the presented HLFC aircraft designs—including the impact of addi-tional maintenance costs for the HLFC system—to further specify the expected costsavings for in-service operations.

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[2] Abbott, I. H., von Doenhoff, A. E., and Stivers Jr., L. S., “Summary of Airfoil Data,”Tech. Rep. NACA-TR-824, NACA Langley Aeronautical Lab., Langley Field, VA,1945.

[3] Abramson, M. A. and Audet, C., “Convergence of Mesh Adaptive Direct Search toSecond-Order Stationary Points,” SIAM Journal on Optimization, Vol. 17, No. 2,2006, pp. 606–619.

[4] Abramson, M. A., Audet, C., Couture, G., Dennis Jr., J. E., Le Digabel, S., andTribes, C., “The NOMAD project [Software],” Retrieved: June 2013. Available athttp://www.gerad.ca/nomad.

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[8] Airbus, Getting to grips with aircraft performance, Airbus Customer Services,Blagnac, France, 2002.

[9] Allison, E., Kroo, I. M., Sturdza, P., Suzuki, Y., and Martins-Rivas, H., “AircraftConceptual Design with Natural Laminar Flow,” 27th Congress of the InternationalCouncil of the Aeronautical Sciences, ICAS, Nice, France, 2010.

[10] Allison, J., Roth, B., Kokkolaras, M., Kroo, I. M., and Papalambros, P. Y., “AircraftFamily Design Using Decomposition-based Methods,” 11th AIAA/ISSMO Multidis-ciplinary Analysis and Optimization Conference, AIAA, Portsmouth, VA, 2006.

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A MICADO parameters and methods

This appendix provides additional information about MICADO XML parameteriza-tion and implemented mass estimation methods.

Table A.1 lists the different disciplines and XML blocks included in the MICADO AiX file(see Sec. 3.1.1), along with a very short summary of the belonging contents and aircraftdesign parameters. Their definitions as well as detailed discussions about the implementeddesign and analysis methods were given in the sections referenced in the third column.

Table A.1: Block composition and contents of Aircraft Exchange (AiX) XML file

XML block Content (lists not exhaustive) Sec.- requirements TLARs, definition of design and study mission 2.1- specifications configurational, cabin, and cargo specifications 2.1- accommodation passengers and crew; cabin and cargo parameters- geometry component geometries (wing, tails, fuselage, etc.), 3.1.1

moveables, structure elements (e.g., spar positions)- propulsion key engine characteristics, reference to engine maps 3.2.2- aerodynamics key aerodynamic parameters, reference to XML polar file 3.2.3- flight mechanics stability and control characteristics, volume coefficients- masses design masses (e.g., MTOW, OWE), component masses, 3.2.4

center of gravity positions, moments of inertia- systems systems parameters, bleed air and power offtakes 3.2.5- performance performance parameters, mission simulation results, 3.2.6

reference to design and study mission XML files 3.2.7- monetary values operating, recurring, and nonrecurring costs 3.2.7- ecological values emissions, noise, and climate impact parameters

191

192 Chapter A. MICADO parameters and methods

Table A.2 lists the mass breakdown used in MICADO, with numbers and names of massgroups and chapters. The right column contains comments and references for the corre-sponding mass prediction methods implemented in MICADO. Own regressions are basedon data from Ref. [283], as well as additionally available manufacturers’ data.

Table A.2: Overview of mass estimation methods implemented in MICADO

Chap. Mass group/chapter name MICADO methods and sourcesStructure

10 Wing own method, see Ref. [300]11 Fuselage method adopted from Ref. [16]13 Horizontal tail method adopted from Ref. [151]14 Vertical tail method adopted from Ref. [151]15 Landing gear method adopted from Ref. [303]16 Pylons own regression, data from Ref. [283]

Power unit20, 22 Equipped engine and nacelle own regression, data from Ref. [283]21 Bleed air system own method, see Ref. [291]25 Fuel system method adopted from Ref. [213]

Systems30 Auxiliary power unit (APU) own regression, data from Ref. [283]31, 32 Hydraulic generation and distribution method adopted from Ref. [306]33 Air conditioning method adopted from Ref. [283]34 Deicing own regression, data from Ref. [283]35 Fire protection method adopted from Ref. [306]36 Flight controls own regression, data from Ref. [283]37 Instruments method adopted from Ref. [306]38 Auto flight system method adopted from Ref. [306]39 Navigation method adopted from Ref. [306]40 Communication method adopted from Ref. [306]41, 42 Electric generation and distribution method adopted from Ref. [306]

Furnishings methods adopted from Ref. [306]50 Furnishings51 Fixed emergency oxygen52 Lighting53 Water installation

Operator items methods adopted from Ref. [306]60 Operator equipment61 Operational equipment

B Conical-flow equations

This appendix provides mathematical equations intended as complementary informa-tion to the descriptions given in Secs. 3.3.2 and 3.3.5. The derivations, formulations,

and assumptions are basically a summary of the primary sources by Lock [170] and Schrauf[259], from which they differ slightly in terms of the herein used notation and symbols.

Derivation of Lock’s equivalence law

In Sec. 3.3.2, Lock’s equivalence law [170] was treated, which relates 3D and 2D pressuredistributions. It considers the 3D flow withM∞ = M∞,3D over a tapered wing at a certainspanwise station as equivalent to the flow over a 2D airfoil at a reduced freestream Machnumber M∞ cosϕ, by postulating equality of local Mach numbers, i.e., M3D,n (x/c) =M2D (x/c). Here, M3D,n (x/c) denotes the Mach number normal to the local isobars. Theunderlying assumptions also imply identity of the isentropic flow relations between localMach number M and pressure coefficients Cp. Thus, with the isentropic-flow equationsfor total pressure ptot and Cp

ptotp

=(

1 + γ − 12 M2

) γγ−1

=: P1 (M) , (B.1)p

p∞= 1 + Cp

γ

2 M2∞ =: P2 (Cp, M∞) , (B.2)

the equivalence between M3D,n (x/c) and M2D (x/c) can be written as [170]

P1 (M3D,n) = P1 (M2D) = P1 (M∞ cosϕ)P2 (Cp,2D, M∞ cosϕ)

= P1 (M∞ cosϕ)P2 (Cp,3D, M∞)

. (B.3)

The herein proposed method uses the reference sweep angle ϕref to obtain the equiva-lent 2D freestream Mach number M∞,2D (see Eq. (3.21)). Thus, if Eq. (B.3) is addition-ally considered for ϕ = ϕref , unknown variables can be eliminated, and the equivalencelaw (3.27) between Cp,3D and Cp,2D = Cp,2Dc (for the conical section) is obtained as follows:

Cp,3D = f − 1γ2M

2∞

+ f Cp,2Dc cos2 ϕref , (B.4)

with f =[

1 + γ−12 M2

∞ cos2 ϕ

1 + γ−12 M2

∞ cos2 ϕref

] γγ−1

= P1 (M∞ cosϕ)P1 (M∞ cosϕref )

. (B.5)

193

194 Chapter B. Conical-flow equations

Compressible conical boundary-layer equations

The compressible conical boundary-layer equations underlie the module COCO (seeSec. 3.3.5) and are described in detail by Schrauf [259]; the original formulation was givenby Kaups and Cebeci [143]. The equation system is an enhancement of the compressibleboundary-layer equations (2.7)–(2.10) in 2D Cartesian coordinates, by introducing theconical-flow assumption with cylindrical polar coordinates (θ, r, z) as shown in Fig. 3.11.While the z-momentum equation writes equally to Eq. (2.9), continuity, circumferentialand radial momentum, as well as energy equation rewrite as follows [131, 259]:

1r

∂

∂θ(ρuθ) + 1

r

∂

∂r(ρrvr) + ∂

∂z(ρw) = 0 (B.6)

ρ

(uθr

∂uθ∂θ

+ vr∂uθ∂r

+ w∂uθ∂z

+ uθvrr

)=− 1

r

∂p

∂θ+ ∂

∂z

(η∂uθ∂z

)(B.7)

ρ

(uθr

∂vr∂θ

+ vr∂vr∂r

+ w∂vr∂z− u2

θ

r

)=− ∂p

∂r+ ∂

∂z

(µ∂vr∂z

)(B.8)

ρcp

(uθr

∂T

∂θ+ vr

∂T

∂r+ w

∂T

∂z

)= uθ

r

∂p

∂θ+ ∂

∂z

(k (T ) ∂T

∂z

)

+ µ

(∂uθ∂z

)2

+(∂vr∂z

)2 , (B.9)

with the velocity components uθ, vr(= −vr), and w in θ, r, and z direction, respectively.The transformation (Levy) variables ξ and η are chosen as [259]

ξ = ξ (x) =x∫

0

µeρeuedx (B.10)

η = η (x, y z) =√r0

r

ue√2ξ

z∫0

ρdz, (B.11)

with the flow variables ue, µe, and ρe at the boundary-layer edge, and r0 as the radial dis-tance from the cone apex O to the respective conical wing section (see Fig. 3.11). Com-pared to the variables used in the Levy-Lees transformation1, the similarity variable ηadditionally depends on the radius r, so that lines with constant η optimally follow thethickening of the boundary layer [259]. The transformation leads to a convenient repre-sentation of the compressible boundary-layer equations containing only four coefficients:The acceleration coefficient corresponds to the Falkner–Skan equations [250], while a sec-ond coefficient comprises viscosity and compressibility. The conicity coefficient becomeszero for untapered, swept wings, and the suction coefficient contains the normal suctionvelocity at the wall ww. For definitions of these coefficients and the complete formulationof the nonlinear differential equation system, the reader may refer to Schrauf [259].

1The Levy-Lees transformation of the boundary-layer equations is, e.g., described in Ref. [250]. The Levyvariables are also applied by Horton and Stock [131] to the conical compressible boundary-layer equations.

C Supplementary data of MICADOlong range reference aircraft design

This appendix presents tables and figures containing supplementary parameters andcharacteristics for the turbulent reference aircraft design discussed in Sec. 4.1.

Table C.1: Top-level aircraft requirements used for MICADO reference design [114]

TLAR Symbol Unit Required valueDesign range Rdes NM 8150Std. passenger capacity PAX − 470Std. passenger payload (mass) [95 kg per PAX] mSPP kg 44650(Initial) cruise Mach number Mcr − 0.85Maximum operating Mach number MMO − 0.89Maximum operating speed VMO kt (CAS) 340Initial cruise altitude (ICA) capability hICA ft ≥ 33000[after take-off @ MTOW, ISA+10◦C]

Time to climb TTC min ≤ 25[after take-off @ MTOW, ISA+10◦C; from 1500 ft to ICA] (should be ≤ 23)

OEI altitude capability (net ceiling) hOEI,max ft ≥ 13000[after take-off @ MTOW, ISA+10◦C, ROCmin = 300 ft/min] (should be ≥ 14000)

Maximum cruise altitude hmax,op ft 43000Take-off field length TOFL ft < 10700[sea level, ISA+15◦C]

Landing distance limit LDL ft < 6800[@ MLW, sea level, ISA, dry runway]

Approach speed Vapp kt 141–165 (Cat. D)[before landing, full flaps] (should be ≤ 145)

Maximum wing span bmax m 80ACN (flex B) − < 75[landing gear requirement: ACN = aircraft classification number; flex = flexible pavement; B = medium (subgrade)]

195

196 Chapter C. Supplementary data of MICADO long range reference aircraft design

Table C.2: Key aircraft parameters of MICADO reference design (suppl. to table 4.3)

Parameter Symbol Unit ValueDesign range R NM 8150Std. passenger payload (mass) mSPP t 44.65Maximum payload (mass) mPL,max t 71.60Cruise Mach number Mcr 0.85Wing loading W/S kg/m2 717.2Thrust-to-weight ratio T/W − 0.257Maximum take-off weight MTOW t 405.3Maximum landing weight MLW t 300.4Operating weight empty OWE t 212.2Manufacturing weight empty MWE t 187.3Maximum zero fuel weight MZFW t 283.8Maximum fuel weight MFW t 207.9Wing area Sref m2 565.0Wing span b m 80.0Mean aerodynamic chord MAC m 9.18Engine type 2× generic engineSea-level static thrust SLST kN (klbf) 511 (115)

Table C.3: Wing geometry parameters of MICADO reference design (see Fig. 4.4a)

Parameter Symbol Unit ValuesWing area Sref m2 565.1Mean aerodynamic chord MAC m 9.18Wing span b m 80.0Aspect ratio Λ − 11.33Parameters at selected spanwise stations* η = 2y/b: root kink tipRel. spanwise position η − 0.08 0.32 0.94 1.00Abs. spanwise position y m 3.3 12.9 37.5 40.0Leading-edge sweep angle ϕLE

◦ (0.0) 33.8 33.8 50.5Quarter-chord sweep angle ϕ25

◦ (0.0) 26.6 31.5 46.3Trailing-edge sweep angle ϕTE

◦ (0.0) 0.0 23.9 28.4Dihedral angle ν ◦ (0.0) 7.72 5.73 5.73Twist angle ε ◦ 3.3 −0.7 −3.3 −5.3Thickness-to-chord ratio t/c % 14.3 10.7 9.5 9.5* Sweep angles and dihedral at spanwise stations η refer to the respective inner adjacent segment.

197

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9Mach number M

0

2000

4000

6000

8000

10000

12000

altit

ude

h, m

50

100

150

200

250

300

350

400

450

500

550

engi

ne n

et t

hrus

t F

N, k

N

(a) Thrust contours at 100%N1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9Mach number M

0

2000

4000

6000

8000

10000

12000

altit

ude

h, m

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

engi

ne fu

el fl

ow m

f, k

g/s

·

(b) Fuel flow contours at 100%N1

Figure C.1: Characteristics of GasTurb engine model for long range aircraft as func-tion of Mach number and altitude (ISA conditions, without offtakes)

Table C.4: Aerodynamic coefficients of MICADO reference design (see Fig. 4.5)

Parameter Symbol Unit ValueDesign cruise conditionsMach number M − 0.85Altitude h ft 35000Reynolds number (MAC) Rec − 61.3 · 106

Aerodynamic coefficients (trimmed @ design cruise point and opt. L/D)Optimum lift-to-drag ratio L/Dopt − 21.42Lift coefficient CL,opt − 0.472Total drag coefficient CD,total − 0.0220 (= 100.0%)Induced drag coefficient CD,ind − 0.0070 (= 31.9%)Viscous drag coefficient CD,visc − 0.0137 (= 62.3%)Wave drag coefficient CD,wave − 0.0013 (= 5.8%)Maximum lift coefficientsMaximum lift coefficient (take-off) CL,max,T/O − 2.3Maximum lift coefficient (landing) CL,max,LDG − 2.6

198 Chapter C. Supplementary data of MICADO long range reference aircraft design

Table C.5: Mass breakdown of MICADO reference design (suppl. to table 4.4)

Chap. No. Mass group/chapter name Unit ValueOperating weight empty (OWE) kg 212184Manufacturing weight empty (MWE) kg 187282Structure kg 123051

10 Wing kg 5527011 Fuselage kg 4181713 Horizontal tail kg 263214 Vertical tail kg 218915 Landing gear kg 1764216 Pylons kg 3501

Power unit kg 2836020, 22 Equipped engine (incl. engine control) and nacelle kg 2702821 Bleed air system kg 34825 Fuel system kg 984

Systems kg 1605030 Auxiliary power unit (APU) kg 61231, 32 Hydraulic generation and distribution kg 318833 Air conditioning kg 210834 Deicing kg 21235 Fire protection kg 48636 Flight controls kg 227237 Instruments kg 28238 Auto flight system kg 45839 Navigation kg 186640 Communication kg 91641, 42 Electric generation and distribution kg 3650

Furnishings kg 1982150 Furnishings kg 1684451 Fixed emergency oxygen kg 54952 Lighting kg 107553 Water installation kg 1353

Operator items kg 2490260 Operator equipment kg 1437961 Operational equipment kg 10523

199

Table C.6: Mission specifications and simulation results (see Figs. 4.8 and 4.9)

Parameter Comment Unit Design Studymission mission

Mission specificationsRange NM 8150 4000Payload t 44.65 44.65Cruise Mach number − 0.85 0.85Cruise climb steps ft 1000 2000Climb Mach number above crossover altitude − 0.83 0.83CAS above FL100 kt (CAS) 300 300CAS below FL100 kt (CAS) 250 250Taxi-out time min 9 9Taxi-in time min 5 5Alternate distance NM 200 200Fuel planning method EU No. 965/2012Mission simulation resultsTake-off weight see Eq. (3.16) t 405.28 328.16Mission fuel see Eq. (3.14) t 149.29 72.18Block fuel see Eq. (3.14) t 138.04 63.26Trip fuel t 136.73 61.94Reserve fuel see Eq. (3.15) t 11.25 8.92Taxi-out fuel t 0.85 0.85Taxi-in fuel t 0.47 0.47Block time h 17.09 8.67Flight time h 16.86 8.43

Table C.7: Comparison of performance parameters with TLARs from tables 4.1/ C.1

TLAR parameter Symbol Unit Req. value: hard [soft] Comp. valueTime to climb TTC min ≤ 25 [≤ 23] 23.2OEI net ceiling hOEI,max ft ≥ 13000 [≥ 14000] 16700Take-off field length TOFL ft < 10700 10607Landing field length LFL ft < 6800 5682Approach speed Vapp kt Cat. D: 141–165 [≤ 145] 144

200 Chapter C. Supplementary data of MICADO long range reference aircraft design

600 640 680 720 0.240.27

0.300.33

60

65

70

75

BF

sm

, 100

0 kg

BF

sm

, 100

0 kg

60 62 64 66 68 70 72 74

wing loading W/S, kg/m2thrust-to-

weight ratio T/W

V app lim

itation

cruise lim.climb lim. TOFL lim.

ref. point 600 640 680 720 0.240.27

0.300.33

60

65

70

75

BF

sm

, 100

0 kg

BF

sm

, 100

0 kg

60 62 64 66 68 70 72 74

wing loading W/S, kg/m2thrust-to-

weight ratio T/W

V app lim

itation

cruise lim.climb lim. TOFL lim.

ref. point

(a) Variation of W/S and T/W

0.7 0.75

0.8 0.85

2428

3236

4044

60 65 70 75 80

BF

sm

, 100

0 kg

BF

sm

, 100

0 kg

60

65

70

75

80

Mach number Mcr lead

ing edge sw

eep angle ϕ LE,°

drag

rise

ref. point

0.7 0.75

0.8 0.85

2428

3236

4044

60 65 70 75 80

BF

sm

, 100

0 kg

BF

sm

, 100

0 kg

60

65

70

75

80

Mach number Mcr lead

ing edge sw

eep angle ϕ LE,°

drag

rise

ref. point

(b) Variation of Mcr and ϕLE

Figure C.2: Overall aircraft design variations for turbulent baseline design

Table C.8: Results of HLFC aircraft design optimizations (suppl. to table 4.8)

Parameter Unit Lower Upper Ref. Turb. HLFC HLFCbound. bound. value design design design

Optimization objective → BFsm BFsm COCsm

↓ Free design variablesMcr − 0.80 0.88 0.85 0.811 0.800 0.836ϕLE,OB

◦ 15 45 33.8 30.0 25.8 28croot m 8 18 14.3 14.1 13.5 12.6ckink m 4 12 7.9 7.8 7.6 7.6ctip m 1 5 2.3 1.8 2.2 2.7sIB (w. fus. seg.) m 5 20 12.9 12.7 12.0 10.7sOB (w/o tip seg.) m 12 40 24.6 24.6 27.2 27.9εkink

◦ −5 2 −0.7 0.7 −0.7 0.3εtip

◦ −9 2 −3.3 −3.1 −2.9 −6.1↓ Resulting/derived design parametersBFsm t 63.3 61.7 55.4 55.7COCsm $/ASK 3.32 3.29 3.11 3.07b m 80.0 78.5 83.3 83.1Λ − 11.3 11.5 12.7 13.0Sref m2 565 537 546 529W/S − 717 734 695 705MTOW t 405 394 380 373OWE t 212 205 208 201mw t 55.3 51.0 54.2 55.7L/Dopt − 21.4 21.8 25.0 23.9mhlfc,tot kg − − 671 708Phlfc,tot kW − − 213 342