22 Propulsion mechanics - T-Online · 2009-02-23 · 22 Propulsion mechanics "Sollten aber einige an meiner Wahrhaftigkeit zwei-feln, so muß ich sie wegen ihrer Ungläubigkeit herzlich

21.4 Dynamometers 1179

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22 Propulsion mechanics

"Sollten aber einige an meiner Wahrhaftigkeit zwei-feln, so muß ich sie wegen ihrer Ungläubigkeit herzlich bemitleiden, und sie bitten, sich lieber zu entfernen, ehe ich meine Schiffsabenteuer beginne, die zwar fast noch 5

wunderbarer, aber doch ebenso authentisch sind."

Karl Friedrich Hieronymus Freiherr von Münch-

hausen (BürgerGA

, 2000/42).

PROBLEMS

Design and evaluation of bodies propelled in fluids, ship hull-propeller configu-10

rations in particular, are traditionally based on the naïve conception of propulsors

producing thrust to overcome the resistance of the bodies to be propelled. For

more or less advanced hull adapted or even integrated propeller configurations

this conception is neither adequate nor useful, full scale in particular.

MODELS 15

In view of this problem the author has developed a rational theory of propulsion,

essentially axiomatic models adequate for the purposes at hand, consisting of the

'universal' axioms of classical mechanics, the momentum and energy balances

valid for all bodies, and additional axiomatic models 'constituting' bodies pro-

pelled in fluids. 20

GOALS/PLANS

In the present treatise, although not primarily addressed to naval architects,

'maritime' details are providing the necessary background. The goal is to develop

only the essentials, to provide examples of model based axiomatic systems, consti-

tutive models of propelled bodies. In order to avoid an unnecessarily clumsy gen-25

eralised epi-language ship terminology will be used.

No attempt will be made to mention all the references to basic work of the au-

thor including the results of projects demonstrating the feasibility of the methods

proposed. A complete bibliography and all papers since about 1990 are to be

found on the website of the author in the sections 'Propulsion in general' and 30

'Ducted propulsors'.

The philosophical and epistemological considerations, which lead to the solu-

tions discussed, are covered in the first chapters of the present treatise. It is

through twenty-five years of dedicated work on the rational theory on propulsion

that the underlying meta-mechanics has been 'really' understood. 35

1180 22 Propulsion mechanics

22.1 Introduction

" … seine [Galileis] Einstellung ist verhältnismäßig leicht zu identifizieren: natürliche Interpretationen sind notwendig."

Paul Feyerabend: Against method (1998/94). 5

PROBLEMS

Propulsion mechanics is still one of the research fields of the author. Thus in

early drafts of this chapter most of the fundamentals had been tacitly assumed 'to

be known to all' (Newton), had been 'treated' implicitly and in the meta-texts. De-

spite or because of a large number of papers on various aspects of the subject the 10

problem was, and still is, to arrive at an explicit, enlightening exposition for the

non-initiated, and maybe for colleagues.

MODELS

The step by step approach and the technique of embedding will be adopted as

has been done more or less explicitly throughout the whole treatise. 15

GOALS/PLANS

The goal and the plan at this stage are to provide a step by step introduction re-

sulting in a detailed plan of the chapter.

22.1.1 Problems of propulsion

" … was diese Männer für einen Einfluß auf meine Ju-20

gend gehabt, und was es mich gekostet, mich gegen sie zu wehren und mich auf eigene Füße in ein wahres Ver-hältnis zur Natur zu stellen."

Johann Wolfgang Goethe: 03.01.1830 (Ecker-

mann, 1911/282). 25

Design and evaluation of bodies propelled in fluids, ship hull-propeller configurations in particular, are traditionally based on the naïve conception of propulsors producing thrust to overcome the resistance of the bodies to be propelled. A now historical account of all aspects of ship propulsion has been given in the Manual 'The Speed and Power of Ships' by David W. Tay-30

lorDW 1910 (1998).

The methodology of William FroudeW and his son Robert Edmund FroudeRE (Lehmann, 1999/148-150), corresponding to the naïve conception and subject of all basic courses in ship theory and of work in all ship model basins worldwide, is not subject of this treatise. Quite to the contrary an at-35

22.1 Introduction 1181

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tempt is being made to overcome the deficiencies of that approach by ra-tionalising it.

According to that methodology hulls and propellers are not only being in-vestigated together as a single system in propulsion tests but separately in hull towing test, for short usually called resistance tests, and propeller open 5

water tests, even if hulls and propellers are not being designed for these conditions.

Thus the flows around hulls and into propulsors in the open water condi-tion are quite different from the flows in the 'behind' condition. Conse-quently, not only for advanced hull and wake adapted propeller configura-10

tions the traditional procedure results in incoherent sets of data. Further this technique cannot be applied full scale under service conditions, but only on model scale and in computational environments.

In view of all these deficiencies the author has developed a rational theory of propulsion, essentially axiomatic models adequate for the purposes at 15

hand, consisting of the 'universal' axioms of classical mechanics, the mo-mentum and energy balances valid for all bodies, and additional axiomatic models, including phenomenological parameters, 'constituting' bodies pro-pelled in fluids.

The development started explicitly with the publication of an axiomatic 20

theory in 1980. From thereon it took twenty-five years of hard work to reach the present state of maturity. But the clarification and exposition of the ideas are still ongoing, closely interlinked processes.

22.1.2 Models of propulsion

"Manchmal ist es ganz hilfreich, naiv zu sein." 25

Pamela RosenbergP, designierte Intendantin der

Berliner Philharmoniker (Tagesspiegel 61 (2005)

18937, 27.08.2005, 23).

22.1.2.1 NO ABSTRACT THEORY

All of the following problems to be solved require more or less intricate 30

models unfolding representation spaces adequate for the purposes at hand. The additional axioms are conveniently abstracted from the theories of ideal propulsors and pumps operating in uniform wakes. But before talking about special models some general conditions these models must meet will be re-called. 35


This will by no means be an axiomatic theory of constitutive models, comparable to Noll's theory of constitutive laws for simple fluids. Naval ar-chitects in industry and even in research would hardly appreciate such an esoteric exposition.

22.1.2.2 BASIC REQUIREMENTS 5

In order to be useful for the description of objective relationships the models must at least be invariant with respect to changes of units. Bucking-ham's Π-Theorem is the expression of this meta-principle, colloquially re-ferred to as 'dimensional analysis' (Birkhoff, 1955/77-90). For ready refer-ence Birkhoff's statement of the theorem is repeated here: 10

The assertion that the relation

Q 0 = f (Q 1 , Q 2 , …. Q n – r … Q n)

is unit-free is equivalent to a condition of the form

Π 0 = φ (Π 1 , Π 2 , … Π n – r)

for suitable dimensionless power-products Π of the Q, where 15

• n denotes the number of influence magnitudes Q, homogeneous

in the basic units, and

• r denotes the number of independent basic units:

in mechanics r = 3.

An important, often forgotten observation is that the theorem says nothing 20

about the number and type of parameters to be chosen and the format of the unit-free function. This 'information' is a matter of experience, past or pre-sent, not necessarily of hydrodynamics. The parameters can be changed to others, in logarithmic scales changing to oblique coordinates. Although eve-rybody is taught the theorem and its implications at school hardly anybody 25

draws the conclusions.

The reduction in the number of parameters by three appears to be large, but the number of mostly geometrical parameters necessary to describe a hydromechanical system of engineering interest is usually very large. As a consequence aggregate or global parameters, typically the displacement and 30

its various moments and 'characteristic' lengths are of interest, the latter usu-ally a matter of more, mostly of less educated guess work trying to antici-pate the results of the experiments to be performed.


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22.1.3 Pragmatism pure

"Es ist alles gesagt, man kann es nur noch kürzer sa-gen."

Peter Kümmel: Beckett. Der Seher. ZEIT

ONLINE (2006) 16, 49. 5

In rare, fundamental cases the situation is even simpler and the problem at hand can be solved pragmatically, even without any reference to experience, e. g., to hydromechanical experiments, physical or numerical. It 'happens' that one of the most fundamental problems of ship theory, the evaluation of the powering performance of a ship at given loading condition and speed is 10

such a simple example.

According to Buckingham's theorem the 'measured' power ratio

K P ≡ P / (ρ D 5 N 3)

is a function

K P = φ (J H) 15

of the hull advance ratio

J H ≡ v H / (D N) .

In view of the limited variability of the data the most general functions to be identified are two-parameter functions. In the absence of any other informa-tion these will be typically linear functions 20

K P = K P 0 + K P H J H .

The unknown hull advance ratio through the water is the difference of the 'measured' advance ratio over ground and the unknown current advance ra-tio

J H = J G − J C . 25

The remaining problem can be solved by assuming the most general model for the current velocity, preferably a function of time linear in the unknown parameters to be identified, maybe harmonic with the tides or just polyno-mial

v C / (D N) = Σ i c i t

i / (D N), i = 0, ... 3 . 30

This completes the constitutive axiomatic model of ships at steady speed tri-als.

Buckingham's theorem says nothing about the values of the parameters. They are to be identified for any individual ship at given loading and


weather conditions from observations in experiments, full or model scale. The few parameters of the axiomatic model can be identified from the few data usually obtained during speed trials. In the detailed procedure discussed in the following physical parameters of a physical model will be identified, normalised only later for visualisation and scrutiny. 5

Contrary to the standardised practice of our grandfathers based on hydro-dynamic considerations the efficient rational evaluation of speed trials gets along without any reference to ship theory, to hydrodynamic theory and to any prior information from previous tests with the scale model or other ships. At this stage it is only mentioned that the same methodology can be 10

used to determine the performance at no wind and no waves. Details of a standard procedure applicable in practice will be subject of the next section.

22.1.4 Inspectional analysis

Not all problems are as simple as the evaluation of traditional speed trials. A rational procedure to arrive professionally, without speculation and 15

guesswork at formats and parameters of the unit-free function is to adopt axiomatically some simple, though adequate, that is sufficiently rich hydro-mechanical model and to perform a dimensional analysis, an 'inspectional' analysis (Birkhoff).

The important observation is that this procedure is essentially normative. 20

The constitutive axiomatic models unfold representation spaces, the phe-nomenological parameters being the 'coordinates' of the systems considered in these spaces. When the author tells hydrodynamicists that their only task is to identify the values of the parameters defined by ship theory, their reac-tions are usually quite emotional. This reaction does not change the situa-25

tion, but supports the argument.

Identification is essentially a matter of experiments, either physical and/or computational, and their evaluation. The important point is that these sub-tasks must be performed professionally, preferably not by naval architects. To put it bluntly: There are too many hydrodynamicists working in ship 30

model basins.

In view of this fact the International Towing Tank Conference (ITTC) had a hard time finally to come back to its original task, to agree on standard procedures, and consequently the Quality Systems Group has established a quality manual according to ISO 900x under its chairman Gerhard Strasser, 35

SVA Vienna.

In that context much more needs to be done on the conceptual level out-lined in the following. Concerning the evaluation of traditional speed trials a


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memorandum on 'Further steps towards a rational standard' has already been forwarded to the ITTC Quality Group. And the rational theory of hull-propeller interactions and the evaluation of quasi-steady trials has been fur-ther developed and published in recent papers presented at Berlin (2005) and at Visakhapatnam (2006). 5

The complete analysis of the powering performance, of the hull-propeller interactions in particular, required for powering performance predictions, is another example of fundamental importance to the profession. For that pur-pose required are a more detailed model and the acquisition of additional, thrust data, necessary for the identification of the additional parameters. 10

The most convenient way to generate an adequate model is the axiomatic use of the hydrodynamic theory of ideal propulsors in ideal displacement and energy wakes. Up to now this has 'essentially' been done implicitly, rather vaguely. The essentially simple basic idea of the rational theory is to do that explicitly. This model provides for conventions, constitutive equa-15

tions implicitly or coherently defining the hull resistance of a ship with pro-peller and the propeller advance speed in the behind condition.

Again hydrodynamicists are up-set by this crude, mechanical engineering use of their sacred science. But this is the only rational way to solve the problems at hand: to replace hull towing tests and propeller open water tests. 20

These tests, if performed in case of advanced hull propeller configurations, hull adapted propulsors and vice versa, provide useless data and, most im-portantly, they cannot be performed on full scale under service conditions.

In case of hull integrated propulsors, ducted propellers and jet propulsors the naïve conception of propulsors producing thrust to overcome the resis-25

tance of the bodies to be propelled, the conceptual framework of interaction in terms of wake and thrust deduction 'breaks down', in fact it becomes un-necessary.

An adequate and fruitful approach to overcome this problem is to con-ceive propulsors as pumps feeding energy into the fluid, to provide for the 30

condition of self-propulsion, of vanishing net-momentum flow into the overall system. Thus an alternative, adequate axiomatic theory can be de-veloped in terms of pump theory, avoiding any reference to the naïve con-ceptions on propulsion. The concept of thrust in particular ceases to be a meaningful design goal and measure of performance. 35

22.1.5 Propulsion: Goals/Plans

"Probleme kann man niemals mit derselben Denkweise lösen, durch die sie entstanden sind."


Albert Einstein (P.M. magazin (2007) 8, 100).

In the present treatise, not primarily addressed to naval architects, mari-time details are not of interest. Thus the goal is to develop only the essen-tials, to provide examples of constitutive equations of propelled bodies and of model based axiomatic systems. In order to avoid an unnecessarily 5

clumsy generalised epi-language ship terminology will be used, the applica-tions to propulsion in air, not only of airships, being straightforward.

The chapter will start with the rational evaluation of traditional ship speed trials treated as a systems identification problem requiring only rudimentary constitutive models, if any. The exposition is purposely arranged at this 10

early stage to demonstrate that, contrary to professional superstition and guesswork, the solution of this fundamental problem does not require any theory of hull propeller interaction, any ship theory, and its essential part, not even any hydromechanical theory as has already been shown.

In order to provide an adequate language for the discussion of propulsion 15

in general an abstract meta-theory of propulsion will be developed in terms of 'invariant' magnitudes, mass and energy flows and energy velocities in particular.

The following part of the chapter will be devoted to open propellers be-hind rather slender ship hulls. As first instance of the meta-theory the fun-20

damental theory of ideal propulsors advancing in ideal fluids at rest will be developed. The presentation will reveal all implications of the theory ob-scured by the traditional teaching.

Subsequently the theory of ideal propulsors in ideal fluids in uniform ideal displacement and energy wake will be developed. This theory is not of 25

interest as such, but will provide the adequate explicit model of an axio-matic theory of hull-propeller interactions.

Next it will be shown how this conceptual framework can be used for the rational evaluation of quasi-steady ship speed trials, provided constitutive equations for wake and thrust deduction are being introduced and adopted, 30

replacing propeller open water and hull towing tests. The theory permits a detailed analysis of hull-propeller interactions in practice, even full scale under trials and service conditions.

The remainder of the chapter will be devoted to hull integrated propul-sors, ducted propellers and jet propulsors, where the conceptual framework 35

of interaction in terms of wake and thrust deduction breaks down, or rather becomes unnecessary. Last but not least, it will be shown that the underly-ing conception of propulsors as pumps permits, different from all other known design procedures without reference to thrust, the design of optimum

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wake adapted propulsor configurations implicitly accounting for all interac-tions.

EVALUATIONS/ASSESSMENTS/CONCLUSIONS

Different from traditional expositions and teaching the introduction already puts

problems and models into perspectives permitting efficient pragmatic solutions of 5

fundamental problems of ship theory so far unsolved.

22.2 Steady speed trials

" 'Sie scheinen also andeuten zu wollen,' versetzte ich, 'daß man um so schlechter beobachte, je mehr man wis-se?' 10

'Wenn das überlieferte Wissen mit Irrtümern verbun-den,' erwiderte Goethe, 'allerdings! Sobald man in der Wissenschaft einer gewissen beschränkten Konfession angehört ist sogleich jede unbefangene treue Auffassung dahin. ...' " 15

Johann Peter Eckermann: Gespräche mit Goethe,

18.05.1824 (1911/379).

PROBLEMS

Traditionally the performance analysis of ships, newly built in particular, is

based on trials, in view of the costs consisting of only a minimum of steady double 20

runs up and down wind and waves. Double runs are necessary to provide for the

necessary variability of the data.

The traditional evaluation according to established and recently standardised

procedures requires a large number of doubtful conventions, mostly tacitly implied

according to the state of the art in naval architecture. Consequently the results ob-25

tained during trials have always been felt to be not very reliable and trustworthy by

all parties involved.

This situation is particularly unsatisfactory as on the basis of these results con-

tractual disputes are to be settled. The recent activities to solve the problems in

proprietary joint industry projects are felt to be steps in the wrong direction. 30

MODELS

The rational performance evaluation proposed is conceived as a problem in ra-

tional resolution of conflicts to be solved by the adoption of an adequate axiomatic

system, coherent conventions to be agreed upon by all parties involved. The neces-

sary transparency is obtained by reducing the number of models to the bare mini-35

mum of highly aggregate models with only very few parameters to be identified

solely from observed performance data consistently applying advanced systems

identification methods.


GOALS

The goal is to show that the problem of performance evaluation can be solved in

terms of elementary mechanics by aggregate models. This approach is strictly con-

trary to the falsely held instinctive beliefs and strategies of naval architects, who

continue to increase the number of sub-models and their intricacy, resulting in ever 5

more parameters to be determined from model tests, suffering of considerable scale

effects, and from other prior information of doubtful relevance.

PLANS

The exposition starts with a minimal set of acceptable conventions or axioms,

global models, permitting the transparent analysis of powering performance of 10

ships based on traditional steady speed trials without reference to results of model

tests and other prior information, as it should be.

Finally it will be indicated how the procedure proposed can be generalised to

permit accounting for changes not only in weather but for changes in loading con-

ditions, trim and draught. 15

22.2.1 Steady trials: traditional approach

"MARTHE [ZU MEPHISTOPHELES]: O sagt mir doch geschwind! Ich möchte gern ein Zeugnis haben, Wo, wie und wann mein Schatz gestorben 20

und begraben. Ich bin von je der Ordnung Freund gewesen, Möcht' ihn auch tot im Wochenblättchen lesen."

Johann Wolfgang Goethe: Faust I. Der Nachba-

rin Haus (BA 08/245). 25

The evaluation of the powering performance of ships based on speed tri-als is one of the basic problems of ship theory. Maybe due to the lack of colour this problem is not fashionable at chairs of ship theory, practitioners being left alone with the 'nasty' fundamentals and the difficult details. In view of the requirements of ISO 900x concerning total quality management 30

and of the legal aspects and implications this situation is felt to be unaccept-able. Continued work towards a rational theory of trials meeting acceptable 'standards' and criteria is necessary.

Traditionally the analysis of the performance of ships, newly built in par-ticular, is based on trials consisting, in view of the costs, of only a minimum 35

of steady runs against and with wind, waves and current. The double runs are required to provide for the necessary variability of the data.


29.10.2008 13:55 h

If at a given time steady conditions are 'assumed' or 'felt' to be reached the speed over ground, the shaft rate of revolutions and torque as well as the relative wind speed and the sea state are measured or otherwise 'observed', mostly crudely guessed, in practice as more or less 'instantaneous' short term averages. 5

The evaluation of these data according to established procedures is based on a large number of conventions: models of hull propeller interaction, of losses in the shafting and of wind and wave resistance according to the state of the art in ship theory requiring values of many parameters to be estimated on the basis of prior information: results of ad hoc model tests, systematic 10

wind tunnel tests, calibrations of wind-meters and others of doubtful rele-vance.

A survey of the traditional methods is provided in the Final Report of 'The Specialist Committee on Speed and Powering Trials' to the 23rd ITTC at Venice (ITTC, 2002/355). The method proposed here has been considered 15

as "a category by itself. It does not really follow the same format as all the other methods and hence was not used in the comparison of factors re-viewed in each method." Whatever 'not really' may imply, 'not at all' would have been adequate.

According to the experience of the author the problem is not so much to 20

analyse the random errors considered by the specialists, but the dominant problem is still to avoid conceptual and systematic errors. And according to Feyerabend's discussion of the 'condition of consistency' in his 'Against method' (1983/39 ff) the alternative approach proposed provides the only avenue to discuss the deficiencies of 'all the other methods'. 25

To the surprise of the author the 'Specialist Committee on Trials and Monitoring' has been discontinued. Evidently the governing bodies of ITTC 'felt' that all problems have been solved. But the very simple, fundamental example discussed in the introduction clearly shows that the present, very intricate practices are based on superfluous assumptions, to put it mildly. 30

But who likes to be told that his deeply rooted beliefs are plain superstition?

The results of the evaluations do not only depend on the observations of the environmental conditions, particularly the biased wind measurements and the crude estimates of the wave data, but on the many partial models adopted and on the values of the corresponding parameters estimated or 35

rather 'guessed' and, last but not least, on the ill-defined numerical proce-dures applied to the ill-conditioned problems to be solved.

This sensitivity is not a problem of the traditional method alone, but an inherent property of the ill-conditioned problem to be solved. And this sen-sitivity is exactly what urgently requires adequate standardisation in order to 40


arrive at comparable, 'objective' results. The author does not share the opin-ion of some English colleagues that the procedure cannot be standardised expressed during the discussion of the Committee Draft ISO/CD 15016.

The sensitivity is particularly unsatisfactory in view of the decisions, the settlement of contractual disputes, to be based on these results. The need for 5

standardisation has resulted in a number of well known codes of practice and recommendations. The latest move has been the Japanese draft of an ISO standard, which in the meantime has become a Draft ISO Standard ISO/DIS 15016 and finally an ISO Standard proper: ISO 15016: 2002-06, despite the serious reservations brought to the attention of all bodies 'in 10

charge'.

The conventional character of the very intricate traditional procedure pro-posed is completely blurred by irrelevant 'physical' details. Instead of ad-dressing the real problems a Japanese/Korean battle has been fought on in-tricate seakeeping theories, without noticing that the problems at hand can-15

not be solved by ever more sophisticated hydrodynamic theories. In particu-lar, the estimation of the added resistance or power required due to waves is based on very crude estimates of the sea state, the wave height and the wave period.

Any attempt to settle all the problems mentioned by increasing the intri-20

cacy of the current practice and standardising it, is doomed to fail. Among practitioners such attempts are widely felt to be not only unsatisfactory, but to be inadequate, addressing none of the fundamental problems mentioned and met in practice. Further, neither the presence of systematic errors in the measurements of power and ship and wind speeds, nor the difficulties in es-25

timating the sea states are being adequately addressed.

22.2.2 Steady speed trials: rational approach

"Eine Idee besteht immer aus zwei Teilen: der Idee und der Ausführung."

Rudolf Diesel: Die Entstehung des Dieselmotors. 30

1913.

22.2.2.1 DEVELOPMENT OF THE APPROACH

Consequently the author has promoted the necessary clarification and ra-tionalisation parallel to the development of the standard. As a first reaction to the Committee Draft ISO/CD 15016 the proposal of an adequate standard 35

has been drafted based on the theory of rational conflict resolution, which calls for utmost transparency. The rationale was and is, even stronger now,


29.10.2008 13:55 h

that an ISO Standard should not just continue to refine past practice, but should meet the highest 'standards' and take advantage of the latest state of the art and technology in every respect.

The work has been continued since, the essential result being the axio-matic or conventional theory explained in many papers and presentations. 5

The latest state of developments over the past five years with links to all the basic material has been published on occassion of the 23rd ITTC at Venice in 2002 and of the VWS Centenary at Berlin in 2003. Further steps towards a rational standard have been presented at the 100th Annual Meeting of STG at Berlin in 2005, at the International Conference on Marine Hydrody-10

namics at Visakhapatnam in 2006 and in a 'Memorandum' (Schmiechen, 2006).

22.2.2.2 PROBLEMS ENCOUNTERED

The starting point is, not as usual the momentum balance, but the energy balance at steady conditions 15

d t E = P sup − P req = P P − P R = 0 ,

using simple 'local' overall 'models' of the shaft power supplied by the pro-peller and shaft powers required due to the resistance in water, wind and waves, and using the techniques of parameter identification.

The necessarily conventional procedure can be rationalised if 20

• the traditional 'partial' models are aggregated to the bare mini-mum number of 'overall' models to be agreed upon,

• with the bare minimum of parameters solely to be identified on the basis of the measurements taken,

• advanced systems identification methods are applied consis-25

tently.

In the proposal developed and the numerical demonstrations provided during the discussions on the ISO/DIS 15016 it has been shown that such a procedure is not only feasible, but provides more consistent results than the method proposed in the ISO standard. 30

The parameters identified ad hoc are measures of correlation between the observed shaft power and the observed 'causes',

• for the power supplied: the frequency of shaft revolutions, the relative speed of the ship through the water;

• for the power required: the relative speeds through the water, 35

through the wind and through the waves.


In view of the very large inertias of ships even extremely small accelera-tions and decelerations can completely upset the momentum and energy balances. Hence, unless unsteady terms are included in the analysis, it has to be guaranteed, prior to further analysis that the values subject to the analysis are definitely corresponding to steady conditions. 5

Evidently this goal is not being reached by practitioners 'taking mean val-ues' at conditions 'considered' to be stationary. Incidentally the problem is exactly the same in model testing as a Japanese investigation and tests with the METEOR model have shown (Schmiechen, 1991, Oral Discussions /28). The present samples of at best eight or ten 'doubtful' averages are just 10

too small in size for serious applications of statistical methods.

Sound performance analyses have to be based on stationary values deter-mined from the time history of the 'instantaneous' data. It is incredible how carelessly this fundamental matter is still being treated. An additional prob-lem, not being noticed if averages are being taken, is the synchronism of the 15

speed data obtained using the Global Positioning System and the other data acquired.

22.2.2.3 FURTHER DEVELOPMENTS

The rational method proposed, being still in its infancy does not yet cope with all the problems and details. It will need the joint effort and agreement 20

of all experts before it can be established as a reference and as a standard. The advantages of the rational procedure are a minimum number of trans-parent conventions and the consistent application of adequate systems iden-tification methods requiring no reference to model test results and other prior data, as it should be. 25

In the interest of the profession, science and technology, and the cos-tumers, yards and owners, a serious discussion not only of the details, but of the fundamentals in the first place, is strongly suggested. Naval architects need to take the discomfort of the industry they are serving very serious and come up themselves with adequate solutions before industry or even outsid-30

ers tell them what they better should do and should do better.

Although the ideas, originally developed as a by-product of the METEOR project nearly twenty years ago, are surprisingly simple and the results of the re-evaluation of data are in close agreement with the traditional results, the procedure is not readily accepted by colleagues worldwide. But in dis-35

cussions following presentations of the proposed rational procedure outsid-ers have already raised the justified question: 'What else have naval archi-tects done so far?'


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22.2.3 Steady speed trials: power supplied, current

22.2.3.1 PROPELLER POWER MODEL

The propeller performance in the behind condition, in the full scale wake, and the current velocity can be identified simultaneously by solving one set of linear equations. 5

For screw propellers the shaft power

P P = 2 π n Q P

can be derived from measured values of the rate of revolutions and of the torque. If the latter are averages of periodically or stochastically oscillating values already this simple formula is a convention. Further conventions are 10

necessary, if instead of the power in the shaft the power 'delivered' at the propeller is considered as is the case in the traditional method based on model propeller open water characteristics.

The data observed in a series of steady runs on opposite courses in the narrow range of variability of the data can be described by the local ap-15

proximate 'Newtonian' power law

P P = p 0 n 3 + p 1 n

2 V H

with the hull speed through the water. This law is complete equivalent to the law

K P = K P 0 + K P H J H 20

introduced earlier. Thus the law in terms of physical magnitudes does not imply any physics, but is suggested in view of appropriate weighting of the data. If the data are not limited to a narrow range the power laws including higher order terms or deriving from some theory may have to be adopted as has been shown in a proprietary project. 25

22.2.3.2 CURRENT MODEL

Further the speed of the ship over ground, with reference to an Earth fixed observation space, can be measured using the Global Positioning System, which is readily available today. But the speed of the ship (hull) through the water cannot be derived directly due to the unknown current velocity. This 30

problem can be solved as follows.

The hull speed can be expressed as the sum of the speed over ground and the current velocity

V H = V G − V C


and by a model for the current velocity as function of time, maybe harmonic with the tides or just polynomial

V C = Σ c i t i , i = 0, ... 3 ,

as stated before, preferably linear in the unknown parameters.

22.2.3.3 PARAMETER IDENTIFICATION 5

The parameters of the power supplied and of the current velocity can be identified from a 'sufficient' number of independent steady states by solving the resulting set of linear equations. In the usual case of only three double runs the number of data is clearly insufficient for statistical analysis. The quality of the data, being of utmost importance, has to be established by 10

careful analysis of the original 'instantaneous' values.

In view of the ill-conditioned problems arising there is no chance to solve the equations with do-it-yourself algorithms, as some colleagues have tried. It took the author two years of intense correspondence and 'research' to find out the reason for their failure to apply the method proposed for the evalua-15

tion of traditional trials.

Singular value decomposition, described earlier, is absolutely necessary. The traditional 'procedures' to solve six, eight or even ten simultaneous, ill-conditioned, 'noisy' equations remain altogether obscure, to say it politely.

If the thrust has been measured together with the torque the parameters of 20

the thrust law

T = t 0 n 2 + t 1 n V H

can be identified as well. As will be shown these thrust data together with the power in the behind condition will permit a more detailed analysis of the powering performance, as soon as an abstract model of the hull-propeller in-25

teractions has been developed and is adopted.

22.2.3.4 NORMALISATION

For visualisation, discussion and scrutiny normalised data are being intro-duced: the power ratio

K P ≡ P / (ρ D 5 n 3) 30

and the thrust ratio

K T ≡ T / (ρ D 4 n 2)

and these are considered as locally linear functions

K P = K P 0 + K P H J H


29.10.2008 13:55 h

and

K T = K T 0 + K T H J H

of only one variable, the hull advance ratio

J H ≡ V H / (D n) .

The analysis can be greatly improved if it is not based on averaged val-5

ues, but on the quasi-instantaneous values preferably of quasi-steady tests, providing for variability and not suppressing all relevant information as is done in traditional steady tests.

22.2.4 Monitoring of trials

22.2.4.1 BASIC MODEL 10

After this 'calibration' the propeller power law in the behind condition can be used to determine the 'instantaneous' values of current velocity for moni-toring purposes. From measured values of the rate of revolution and of the torque the speed of the ship through the water is obtained according to the explicit rule 15

V H = P P / (p 1 n

2) − p 0 n / p 1 .

More important in the present context is the monitoring of the trials them-selves. Even if the conditions at a run are being 'considered' to be steady they are definitely not, due to the omnipresent 'noise', random variations of wind and waves. But due to the large inertias of ships the states change only 20

quasi-steadily.

Accordingly the instantaneous power ratios during individual runs, usu-ally of short duration compared to the time scale of changes of the current velocity, are linear functions

K P = K P 0 + K P H (J G − J C) 25

= (K P 0 − K P H J C) + K P H J G

of the instantaneous hull advance ratios

J H = J G − J C ,

in general differing in the constant term due to changes of the current veloc-ity during the trials, but coinciding in the linear term, being 'parallel' for all 30

runs.


22.2.4.2 CONSEQUENCES

Consequently, in the absence of current the data of all runs will 'line up', for constant current, the data will line up separately for the runs up and down the current, respectively, finally, in the general case of changing cur-rent velocity, there will be offsets between the data of the runs in the two 5

groups.

In view of the necessary quality of the data and the costs of trials the monitoring has to be performed online. Only this procedure permits imme-diate detection of malfunctions of the measurement system, to repair the system and to repeat the run when this is still possible. 10

After the 'calibration' the propeller power law in the behind condition can also be used to establish the deviation from the contracted propeller per-formance without reference to weather conditions. This proposal was fiercely turned down immediately after it had been suggested by the author.

Usually not only the propeller performance is contracted, but the per-15

formance of the ship under given weather conditions. 'Accordingly' the ap-proach described has been extended to identify these conditions as well.

22.2.5 Steady speed trials: power required

22.2.5.1 PRINCIPLES OF PROCEDURE

The shaft power required is due to the motion of the vessel through water, 20

waves and wind. As in the case of the power supplied the parameters of simple 'local' overall models can be identified simultaneously by solving another set of linear equations and can be used to determine the speed-power relationship at conditions different from the trials conditions, typi-cally at the no wave and no wind condition. 25

Identifying parameters of models from observed data, even visually ob-served wave data, has the advantage that systematic errors in the observa-tions are to a great extent 'automatically' accounted for.

In the very intricate traditional methods and the ISO method proposed based on physical theories and physical parameters this does not apply, al-30

though they are using the same wind measurements and the same crude wave observations available. This fact is one major reason for the concerns about the ISO method expressed nearly unisonously by experts in shipyards and institutions.


29.10.2008 13:55 h

The power required for the motion through the water is 'locally', 'in the vicinity' of the operating conditions', sufficiently modelled by the bi-quadratic parabola

P Water = Σ c Water i V H

i , i = 2, 3, 4.

In final tests it has been found that any simpler 'law', using only two pa-5

rameters, will lead to difficulties.

The power due to motion through the wind is as usual sufficiently mod-elled by the law

P A.Wind = c A Wind C A Wind

using the short hand notation 10

C A.Wind = [ρ Air A Wind V Wind.R | V

Wind.R

| /2] V H

for the aggregate 'cause' of the power due to wind with the relative wind speed, if the wind direction is basically from ahead or behind. In general the additional law needs to be introduced to account for the 'directional' coeffi-cient of wind resistance. 15

Slightly more intricate is the added power due to the operation in waves. The simple law

P A.Wave = c A.Wave C A.Wave

using the short hand notation

C A.Wave = [ρ h Wave 2 V Wave.R | V Wave.R

| /2] V H 20

for the aggregate 'cause' of the power due to waves with the observed wave height and the relative wave speed derived from the observed wave period, similar to the law of the shaft power due to wind, is being suggested and has been used in the re-evaluation of the ISO/DIS example. An additional law for the transverse waves may be necessary. 25

As in the case of the power supplied and of the current the models pro-posed are open for discussion and for improvement. They are the conven-tions to be agreed upon! The 'coefficients' or parameters introduced are not identical and their values are not to be compared with those of the coeffi-cients of the wind and wave resistance used in the traditional procedures! 30

22.2.5.2 SINGULARITY

In the usual case of nearly perfect correlation of the aggregate wind and wave causes the problem becomes singular, implying that infinitely many mathematically correct solutions exist. In cases the down wind condition may very nearly equal the no wind and no wave condition, the sometimes 35


so-called vacuum condition. But this fact is not a good starting point for dealing professionally with the singular problem!

A straightforward solution is obtained if the parameter of added power due to wind is arbitrarily assumed. Accordingly all the subsequent results depend on the value assumed for the wind power parameter. Among the re-5

sults is the standard deviation of the residua in solving the set of linear equa-tions. Due to the very crude 'observations' of the waves this standard devia-tion is much larger than that in identifying the propeller characteristic. The result of interest is of course the power required at the contract condition, at the service speed and the no wind and no wave condition. 10

In an example the standard deviation of the residuum remained essentially unchanged for different values of the wind parameter, while the values of the contract power at the contract condition exhibited only very small changes depending on the value of the wind power parameter. Thus the value chosen for the wind power parameter does not really matter, it does 15

not significantly affect the result of interest.

The problem to select a satisfactory, a meaningful, solution, to provide a rationale for deciding on the value of the wind power parameter, can only be solved by convention. Formal 'solutions' suggested in earlier expositions are hardly meaningful in physical terms. In the given engineering context of 20

evaluating trials the convention

c A.Wind = 1

is suggested.

This convention implies that the value of the coefficient of wind resis-tance is assumed to equal the value of the propulsive efficiency. And look-25

ing at the values of the coefficient of wind resistance published in the stan-dard ISO 15016 this assumption appears to be acceptable in general. And as stated earlier small deviations from this assumption have only a small effect on the final result of interest, the power at the service speed and the no wind and wave condition. 30

22.2.5.3 SPECIAL CASE

If the down wind condition very nearly equals the no wind and no waves condition, the so-called 'vacuum condition', this fact may provide the only solution in cases where only crude estimates of wind and wave data are available and where other procedures break down. In these cases the 'windy' 35

wind and wave data can safely be 'forgotten'. For the purposes of power prediction only the added power due to motion through the air needs to be estimated using the above convention. In these cases detailed analyses of the


29.10.2008 13:55 h

propulsive performance are 'of course' not possible. An example of this type has been published on the website of the author.

22.2.6 Steady speed trials: contracted conditions

After the parameters of the local laws of required shaft power have been identified from the trial data the speed-power relationships can be estab-5

lished for the trial conditions, typically no waves and no wind:

P P 0 = P P water + P P air = Σ c Water i V H i + c A wind V H

3 .

For given hull speed and propeller power the frequency of revolution is ob-tained as solution of the power equation

P P = p 0 n 3 + p 1 n

2 V H . 10

The power and the rate of revolution as functions of speed through the water are usually compared with the contracted values derived from predic-tions based on model tests. Using the parameters identified speed-power and speed-revolution relationships at conditions other than the contracted can be crudely 'estimated' as well in the same simple fashion within the range of 15

validity of the parameters.

For visualisation, discussion and scrutiny these data are again normalised. The power number

C P ≡ P / (ρ D 2 V H 3)

and the hull advance ratio are plotted as functions of the Froude number 20

based on the ship length

F n = V H / (g L) 1/2

or based on the water depth in case of shallow water as in the CORSAIR tests.

A survey of recent developments of the rational procedure provides ac-25

cess to numerous other examples as does the section 'On the Evaluation of Trials' in the 'Recent Papers' on the website of the author.

22.2.7 Steady speed trials: verification, 'validation'

It is common practice to verify an analysis procedure with test data gen-erated by the corresponding inverse synthesis procedure. Such tests with 30

'simulated' data are the minimum required in view of programming mistakes and the noise to be dealt with.


But this technique cannot be used to validate a method. Even provided the simulated data are being generated correctly and according to the rules set forth, they are not useful to verify or even to validate any 'alternative' proce-dure. The numerical results of evaluations with alternative procedures differ 'by definition' from the results according to the 'reference' method. 5

Evidently these differences do not 'prove' the validity of the 'reference' procedure or any alternative procedure in real life situations with real data. In order to show the adequacy of the rational method proposed the author has evaluated all sets of real data he could get hold of, all the examples originally to be found on his website, now provided upon request, in any 10

case including the data and all details of the evaluations.

But to date nobody cares to look at these examples. Instead, every party comes up with new data, incomplete as these always are and with their own evaluation, asking their results to be reproduced. The problem is that the other methods are hardly ever published in sufficient detail, so usually they 15

cannot be scrutinised. The yards may have an interest that the situation will remain that way forever!

So computing new examples will never resolve the 'problem' of the au-thor, to convince the community, that the rational method has the advan-tages of being more adequate, more transparent and providing not only 20

more, but more consistent results. In order to evaluate the different methods one would have to analyse them formally, not numerically. This would be a very nice student's exercise, but an irresponsible waste of effort in the light of the principles set forth.

In order to reach the goal one has to forget about the data and try to un-25

derstand the essence of the difficult problem to be solved and try to under-stand the very clear-cut solution proposed including its capability to deal with the few data at hand, not only crude as the wave data usually are, but maybe biased as the wind data usually are.

The intensive studies so far show, that the problems in detail remain diffi-30

cult enough. And most of them need to be addressed and solved, even if the evaluation is following the traditional procedure. In the ISO standard the problems have not even been mentioned, forget about addressed, although they have been pointed out by some participating bodies and by the author.

Not the small numerical differences in the results are of interest, but the 35

big differences in the models and, even more so, in the principles! The pro-cedure proposed is based on a minimum number of simple explicit and ac-ceptable global models, the few parameters to be identified by consistent systems identification methods, thus requiring no reference to model test re-sults and to any other prior information, as it should be! Not 'acceptable' 40


29.10.2008 13:55 h

numerical differences between results of various methods, but new conven-tions have to be agreed upon!

22.2.8 ISO/DIS 15016 example

Despite fundamental deficiencies and inconsistencies, even in the exam-ple provided, trials being interrupted by a passing typhoon, the new ISO/CD 5

15016 example provides a comprehensive test case for the rational proce-dure proposed and developed in the course of the discussion of the recent activities to standardise the evaluation of ship speed trials.

There remain differences in the evaluations still to be analysed. Independ-ent of this analysis the differences in magnitude and, particularly, in trend of 10

the normalised results between the proposed rational and the proposed ISO evaluations can be ascribed to inconsistencies in the ISO procedure. Some effects may reflect laminarity effects at slow speed model tests.

A problem arises in analysing the required power. At extreme weather conditions the residua are not as small as for the supplied power. The reason 15

is doubtless the poor resolution of the wave observation. If the crude model is kept the residua have to be accounted for.

From the data at hand the values of the added power due to waves being identified according to the rational method are more than twice as large as the 'nominal' values computed according to the proposed ISO method. And 20

the latter has been particularly conceived to deal with this problem, just with reference to the very crude data of wave observation, but without any refer-ence to the observed data of shaft power!

In order to avoid any discussion on purposely selecting data the data of all ten runs have been included in the evaluation. This has the advantage to in-25

crease the size of the sample for statistical evaluations. In addition to the overall evaluation ten evaluations have been added of the ten possible sets of data including each only nine runs.

The stability of the results is very good, showing the nearly perfect con-sistency of the data, originally with only one exception. This exception has 30

been traced back to a misprint in the data, finally admitted by the Japanese group responsible.


22.2.9 Steady speed trials: further developments

22.2.9.1 QUASI-STEASDY TRIALS

Many problems in the evaluation of traditional trials are due to waiting for steady conditions, i. e., ignoring all interesting information, and using ill-defined average values. In the METEOR and CORSAIR trials quasi-5

steady test manoeuvres have been shown to be much superior to steady test-ing, providing not only much more information, but at the same time the necessary references for the suppression of noise, even at service conditions in heavy weather, without picking up systematic errors due to feed-back of noise. 10

Noting that often the time constant of the propulsor is much smaller than that of the vessel, the requirement of steady states, which are difficult to es-tablish and to guarantee, can be relaxed and the full energy balance

P P = P R + d t E

with the basic definition 15

d t E = c inert (d t V H) V H

can be used, if the changes of kinetic energy are properly monitored and ac-counted for.

In general the additional parameter may be identified together with the other parameters of the required power according to the basic definition. 20

The speed through the water has already been identified with the parameters of the delivered power law and the acceleration may be determined directly from the GPS measurements

d t V H ≈ d t V G ,

the time rate of change of the current assumed to be much smaller, and pro-25

vided utmost care is taken in differentiation. If longitudinal inertia of the ship, including the hydrodynamic inertia, can be estimated reliably on the basis of other data this method provides a check of the propulsive effi-ciency.

The rate of change of the kinetic energy may be conceived as the power 30

required due to the 'inertial resistance'. Due to the large inertias of ships ex-tremely small accelerations may upset the energy balance, if they are not appropriately accounted for! Practitioners are well aware of this effect and 'take advantage' of it, if 'possible', if the contractor does not notice.


29.10.2008 13:55 h

22.2.9.2 THRUST MEASURMENTS

As has been shown further in the METEOR and CORSAIR trials the ad-ditional measurement of thrust permits a complete analysis of the hull-propeller interactions. But it may take another generation before the theo-retical and commercial potential of this transparent technology is taken ad-5

vantage of.

It can be envisaged that in future the method will be applied for the evaluation of model tests and trials and for monitoring of ship performance in service, and thus eventually increasing and improving the data base on scale effects. Validation of CFD codes introduced into ship design can be 10

successfully achieved only along this route.

As has been shown in the METEOR project reliable thrust measurements are possible by using calibrated hollow shafts. If shafts are designed to in-clude short hollow sections these are not expensive. All attempts to circum-vent this technique by 'simpler' systems have been costly failures. 15

22.2.9.3 WAY INTO PRACTICE

As a new paradigm on ship speed trials evaluation the method proposed may take quite some time to make its way into practice, although the tech-nology is available. But in view of modern optimum ship design it is more than timely that the present, unsatisfactory practice is supplemented and, 20

maybe some day, replaced by the more transparent, more rational and 'more physical', still conventional procedure. The models used are the most basic possible constitutive conventions, but they may serve the purpose until somebody comes up with more adequate proposals.

As the title of the recent memorandum states the present exposition is 25

providing further steps and clarifications towards a rational standard for evaluating ship speed trials. The author has not updated his early drafts of such a standard, but strongly supports and promotes an early update in order to have it ready for consideration at the forthcoming update of the present ISO 15016: 2002-06. 30

The argument that such drastic changes of the conventions and standards meets with psychological problems on the side of the clients is not valid. The fact is that the problems are those of the experts. Clients have for a long time been asking for a more transparent procedure in evaluating speed trials and are willing to pay for it, as the joint industry projects at MARIN in 35

Wageningen shows.

All related studies, including the details of all examples investigated, and all presentations so far are to be found under the 'Recent Papers' in the sec-


tions 'On the Evaluation of Ship Speed Trials', 'On the Propulsion Tests with METEOR' and 'On the Propulsion Tests with CORSAIR' on the website of the author. References in brackets are referring to documents on the website with hyperlinks directly to the documents. Background information is to be found in the 'Bibliographies' related to 'General' and 'Propulsion'. 5

EVALUATIONS/ASSESSMENTS

The analysis of the powering performance of ships based on the results of tradi-

tional speed trials can be drastically rationalised by adopting a minimal set of ac-

ceptable aggregate models with a minimum set of parameters identifiable from the

few data at hand. 10

The identification of the corresponding minimal sets of parameters is a matter of

solving two ill-conditioned sets of linear equations for the power supplied or deliv-

ered and the powers required, respectively. The parameters identified permit to

predict the powering performance at conditions differing from the trials conditions,

at the contracted conditions in particular. 15

The data-base and the confidence in the results can be greatly improved by use

of data to be acquired at quasi-steady runs and including the inertial term.

CONCLUSIONS

In order to obtain more detailed insights into the propulsive performance of

ships more detailed constitutive axiomatic models beyond those discussed so far 20

are required. Further not only the power has to be measured but the thrust as well

and quasi-steady tests become mandatory to provide for the necessary variability

of the data and the suppression of feed back of noise.

22.3 Meta-theory of propulsion

"Wiederum andere halten zu sehr auf Fakta und sam-25

meln deren zu einer Unzahl, wodurch nichts bewiesen wird. Im ganzen fehlt der theoretische Geist, der fähig wäre, zu Urphänomenen durchzudringen und der einzel-nen Erscheinungen Herr zu werden."

Johann Wolfgang Goethe: 16.12.1828 (Ecker-30

mann, 1911/223).

PROBLEMS

Traditional teaching of the fundamentals of propulsion is based on the naïve

concept of propellers as thrusters overcoming the resistance of the hulls to be pro-

pelled. For most advanced hull-propulsor configurations this concept is completely 35

inadequate.

22.3 Meta-theory of propulsion 1205

29.10.2008 13:55 h

MODELS

Much more adequate and convenient is to conceive propulsors as pumps feeding

energy into the flow providing for vanishing momentum flow into the overall ship

system.

GOALS/PLANS 5

The goal is to provide the theory of this conception, the meta-theory of propul-

sion, permitting the adequate discussion of the following instances: ideal propul-

sors in open water and in wakes behind ships, ducted propellers in open water and

hull integrated.

22.3.1 Introduction 10

Traditional teaching of the fundamentals of propulsion starts with ideal propellers in 'open' water, considered as actuator discs, and the Rankine-Froude momentum theory of their ideal jets. But in practice neither fluids nor propulsors and their jets are ideal, jet configurations are non-permanent, maybe unstable, and in many cases open conditions are practically impossi-15

ble, typically on full scale, or they are physically impossible, as for all hull integrated propulsors, or they are not particularly meaningful, as for all screw propellers and all ducted propellers.

In all these cases the theory of ideal propulsors is f no direct use, but may be conceived as an instance of an abstract meta-theory of propulsors or vice 20

versa as model of an axiomatic theory. Consequently the axiomatic theory is abstracted from the above theory, which serves as a sufficiently intricate model.

Although this is implied by the traditional teaching and in all engineering considerations, it has never before been done explicitly and coherently. The 25

abstraction is conveniently avoiding any reference to the naïve conception of propulsion, the concept of thrust in particular, being no longer design goal and measure of performance.

This approach is in line with a statement L. I. Sedow in his opening ad-dress at the IUTAM Symposium in Leningrad 1971: 30

"Bekanntlich haben Schiffstheoretiker immer die gegenseitige Beeinflus-sung von Schiff und Propeller studiert und berücksichtigt. Jetzt jedoch be-steht der Kern der Sache nicht in der Betrachtung des Zusammenwirkens getrennt entworfener Teile, sondern in dem Entwurf des bewegten Systems als einer Einheit. 35

Während wir bis jetzt über Schub und. Widerstand eines Fahrzeuges zu sprechen pflegten, werden wir in nächster Zukunft nur von einer Verwirkli-chung eines gewünschten stationären Bewegungssystems mit einer resultie-


renden hydrodynamischen Kraft gleich Null reden. Die Frage der Untertei-lung dieser Kraft in Widerstand und Schub gewinnt einen künstlich ange-nommenen Charakter und verliert ihre Bedeutung." Translation: Georg

Weinblum.

As has been explained in detail an abstract theory is essentially a formal 5

language consisting of basic concepts, basic propositions, i. e., the axioms, derived concepts and derived propositions, i. e., the theorems. In order to be useful for the purposes of comparing different types of propulsors the theory will be phrased in terms of 'invariant' magnitudes, in terms of volume or mass and energy flows, carefully avoiding any reference to thrust. 10

22.3.2 Axiomatic system

22.3.2.1 BASIC CONCEPTS

The basic concepts are those used in the theory of ideal propulsors, and the corresponding pump theory. In detail the minimum set of interest here is: the speed of the ship V H relative to the water at rest at infinity, the effec-15

tive resistance R E of the hull, the power delivered P P , the density of the water ρ , the volume flow rate Q , the energy flow at the entry E F

E and the energy flow at the exit E F

J of the propulsor.

In interpretations of the abstract theory the concepts introduced may be integral values over the entry and the exit sections to be agreed upon as ade-20

quate for the purpose at hand.

For equivalent propulsors, being formal constructs, not real propulsors, the basic magnitudes outside the displacement wakes ‘far behind, in the en-ergy wake alone’ are the same. The concept of equivalent propulsors, one of the most fruitful concepts in ship theory, has been introduced by Fresenius 25

and has first been exploited systematically by Fritz Horn at Berlin.

22.3.2.2 DERIVED CONCEPTS

Before introducing any axiom it is convenient to introduce derived con-cepts. If phrased in terms of energy velocities

V X ≡ [2 E F X

/ (ρ Q)] 1/2 30

and the corresponding energy wake fractions

w X ≡ 1 − V X / V H .

the theory becomes particularly suggestive.

With the corresponding energy densities


29.10.2008 13:55 h

e X ≡ E F X

/ Q ≡ ρ V X 2 /2

the propulsor 'head' becomes

∆ e ≡ e J − e E ≡ P J

/ Q ≡ ρ (V J 2 − V E

2) /2

and thus the concept of jet power

P J ≡ E F J − E F

E ≡ Q ∆ e . 5

Further the concepts of the corresponding 'invariant' momentum’ flows

M X ≡ ρ Q V X ≡ (2 ρ Q E F X) 1/2

are introduced. They permit to switch from the discussion in terms of energy flows and powers to the discussion in terms of momentum flows and 'forces'. 10

In view of the fact that the basic concepts introduced are of integral nature the derived 'specific' concepts represent averages, maybe time and space av-erages.

22.3.2.3 AXIOMS

The axioms of the meta-theory of propulsion are the momentum balance 15

m d t V H + R E = T E + F

and the 'law' for the effective thrust

T E = M J − M E = ρ Q (V J − V E) .

At steady self-propelled conditions the inertial term and the external force F vanish, so that the momentum balance reduces to 20

R E = T E ,

The equation for the effective thrust is not a formal definition of the concept but an 'implicit', an 'axiomatic definition' in Hilbert's terms, a coherent defi-nition in the context of the language developed.

In earlier expositions of the axioms the author missed to distinguish 25

clearly between the effective resistance and the effective thrust and just used the resulting balance

R E = ρ Q (V J − V E) .

at steady self-propelled conditions.


22.3.3 Derived concepts, theorems

22.3.3.1 PERFORMANCE MEASURES

Of particular interest among further derived concepts are the three per-formance measures, the internal efficiency

η J P ≡ P J / P P , 5

the configuration efficiency

η TE J ≡ T E V H / P J

and the product of the two, the propulsive efficiency

η TE P ≡ η TE J η J P .

In the present context the internal efficiency, comprising the efficiencies 10

of the 'pumps' proper, maybe rotor-stator configurations, and the 'ducts', consisting of inlets, may be diffusers, and outlets, may be nozzles, will not be discussed in detail, but will be considered as 'given' or to be identified.

22.3.3.2 PROPULSIVE EFFICIENCY

In terms of the energy velocities the configuration efficiency is 15

η TE J = 2 V H / (V E + V J) = 2 V H

/ (2 V E + ∆ V) ,

with the difference

∆ V ≡ V J − V E ,

and thus explicitly

η TE J = 1 / (1 − w E + τ E /2), 20

with the 'vorticity' parameter

τ E ≡ ∆ V / V H = T E / (ρ Q V H) .

being a measure of the propeller loading often more convenient than the normalised propulsor head.

This little known expression confirms the well known rule that the con-25

figuration efficiency increases with increasing mass flow through the pro-pulsor. Further it clearly shows that the configuration efficiency is inde-pendent of hull-propeller interactions contrary to convictions falsely held by most naval architects.

Thus the propulsive efficiency 30

η TE J = η J P / (1 − w E + τ E

/2),


29.10.2008 13:55 h

depends on three parameters: the pump efficiency, the energy wake fraction and the 'vorticity' parameter.

In terms of the normalised propulsor 'head'

ε E ≡ ∆ e / (ρ V H 2 /2)

the vorticity parameter is 5

τ E = [(1 − w E) 2 + ε E)] 1/2 − (1 − w E) ,

and thus in first approximation

τ E ≈ ε E / [2 (1 − w E)] .

Concerning the notation it important to note that the normalised propulsor 'head' is identical with the thrust loading ratio (Schubbelastungsgrad) only if 10

the propulsor model adopted is the actuator disc, a choice not particularly adequate in general. In order to avoid any confusion the author saw no other choice than to abandon the traditional symbol and to use a different symbol to denote the energy loading ratio, a much more general concept.

In accordance with the motto taken from Goethe's conversations, all these 15

explicit relationships resulting from inspectional analysis cannot be arrived at by 'induction'. The expression for the 'vorticity' parameter clearly shows that only the effective thrust is energetically relevant. The 'vorticity' parame-ter is a fundamental parameter not 'normally' used by naval architects.

22.3.3.3 THEOREMS 20

The essential result is that all propulsors, essentially pumps, producing equal jets 'far behind', outside the displacement wake, are equivalent, inde-pendent of the thrust they develop! The configuration efficiency, the true measure of performance, is the same for all of them.

Along this line of thought a design procedure for wake adapted ducted 25

propulsors has been developed and successfully tested (Schmiechen, 1994). The advantage of this procedure is that all interactions are accounted for implicitly.

Positive energy wake is not a gift of heaven, but is produced by the vessel itself, by skin friction. Thus the rule to take advantage of the energy wake 30

does not imply that one should purposely produce such wake although the configuration efficiency increases with increasing energy wake fraction. At the same time the effective resistance increases and thus the vorticity pa-rameter.


22.3.3.4 LIMITING CASE

In the limiting case of deeply submerged vehicles the energy wake repre-sents the whole resistance. Assuming uniform wake flow

V E = (1 − w E) V H

V J = V H 5

the frictional resistance becomes

R F = ρ Q F [V H − V H (1 − w E)] = ρ Q F V H w E .

Usually there are other components of resistance, typically wave resistance, and other 'propulsive' forces, typically wind from behind, acting on a vessel balanced by the effective thrust, at steady condition 10

T E = R E − F = R F + R R − F .

If in the absence of other resistance components and other propulsive forces the propulsor digests the whole energy wake the configuration effi-ciency

η TE J = 1 / (1 − w E /2) 15

is maximum. With increasing energy wake fraction the resistance increases and thus the power required. In the limiting case considered the jet power

P J = ρ Q R V H 2 w E (1 − w E

/2) = ρ Q R V H 2 (w E − w E

2 /2)

increases only slightly less than proportional to the wake fraction.

Under given circumstances the jet power has a minimum value and the 20

really interesting question is how close a given design comes to that value. The traditional practice to fit submarines, torpedoes and airships with gently tapered tails is not optimal as it involves flow deceleration with correspond-ing energy losses. Advanced designs show hull diameters increasing up to the intake of hull integrated propulsors. 25

All these considerations support the departure from the naïve concept of propulsors as thrusters overcoming the resistance of bodies to be propelled. Much more adequate is to conceive propulsors as pumps feeding energy into mass flows, preferably drawn from the energy wakes. The condition of self-propulsion is the condition of vanishing net momentum flow into the hull-30

propulsor system.


As required this abstract theory in terms of energy flows or rather energy veloci-

ties permits to discuss propulsion without reference to thrust. The theorem on the

configuration efficiency derived clearly shows that hull-propulsor interactions due 35

22.4 Ideal propulsors: open 1211

29.10.2008 13:55 h

to displacement effects do not affect the propulsive performance. If such effects are

observed one is not comparing equivalent propulsors but apples and pears.

CONCLUSIONS

Before the naïve conception of propulsion is left it is rationally reconstructed, by

the way providing a number of fundamental insights and solutions. 5

22.4 Ideal propulsors: open

PROBLEMS

Traditionally the theory of ideal propulsors, modelled as actuator discs, in ideal

fluids is taught as introduction to propulsion theory.

MODELS 10

In the present context the theory of ideal propulsors is treated as the first in-

stance of the meta-theory of propulsion. The basic case considered is that of pro-

pulsors of any 'design' in 'open water', not interacting with a hull to be propelled,

the ideal fluid at large being at rest in the observation space.

GOALS 15

The goal is an exposition clearly showing the implications hardly known al-

though the theory is taught at all schools of naval architecture.

PLANS

After discussion of the momentum, the energy and the vortex theory the pump

theory will be introduced. 20

22.4.1 Momentum theory

22.4.1.1 CAUSES AND EFFECTS

The fundamental theory of ideal propulsors is the momentum theory (Strahltheorie) of Rankine-Froude. Ideal propulsors advancing at constant speed into ideal fluids at rest are usually nearly exclusively modelled as ac-25

tuator discs in view of open water screw propellers. This view is much too narrow, as it does not permit to gain insights into the important aspects and implications of the theory.

In accordance with the momentum balance over an integration volume fixed in an observation space moving with the propulsor it is of primary im-30

portance to distinguish clearly between the effect, the propulsor race or the jet, and its cause, the propulsor itself, generating the jet.


In traditional expositions this distinction of propulsors and their effects is not being made, but the physically unsatisfactory model of the actuator disc is introduced right at the beginning, although other, more satisfactory mod-els for propulsors of finite loading, force fields, maybe in ducts, can be con-structed (Schmiechen, 1978) and are now being used in CFD computations 5

(Schmiechen, 1988.p).

22.4.1.2 MOMENTUM BLANCE

The relevant paragraph from the discussion of the momentum balance at large is repeated here for ready reference:

For steady flows in ideal fluids the boundary is chosen at such a distance 10

that the diffusive momentum flow, the pressure integral vanishes in the time average

M D fluid i = − ∫ p dA i = 0 i

and the balance in terms of time averaged magnitudes reduces to the thrust equation 15

T i ≡ − (M D.solid i + M P

i) = M C i .

The interesting point is that the thrust depends on the 'output' only and not on the details of its generation. Propulsors with equal output are equivalent. The freedom of generating models according to Plato's metaphor is at the same time the freedom of engineers to produce a given output with different 20

designs. 'Hamburgers' should not confuse this great freedom with their 'Große Freiheit'.

An ideal propulsor moves with speed v 0 into an ideal fluid of density ρ , in general at rest. Consequently the velocity of the volume flow Q is − v 0 far ahead of the propulsor, where the pressure integral vanishes. 25

In the technical jargon the volume flow is called 'volume flow rate', which is a pleonasm. The basic concept of flow implies 'rate'. The corresponding notation 'Q dot ', permitted by the German standards, is totally misleading. Standardly the 'dot' denotes time derivatives, and there is no vessel of vol-ume Q in the ocean from which the flow 'derives'. 30

The propulsor produces a steady flow with uniform velocity − v 2 far be-hind the propulsor, where again the pressure integral vanishes. For conven-ience it is assumed that the jets are circular cylinders. The stability of these flows is not subject of this theory.

Considering only the one-dimensional case the vector notation can be 35

dropped and the thrust equation is obtained in the usual format

T = M C = ρ Q (v 2 − v 0) ,


29.10.2008 13:55 h

remembering that T is a reaction and that the convective momentum flow into the integration space is counted positive.

22.4.2 Ideal propulsor

In view of the open screw propeller the usual model of an ideal propulsor is the so called actuator disc, a singular external pressure jump resulting in a 5

corresponding jump of energy density in the fluid.

The disadvantage of this model is its edge singularity studied by Sparen-berg and his student (SchmidtHG

, 1977). The edge singularity can be avoided if a duct is being introduced. In this case there are pressure differences at the duct already in the ideal case defined by vanishing net-thrust. In this case 10

the vortex distributions at duct entry and duct exit are counter-rotating, the thrusts compensating each other.

A much more instructive and convenient propeller model than the singu-lar actuator disc is an extended potential force field producing only a circu-lar vortex sheet (Schmiechen, 1978). How to construct such potential force 15

fields of limited extension has been described in the reference quoted.

At the edge of the force field a velocity difference, the vortex sheet gradually builds up, but there are no pressure differences across the sheet. Thus an infinitely thin duct at the edge of the ideal force field does not 'pro-duce' any thrust. Only if the generating line of the duct differs from the ideal 20

flow line local pressure differences occur and net thrust may be 'produced' at the duct. In case of non-shock-free a singularity occurs at the leading edge contributing to the thrust as shown by Föttinger in 1918.

At non-ideal ducts the pressure differences correspond to additional (!) velocity differences, i. e. additional (!) vortex distributions along the gener-25

ating lines. The relationship between the pressure and the vortex distribu-tions is given by the vortex velocity, the average of the internal and external velocities. As the resulting local force is normal to the flow the local forces and thus the net thrust is powerless. Essentially the same stories apply in cases of ducts with finite displacements. 30

Potential force fields have been produced in a Japanese project using magneto-hydrodynamics effects. Usually they are implemented by ideal pump stages, rotors and stators, or vice versa, ideally with infinite numbers of frictionless blades. The rotors, feeding the energy into the fluids, produce potential vortices, the rotational momentum (Drall) of which is 'extracted', 35

converted into thrust in the stators. In case of finite numbers of frictionless blades the situation remains essentially unchanged.


The jet remains essentially ideal except at the edge where the vortex sheet is no longer ideally continuous but consists of discrete screw and line vor-tices, such that the axial vorticity vanishes as in the ideal case. In case of real blades, complicated by gaps at the rotor-tips and the boundary layers at blades and ducts, CFD and overlaying optimisation methods provide the 5

adequate tools for the final design of the blades and the duct.

22.4.3 Jet power, efficiency

In terms of the meta-theory the velocities of the mass flow at infinity cor-respond to the energy velocities at the entrance

V E = v 0 10

and in the jet

V J = v 2 ,

respectively. Accordingly the effective thrust equals the thrust

T E = T

and with the internal efficiency 15

η J P = 1

of the ideal propulsor the power delivered equals the jet power

P P = P J = Q ∆ e .

Due to the absence of an energy wake

w E = 0 20

the speed of the system equals the velocity ahead

V H = V E = v 0 .

In the absence of a hull it will be convenient to introduce the propeller (ad-vance) speed

V P = V H . 25

Consequently the configuration efficiency equals the propulsive or jet ef-ficiency of the propulsor

η TE P = η TE J η J P = η T J ≡ T V E / P J ,

which becomes

η T J = 2 v 0 (v 2 − v 0) / (v 2

2 − v 0 2) 30

= 2 v 0 / (v 2

+ v 0) = 2 v 0 / [2 v 0 + (v 2

− v 0)] ,


29.10.2008 13:55 h

for all equivalent ideal propulsors producing equal jets. Thus the propulsive or jet efficiency of ideal propulsors

η T J = 1 / (1 + τ Ε /2) ,

solely depends on the vorticity ratio

τ Ε = τ ≡ (v 2 − v 0) / v 0 . 5

Introducing the power or energy load ratio

ε Ε = ∆ e / (ρ v 0 2 /2)

of the propulsor the vorticity ratio is

τ Ε = (1 + ε E) 1/2 − 1

and thus the jet efficiency becomes 10

η T J = 2 / (1 + (1 + ε E) 1/2) .

Already the presentation of these few elementary facts in lectures at Ger-man universities has caused considerable, emotional discussions, painful departures from beloved instinctive, but hopelessly confused beliefs. The whole theory applies to any ideal propulsor, feeding energy uniformly into a 15

mass flow, independent of its design.

One of the reasons for the emotional reactions is that in case of the only, 'universally' adopted propeller model, the actuator disc, the energy load ratio happens to equal the thrust load ratio, thus traditionally denoted by

c T ≡ 2 T / (ρ Q V P) ≡ 2 A P ∆ e / (ρ A P V P 2) 20

= 2 ∆ e / (ρ V P 2) ≡ ε E ,

the flow velocity at the propeller happens to equal the group velocity of the jet generated.

As will be shown, the thrust load ratio is an ill-defined concept, not useful for the evaluation of propulsors in general. The discussion on Grim's 'Leid'-25

Rad, which has aroused some interest, provides a simple example (Schmie-chen, 1966).

22.4.4 Vortex theory

The ideal propulsors are shedding vorticity. The velocity

v 1 = (v 2 + v 0) /2 30

is the group or energy velocity of the vortex sheet with density of vorticity

γ = v 2 − v 0 .


This singular sheet separates the jet flow with energy density

∆ e = ρ (v 2

2 − v 0 2) /2 = ρ γ v 1

from the surrounding fluid.

In terms of the energy velocity the jet efficiency of the propeller is simply

η T J = v 0 / v 1 , 5

a rule which holds in general for any type of vortex street. The group veloc-ity is the 'integrating' factor of the vortex street similar to the absolute tem-perature is in thermodynamics. If the group velocity can be easily observed, as at rowing boats, the efficiency can be determined according to this law without thrust and power measurements, from kinematical observations 10

only!

Very often 'advanced' vortex theory is considered to have left 'old fash-ioned' momentum theory behind, although both are two sides of the same medal (Gunsteren, 1973). All inventors claiming that their propulsors do not produce vortices have missed the basic lectures in hydromechanics. Only in 15

the limiting, not particularly interesting case of vanishing thrust there are no vortices produced. The problem of propulsor design is to produce optimum vortex configurations in optimum fashions.

22.4.5 Pump theory

This exposition shows that even in this case the propulsor may be consid-20

ered as a pump, which can be treated in terms of volume flow and energy density, 'head' in engineering jargon, or in terms of mass flow and mass spe-cific energy, in ideal fluids invariant with respect to the choice of the inte-gration boundary. This aspect is of fundamental importance for the design and the evaluation of propulsors. 25

While usually in pumps the thrust is a nasty by-product, in propulsors it is falsely considered to be of primary concern. In pump design the thrust is treated implicitly. This can be done in propulsor design as well, permitting to account implicitly for all intricate hull-propeller interactions (Schmie-chen, 1994). 30

That the thrust is a nasty by-product applies in particular to the thrust of ducts. Contrary to the widely, but falsely held instinctive belief the purpose of ducts is not to provide thrust but to avoid edge singularities, thus permit-ting to realise nearly ideal propulsor performance.

22.5 Ideal propulsors: behind 1217

29.10.2008 13:55 h

According to the momentum theory the thrust of ducts depends solely on the ratio of the actuator area to the jet area, independent of the form and pro-file of the ducts provided flow separation and cavitation are avoided.

With the actuator thrust

T A = ρ A A ∆ e = ρ A A (v 2 2 − v 0

2) /2 5

and the total thrust

T P = ρ A 2 v 2 (v 2 − v 0) ,

the relative thrust of the actuator is

T A / T = A A

/ A 2 (1 + v 0 / v 2)

/2 = A A / A 2

/ η T J

and thus the relative thrust of the duct 10

T D / T = 1 − T A

/ T = 1 − A A / A 2

/ η T J .

Consequently, the smaller the actuator and the smaller the propulsor loading the higher the thrust at the duct, but the higher the frictional losses and the dangers of flow separation and of cavitation.

All pumps producing equal jets 'far behind' are equivalent! As will be 15

seen this concept due to Fresenius (1921) is extremely powerful for propul-sors in uniform wakes and in 'real', non-uniform wakes.

Evaluating real ducted propulsors in open water turned out to be more dif-ficult in detail than expected. Only recently a proposal for a rational proce-dure has been developed and applied (Schmiechen, 2007). 20

EVALUATIONS/ASSESSMENTS/CONCLUSIONS

The detailed exposition of the theory of ideal propulsors shows that the tradi-

tional teaching does not explain the essential features and does not exploit the full

potential of the theory.


"Halbe Theorie führt von der Praxis ab − ganze zu ihr zurück."

Novalis (2001/96).

PROBLEMS

Usually propulsors do not operate in open conditions but usually behind hulls of 30

ships causing displacement and energy wakes.


MODELS

In order to study the effects of the wakes on propulsor performance ideal pro-

pulsors in ideal displacement, ideal energy and ideal mixed wakes are being con-

sidered. The powering performance will be obtained by constructing equivalent

ideal propulsors outside the wakes. 5

GOALS

Again the goal is to develop the theory in view of the implications and its use as

a model in the axiomatic theory of hull-propulsor interactions. The essentials of

this theory have been discussed by Fresenius (1921), basically in the same way and

already stressing many fundamental points. 10

PLANS

After discussion of the configuration and hull efficiencies in terms of the wake

and thrust deduction fractions the thrust deduction fraction will be considered as

function of the wake fraction and the wake ratio, the displacement influence ratio.

The global approximation of this function provides for a simple thrust deduction 15

axiom which has first been used in a pragmatical approximation in the METEOR

project.

22.5.1 Equivalent propulsors

In general propulsors do not operate in open water but in wakes. The fun-damental concept for the study of the propeller in the wake, on a modified 20

pressure level, is that of the equivalent propulsor operating outside the wake. Equivalent propulsors do not need to have the same losses, ideally they have no losses. Thus in referring to them only the jet performance has to be taken into account!

In accordance with our instinctive beliefs the equivalent propulsor is de-25

fined by the constitutive equations in terms of the volume flow

Q E = Q

and the energy density

∆ e E = ∆ e ,

provided that the equivalent propulsor produces the same jet as the original 30

propulsor after its jet has left the wake.

The conditions of equivalence correspond to the energy equation

∆ e = ρ (v J 2 − v E

2) /2 = ρ (v 2 2 − v 0

2) /2

and the power equation

P J = Q E ∆ e E = Q ∆ e , 35


29.10.2008 13:55 h

respectively.

22.5.2 Displacement wakes

In the simplest case the wake is uniform 'displacement' wake. The termi-nology is referring to the fact that such wake is usually due to the displace-ment flow around the hull of a vessel. In the present context it is not impor-5

tant to know how this wake is generated, but to assume the wake to be infi-nite.

Consequently ideal propulsors in the wake are exactly behaving as before, but on a pressure level different from that outside the wake, the simple in-stantiation to be replaced by the BernoulliJ equations in the volume flow 10

ahead

e E = ρ v 0 2 /2 + ∆ p = ρ V E

2 /2 ,

and behind the propulsor

e J = ρ v 2 2 /2 + ∆ p = ρ V J

2 /2 ,

meeting the condition of equivalent propulsors 15

∆ e = ρ (v 2

2 − v 0 2) /2 = ρ (V J

2 − V E 2) /2 .

Due to the absence of energy wake

w E = 0

the advance speed of the equivalent propulsor equals the energy velocity

V PE = V E , 20

but the advance speed of the propulsor in the wake is reduced by the dis-placement wake fraction

V P = v 0 ≡ (1 − w D) V E .

The pressure level at which the propeller operates in the wake becomes

∆ p = ρ (V E 2 − v 0

2) /2 = (1 − (1 − w D) 2) ρ V E 2 /2 , 25

in first approximation

∆ p ≈ w D ρ V E 2 .

This pressure level is hardly ever mentioned.

Particularly in cavitation testing in traditional cavitation tunnels it is not accounted for, different from the vapour pressure, which is of the same or-30

der of magnitude and is meticulously monitored. The reason is that separa-


tion of the wake components is not even attempted in traditional perform-ance testing and analysis.

22.5.3 Thrust deduction

While the jet powers of the two equivalent propulsors are equal by defini-tion their thrusts are not. The thrust of the equivalent propulsor 5

T E ≡ T (1 − t) .

is smaller than that of the propeller in positive displacement wake. From the definitions of the nominal areas of the actuator discs

Α PE ≡ T E / ∆

e

Α P ≡ T / ∆ e 10

the relationship

Α PE / Α P = T E

/ T = 1 − t .

is obtained. Accordingly the nominal area of the equivalent actuator disc is as much smaller as the thrust is smaller than the corresponding magnitudes of the propeller in the displacement wake. 15

While the name 'thrust deduction fraction' is correct, the concept is tradi-tionally introduced in terms of the resistance of the vehicle to be propelled. This is a misleading confusion of the definition of the thrust deduction with the momentum balance.

In German even the terminology reflects this confusion. 'Sog' (suction) 20

S ≡ T − T E

and 'Sogzahl', alias 'Sogziffer'

t ≡ (T − T E) / T

are grossly misleading, implying without due notice the momentum balance

R = T E 25

and further Froude's convention

R = R T ,

the interpretation of the resistance in terms of the towing resistance of the hull alone provided that concept can be operationally interpreted.

As has been pointed out in the paper presented at the Centenary of the 30

Opening of VWS 2003 the thrust deduction is 'trivially' balanced by the suc-tion at the hull, both representing an energetically neutral short circuit.


29.10.2008 13:55 h

'Looking' towards the hull, at the suction is truly looking in the wrong direc-tion, missing the essentials happening behind the ship, outside the displace-ment wake.

22.5.4 Configuration efficiencies

As both equivalent propulsors produce the same jet in the far field their 5

configuration efficiencies

η TE J ≡ T E V E / P J = (1 − t) / (1 − w D) (T V P

/ P J) ≡ η TE T η T J

are the same. So, by definition of the equivalent propeller, whatever may happen in the wake is irrelevant for the energy balance! Fresenius has al-ready clearly stated this fact. 10

The ratio of the two jet efficiencies

η TE T ≡ (1 − t) / (1 − w D) = η TE J / η T J

is traditionally called hull efficiency for the reason stated, displacement wakes occurring in practice near hulls of ships. Expressing the two jet effi-ciencies in terms of the energy load ratio of the propeller in the wake 15

η TE J = 2 / (1 + (1 + ε (1 − w D) 2) 1/2)

and

η T J = 2 / (1 + (1 + ε) 1/2) ,

the definition provides the explicit expression

t = 1 − (1 − w D) (1 + (1 + ε) 1/2) / (1 + (1 + ε (1 − w D) 2) 1/2) 20

for the thrust deduction fraction as a function of the energy load ratio and the displacement wake fraction.

For positive displacement wake fraction the hull efficiency is

η TE T ≡ (1 − t) / (1 − w D) > 1

and consequently the thrust deduction fraction is smaller than the displace-25

ment wake fraction

t < w D .

The hull efficiency is not an efficiency proper and consequently is cau-tiously called 'hull influence ratio' (Rumpf-Einflussgrad) in German.

The values usually larger than 1 have nourished the hope that something 30

is 'to be gained' for nothing. But as has been mentioned the displacement wake fraction and the thrust deduction fraction 'neutralise' each other as far


as the energy balance is concerned. Not the jet efficiency but the configura-tion efficiency of the equivalent propulsor is the 'true' and invariant measure for the performance of a given configuration.

The same remarks hold for negative displacement wake fractions result-ing in negative thrust deduction fractions. In this case the propeller thrust is 5

smaller than the effective or equivalent thrust balancing the resistance of a vessel in steady motion. Often this case is considered to be physically im-possible, considered to represent a sort of perpetuum mobile. But this falsely held instinctive belief is not supported by the theory of interaction.

22.5.5 Thrust deduction: transformed 10

The law for the thrust deduction fraction can be transformed by introduc-ing other parameters instead of the energy load ratio and the displacement wake fraction. One such set of interesting physical parameters is the vortic-ity ratio

τ = (1 + ε) 1/2 − 1 15

and the displacement influence ratio or wake ratio

χ ≡ w D / (1 − w) .

In terms of these parameters the thrust deduction fraction is explicitly

t = [1 + τ + χ − [(1 + τ + χ ) 2 − 2 τ χ] 1/2

] / τ .

This relation has been derived by Horn in 1956 and has since been re-20

derived many times, by the author in 1978.

An extremely simple and useful global approximation of this relation

t = 0.58 χ η T J

holds in the ranges

η T J = 0 ... 1 25

χ = 0 ... 1

within a few percent. It is the plausible basis of a very pragmatic thrust de-duction axiom to be discussed further down (Schmiechen, 2005.p). Depend-ing on the purpose at hand and the parameter range of interest other, more precise local approximations may be derived. 30

22.5.6 Thrust deduction: limit

Less useful in practice, but of historical interest is the local approximation


29.10.2008 13:55 h

t ≈ χ / (1 + τ + χ) ,

which holds under the condition

2 τ χ << (1 + τ + χ) 2 .

In Dickmann's 'legendary paper' (Nowacki, 1972) of 1939 the considerations are limited to propulsors of vanishing load ratio. Dickmann's result was 5

t ≈ χ / (1 + τ / 2 + χ)

and Horn (1956) has already noticed, that it is based on the unnecessary ap-proximation of vanishing load ratio. Dickmann forgot his own approxima-tion and used his result not only for small load ratios but up to values of 3 !

Concerning the energetic situation Dickmann's statements are 'unclean'. 10

He expressed the opinion that the influence of a positive displacement wake is negative. This is true only if propellers of equal size, if apples and pears are being compared. Fresenius has clearly described that equivalent propel-lers are not of equal size.

Later Nowacki and Sharma have again used Dickmann's approximation 15

and obtained the approximation (1972)

t ≈ χ / (1 + τ /2) .

If, following Horn, the condition of vanishing load ratio, the approximation

Q S / (A v 0) = τ

for the equivalent sink strength, is replaced by the correct relation 20

Q S / (A v 0) = τ (1 + τ /2)

/ (1 + τ)

valid for all load ratios, the result is

t ≈ χ / (1 + τ) = χ / (1 + ε E) 1/2 .

The missing of the wake ratio in the numerator may be due to linearisations necessary in those days. 25

Even these simple considerations permit to clarify the essential aspects of hull-propeller interactions, although a hull proper has not yet been intro-duced.

22.5.7 Energy and mixed wakes

22.5.7.1 ENERGY WAKE ALONE 30

In practice propulsors operate not only in displacement wakes, but in wakes composed of displacement and energy wakes. The equivalent propul-


sor 'far behind', outside the displacement wake, operates in the energy wake alone at the speed

V PE = V E = V H (1 − w E)

Consequently the configuration efficiency is

η TE J ≡ T E V H / P J = 1 / (1 − w E) (T E V E

/ P J) 5

with the hull influence factor

η TE T = 1 / (1 − w E) .

Propulsors far behind do not 'interact' with the hulls.

22.5.7.2 MIXED WAKES

The performance of the ideal propulsor in the mixed wake is obtained by 10

comparison with the equivalent propeller studied before. Again the condi-tion of equal configuration efficiency is the starting point:

(1 − t) / (1 − w) (T V P / P J) = 1 / (1 − w E) (T E V PE

/ P J) .

Consequently the explicit relation for the thrust deduction fraction is

t = 1 − (1 − w) (1 + (1 + ε) 1/2) / 15

/ [(1 − w E) (1 + (1 + ε (1 − w) 2/(1 − w E) 2) 1/2)]

with the total wake fraction

w = w D + w E .

This results in exactly the same relation

t = [1 + τ + χ − [(1 + τ + χ ) 2 − 2 τ χ] 1/2

] / τ . 20

as for the propulsor in the displacement wake but with the factor (1 − w D) replaced by the factor (1 − w) / (1 − w E) resulting in the complete definition of wake ratio

χ ≡ (1 − w E) / (1 − w) = w D / (1 − w E − w D) .

The result deduced by elementary algebra starting from the invariance of the 25

configuration efficiency for equivalent propellers, could have obtained al-ready by Fresenius.

22.5.8 Real propulsors in real wakes

There are no ideal propulsors and there are no ideal uniform wakes be-hind ship hulls. Thus the above theory is not of direct use, but may be and 30


29.10.2008 13:55 h

will be used as the model of an axiomatic theory of real propulsors operat-ing in real, non-uniform wakes.

Consequently the axiomatic theory is abstracted from the above theory, which serves as a sufficiently rich model. Although this is implied by the traditional teaching and in all engineering considerations, to the knowledge 5

of the author it has never before been done explicitly and coherently.

Accordingly the thrust deduction fraction will be considered as a function of two parameters in close accordance with the result of inspectional analy-sis stated before. All former attempts to establish a relationship between wake and thrust deduction fractions were doomed to fail due to two reasons: 10

• Firstly, the traditional way of testing is much too crude to pro-vide the data necessary. The essential parameter, the wake ratio, is not identifiable from data taken in traditional ship model test-ing. So all the 'historical' data cannot even be re-evaluated!

• Secondly, even with sound data, the above law could never 15

have been arrived at by 'induction'.

Further the values of the wake ratio are different on model and on full scale due to scale effects in the wakes. Consequently the values of the thrust deduction fraction are different at the condition of equal load ratio on model and on full scale, contrary to the traditional 'axiom' of model ship correla-20

tion, which 'postulates' equal values on model and on full scale.

In order to dismantle this tribal lore one has to recall Froude's procedure, which is still followed in the 'continental method to account for scale ef-fects'. In model testing a towing force, called 'frictional deduction', is ap-plied to relieve the model propeller in a standardised way and nothing more. 25

This is the crudest possible, and over a century extremely successful prag-matism, but it clearly establishes neither equal load ratios nor equal wake ra-tios nor equal thrust deduction fractions on model and full scale.

This and other inconsistencies of the traditional evaluation of ship per-formance have triggered the work of the author on a rational theory of pro-30

pulsion to be discussed now and showing that a consistent and satisfactory rational procedure and at the same time an extremely efficient procedure is not only possible in principle, but in practice as well.


The theory of ideal propulsors in uniform wakes provides a number of theorems 35

of great interest, but not usually taught to naval architects to-be.


CONCLUSIONS

The theory developed provides a sufficiently rich model for an axiomatic theory

and thus the assessment of the hull-propeller interactions in case of real propellers

in real wakes on model and on full scale.

22.6 Quasi-steady trials 5

"In jenen Jahren, wohin gedachter Aufsatz fallen möchte, war ich hauptsächlich mit vergleichender Ana-tomie beschäftigt und gab mir 1786 unsägliche Mühe, bei anderen an meiner Überzeugung: dem Menschen dürfe der Zwischenknochen nicht abgesprochen werden, Teil-10

nahme zu erregen. Die Wichtigkeit dieser Behauptung wollten selbst sehr gute Köpfe nicht einsehen, die Rich-tigkeit leugneten die besten Beobachter, und ich mußte, wie in so vielen andern Dingen, im stillen meinen Weg für mich fortgehen." 15

Johann Wolfgang Goethe: Erläuterungen zu dem

aphoristischen Aufsatz 'Die Natur', 1828 (1960/48-

49; GA 16/925).

PROBLEMS

In order to overcome the deficiencies of Froude's method for the analysis of the 20

powering performance based on propeller open water tests and on hull towing tests

the theory of propellers in uniform wakes has to be applied to real propellers in

real wakes.

MODELS

The models for the identification of the basic interactions, wake and thrust de-25

duction, are the energy balance for the propeller and the momentum balance for

the ship together with additional axioms replacing the propeller open water tests

and the hull towing tests.

GOALS

The goal is to provide an exposition of the problems and their solution in terms 30

so convincing, 'dass selbst sehr gute Köpfe die Wichtigkeit dieser Behauptung ein-

sehen und die besten Beobachter die Richtigkeit nicht länger leugnen können'.

PLANS

The plan is to develop only the details of the rational interpretations of wake and

thrust deduction fractions. The determination of the values for all other magnitudes 35

is a matter of elementary algebra.


29.10.2008 13:55 h

22.6.1 Propellers behind

As has been explained by the author in many papers the traditional tech-nique of physical separation and subsequent separate investigation of hull and propulsor is no longer adequate for integrated hull-propulsor configura-tions, in the simplest case wake adapted screw propellers. Further this tech-5

nique is not applicable on full scale under service conditions for which the data are of interest.

The axiomatic model of hull-propeller interaction corresponds in all de-tails exactly to the hydrodynamic theory of ideal propulsors in uniform en-ergy and displacement wakes. In this limiting case it becomes identical with 10

that theory as necessary. Surprisingly that theory is hardly known explicitly, although it provides important insights into hull-propeller interactions.

For real screw propellers in non-uniform wake the 'ideal' theory may be considered as an approximation of the actual situation. But much more in-teresting and important is the approach, proposed by the author in 1980, to 15

use it as model of an axiomatic system for the implicit or coherent definition of magnitudes, which cannot be defined otherwise, namely the propeller ad-vance speed in behind conditions and the hull resistance at operational con-ditions.

In the case of an open screw propeller it has been shown in detail how an 20

equivalent ideal propulsor with internal losses can be constructed from data observed in a limited range of quasi-steady operation. For the screw propel-ler in the behind condition the wake fraction and thrust deduction fraction have to be identified, if a detailed analysis of the propulsive performance is of interest. 25

In traditional ship model testing the constitutive axioms permitting to de-termine wake and thrust deduction fractions are:

• the propeller advance speed equals the open water advance speed at the same thrust or torque,

• the resistance under propelled conditions equals the towing re-30

sistance of the hull.

Both these axioms are more or less 'evident' for slender hulls, but not in general, and most importantly, both cannot be 'applied' at full scale ships under service conditions.

This problem can only be resolved by replacing the traditional propeller 35

open water tests and hull towing tests and the axioms stated by more appro-priate axioms, i. e., plausible conventions. From a logical point of view plausibility is not necessary but in view of applications in continuation of


past practice plausibility not only of the axioms but of the related resulting values is of utmost importance, pre-requite for acceptance by the commu-nity.

The wake and thrust deduction axioms are fundamental for evaluating the powering performance of full scale ships objectively, without any reference 5

to model test results, which may have been used for the performance predic-tion and on which in turn the contract conditions may have been based.

For a complete analysis of the powering performance it is not sufficient to perform trials in the traditional way with the 'addition' of reliable thrust measurements but, at least on full scale, quasi-steady changes of state have 10

to be performed resulting in inertial 'forces' serving as 'external' forces nec-essary for the identification of the thrust deduction fraction.

In order to avoid clumsy terminology in the following the jargon 'un-known parameter' is being used for short where 'unknown value of parame-ter' would be correct. 15

22.6.2 Energy balance

22.6.2.1 BASIC AND DERIVED CONCEPTS

The basic equation for the determination of the total wake fraction is the energy balance of the propeller

T V P = η T J η J P P P 20

at steady conditions, with the propeller advance speed

V P ≡ V (1 – w) ,

the propulsive propeller efficiency or propeller jet efficiency

η T J ≡ P T / P J

and the hydraulic propeller efficiency or propeller pump efficiency 25

η J P ≡ P J / P P .

The jet efficiency is often called the ideal propeller efficiency. According to the present exposition this jargon is felt to be misleading. The concept of pump efficiency is rarely used by naval architects although it provides a sound measure for the 'quality' of a propeller design. In view of the very 30

large inertia of most ships it is sufficient to consider 'steady' propeller condi-tions, established quasi-instantaneously from 'the ship's point of view' with its large time constant.


29.10.2008 13:55 h

22.6.2.2 JET EFFICIENCY AXIOM

If the 'apparent' propeller efficiency

η ≡ T V H / P ≡ K T J H

/ K P

and the 'apparent' energy load ratio

ε E ≡ 8 T / (ρ π D 2 V H 2) ≡ 8 K T

/ (π J H 2) 5

are introduced, both depending on measured values only, the theoretical function for the jet efficiency of an ideal propulsor in uniform wake, here adopted as axiom, becomes

η (1 − w) / η J P = 1 / (1 + (1 + ε E / (1 − w) 2) 1/2) .

Solved for the wake fraction the energy balance results in 10

w = 1 − η J P / η + ε η / (4 η J P) ,

the details of the derivation to be found in the file .../hpi_aswt.pdf .

Following Froude the propeller advance speed in the behind condition, in non-uniform flow, is axiomatically taken to equal the advance speed in the open condition, though in uniform flow, at the same thrust or the same 15

torque or some intermediate condition to be agreed upon.

The ambiguity of the definition has caused endless fruitless discussions concerning the 'correct' definition of the wake fraction. Further this axiom is only acceptable in case of slender hull forms, it is not acceptable in case of hull integrated propulsor configurations, and most important, it may be ac-20

ceptable, but it is not practical at full scale, propeller open water tests at full scale being 'impossible'.

All the problems encountered along the traditional approach can be avoided if the wake fraction is defined uniquely by the formula derived be-fore and is identified accordingly. Subsequently the propeller advance speed 25

and all the efficiencies of interest can be determined.

22.6.2.3 PUMP EFFICIENCY AXIOM

But there remains one problem to be solved: the hydraulic efficiency of the propeller has to be known. Accordingly the above axiom has to be com-plemented by an axiom for the hydraulic or pump efficiency. 30

In the narrow operational range of interest the axiom of constant hydrau-lic efficiency

η J P = const

is the crudest possible and plausible, provided the system is operating at de-sign condition. 35


This axiom is not plausible if finite ranges of load conditions are under considerations, but it has the advantage to limit the complexity of the model, permitting to get along with only two phenomenological parameters to be identified in a robust procedure.

The author has subjected the procedure to further extended conceptual 5

and numerical analyses triggered by detailed questions (Wagner, 2008). Fundamental issues have been clarified and finally, after various diversions, the correct application of the pump efficiency axiom has been implemented.

As a consequence of the axiom adopted all attempts to identify the two parameters based on data from a randomly selected set of operating condi-10

tions, maybe just two, are doomed to fail 'by definition', due to the model purposely simplified.

Thus in order to obtain meaningful results the range of operating condi-tions has to be shifted until the axiom is met as has been done in the final analysis of the 'model' test, to be discussed. 15

This procedure looks as if invented ad hoc, but it is indeed the procedure generally followed in systems identification, provided it is performed pro-fessionally. Any model implies limiting assumptions and after the identifi-cation of the parameters experts routinely check whether the underlying as-sumptions are met. Typical examples of such assumptions are the linearity 20

of balances and the normal distributions of noise during their calibrations.

In other contexts the procedure outlined is called 'testing of hypotheses'. In the present context this terminology is felt to be misleading. The 'disturb-ing' feature here is that the 'hypothesis', the simplification of the model is purposely very crude in order to permit a robust identification procedure. 25

This simple local axiom replaces the earlier very clumsy axioms coher-ently defining a global loss parabola (.../hpi_lpa.pdf) and resulting in a very unreliable procedure for the determination of the wake fraction, lacking the robustness necessary for everyday application in towing tanks and on board ships. 30

As has been shown in an earlier evaluation of the 'model' test the axiom can be relaxed a posteriori. If a rather wide range of the hull advance ratio is covered the pump efficiency of the propeller is not constant over the whole range, but has been approximated by a parabolic function of the ad-vance ratio, the parameters identified in a subsequent procedure. But this 35

procedure is now to be considered obsolete.


29.10.2008 13:55 h

22.6.3 Local wake axioms

22.6.3.1 NOMINAL WAKE FRACTION

At this stage the pump efficiency is an unknown propulsion parameter to be identified. Thus the pump efficiency axiom as it stands does not permit to identify the wake fraction, an additional wake axiom is necessary. 5

Simple, robust determination of the wake fraction can be based on the 'lo-cal' wake axiom

w = w T J η T J

with another propulsion parameter, the nominal wake fraction, relating the wake fraction to the propeller loading, measured in terms of the jet effi-10

ciency of the propeller.

Traditionally the nominal wake fraction is identified from local measure-ments in the propeller plane at hull towing tests. Here it is defined as the wake fraction at vanishing propeller thrust, at unit jet efficiency. Thus its value can be identified at model and at full scale. 15

Warning! The statement 'can be identified' does not imply that it can be identified at the physical state of vanishing propeller thrust, as Abkowitz has proposed (1988). In the physical state of vanishing thrust the flow condi-tions are in general no longer those prevailing under operational conditions. Further extreme engine manoeuvres suggested are not very popular with 20

chief engineers.

The jet efficiency is a 'dynamical' inverse measure of the propeller load-ing considered to be 'more meaningful' than the hull advance ratio, a 'kin-ematical' inverse measure of the propeller loading. The hull advance ratio has been used by the author as a convenient substitute as long as he could 25

not reliably determine the jet efficiency.

The nominal wake fraction is again axiomatically assumed to be constant

w T J = const .

The structure of these ad hoc axioms is based on the plausible argument that the wake decreases with increasing propeller load ratio, vanishing at infinite 30

load ratio.

But these axioms are still lacking a theoretical foundation, comparable with the foundation of the thrust deduction axioms to be discussed in the pertinent sections to follow.


22.6.3.2 PARAMETER IDENTIFICATION

The two parameters can now be identified by equating the wake fraction

w 0 (η J P) = 1 − η J P / η + ε η / (4 η J P)

according to the energy balance and the wake fraction

w 1 (η J P , w T J) = w T J η (1 − w) / η J P 5

according to the wake axioms. The equation

w 0 (η J P) = w 1 (η J P , w T J)

holds for any condition, thus it represents a system of non-linear equations to be solved iteratively.

It is explicitly repeated here that the limiting condition of constant hy-10

draulic efficiency, introduced to permit robust identification of the parame-ters, has to be observed.

22.6.3.3 FUNDAMENTAL PROBLEM SOLVED

In plausibility tests using performance data of a propeller in open water it has been shown that from the measured values of the frequency of revolu-15

tions, of the thrust and of the torque the speed of the propeller in open water can be re-constructed with great precision. Data and test results are to be found on the website of the author in the file 'Wake axioms'.

This result is of utmost theoretical and practical importance! For real pro-pellers in real wakes the concept of the propeller advance speed is a strictly 20

'theoretical' concept, not accessible to direct measurements. There is no un-disturbed flow, no open water ahead of the propeller, ahead of the propeller is the hull.

In the context of the present treatise, consistently focussing attention on 'motions' rather than 'configurations' in accordance with KaneTR (1985/X), 25

this is another example that the concept of speed, considered as a fundamen-tal state magnitude, can be rendered operational without reference to dis-tances travelled, not 'kinematically', but strictly 'dynamically', based only on measurements of rate of revolutions, thrust and torque of the propeller.

This result may have fundamental implications, maybe providing the 30

theoretical foundation sought for the local wake axioms.

22.6.3.4 SUBSEQUENT EVALUATIONS

After the wake has been determined the jet efficiency and thus the group velocity of the vortex street generated may be determined. The latter equals


29.10.2008 13:55 h

the flow velocity in the 'propeller plane', and permits to determine the flow rate.

In the re-evaluation of the 'model'-test and the METEOR ship and model data the method has been shown to be robust. All values including the scale effects in the wake fraction are in accordance with the 'expected' effects. 5

The details are to be found in the numerical tests on the website of the au-thor under 'News on propulsion'.

After all the procedure is meeting the standards envisaged and the nu-merical tests revealed that the earlier evaluation of the 'model' test acciden-tally provided 'correct results'. The hydraulic efficiency 'happened' to be 10

maximal in the randomly selected range of data investigated!

22.6.4 Alternative approaches

The following coverage of alternative approaches purposely provides de-tails of the complexity of the conceptual and numerical exercises performed.

22.6.4.1 SINGULARITY 15

After some preliminary 'fumbling' with ill-defined problems and ill-defined test data the reconstruction has been re-started from scratch based on the principle of objectivity, requiring the equivalent open water perform-ance to be independent of the randomly given sample of steady working conditions of the propeller. 20

And the first, fundamental results based on the original test data con-firmed the observation of Dr. Wagner that the problem of identifying the wake as originally stated is not only ill-conditioned, but that it is strictly singular.

With sets of data J H , K T , K P given the wake axiom for the propeller in 25

the behind condition

w = w T J η T J

with the nominal wake fraction

w T J = const

permits to identify equivalent open water conditions still depending on the 30

value of the nominal wake fraction.

The starting points are the same as before, the explicit law of the jet effi-ciency

η T J = 2 / [1+ (1+ ε E) 1/2]


with the energy loading

ε E ≡ 8 k T (J P) / (π J P 2) ,

adopted as an axiom and the axiom of the wake fraction

J P = J H (1 − w) .

The operational interpretation of these axioms requires that the speed 5

through the water and the thrust can be measured. These problems can be solved if in traditional steady trials the propeller in behind condition at the given load condition is calibrated as has been explained.

With a value of the nominal wake fraction assumed the equation

2 k T (J H) / [π J H 2 (1 − w T J η T J)

2] = 1 / η T J 2 − 1 / η T J 10

results for any hull advance ratio in the jet efficiency and thus in all other magnitudes of interest. In practice the values of the nominal wake fraction can vary only in a very limited range corresponding to the limited range of the maximum hydraulic efficiencies around 0.8 of advanced wake adapted propeller designs. 15

Of practical interest is the following observation. Contrary to the fictitious undisturbed flow velocity ahead of the propeller in the behind condition the physical flow velocity in the propeller plane, being proportional to the pump efficiency, depends only very little on the nominal wake fraction. Thus, in view of its limited range the nominal wake fraction is not really crucial as 20

far as design and evaluation of propellers is concerned.

22.6.4.2 NOMINAL WAKE FRACTION

That the problem is singular, providing consistent solutions for any value of the nominal wake fraction can be resolved only by an additional axiom as stated before, a convention to be agreed by the community concerned. This 25

is not a problem of the present proposal, but a fundamental problem of the traditional method as well.

Determining the nominal wake fraction according to Froude's method, re-ferring to the open water performance of the propeller, leads to the unre-solved problems that thrust and torque identities lead to different results in 30

model tests due to the non-uniformity of the wake, and that this reference is possible only on model scale.

During the development of the rational procedure over the decades a large number of different proposals have been made ad hoc, all leading to sensi-ble results, but all lacking the intuitive appeal and the robustness of Froude's 35

solution as has been stated explicitly by the author on many occasions.


29.10.2008 13:55 h

Thus the point was not to repeat this observation ad infinitum but to come up, with further, more satisfactory and generally acceptable proposals. There is no other way to identify full scale performance. And scale effects can only be identified if ship and model performances are determined ac-cording to the same method. 5

In the basic tests of the procedure the selection of the nominal wake frac-tion has tentatively been based on the relative location of the maximum hy-draulic efficiency assumed to be 0.558. The disadvantage of such a proposal is that it requires the extrapolation, which had been abandoned before. Thus the former convention, assuming the maximum pump efficiency in the range 10

of data, was definitely more robust and has been shown to solve the problem if applied correctly.

22.6.4.3 AN 'INTUITIVE' APPROACH

Instead of referring to the hydraulic losses of the propeller another, very intuitive approach tested has been to determine the nominal wake fraction 15

directly based on the propeller pitch and the propeller advance speed at the zero thrust condition.

As long as no other data are available the necessary calibration constant may be taken from open water tests with model propellers as in Froude's procedure. If propeller profile data are available the calibration constant 20

may be estimated according to a simple rule proposed, independent of open water tests, impossible on full scale anyway. This rule has been explained and successfully tested at the end of the test file.

This intuitive method is transparently linking up with the past practice and thus maybe acceptable for the community concerned. But further checks 25

have shown that the procedure, again requiring extrapolation, is applicable only in case of ordinary screw propellers but not in general, e. g., in the model test performed with a CP propeller model.

22.6.5 Momentum balance

22.6.5.1 BASIC AND DERIVED CONCEPTS 30

The basic equation for the determination of the thrust deduction fraction is the momentum balance of the ship

m d t V H + R (V H) = F + T E

at quasi-steady conditions, m denoting the total longitudinal inertia F denot-ing all external 'forces', maybe a 'frictional deduction', as applied in model 35


tests according to the continental method, or wind and wave resistance, and with the effective propeller thrust

T E ≡ T (1 – t) .

Naval architects rarely, if ever, use the concept of effective thrust, al-though it provides the only rational basis for talking about thrust deduction. 5

The English name hints at least in the right direction, while the German name, Sog, is grossly misleading as has been explained in detail earlier.

For the following considerations the translational inertia of the ship, in-cluding the aggregate inertia of the surrounding water, the 'added mass', is considered to be given and the acceleration is considered to be derived accu-10

rately from the speed over ground measured by means of the Global Posi-tioning System.

At a later stage the total longitudinal inertia may be introduced as another parameter to be identified. In the 'model' test evaluated the very small longi-tudinal hydrodynamic inertia could not be identified reliably. 15

22.6.5.2 RESISTANCE AXIOM

Thus the average thrust deduction fraction may be determined provided the law of the resistance is known. Accordingly the above axiom has to be complemented by an axiom for the resistance of the ship.

Following Froude the resistance is traditionally axiomatically taken to 20

equal the towing resistance. But this axiom is again only acceptable in case of slender hull forms, it is not acceptable in case of hull integrated propulsor configurations, and most important, but it is not practical at full scale, hull towing tests at full scale being 'impossible'.

Thus, in order to escape the dead lock the local axiom 25

R (V H) = r 0 + r 1 ∆ V H + r 2 ∆

V H 2

for the dependence of the resistance on the speed through the water

∆ V H = V H − V H mean

is adopted. If the range of speed covered is small a linear resistance axiom may be sufficient, if the range is large a higher order law has been shown to 30

be necessary.


29.10.2008 13:55 h


22.6.6.1 THRUST DEDUCTION AXIOMS

At this stage the resistance is a function with three unknown parameters to be identified. Thus the resistance axiom as it stands does not permit to identify the thrust deduction fraction, an additional thrust deduction axiom 5

is necessary.

According to the global approximation of the thrust deduction theorem the simple robust local thrust deduction axiom

t = t T J η T J

with the constant parameter 10

t T J = const ,

the nominal thrust deduction fraction, the thrust deduction fraction at unit jet efficiency, at vanishing propeller thrust has been adopted.

Traditionally the nominal thrust fraction is hardly ever referred to. One of the reasons may be that, not only for people talking in terms of suction, of 15

'Sog', disturbingly the value of the thrust deduction fraction, the 'Sogzahl', is largest at vanishing thrust.

The same warning applies here as in case of the nominal wake fraction. The statement 'can be identified' does not imply that it can be identified at the physical state of vanishing propeller thrust. In the physical state of van-20

ishing thrust the flow conditions are in general no longer those prevailing under operational conditions.

According to the global approximation of the thrust deduction theorem the value of the nominal thrust deduction fraction depends on the wake ratio

t T J = 0.58 χ . 25

Earlier, before the local wake axioms had been established and the jet ef-ficiency could be determined reliably, the axiom

t = t H J H

for the thrust deduction fraction has been used on model and full scale in evaluating the powering performance. 30

In model tests it has been observed that the resulting values of the 'effec-tive' resistance have always been very close to the values of the towing re-sistance. This observation may convince practioners of the traditional ap-proach to adopt the approach proposed and take advantage of the more reli-able and efficient testing on model scale. 35


22.6.6.2 RESISTANCE AXIOM

Introducing the resistance and the thrust deduction axioms into the mo-mentum balance results in the equation

r 0 + r 1 ∆ V H + r 2 ∆

V H 2 + t T J η T J T = T + F − m d t

V H .

This equation holds for any condition and thus represents a set of linear 5

equations for the unknown parameters.

As has been observed earlier the thrust deduction axiom in accordance with the global approximation of the thrust deduction theorem is too crude to permit the identification of reasonable values of the energy wake fraction. Accordingly further attempts have been made to replace that axiom, though 10

without success so far. Further down a pragmatic approach will be sketched.

But by the way it has been noticed that the value of the longitudinal hy-drodynamic inertia crucially affects the momentum balance. With a more appropriate value than formerly assumed the final results are in nearly per-fect agreement with those obtained in the traditional way based on results of 15

propeller open water and hull towing tests.

Further it has been observed that the inertia identified strongly depends on the bandwidth of the filter applied to the raw data. Accordingly a procedure has been developed to extrapolate from quasi-steady conditions to the steady condition of interest. 20

22.6.6.3 CONVENTIONS TO BE AGREED UPON

As has been stressed over and over again the whole procedure is 'highly' conventional, as is the traditional procedure, but that there is no other way to solve the problem of full scale powering performance analysis.

In order to arrive at conventions proper the proposals so far need to be 25

discussed and agreed upon by the community concerned. As has been men-tioned over and over again those (who should be) concerned are not yet con-cerned.

22.6.7 Powering performance

22.6.7.1 FEASIBILITY 30

In order to show the feasibility of the procedure a quasi-steady propulsion test has been performed on model scale (1987) and finally been evaluated fifteen years later. The resulting values are in very close agreement with those identified according to the traditional procedure based on propeller open water and hull towing tests. 35


29.10.2008 13:55 h

As has been stressed over and over again this agreement is not necessary in principle, but it is of course pre-requisite for the method proposed to be accepted by the community, not only for nostalgic reasons but in view of the necessary references to past experience.

In tests with the research vessel METEOR the method has been shown to 5

be practical full scale, and in tests with the experimental surface effect ship CORSAIR/MEKAT the method has been shown to be the only physically meaningful.

22.6.7.2 SCALE EFFECTS

In the METEOR project the scale effects identified in wake fraction and 10

thrust deduction fraction are in accordance with the expected effects. As has been mentioned, in the traditional procedure these scale effects in thrust de-duction fraction are being 'ignored' axiomatically!

The axiom that the thrust deduction fraction is the same on model and on full scale has been 'practically confirmed' over and over again. The main 15

reason is that the theoretical models and the measurements as well as their evaluations so far have been much too crude to permit a more detailed analysis.

22.6.7.3 ENERGY WAKE FRACTION

As has been mentioned the values of the energy wake fraction identified 20

are still 'not quite' realistic. Future work has to start from here on, particu-larly in view of the scaling problem, which has not yet been treated by the author.

The reason for the problems encountered may be due to the fact that the convention of uniform energy wake is not acceptable, that the method pro-25

posed reaches its limits.

A very crude solution in line with the aggregate approach is to determine the 'global' approximation of the thrust deduction theorem

t = const χ η T J

in the range of states investigated and arrive at the value 30

χ = t / (const η T J) = t T J / const

of the wake ratio

χ ≡ (1 − w E) / (1 − w)

in terms of the magnitudes identified so far.


Subsequently the values of energy wake fractions are obtained according to the above identity

w E = 1 − χ (1 − w) ,

and thus explicitly

w E = 1 − t T J (1 − w T J η T J) / const . 5

22.6.8 'History'

"Wenn der Mann, überzeugt von dem Gehalt seiner Vorsätze, sich nach außen wendet und von der Welt ver-langt, nicht etwa nur, daß sie mit seinen Vorstellungen übereinkommen solle, sondern daß sie sich nach ihm be-10

quemen, ihnen gehorchen, sie realisieren müsse; dann er-gibt sich erst für ihn die wichtige Erfahrung, ob er sich in seinem Unternehmen geirrt, oder ob seine Zeit das Wahre nicht erkennen mag."

Johann Wolfgang Goethe: Naturphilosophie 15

(1960/44).

22.6.8.1 FROUDE'S METHODOLOGY RATIONALISED

Horn's attempts, starting in 1935, to overcome the deficiencies of Froude's method for the analysis of ship hull-propeller interactions has been discon-tinued not only due to the war but due to inadequate theoretical, experimen-20

tal and computational tools at that time.

Based on earlier experimental and theoretical work of the author, on ducted propellers, on pump jets and on the evaluation of propulsors in gen-eral, Horn's attempts have been started anew in 1980 with the publication of an axiomatic theory, dedicated to Horn commemorating his 100th birthday. 25

The central ideas were

• to use the theory of ideal propulsors in uniform wakes as an axiomatic system and

• to exploit the concept of equivalent propulsors due to Fresenius (1921) and successfully applied by Horn before (1957). 30

Under the motto 'Wake and thrust deduction from propulsion tests alone' the development reached its first climax in 1988 with the METEOR tests in the Arctic Sea. The results including the complete analysis of all hull-propeller interactions under service conditions have been reported and dis-cussed at the international workshop '2nd INTERACTION Berlin 1991', 35


29.10.2008 13:55 h

among the participants the members of the ITTC Powering Performance Committee.

22.6.8.2 INTERLUDE: DUCTED PROPULSORS

In subsequent projects on the design and the evaluation of ducted propel-lers all interactions have been treated implicitly, as in pump design, thrust 5

being no longer a design goal. Since the Japanese ISO proposal of 1999 concerning the evaluation of traditional steady speed trials the focus changed back to full scale trials. A transparent systems identification proce-dure has been developed, which no longer relies on model test results or any other prior data, as it must be. 10

22.6.8.3 LOCAL WAKE AXIOMS

In 2002 the initial wake and thrust deduction conventions have been suc-cessfully further developed to theoretically more acceptable axioms and practically to more robust procedures. These permit the reliable analysis of all interactions from short quasi-steady tests with models and ships under 15

service conditions, provided the thrust has been measured together with the torque.

As has already been mentioned the plausibility of the local wake axioms has been tested based on the open water performance of a model propeller. Data and test results are to be found on the Website of the author. 20

As an example a model test performed prior to the METEOR tests has been re-evaluated. The corresponding re-analysis of the METEOR ship and model data has provided reliable values of the scale effects in wake and thrust deduction, worldwide for the first time.

22.6.8.4 REVIEWS OF RESULTS 25

The history and the basic ideas and results of the 'Rational Theory of Pro-pulsion' have recently been summarised in the contribution of the author to the STG Meeting commemorating the Opening of VWS in 1903 (2003.p) and in the paper '25 Jahre Rationale Theorie der Propulsion. Fritz Horn zum 125. Geburtstag' prepared for presentation at the STG Summer Meeting 30

2005 and finally presented at the 100th Annual Meeting of STG (2005.2). All papers and their presentations are to be found on the website of the au-thor in the relevant contexts.

Before the local wake axioms have been adopted a global loss parabola has been constructed. The details are only of historical interest and to be 35

found on the website of the author. Here it is of interest that the axiomatic model for the construction of equivalent propellers in the open condition is


possible, but that the procedure proposed along this line thought was not ro-bust.


The theory of ideal propellers has been used as the model of an axiomatic theory

of hull-propeller interactions. In order to provide for the 'independent' evaluation 5

of the performance of full scale ships axioms 'constituting' ships with propellers

are being necessary.

Plausible, local axioms have been constructed and shown to lead in robust pro-

cedures on model scale to results in very close agreement with results of the tradi-

tional procedures for a rather traditional hull form and, most important, it can be 10

applied on full scale as has been shown in the METEOR project already in 1988.

CONCLUSIONS

While the traditional method is inadequate for wake adapted propellers and ad-

vanced hull forms and is not applicable on full scale even for traditional hull forms

the method proposed based on the axioms does not suffer from these deficiencies. 15

According to the exposition the method is not universal; it has to be adapted to

special types of hull-propeller configurations. This has been shown paradigmati-

cally in case of the CORSAIR/MEKAT, an experimental air-cushion vehicle of

Blohm+Voss with partially submerged propellers.

22.7 Hull-integrated propulsors 20

PROBLEMS

So far the naïve concept of propulsors as thrusters overcoming the resistance

has been followed. The conceptual framework of hull propeller interaction in terms

of wake and thrust deduction is no longer adequate if the propulsors are more or

less hull integrated as in case of ducted propellers or pump jets. 25

The concepts of wake and thrust deduction are no longer necessary, they become

meaningless, they can no longer be interpreted operationally. Similarly the meta-

theory remains a play with glass beads unless the few concepts introduced are op-

erationally interpreted.

MODELS 30

As simplest model of a hull integrated propulsor a ducted propeller is adopted

GOALS/PLANS

After discussion of propulsor models in general the operation of ideal ducted

propellers in open water and behind ships is analysed. The section closes with an

outline of the interpretation of the theory as necessary. 35


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22.7.1 Propulsor models

In traditional expositions the only propulsor model considered is that of the actuator disc with a pressure discontinuity

∆ p ≡ Τ/A 1 = ∆

e

due to a force field of infinite strength at a disc of area 5

A 1 = Q / v 1 .

And the impression is given that the actuator disc is 'the' ideal propulsor. But this instinctive belief perpetuated by traditional teaching is falsely held.

The disadvantage of this unrealistic model is that it has an edge singular-ity, which has been investigated by SchmidtHG (1977) and Sparenberg. In-10

stead of studying this nasty effect engineers rather tend to avoid it by adopt-ing force fields as propulsor models, in practice in ducts as already men-tioned by Fresenius. The author has shown paradigmatically how force fields replacing actuator discs can be constructed (Schmiechen, 1978).

In the simple case treated the flow outside the force field and the jet gen-15

erated is a potential flow caused by a singular sink of strength

Q S = (A 0 − A 2) v 0 = Q (1 − v 0 / v 2) = Q (1 − 1 / (1 + ε) 1/2) ,

the areas being the cross section of the volume flow far ahead of the propul-sor and far behind the propulsor. The name 'equivalent' sink for this type of sink is completely misleading. The sink is not 'equivalent' to a propulsor in 20

the sense to be discussed immediately, but only concerning the flow outside all interesting regions of the flow, outside the force field and the jet gener-ated.

And this statement is true despite the fact that the singular sink in the uni-form flow provides the thrust 25

T S = ρ Q S v 0 = ρ = ρ Q v 0 (1 − v 0 / v 2) .

But this thrust is different from the thrust of the ideal propulsor.

For 'safety's sake' it is repeated here: Sinks are not propulsor models but provide models for some aspects of the flow around propulsors. Only in the limiting case of vanishing thrust, and thus of vanishing interest, both models 30

coincide.


22.7.2 Ducted propellers

Force fields of the type mentioned are most conveniently 'realised' in ducts. The purpose of ducts is not to produce thrust but to prevent edge sin-gularities thus permitting to come as close as possible to ideal conditions.

According to the momentum theory the thrust of the duct 5

T D = T T − T A = (A 1 − A A) ∆ p

is the difference between the total thrust and the thrust at the actuator, again conceived as a singular force field resulting in a discontinuous pressure jump

∆ p = ∆ e 10

as before.

Contrary to an instinctive belief widely held among naval architects this thrust is not a 'gain' for 'nothing' and this thrust does not depend on the shape of the duct, provided that the jet produced is ideal, that no flow sepa-ration occurs at the duct. 15

For practical reasons, among others ease of removal of the actuator, the actuator area is often chosen equal to the final jet area

A A = A 2 .

This choice has the disadvantage that the pressure ahead of the actuator, which is important for eventual cavitation, is only 20

p 1− = p 0 − ρ (v 2 2 − v 0

2) /2 = p 0 − ∆ e .

Despite the disadvantage of small actuators, resulting in danger of cavita-tion, and the disadvantage of deceleration of flows, resulting in danger of separation, ducts with exit areas larger than the actuators

A A < A 2 25

have been fashionable in places, 'for reasons of hull design'.

In this case the velocity at the actuator is further increased

v A = Q / A A > v 2

and the pressure ahead of the actuator is further lowered

p 1− = p 0 − ρ (v A 2 − v 0

2) /2 < p 0 − ∆ e . 30

The thrust of the duct is increased as well but as already mentioned this is a fictitious 'gain'.


29.10.2008 13:55 h

To add one disadvantage to another is felt not to be particularly ingenious. Optimum performance is obtained with continuously accelerating flows in nozzles proper. Thus the name 'Düsen-Propeller' in German is perfectly well chosen.

If the area of the actuator is chosen according to the area of the open ac-5

tuator disc

A A = A 1

the thrust of the duct vanishes, but the pressure ahead of the actuator is in-creased

p 1− = p 0 − ρ (v 1 2 − v 0

2) /2 > p 0 − ∆ e 10

and the advantage of the duct, preventing the edge singularity, remains un-changed. Attempts to increase the size of the actuator even further in order to prevent cavitation have not been successful due to the difficulties encoun-tered with the deceleration of flows.

Although ducted propellers are designed and tested nearly exclusively in 15

the open condition this is totally inappropriate in view of hull-propulsor in-teractions as will be shown.

22.7.3 Internal losses

The theory developed remains unchanged if the ideal propulsor has inter-nal losses. The power 20

P P = − E C − E P = P J + P L

provided or delivered has now not only to cover the ideal jet power

P J ≡ − E C

but the 'lost' power

P L ≡ − E P 25

dissipated inside the propulsor.

The corresponding efficiency

η J P ≡ P J / P P = P J

/ (P J + P L) = η T P / η T J

is called the hydraulic or pump efficiency and equals the ratio of the jet effi-ciency 30

η T P ≡ T V P / P P ,

and the jet efficiency


η J P ≡ T V P / P J .

of the propulsor.

The losses are irrelevant for the jet efficiency as they have no mechanical effect except maybe micro-turbulence to be accounted for by the diffusive momentum outflow if necessary. 5

Usually the important distinction between propulsor jet and pump effi-ciencies is not being made in naval architecture, although only the hydraulic efficiency is an adequate measure for the quality of a propulsor.

22.7.4 Propulsor theory interpreted

The advantage of the abstract theory is that it can be used for any type of 10

hull integrated propulsors in wakes, in non-uniform inflows. While in ideal fluids and flows considered before the results are invariant with respect to the choice of the entry and exit boundaries the same does not apply for real propulsors in real fluids and flows. Consequently the axioms have to be supplemented by agreements concerning the entry and exit boundaries. 15

In view of the difficulties to measure the total energy flows at the agreed entry and exit boundaries of the propulsor the convective flows of the total energy including the pressure but not the deviatoric stress field are taken as approximations as before for the momentum flows.

The problems to measure the mass and convective energy flows remain 20

formidable enough, so that further standards, conventions and agreements are necessary in any case. The naïve hope to solve all these problems by la-ser Doppler velocimetry is based on wishful thinking, forgetting that the pressure has to be known as well.

Local measurements, even provided they are technically possible, are 25

much too intricate in most routine applications. Integral measurements are preferred, where possible, and require modifications of the axiomatic model. The same problems have been faced by the pump industry and subsequently standards have been established.

In the foregoing the conditions far ahead and far behind the propulsor 30

have been referred to. For practical applications this is often inconvenient, even for propulsors, which can be conceived in the open condition, moving independently of the vessel they are propelling.

One way to deal with this problem is to use the more general version of the momentum balance including pressure integrals, not to mention or rather 35

including the potential energy. This very intricate procedure is well estab-


29.10.2008 13:55 h

lished (Schlichting, 1965/699 ff) and has been applied in evaluating the per-formance of a model propulsor (Schmiechen, 1992.p).

In this case the velocities far ahead and far behind may be conceived as energy velocities to be constructed according to the rules

e X = ρ v X 2 /2 + p X ≡ ρ V X

2 /2 5

in terms of the energy densities in the entry and exit sections.

22.7.5 Basic procedure

In ducted systems considering pressure measurements not only at the en-try and exit sections X but at nearby sections Y and assuming negligible en-ergy losses 10

e X = ρ v X 2 /2 + p X = ρ v Y

2 /2 + p Y

the condition

Q = A X v X = A Y v Y

permits to identify the densities of the kinetic energies

ρ v X 2 /2 = (p X − p Y) / (A X

2 / A Y 2 − 1) 15

and thus not only the densities of the total energies

e X = ρ v X 2 /2 + p X

but the velocities and thus the volume flow

Q = A X v X .

In textbooks on hydrodynamics this theory is treated under the heading 20

'venturi-meter' (KayJM, 1963/24 f). The results permit the complete perform-ance evaluation according to the meta-theory of propulsion. In practical ap-plications the ad hoc venturi-meters have to be calibrated under operating conditions.

Performance testing and evaluation of jet propulsors is of considerable in-25

terest to ship model basins. While the ITTC Committee on Unconventional Propulsors under the chairman Claus Kruppa was closely following the evaluation of jet propulsion in terms of energy flows the Committee serving the 23rd ITTC went back to momentum flows.

EVALUATIONS/ASSESSMENTS 30

The operation of ducted propellers behind hulls results in hydrodynamical short

circuits, at best energetically neutral. This example shows that thrust at the duct is

indeed a nasty by-product.


Testing of jet propulsors can in principle be performed as pump testing using

venturi set ups in the inlet and the outlet.

CONCLUSIONS

So far the performance testing and evaluation of given systems has been of pri-

mary concern. In view of advanced design methods and of the related conceptual 5

and operational problems encountered the importance of the subject is grossly un-

derestimated and accordingly the necessary developments are not adequately taken

care of.

The chapter will close with a section on the design of ducted propulsors, where

very powerful computational tools are available now but again the conceptual 10

problems and the solutions proposed are not adequately taken care of and taken

advantage of, respectively.

22.8 Ducted propeller design

PROBLEMS

The problem is to develop methods for design and evaluation of wake adapted 15

ducted propellers, water jet propulsors in general without explicit reference to

thrust and hull-duct-propeller interactions.

MODELS

By treating propulsors consistently as pumps all interactions between hull and

propulsor, consisting of a duct and an actuator, a pump stage, the latter consisting 20

of a rotor and, maybe, a stator, are accounted for implicitly, different from all

other known design and evaluation methods.

GOALS/PLANS

Only the basic principles will be developed. Details, being not of interest to the

general reader, are to be found in papers on the website of the author. 25

22.8.1 Propulsors are pumps

In ordinary propeller design for thrust the thrust deduction fractions have to be known in advance. This knowledge is not available for advanced hull integrated propulsor designs. In view of the large number of parameters it is impossible to provide for the data base necessary and for the operational in-30

terpretation, not only necessary for the validation of the design procedures.

The foregoing considerations support the departure from the naïve con-ception of propulsors being thrusters overcoming the resistance of the bod-ies to be propelled. Much more adequate is to conceive propulsors as pumps

22.8 Ducted propeller design 1249

29.10.2008 13:55 h

feeding energy into a volume flow, preferably the energy wakes as has been seen.

The condition of self-propulsion is the condition of vanishing net momen-tum flow into the hull-propulsor system. This concept underlying all the work of the author and this position has prominently been expressed by Se-5

dow in the quotation provided earlier.

22.8.2 Equivalent propulsors

Design or selection and evaluation of ducted propellers are usually based on the conceptual model of the open water condition, although this model is hopelessly inadequate for the problems at hand. It accounts neither for the 10

vorticity in the wake of the hull ahead of the propulsor nor, even more im-portantly, for the fact, that nearly all the interactions take place as a hydro-dynamical short circuit between hull and duct.

The above mentioned problems can be solved, if instead of the conceptual model of the propeller in open water the conceptual model of the equivalent 15

propeller in the energy wake alone, in plausible terms: the equivalent pro-peller 'far behind the ship', if there would be no diffusive decay of the wake, is introduced, which accounts for all interactions implicitly.

This model is not a physically realisable propeller, but an extremely pow-erful conceptual tool, which has been used by Horn in Germany for the 20

study of hull-propeller interactions. In Russia the same model is used, sur-prisingly with different results.

A paper presented at the meeting of the Centenary of the Krylov Ship Re-search Institute at St. Petersburg was intended to continue the discussion with Victor Bavin and others (Schmiechen, 1994.p). But the hope to clarify 25

and eventually remove the discrepancies and has not been fulfilled.

Although this concept is based on the well-known principles of hydrome-chanics, the balances of mass, momentum, and energy, naval architects are not ready to accept it yet. The reason is that they traditionally are treating in-teractions as if hull and propeller could be investigated separately, which 30

may have been reasonable for the traditional configurations of slender ships with open screw propellers, but is no longer acceptable for most hull- and wake-adapted propulsor designs today.

22.8.3 Feasibility study

In a project at VWS, the Berlin Model Basin, two ducted propellers for a 35

body of revolution have been designed and investigated under service con-


ditions on the basis of methods developed earlier. Methods for the evalua-tion of the propulsive performance of ships based on propulsion tests under service conditions alone have been developed by the author since thirty years (1968, 1970). The corresponding design procedures have been devel-oped later over nearly ten years (1983/1993). 5

The goal of the project was the detailed development of the design proce-dure proposed earlier down to the numerically controlled production of the blades and of the evaluation procedure. In future the procedures developed will have to be integrated into expert systems for propeller design in order to permit wider use by designers. 10

The results of the project have been documented in reports of the Ver-suchsanstalt für Wasserbau und Schiffbau (Schmiechen, Voss, Engler, 1992; Schmiechen, Goetz, 1993) and the Forschungszentrum des Deutschen Schiffbaus.

Although the performance of the propellers was acceptable, the measure-15

ments in the large circulation tunnel of VWS produced values still slightly differing from the design values. The main reason for these discrepancies may be attributed to the crude method of blade design used. In future it will have to be replaced by CFD methods. In this short summary only the basic concepts and some results will be outlined. 20

In order to avoid confusion the whole propulsive system will be called propulsor and its components will be referred to as duct and actuator or pump stage, the latter 'ideally' consisting of rotor and stator.

22.8.4 Thrust distribution

If the area of the pump equals that of the jet, i. e., if the velocity in the 25

pump equals the jet velocity the relative thrust at the duct depends on the loading coefficient. The usual 'conclusion' is that a duct produces extra thrust, up to 100 % at bollard condition. Evidently this gain is only apparent. There is no perpetuum mobile, not even in hydrodynamics!

Only formally the ideal propulsor reduces to the usual actuator disc with-30

out duct. The duct does in fact retain its function, permitting optimum head distribution, the circulation not dropping off towards the tips. And this is evidently the major advantage of ducts and not the apparent gain in thrust.

The distribution of thrust between actuator and duct is more or less arbi-trary and a matter of various aspects, it does not affect the energy balance 'at 35

all'. In practice this is of course not quite true in view of the pump efficiency depending on the flow conditions in detail.


29.10.2008 13:55 h

But this line of thought (1968/1980) will not be followed here. In view of the length of ducts the concept of open water condition is quite inappropri-ate, for partial ducts in tunnels and for jet propulsors it is completely inade-quate. For fundamental considerations only the concept of uniform wake without the assumption of parallel flow may be maintained. 5

In this case the condition of self propulsion may be formulated as mo-mentum balance

m d t V H + R E = T E + F

with the effective resistance and the effective thrust, the interpretation of both quantities in terms of measurements has yet to be defined. The inertial 10

resistance has been kept in view of the fact that it may contribute substan-tially to the momentum balance, for large values of the total longitudinal in-ertia even at extremely small values of the acceleration.

In general an external towing force cannot be distinguished from the re-sistance, but it may be useful to keep track of it separately if possible, if it is 15

known from measurements.


While for non-ducted propellers the global thrust deduction fraction ac-cording to the traditional 'definition', the momentum balance

R E = T (1 − t) 20

for steady open water conditions without extra external forces, can be kept as convention, even if it is physically not meaningful, this is neither possible for ducted propellers nor for jet propulsors.

This at first sight surprising fact has a simple, plausible reason, which is to be found in the mechanism of the thrust and suction generation, which is 25

exactly the same for both, namely the pressure reduction in the duct inlet, which depends on the velocity increase in the duct inlet, which in turn de-pends on the opening of the duct inlet.

This very simple model based on experimental evidence, not published at its discovery (1961), but locked away in a basement (2003), was actually the 30

starting point of the rational theory of hull-propeller interactions (1969/1980), which has been developed in many directions since then.

The thrust at the duct and the corresponding suction at the hull constitute a powerless short circuit without affecting the propulsive performance. The consequence of this finding is that a duct with larger thrust is not necessarily 35

an advantage, as it implies higher flow velocities and consequently larger


frictional losses as well as the need for stronger support of the duct as com-pared with a duct 'producing' less thrust.

After 'experts' for nearly fifty years had 'denied' the correctness of the ob-servations and their interpretation, not meeting their falsely held instinctive beliefs, the same finding has been confirmed by tests at the Schiffbau-5

Versuchsanstalt Potsdam (Heinke, 2007).

The scheme for the evaluation of propulsors based on mass and energy fluxes as proposed (1969) has been used by Masilge (1991) in an investiga-tion of a pump jet in an inadequately modified form, the attempt being made to 'obtain' the same values for the towing resistance of the hull with closed 10

duct system and for the effective resistance.

22.8.6 Basic design

The procedure for preliminary propeller design, i. e., for the determina-tion of the main dimensions has been described in previous papers (1983, 1987, and 1988) and shall not be repeated here. Only the basic ideas will be 15

recalled.

For the equivalent propeller the interactions are determined by the distri-bution of the energy density in the mass flow, which can be obtained, at least approximately, from the local measurements at the towing condition, as has been done in the project, or from corresponding boundary layer com-20

putational results.

Observing the optimum condition of uniform energy density at the exit, for any values of effective resistance and total mass flow the distribution of circulation at stator and rotor may be determined, at this stage in the invari-ant format as functions of the local mass flow and the frequency of revolu-25

tion.

In the original work the actuator in the duct was modelled as a force field in order to determine the outer flow around the body and the duct (1987, 1988). The model of the force field for propellers has now been widely adopted not only for the solution of the Euler equation but of the Navier-30

Stokes equation as well.

As has been found from simple considerations the computation of the whole flow field is not necessary for the present configuration. The flows at the entrance and exit of the duct are completely determined by the balances of mass and energy, contrary to most other procedures for any loading of the 35

propulsor without approximation.


29.10.2008 13:55 h

In the procedure the hull is still assumed to be given, e. g., optimised in some way independent of the propulsor. Usually shapes are determined without flow separation. But this is of course not necessary. Bodies have been designed and successfully tested with flows accelerated up to the pro-pulsor entry. 5

The practical procedure of propeller design consists of few simple equa-tions. Provided the propeller absorbs the total wake then the relation

V E = 3/4 V H

holds for the mean energy velocity at the intake, V H denoting the ship or hull speed. 10

From the condition of self propulsion

R E = TE = ρ Q ( V J − V E)

the jet efficiency

V J = V E + V R

is obtained with the velocity increase 15

V R = R E / (ρ Q) .

For the velocity at the inlet of the duct the mean velocity is arbitrarily, but not accidentally chosen to be

V 0 = (V E + V J)

/2

in accordance with the design criterion of continuous acceleration of the 20

flow.

For given effective resistance and volume flow the entrance area of the duct is

A 0 = Q / V 0

and with the velocity 25

V 6 = 0.95 V J

at the exit the corresponding area is

A 6

= Q / V 6 .

For a selected conical body contour the inner duct contour is thus given as well. 30

The volume flow over the wake may be approximately determined from the frictional resistance according to the equation

Q P = 4 R F / (ρ V H) .


The propulsors have in fact been designed for a larger resistance in order to avoid the notoriously small propeller loading in self propulsion of deeply submerged bodies, but the design value

R E / (2 ρ Q V H) = R E

/ (8 R f) = 1/4

is still pretty small for ducted propellers. 5

The Cordier line linking the frequency of revolution and the diameter has been crudely approximated by the equation

N D 2 = 2.5 Q 1/2 (∆ e / ρ) 1/4 ,

where the 'kinematical' head is

∆ e / ρ = V E V R + V R

2 /2. 10

In order to design the blades of stator and rotor the pump has been di-vided into ten elementary conical pumps and standard techniques of profile selection have been used although they were felt not to be adequate for the conical flow situation. For the tests a duct supported by a five bladed stator and two rotors with three and six blades, respectively, have been designed 15

and manufactured under numerical control.

Both propulsor configurations have been tested, the results showing no significant differences. The values obtained were still different from the de-sign values, the differences to be attributed to the much too simple minded blade design, which will have to be replaced by CFD procedures in future 20

research and development projects.

22.8.7 Review

At VWS, the Berlin Model Basin, procedures for the design and evalua-tion of ducted propellers have been developed, which treat propulsors con-sistently as pumps and permit to account implicitly for all hull-propulsor in-25

teractions. According to these procedures two ducted propellers have been designed, manufactured, and tested.

Although the values measured did not exactly meet the design values the results prove that the design procedure is not only practical, but in the first attempt lead to an acceptable propulsor, and the tests showed that the corre-30

sponding evaluation procedure leads to meaningful results.

Further it has been shown that the evaluation according to the rational method outlined results in values for the ducted propellers investigated. The reason is the method is based on mass and energy flows and avoids refer-ence to energetically irrelevant global displacement effects and local pres-35

sure effects.


29.10.2008 13:55 h

An evaluation on the basis of measured velocities alone is not possible. The reliable computation of the pressure values in the race of the propulsor, even in the case of the axis-symmetrical body, was not possible.

22.8.8 Outlook

The proposed procedures for the preliminary design of ducted propellers 5

and of rotor and stator blades are very transparent. But the crude procedure for blade design needs to be replaced by CFD methods. For the validation of the numerical methods many more detailed flow measurements will be nec-essary, for the evaluation of the propulsors additional pressure measure-ments are necessary. 10

Recent developments of ducted propulsors using CFD techniques are not taking advantage of the approach outlined and shown to be feasible, but are still concerned with open water propulsors. Two of these developments, at Heidenheim (Jürgens, 2006) and at Duisburg (Steden, 2007), have been ana-lysed and discussed by the author at the Annual Meetings of STG and sub-15

sequent private meetings, all the details to be found on the website of the au-thor.

The approach suggested has not yet been applied to traditional propeller configurations without ducts etc. But it is felt that so called 'holistic' designs would greatly gain from its application and become truly holistic (Abdel-20

Maksud, 2008).

Not only in view of measurements on full scale ships the conventional methods based on integral measurements have to be further developed. At present the method based on the concept of the equivalent open water pro-pulsor has reached a certain state of maturity. 25

But in its present form developed basically for 'open' propellers, i. e., without ducts, it is not adequate. Specialised model test techniques for inland ships as proposed by von der SteinN and developed and applied at the Duisburg Model Basis are not solving the problem in general (2005).

One of the reasons is that the thrust at the rotor is not necessarily a meas-30

ure for the 'head' of the pump. So generalisations will have to be conceived. More adequate appears the evaluation of ducted propellers as water jet pro-pulsors as outlined in the basic paper. But for the evaluation on the basis of measured integral values under service conditions appropriate axioms, i. e., conventions, have to be developed and to be agreed upon. 35

The complete list of references, in particular those papers of the author documenting the development of the design and evaluation procedures, are to be found in the two reports on the project (Schmiechen, 1993) and in the


newly established section on 'Ducted propulsors' on the website of the au-thor.


It has been shown that wake adapted hull integrated propulsors can be designed

on the basis of first principles and of pump theory. In a project at VWS the proce-5

dure has been demonstrated to produce results very closely meeting the design

goals.

CONCLUSIONS

For most practical purposes, even on model scale, the evaluation based on local

measurements is much too involved. Conventional techniques based on integral 10

measurements as in case of open propellers applicable on model and full scale are

in urgent need.

CLOSURE OF CHAPTER


It has been shown that the rational theory of propulsion based on conception of 15

equivalent propulsors provides solutions for a number of fundamental theoretical

and practical problems, including:

• the evaluation of traditional steady speed trials without refer-

ence to hydrodynamic theory and model test results,

• the complete analysis of the powering performance of models 20

and ships under service conditions solely using quasi-steady tri-

als and

• the design of wake adapted ducted propellers including all in-

teractions between hulls, ducts and actuators.

The work is documented on the website of the author, most recent papers and 25

studies of details since about 1990 being directly accessible. An overview is to be

found in a paper dedicated to Horn commemorating his 125th birthday

(Schmiechen, 2005.p) and a theme lecture on Propulsor Hydrodynamics

(Schmiechen, 2006).

CONCLUSIONS 30

The conceptual frame work of the exposition is in large parts identical with that

of naval architects, but its interpretation has been rationalised and cleaned from

the traditional tribal folklore (Truesdell, Feyerabend) and 'unnecessary additions'

(Newton, Mach, RussellB).

So far only the groundwork has been done. The basic examples, conceptual solu-35

tions and studies of their feasibility do not solve all problems, but are paradigmatic

in character, promising dramatic technological and commercial advantages.


29.10.2008 13:55 h

For applications in research and industry the axiomatic conventions have to be

accepted and the procedures have to be developed by the community concerned.

Surprisingly those who have the problems and are in urgent need of solutions are

only slowly starting to take advantage of the approaches proposed and demon-

strated to be practical. 5

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