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IICCEEWWIINNGG –– AA MMeesshh GGeenneerraattiioonn SSyysstteemm ffoorr CCoommpplleexx TThhrreeee--DDiimmeennssiioonnaall IIcceedd WWiinngg CCoonnffiigguurraattiioonnss Year 2 Effort: Icing Effects Studies for a Three-Dimensional Wing NNAASSAA CCoonnttrraacctt NNAAGG33--22556622

David Thompson, Satish Chalasani, and Prasad Mogili Computational Simulation and Design Center Mississippi State University Mississippi State, Mississippi April 2003

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Abstract

The problem of flow field simulation for iced wing configurations is a complex one that severely taxes existing capabilities for geometry modeling, mesh generation, and flow solution. The objective of this two-year effort is to evaluate current capabilities for simulation of high Reynolds number viscous flow around three-dimensional wings with ice accretions. In this report, we focus on the activities associated with the second year. More information regarding the first year activities can be found in the Year 1 report. During the second year, the primary objectives of this research were: 1) to evaluate the effectiveness of current computational fluid dynamics technology for predicting flow fields for a wing with a glaze ice accretion and 2) to investigate the effects of spanwise variation of ice shapes on the resulting computed flow fields. Steady-state solutions of the Reynolds-averaged Navier-Stokes (RANS) equations were computed using the Cobalt flow solver for a constant-section, rectangular wing with and without an extruded two-dimensional ice shape. The one equation Spalart-Allmaras turbulence model was used. The results were compared with data obtained from a recent wind tunnel test. The results predicted for the clean wing showed good agreement with experimental pressure data. Results predicted for the extruded wing indicate that the steady RANS solutions underpredicted the lift coefficient when compared to the experimental data. The differences widen as the recirculation zone expands aft of the upper ice horn with increasing angle of attack. Mesh refinement improves the results somewhat but differences remain. The drag, however, being primarily due to form or pressure drag, was well predicted. A spanwise variation in ice shape was obtained by developing a blending function that merged the ice shape with the clean wing using a sinusoidal spanwise variation. Computed results suggest that, for this case, the results predicted by the extruded shape provide conservative estimates for the performance degradation of the wing. Additionally, several issues were raised regarding the mesh generation process. Finally, we continued investigated employing level-set-based techniques to perform surface extraction from point cloud data. While promising, our approach still requires additional work before it can be deployed as a robust system.

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Contents

1. Introduction 5 2. Review of Year 1 Activities 6 3. Year 2 Activities 7 3.1 Problem Statement 8 3.2 Geometry Modeling 9 3.3 Mesh Generation 10 3.4 Numerical Flow Solution 12 4. Results 13 4.1 Clean Wing – Comparison with Experimental Data 13 4.2 Extruded Wing – Comparison with Experimental Data 15 4.3 Effects of Spanwise Variation 18 5. Surface Extraction 25 5.1 Introduction to Level Sets 27 5.2 Preliminary Results 27 6. Summary 28 7. References 29

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List of Figures

1 Case 944 ice shape used in this study 8 2 Iced wing geometries showing effects of ω 10 3 Effect of δ variation on resulting wing shape 11 4 Midspan cutting plane of mesh for wing with extruded ice shape 12 5 Convergence history for clean wing at α=6o 13 6 Comparison of Cobalt solutions with experimental data for the clean

wing 14

7 A pressure-based comparison of predicted results and experimental data

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8 Convergence history for extruded wing at α=6o 16 9 Comparison of Cobalt solutions with experimental data for the

extruded wing 16

10 Comparison of predicted midspan wing pressures with experimental data for different angles of attack

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11 Extruded wing pressure coefficients at α=6o 18 12 Lift and drag coefficients for the four geometries shown in Figure 2 19 13 Separation (red) and attachment (blue) lines for the extruded wing –

flow is from left to right 20

14 Separation (red) and attachment (blue) lines for the “8-cycle” wing – flow is from left to right

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15 Separation (red) and attachment (blue) lines for the “4-cycle” wing – flow is from left to right

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16 Detail of upper surface of “8-cycle” wing showing separation and attachment lines and velocity vectors near the surface at α=0o – flow is from left to right

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17 Flow field solution for “8-cycle” wing with δ=0.5 at α=6o 24 18 Effects of mesh refinement on flow field structures for extruded wing

at α=6o 26

19 Surface extracted from noisy point cloud data 27

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List of Tables

1 Mesh statistics for representative cases 11 2 Effect of mesh spacing on clean wing solution – angle of attack of six

degrees 15

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1. Introduction

There are two distinct applications related to the aircraft icing problem in which computational fluid dynamics (CFD) can play a significant role.1 First is the prediction of ice accretion using a code such as LEWICE2 coupled with a viscous flow solver. The second application is a detailed flow field analysis to determine the effects of ice accretion on aircraft performance. We focus on the second application, “icing effects,” in this report. One of the challenges regarding the simulation of iced wing flow fields is adequate representation of the ice accretion. Even though the volume of the ice accretion may be small in comparison to that of the wing, it may significantly affect the global nature of the flow field. For example, even small glaze ice accretions with “horns” may induce significant regions of flow separation. Although computational fluid dynamics tools have made great strides in recent years, there are several unanswered questions regarding their capabilities for predicting the flow around wings with ice accretions. The ability of geometry/mesh generation tools to adequately address the unique needs of an iced wing flow simulation is also much in question. There are significant issues related to surface modeling including questions regarding the quality of a NURBS representation of the surface. Additionally, within the constraints of accuracy, efficiency, and flexibility, questions remain as to what type of mesh is appropriate for a complex iced-wing configuration. Finally, there are numerous questions related to turbulence modeling, e.g., regions of massive separations and surface roughness. In general, detailed three-dimensional simulations of the flow around an iced wing are relatively rare due to the enormous expenditure of resources needed to obtain a quality solution. In one such effort, Chung, et. al.3 demonstrated the potential of CFD by predicting the aerodynamic characteristics of an aircraft involved in an accident attributed to icing. Two-dimensional ice shapes were digitized from results obtained in the NASA GRC Icing Research Tunnel. An artificial three-dimensional geometry was generated by extruding a two-dimensional ice shape in the spanwise direction and fairing the shape at the tip. A two-block, structured grid with noncontiguous overlapping interfaces was used in the study. The flow field solution was computed using the general-purpose code NPARC.4 Here we report on a numerical icing effects study. Steady-state solutions of the Reynolds-averaged Navier-Stokes (RANS) equations were computed using the Cobalt flow solver5 for a constant-section, rectangular wing with an extruded two-dimensional ice shape. The one-equation Spalart-Allmaras turbulence model6 was used. The results were compared with data obtained from a recent wind tunnel test.7 The effects of spanwise variation in the ice shape on the resulting flow field were also investigated by computing flow fields for synthetic ice shapes generated by merging the two-dimensional ice shape with the clean wing using a sinusoidal blending function and comparing these results with clean wing and extruded wing predictions. Although we briefly describe activities from Year 1,

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our focus in this report is on activities associated with the second year. More information regarding the first year activities can be found in the Year 1 report.8 2. Review of Year 1 Activities

To date, there have been only limited numerical three-dimensional icing-effects studies. Due to this limited experience, the Year 1 emphasis was placed on identifying a sound, overall approach to surface mesh generation/volume mesh generation/flow solution rather than developing new technologies. Below is a brief summary of activities accomplished during Year 1:

• An approach to generate a fully three-dimensional NURBS representation of the point-cloud data was developed using the “ImageWare Surfacer”9 software package.

• An approach using a pseudo three-dimensional lofted geometry representation with the “ImageWare Surfacer” software package was also investigated.

• A technique utilizing medical imaging technology10 was applied to filter chordwise iced-wing sections. The approach met with mixed, although promising results.

• Several meshes for iced wing configurations were developed using the existing mesh generation package SolidMesh.11

• New topologically-adaptive surface and volume mesh generation algorithms12 were applied to the iced wing problem.

• A flow solution for an iced wing configuration was generated using the Cobalt5 flow solver.

• Strategies were developed for geometry modeling and mesh generation specific to the iced wing problem.

Importantly, we were able to demonstrate the complete problem solution process—from point cloud to flow solution. These efforts are described more fully in the Year 1 report. As noted above, we developed a strategy for attacking the problem of CFD for iced wing configurations. The recommendations listed below are the basis of this strategy:8

• Continue to develop an automated surface-filtering module using level set theory. We believe this capability will be useful regardless of the approach used to represent the surface.

• Continue to refine the pseudo-three dimensional surface modeling approach. In particular, develop an automated procedure to generate data slices. One possible approach would be to use a three-dimensional level-set filtering technique on the point cloud data whereby the chordwise slices could be extracted automatically.

• Continue to identify software that is available as a long-term solution to the iced wing mesh generation problem. Several candidates are currently being investigated. SolidMesh appears to be an acceptable interim solution.

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• It is our opinion that, at some point, iced-wing specific mesh generation software should be developed. What is lacking in current mesh generation software packages is intuitive control of point placement. However, this effort should be postponed until the utility of computational fluid dynamics simulations is established for iced wing simulations and a clear understanding of the potential benefits of such a system is established.

• Cobalt should continue to be used to generate flow field solutions. • Evaluate the effectiveness of computational fluid dynamics techniques for iced

wing simulations by comparison of computed results with experimental data. We recommend that the experimental investigation include procedures to establish the general structure of the flow field.

• Determine, by comparison with experimental data, if the significant spanwise flow components reported here are real features rather than computational anomalies.

The proposed Year 2 objectives were developed based on the implementation of these recommendations. 3. Year 2 Activities

There are four main objectives associated with the proposed Year 2 effort:

• Demonstrate the pseudo three-dimensional lofting technique for new point cloud data (to be provided by NASA GRC in April 2002).

• Develop a better understanding of three-dimensional iced wing flow fields by extensive interrogation of computed flow fields and comparison with available experimental data.

• Evaluate the sensitivity of the flow solution with respect to (1) mesh density and (2) spanwise resolution of the geometry representation.

• Develop two-dimensional curve and three-dimensional surface extraction algorithms based on level-set theory.

The full simulation process was to be performed for newly scanned data using the strategy developed in Year 1. Because of unforeseen circumstances, NASA GRC was unable to provide the new point cloud data in April 2002. Therefore, NASA GRC and the ERC agreed to modify the scope and direction of the effort during Year 2. Since NASA GRC personnel were performing a test at the NASA LRC LTPT for an extruded (two-dimensional) ice shape, it was decided to simulate the associated clean wing and the extruded wing and compare the computed results with the experimental data. Additionally, a method was developed to generate a synthetic ice shape by merging an experimentally determined ice and a clean wing shape in a parametric manner. The modified objectives of Year 2 effort are:

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• Evaluate the accuracy of the proposed approach by comparison of computed results with experimental data for a clean wing.

• Evaluate the accuracy of the proposed approach by comparison of computed results with experimental data for a wing with an extruded two-dimensional ice shape.

• Evaluate the effects of spanwise geometry variation by parametrically varying the process of merging a two-dimensional ice shape with clean wing.

• Evaluate the sensitivity of the flow solution with respect to (1) mesh density and (2) spanwise resolution of the geometry representation.

• Develop two-dimensional curve and three-dimensional surface extraction algorithms based on level-set theory.

3.1 Problem Statement The iced wing problem is a complex one that involves several steps. In order to motivate our approach, we now provide a problem definition. Given a geometric definition of a wing with an ice accretion:

• Develop a representation of the surface that is suitable for generating a surface mesh.

• Specify the artificial boundaries needed to define the computational domain, e.g., outer boundary and symmetry boundaries.

• Generate a mesh and specify boundary conditions on the bounding surfaces of the computational domain

• Generate a mesh in the interior of the computational domain • Generate a flow solution

Since the wing employed for the test program was mounted between walls, the geometry modeled in this study did not include wing tips. The specific two-dimensional ice shape used in this study represents a glaze ice accretion on a business jet airfoil7 and is shown in Figure 1. There are significant upper and lower surface horns as well as a lower surface accretion due to runback. It is designated as Case 944 ice.

Figure 1. Case 944 ice shape used in this study

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3.2 Geometry Modeling We developed a technique to generate a wing with a synthetic three-dimensional ice accretion given an airfoil definition and a two-dimensional ice shape. The algorithm interpolates between the clean shape and the ice shape using a sinusoidal weighting that depends on the spanwise location. Given a point on an airfoil with an ice accretion (xiced,yiced) and the point on the corresponding clean airfoil (xclean,yclean) definition that is closest to (xiced,yiced), interpolate between the iced shape and the clean shape using a factor that depends on the spanwise position

( ) ( )

( ) ( )zyyyy

zxxxx

cleanicedcleannew

cleanicedcleannew

σ

σ

×−+=

×−+=

(1)

where σ(z) is defined as

( )

−

+= 12cos

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1,0.0maxbz

z ωπδσ . (2)

δ is the deviation, z is the spanwise position, ω is the frequency of the oscillation, and b is the half span of the wing. Note that the max function ensures that σ(z) is nonegative. The function multiplying the deviation δ varies between 0 and –2 so that the maximum value of σ(z) is 1 and the minimum value is 1-δ with a sinusoidal variation in between. If σ(z) is unity, the iced shape is returned. If σ(z) is zero, the clean shape is returned. It should be noted that for ice shapes that are described by multi-valued functions, i.e., a normal from the clean airfoil surface intersects the ice shape more than once; the above procedure may produce a “folded” surface if larger values of the deviation parameter δ are used. The Case 944 ice shape is one such surface. Figure 2 shows four geometries. The “4-cycle” and “8-cycle” cases were generated using δ=0.2. These cases were selected because the resulting ice shapes exhibit spanwise variations that resemble realistic three-dimensional ice accretions. Figure 3 shows the effects of varying δ. Figures 3(a) and 3(b) show valid surfaces generated using small values of the deviation parameter δ, 0.2 and 0.5 respectively. On the other hand, the surfaces shown in Figures 3(c) and 3(d) are “folded” because of the relatively large values of δ, 1.0 and 1.25 respectively. The program developed to automate this procedure, extrudeWing, has been delivered to NASA GRC. The output of extrudeWing is a file containing a structured quadrilateral surface mesh in Plot3d format. The surface mesh is then input to SolidMesh and a NURBS representation of the surface is generated thereby facilitating the mesh generation process.

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3.3 Mesh Generation The surface and volume meshes were generated using the program SolidMesh. In essence, SolidMesh is an interface to a surface mesh generation routine and the unstructured volume mesh generation code AFLR3.11 AFLR3 uses an advancing front algorithm to insert a point in the mesh and then performs a local reconnection to generate high quality elements. A new point is inserted and the process is repeated. For each configuration, an all-triangle surface mesh is generated. Then, a hybrid volume mesh is generated. A hybrid mesh consisting of extruded triangular prisms and tetrahedral elements was chosen because of its potential for improved efficiency and accuracy in comparison to an unstructured purely tetrahedral mesh. Table 1 shows statistics for eight meshes employed in this study. Unless noted in the text, the distance to the first point off the wall was taken to be 1x10-6, which corresponds to an average y+ value less than 0.1. This value is well within the recommended values for the turbulence model employed.

Figure 2(a). Clean wing section

Figure 2(b). Extruded wing section

Figure 2(c). “4-cycle” wing section

δ=0.2, ω=4

Figure 2(d). “8-cycle” wing section δ=0.2, ω =8

Figure 2. Iced wing geometries showing effects of ω

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Figure 3(a). “8-cycle” wing section

δ=0.2, ω =8

Figure 3(b). “8-cycle” wing section δ=0.5, ω =8

Figure 3(c). “8-cycle” wing section

δ=1.0, ω =8

Figure 3(d). “8-cycle” wing section δ=1.25, ω =8

Figure 3. Effect of δ variation on resulting wing shape

# Nodes # Faces # Cells Clean wing (baseline) 378,041 2,360,974 1,023,032 Clean wing (Rev 1) 328,011 2,119,287 927,673 Clean wing (Rev 2) 630,285 4,711,884 2,150,999 Extruded wing 890,958 5,299,738 2,258,447 Extruded wing (refined) 2,817,169 17,448,060 7,528,540 4-Cycle wing (δ=0.2) 904,680 5,368,010 2,285,734 8-Cycle wing (δ=0.2) 903,654 5,360,055 2,281,964 8-Cycle wing (δ=0.5) 1,834,095 11,566,857 5,026,724

Table1. Mesh statistics for representative cases

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Figure 4 shows midspan cross-sections through the basic and refined meshes generated for the wing with the extruded ice shape. Note that these are cutting planes so that the line segments that appear represent intersections of faces with the cutting plane. However, the connectivity of the mesh is still evident and the prism layer near the body surface is clearly visible. Also, Figure 4(a) shows the faceted surface represented by the triangular surface mesh on the extruded wing. Notice that even though the surface definition is two-dimensional, the resulting faceted surface exhibits a spanwise variation due to the unstructured nature of the mesh. Also, the mesh in the region downstream of the upper horn is relatively coarse. Refining the surface mesh reduces the sizes of the facets and improves the mesh density in the separated region as shown in Figure 4(b). 3.4 Numerical Flow Solution The flow solver employed in this effort is the noncommercial version of Cobalt.5 The Cobalt flow solver was designed for general unstructured meshes. It employs a nonlinear Riemann solver for the inviscid flux computations and can be run either in explicit or implicit mode. In all cases reported here, the solution to the RANS equations was obtained using implicit local time stepping and does not in any way represent a time-accurate solution. Several turbulence models are available including the Spalart-Almaras one-equation model6 that was used for the computations reported here.

Figure 4(a). Basic mesh for extruded ice

shape Figure 4(b). Refined mesh for extruded ice

shape

Figure 4. Midspan cutting plane of mesh for wing with extruded ice shape

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4. Results

In this section we present comparisons of predicted RANS results with experimental data for the rectangular wing with and without the extruded ice shape. The wing section is that of a business jet and the ice shape is the 944 glaze ice shape7 shown in Figure 1. We also include a discussion on the effects of spanwise variation of the ice shape as described in Section 3.2 on the computed results. We have computed steady-state RANS solutions using the Cobalt flow solver with the Spalart-Allmaras turbulence model for the following conditions: M=0.12, Re/L=3.8x106/m which, with a chord length of 0.9144m, yields Re=3.5x106, and angles of attack of 0o, 2 o, 4 o, and 6 o. The clean wing cases correspond to Run 9 in the experimental data. The extruded wing cases correspond to Run 41. All cases reported below were run on 64 processors on the EMPIRE cluster at the ERC at Mississippi State University. No attempt was made to determine optimum input parameters for Cobalt. Solution times varied considerably for the different cases considered depending on flow field complexity and mesh size. 4.1 Clean Wing – Comparison with Experimental Data The first step in the analysis of the solution is to determine whether the numerical solution is converged and whether it represents a steady state solution. The six-degree angle of attack case was selected to illustrate the convergence of the solution for a representative case. Figure 5(a) shows the L2 residual was reduced by approximately two orders of magnitude. Additionally, in Figure 5(b), we note that the lift has converged.

We now compare the predicted lift and drag coefficients with experimental data. As shown in Figure 6(a), the lift is over predicted relative to the experimental data, as is the lift curve slope. Figure 6(b) shows a comparison of the predicted drag coefficient and the

Figure 5(a). L2 residual history Figure 5(b). Lift history

Figure 5. Convergence history for clean wing at α=6o

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experimental data. The predicted drag force is, likewise, consistently larger than the experimental value. Figure 7(a) shows a comparison of the predicted chordwise pressure distribution at the wing midspan with experimental data at a six-degree angle of attack. The agreement between predicted results and experimental data for other angles of attack was similar. In light of this pressure data, the differences in the predicted and experimental lift coefficients are somewhat difficult to explain. To investigate these discrepancies, a short program was written to integrate the pressure coefficient data. Figure 7(b) shows a

Figure 6(a). Wing lift coefficient versus

angle of attack Figure 6(b). Wing drag coefficient versus

angle of attack

Figure 6. Comparison of Cobalt solutions with experimental data for the clean wing

Figure 7(a). Clean wing pressure

coefficients at α=6o Figure 7(b). Comparison of integrated

pressures

Figure 7. A pressure-based comparison of predicted results and experimental data

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comparison of the experimental lift coefficient, the lift coefficient obtained by integrating the experimental pressure coefficients, and the lift coefficient obtained by integrating the predicted pressure coefficients. In this figure, the agreement between predicted and experimental integrated lift values is much improved. At this time, the discrepancies shown in Figure 6(a) and 7(b) have not been resolved. It should be noted that there was no significant spanwise variation in the predicted pressure coefficients. To evaluate the effects of mesh resolution on the predicted drag, several meshes were generated and used to compute solutions. The results are summarized for an angle of attack of six degrees in Table 2. There was some concern that the position of the first point (y+<0.1) was actually too close to the surface for the Spalart-Allmaras turbulence model. The mesh denoted as “Rev 1” in Table 2 uses the baseline surface mesh with the the distance to the first point off the wall increased by an order of magnitude. The number of points, etc., in the mesh decreased because fewer points were needed to discretize the domain. The mesh labeled “Rev 2” in Table 2 employed the larger distance to the first point but increased the number of points on the surface of the wing by approximately 50%. Notice that the only significant effect evident in the wing drag data is that increasing the number of points on the surface reduced the drag coefficient. A less prominent effect was that increasing the average y+ value increased the error in the wing drag. This suggests that for the approach being employed here, it is necessary to use a very small y+ value with as many points on the surface as practical. 4.2 Extruded Wing – Comparison with Experimental Data We now present a comparison of predicted results with experimental data for the wing with the extruded ice shape hereafter referred to as the “extruded wing.” Figure 8 shows the convergence history for the extruded wing at an angle of attack of six degrees. In Figure 8(a), the L2 residual shows nearly a three-order of magnitude decrease over the course of the solution. However, as shown in Figure 8(b), the lift shows a few small oscillations (less than one percent of the lift) after several thousand iterations. The solution was continued up to 20,000 iterations and no significant changes were observed. This convergence is encouraging given the extensive region of recirculating flow. Figure 9 shows a comparison of the wing lift and drag coefficients predicted using the basic mesh with experimental data. As shown in Figure 9(a), the lift coefficient is significantly underpredicted relative to the experimental data as is the lift curve slope.

Mesh Avg. y+ # Nodes # Faces # Cells Wing CD Baseline 0.059 378,041 2,360,974 1,023,032 1.7737E-02 Rev 1 0.64 328,011 2,119,287 927,673 1.8427E-02 Rev 2 0.78 630,285 4,711,884 2,150,999 1.3925E-02 Experimental data

NA NA NA NA 8.6610E-03

Table 2. Effect of mesh spacing on clean wing solution – angle of attack of six degrees

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On the other hand, as shown in Figure 9(b), the predicted drag coefficient shows very good agreement with the experimental data. This agreement can be attributed to the fact that the drag is primarily composed of form or pressure drag for this configuration, i.e., the ice shape is a bluff body. Figure 10 shows a comparison of predicted midspan pressure coefficients and experimental data for four different angles of attack. It should be noted that there is only a slight spanwise variation in the pressure at any given chordwise position. Figures 10(a)-10(d) show that, as the angle of attack is increased, the strength of the recirculation

Figure 8(a). L2 residual history Figure 8(b). Lift history

Figure 8. Convergence history for extruded wing at α=6o

Figure 9(a). Wing lift coefficient versus

angle of attack Figure 9(b). Wing drag coefficient versus

angle of attack

Figure 9. Comparison of Cobalt solutions with experimental data for the extruded wing

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increases in the experimental data as evidenced by the increasing size “bump” in the pressure coefficient distribution. This same behavior appears in the predicted results but not to the degree exhibited by the experimental data. The pressure data suggest that the reattachment for the flow moves aft as the angle of attack is increased as expected. The descrepancies in the predicted pressure coefficients are consistent with those in the lift coefficients. Additionally, it should be noted that differences in the upper surface pressures occur even at the lower angles of attack. The predicted results agree reasonably well with the experimental data on the lower surface although differences become more apparent at the higher angles of attack.

Figure 10(a). α=0o

Figure 10(b). α=2o

Figure 10(c). α=4o

Figure 10(d). α=6o

Figure 10. Comparison of predicted midspan wing pressures with experimental data for different angles of attack

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To illustrate the effects of mesh refinement on the pressure distribution, Figure 11 shows a comparison of the predicted pressure coefficients at midspan and experimental data for the extruded wing at a six-degree angle of attack for the basic mesh and the refined mesh. As shown in the figure, mesh refinement improves agreement with experimental data and produces a strengthened recirculation region. This results suggests that further mesh refinement may be neccesary. However, it may be that a steady RANS solution will not accurately capture the recirculating region and an alternative procedure such as an unsteady Detatched Eddy simulation (DES)13,14 may be necessary. 4.3 Effects of Spanwise Variation We now consider the effects of spanwise variation in the ice shape. The configurations employed here are the four configurations shown in Figure 2 – the clean wing, the extruded wing, the “4-cycle” wing, and the “8-cycle” wing both with δ=0.2. These cases represent reasonable three-dimensional ice shapes. We have also included results from a single solution for the “8-cycle” wing with δ=0.5 at six degree angle of attack. It is well known and appreciated that truly two-dimensional flow separation does not occur in nature. Therefore, we anticipate some degree of spanwise flow even for the extruded wing. On the other hand, the clean wing solution exhibits no flow separation at the conditions considered and, accordingly, very little spanwise flow. It should be noted that the faceting associated with the discrete surface triangulation (which results in a realistic ice shape) does introduce a spanwise variation in the clean wing and the extruded wing. Figure 12 shows plots of the lift and drag coefficients versus angle of attack for each of the four configurations. Not surprisingly, the general effect of the ice accretion is to decrease the lift and increase the drag. In these cases, the predicted lift and drag coefficients are bounded by the clean wing results and the extruded wing results. Thus, the extruded wing provides a conservative estimate of the lift degradation and

Figure 11. Extruded wing pressure coefficients at α=6o

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corresponding drag increase. However, this conclusion has not been substantiated for other configurations and should not be extrapolated at this time. Additionally, the spanwise variation appears to have minimal effect on the integrated force coefficients. One of our objectives was to determine if the three-dimensional nature of the ice shapes significantly affects the characteristics of the flow separation. We now investigate how the structure of the flow field is affected by the spanwise variation in the ice shape. We use a critical point-based technique to determine the locations of the separation and attachment lines.15 This technique evaluates the eigenvalues of the velocity gradient tensor to determine the characteristics of the streamlines near the surface. The results are similar to an interpretation of a surface oil flow. When surface flow streamlines converge, it suggests that fluid is leaving the surface, e.g., a flow separation is occurring. When these streamlines diverge, fluid is impinging on the surface suggesting an attachment. Figures 13-15 show the separation lines (red) and attachment lines (blue) on the lower surface (left column) and upper surface (right column) at four angles of attack for the extruded wing (Figure 13), the “8-cycle” wing (Figure 14), and the “4-cycle” wing (Figure 15). The images, although somewhat noisy due to the fact velocity gradients are employed to classify the points, generally show the expected results. For each case, the images in the left column show that the attachment line moves forward (to the left) with increasing angle of attack. The images in the right column show the attachment line moves aft (to the right) with increasing angle of attack. In the six-degree angle of attack cases, the flow reattaches just ahead of the trailing edge. Figures 13-15 show that the structure of the flow field is very similar for each geometry case even though the geometries are different. Again, this suggests that simulating the extruded wing may be adequate for icing effects studies.

Figure 12. Lift and drag coefficients for the four geometries shown in Figure 2

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Lower surface Upper surface

α=0o

α=2o

α=4o

α=6o

Figure 13. Separation (red) and attachment (blue) lines for the extruded wing – flow is from left to right

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Lower surface Upper surface

α=0o

α=2o

α=4o

α=6o

Figure 14. Separation (red) and attachment (blue) lines for the “8-cycle” wing – flow is from left to right

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Lower surface Upper surface

α=0o

α=2o

α=4o

α=6o

Figure 15. Separation (red) and attachment (blue) lines for the “4-cycle” wing – flow is from left to right

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Figure 16. Detail of upper surface of “8-cycle” wing showing separation and attachment

lines and velocity vectors near the surface at α=0o – flow is from left to right

Also of interest is that separation lines perpendicular to the primary attachment lines appear on both the upper and lower surfaces indicating separations that are parallel to the flow. Due to their coherence and persistence, we believe these structures are present in the computed flow fields and are not artifacts of the procedure. In general, these structures show more coherence at the lower angles of attack. The frequency of these features appears to be related to the geometric definition. Note that they occur most frequently for the “8-cycle,” less for the “4-cycle,” and less still for the extruded wing. Therefore, we believe that are related to the spanwise variation in the geometry. Supporting this contention is the detailed image shown on the left in Figure 16. Here we see the separation and attachment lines along with the velocity vectors near the surface. We observe that the velocity vectors do diverge along the length of the attachment (blue) line. We also observe that the velocity vectors converge along the lengths of each of the separation (red) lines. We have not been able to identify the features as being associated with vortices induced by the spanwise geometry variation. Streamline traces, while producing interesting patterns, and other vortex detection methods are somewhat inconclusive. This may perhaps be due to the mesh resolution employed for these computations.

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Lower surface Upper surface

Figure 17(a). Separation and attachment lines

Figure 17(b). Isosurfaces of spanwise velocity component – yellow in negative z

direction and purple in positive z direction

Figure 17. Flow field solution for “8-cycle” wing with δ=0.5 at α=6o

To further support our hypothesis, we computed the solution for the “8-cycle” wing with δ=0.5 to evaluate the effects of increasing the magnitude of the variation in the geometry. The solutions shown in Figure 14 and 16 were obtained on a geometry generated with δ=0.2. The idea was to strengthen these features by increasing the size of the “depressions” in the wing definition. Recall that δ controls the maximum deviation from the given ice shape (Equation (2)). It should be noted that significantly more elements were needed to appropriately discretize the surface for this configuration which resulted in a more dense mesh (see the 5th row in Table 1). In Figure 17(a), we show the separation and attachment lines as in previous figures. However, in this case, prominently cyclical separation and attachment lines coincide with the peaks and valleys of the defined ice shape (somewhat evident in the figure at the wing leading edge). In this case, the geometry variation and resulting induced secondary flows cause the primary flow to attach much sooner than the other six-degree cases. To further illustrate the strengthened periodic behavior of the flow field, we also show isosurfaces of the spanwise velocity component in Figure 17(b). The isosurfaces show a strongly periodic pattern where yellow is the isosurface for one meter per second in the negative z direction and purple is for one meter per second in the positive z direction. Therefore, we believe our conclusion regarding the chordwise features in Figures 13-16 is sound. Those features are weaker because there is less spanwise variation in the geometry.

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We now demonstrate the effects of mesh refinement on the solution for the extruded wing at six-degree angle of attack. Figure 18 shows the separation and attachment lines and spanwise velocity isosurfaces for the extruded wing at six degrees angle of attack for the basic mesh and the refined mesh. Aside from the fact that the features are “cleaner” for the refined mesh computation, there are several other differences worth noting. First, comparing the separation/attachment line plots we see that there are remnants of the axial separation and attachment lines in the solution computed on the basic mesh that are not present in the refined mesh solution. Further, we note that the spanwise velocity flow fields are significantly different for both the upper and lower surfaces. Of course, some, but not all, of these differences can be attributed to the difference in resolution of the volume mesh, i.e., in the flow field. We propose these differences are strongly influenced by the surface represented by the mesh itself. The axial patterns present in Figure 13 (results for the extruded wing) correspond to weak features even though there is no spanwise variation in the geometry definition. However, due to the use of an unstructured triangular surface mesh, spanwise variations are introduced into the meshed representation of the geometry. This is evident in Figures 4(a) and 4(b) where the basic mesh employs relatively fewer surface triangles and results in a highly-faceted surface representation and the refined mesh employs many more surface triangles and produces a relatively smooth representation of the surface. In this case, aside from the scarcity of points in the recirculating region downstream of the horn, we expect that the smoother representation of the extruded shape will produce a solution that compares more favorably with the experimental data. We argue, although not too forcefully due to flow field resolution issues, that the flow field solutions presented in Figure 10 for the extruded wing represent appropriate solutions for the faceted geometry that was actually represented by the surface mesh. It should be noted that for a more realistic ice shape, the faceted geometry might better represent the ice shape. This has further implications we will discuss in the Summary. 5. Surface Extraction

As part of the two-year effort, we investigated the use of different image processing techniques to automatically “filter” the scanned point cloud data that describes the iced wing. During Year 1, we developed a level-set based16 curve extraction routine based on the assumption that data points that must be filtered are not located below the actual surface. This approach did suffer some problems as outlined in the Year 1 report.8 During Year 2, a new approach was implemented in three dimensions and applied it to the three-dimensional point cloud data. In the second year, a “shrink wrap” approach17 was employed to evolve a surface that enclosed the point cloud to the point cloud surface. The idea is that isolated points will “puncture” the shrink-wrap and not be captured as part of the surface. We now briefly discuss level sets and provide context for the algorithm we have developed in collaboration with Raghu Machiraju at The Ohio State University.

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Lower surface Upper surface

Figure 18(a). Extruded wing – basic mesh

Figure 18(b). Extruded wing – refined mesh

Figure 18. Effects of mesh refinement on flow field structures for extruded wing at α=6o

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5.1 Introduction to Level Sets In the context of surface extraction, we basically want to segment a region by locating bounding surface. However, we also want to extract a set of points on this bounding surface. The basic idea behind any level set method is to perform front tracking – a task normally performed using a Lagrangian formulation – using an Eulerian formulation. The main advantage is that the level set approach can be used in two or three dimensions making it possible to perform curve and surface extractions. Additionally, in the level set approach, it is not necessary to explicitly consider topological changes in the front. Topological changes occur implicitly in the level set formulation. Additionally, we employ a total-variation preserving (TVP) algorithm18 to ensure that the inherent roughness of the iced surface is not smoothed excessively. We refer the reader to a recent publication19 for more details regarding the approach. 5.2 Preliminary Results To illustrate the advantages as well as the shortcomings of this approach, we have included the surface extracted from a noisy scan of an iced wing configuration as shown in Figure 19. Note that in the figure, the ice shape is reconstructed reasonably well and the obvious outliers are removed. However, the noise on the upper surface of the airfoil aft of the quarter chord has been “wrapped” but is still present in the surface definition. We believe this to be a mesh resolution issue. While these results are preliminary, they are promising. It may be possible to develop a semi-automatic approach where multiple surfaces are defined using the level-set based technique and the user then selects the surfaces of interest. More work remains before this technique can be used as a reliable tool.

Figure 19. Surface extracted from noisy point cloud data

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6. Summary

The problem of flow field simulation for iced wing configurations is a complex one that severely taxes existing capabilities for geometry modeling, mesh generation, and flow solution. The overall objective of this two-year effort was to evaluate current capabilities for simulation of high Reynolds number viscous flow around three-dimensional wings with ice accretions. During the second year, the primary objectives of this research were: 1) to evaluate the effectiveness of current computational fluid dynamics technology for predicting flow fields for a wing with a glaze ice accretion and 2) to investigate the effects of spanwise variation of ice shapes on the resulting computed flow fields. Steady-state solutions of the Reynolds-averaged Navier-Stokes (RANS) equations were computed using the Cobalt flow solver with the Spalart-Allmaras turbulence model for a constant-section, rectangular wing with and without an extruded two-dimensional ice shape. The results predicted for the clean wing showed good agreement with experimental pressure data. There was also good agreement between lift coefficient values obtained by integrating the predicted and experimental pressure coefficients. For the extruded wing, results indicate that the steady RANS solutions underpredicted the lift coefficient when compared to the experimental data. The differences widen as the recirculation zone expands aft of the upper ice horn with increasing angle of attack. Mesh refinement improves the agreement somewhat but differences remain. The drag, however, being primarily due to form or pressure drag, was well predicted. The results reported here indicate that it is possible to simulate complex three-dimensional iced wing flow fields using a steady RANS approach. The accuracy of the predicted results is still open to question. The results also suggest that further refinement may be needed or that an alternative approach, such as unsteady DES, may be necessary. To achieve the second objective, a spanwise variation in ice shape was obtained by developing a blending function that merged the ice shape with the clean wing using a sinusoidal spanwise variation. Computed results suggest that, for these case, the results predicted by the extruded shape provide conservative estimates for the performance degradation of the wing. However, this conclusion should be tempered somewhat given the level of agreement between predicted results and experimental data for the extruded wing. It should be noted that although gross quantities such as lift and drag did not show significant differences, the details of the flow fields were quite different. Additionally, our study raised several issues regarding the mesh generation procedures. The wing with the extruded ice shape is really a two-dimensional geometry, i.e., the curvature in the chordwise direction is much larger than the curvature in the spanwise direction. For efficiency, it makes more sense to use anisotropic mesh elements to discretize the wing surface. Currently, we use isotropic triangles, which requires an excessive number of surface triangles to adequately resolve the ice shape. More efficient computations could be performed using a surface mesh with anisotropic elements. Further, our results showed that weak axial vortices were generated by the random variation introduced by an unstructured triangular surface mesh. When the surface and volume meshes were refined, the axial structures disappeared. We can conclude that for

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the relatively smooth extruded shape, it is necessary that the surface representation produced by the mesh generation approximate this smooth surface. As mentioned earlier in the text, this suggests the use of anisotropic quadrilateral elements for efficiency as well as accuracy. For realistic, truly three-dimensional ice shapes, the isotropic triangular elements are more appropriate and introduce a random surface roughness that may be desirable. This is particularly true if the surface has been smoothed as part of the geometry modeling process. We also reported on the development of a level-set based technique to extract surfaces from scanned point cloud data. Our preliminary results are promising. However, much work remains to develop a robust tool. 7. References

1. Y. Choo, K. D. Lee, D. S. Thompson, and M. Vickerman, “Geometry Modeling and

Grid Generation for ‘Icing Effects’ and ‘Ice Accretion’ Simulations on Airfoils,” Proceedings of the 7th International Conference on Numerical Grid Generation in Computational Field Simulations, Whistler, B.C., pp. 1061-1070, 2000.

2. W. B. Wright, “Users Manual for the NASA Lewis Ice Accretion Code LEWICE 2.0,” NASA CR-1999-209409, September 1999.

3. J. Chung, Y. Choo, A. Reehorst, M. Potapczuk, and J. Slater, “Numerical Study of Aircraft Controllability Under Certain Icing Conditions,” AIAA Paper 99-0375, Presented at 37th Aerospace Sciences Meeting, Reno, NV, January 1999.

4. NPARC User's Guide Version 3.0, NPARC Alliance, September 1996. 5. R. F. Tomaro, W. Z. Strang, and L. N. Sankar, “An Implicit Algorithm for Solving

Time Dependent Flows on Unstructured Meshes,” AIAA Paper 97-0333, Presented at 35th Aerospace Sciences Meeting and Exhibit, Reno, NV, January 1997.

6. P. R. Spalart and S. R. Allmaras, “A One-Equation Turbulence Model for Aerodynamic Flows,” La Recherche Aerospatiale, vol. 1, pp. 5-21, 1994.

7. H. Addy, J. Zoeckler, A. Broeren, “A Wind Tunnel Study of Icing Effects on a Business Jet Airfoil,” AIAA Paper 2003-0727, Presented at the 41st Aerospace Sciences Meeting and Exhibit, Reno, NV, January 6-9, 2003.

8. D. Thompson, S. Chalasani, S. Gopalsamy, and B. Soni, “Geometry Modeling and Mesh Generation Stratigies for Complex Three-Dimensional Iced Wing Configurations: Year 1 Report (NAG3-2562),” Technical report, NASA GRC, February 2002.

9. ImageWare, http://ww.sdrc.com/imageware, 2000. 10. R. Malladi, J. A. Sethian, and B. C. Vemuri, “Shape Modeling with Front

Propagation: A Level Set Approach,” IEEE Trans. Pattern Analysis and Machine Intelligence, 17(2)"158-175, February 1995.

11. D. Marcum, “Unstructured Grid Generation using Automatic Point Insertion and Local Reconnection,” Handbook of Grid Generation, J. F. Thompson, B. K. Soni, and N. Weatherill, eds, CRC Press, Boca Raton, FL, 1998

12. S. Chalasani, D. Thompson, and B. Soni, "Topological Adaptivity for Mesh Quality Improvement," Proceedings of the 8th International Conference on Numerical Grid

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Generation in Computational Field Simulations (available on CD), Honolulu, HI, June 2002.

13. M. Strelets, “Detached Eddy Simulation of Massively Separated flows,” AIAA Paper 2001-0879, Presented at 39th Aerospace Sciences Meeting and Exhibit, Reno, NV, January 2001.

14. K. D. Squires, J. R. Forsythe, S. A. Morton, W. Z. Strang, K. E. Wurtzler, R. F. Tomaro, M. J. Grismer, and P. R. Spalart, “Progress on Detached-Eddy Simulation of Massively Separated Flows,” AIAA Paper 2002-1021, Presented at 40th Aerospace Sciences Meeting and Exhibit, Reno, NV, January 2002.

15. D. Kenwright, “Automatic Detection of Open and Closed Separation and Attachment Lines,” Proc. Visualization ’96, pp. 151-158, 1998.

16. J. A. Sethian, Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science. Cambridge University Press, 2nd ed, 1999.

17. H. Zhao, S. Osher, and R.Fedkiw, “Fast Surface Reconstruction using the Level Set Method,” Proc. IEEE Workshop on Variational and Level Set Methods in Computer Vision (VLSM 2001), pg.194-201, July 2001.

18. S. Osher and L. I. Rudin, “Feature-Oriented Image Enhancement using Shock Filters,” SIAM J. Num. Anal, vol. 27, pg. 19-940, 1990.

19. Y. Kim, R. Machiraju, and D. Thompson, “Roughness Preserving Interface Construction,” submitted to the IEEE Visualization ’03 Conference, Oct. 2003.