Computational Simulation of Flow Over a High-Lift Trapezoidal Wing

Abhishek Kharea,1, Raashid Baiga, Rajesh Ranjana, Stimit Shaha, S Pavithrana, Kishor Nikama,1, Anutosh Moitrab

aComputational Research Laboratories Ltd., Pune, IndiabThe Boeing Company, Seattle, USA

Abstract: Reynolds Averaged Navier-Stokes simulation of a trapezoidal three element highlift wing, using CFD++, is presented in this paper. Parametric study of grid and solver effectshas been done. Requirements of the grid refinement at critical locations of the geometry arediscussed. Optimized volume stretching ratio has been identified through the grid indepen-dence study. Simulations using various turbulence models available in CFD++ with variousgrids have been performed and results are documented. Predicted trends of lift coefficient CL

and its maximum value are in close agreement with experimental data.

Key words: NASA Trapezoidal Wing, High Lift Systems

1. INTRODUCTION

High-lift systems are indispensable part of commercial jettransports. These systems enable the commercial airplanesto efficiently perform their low speed operations, which fur-ther affect takeoff and landing field length, approach speedetc. Therefore efficient design of high-lift system is a criticalpart of the design cycle of the commercial transport airplanes.Simulating high-lift flows using computational codes is in-deed a challenging task because of the complexities of thegeometry and flow physics involved. For example complexphysics includes attachment line transition, relaminarization,viscous wake interactions, confluent boundary layers, separa-tion and reattachment. Trapezoidal wing is an open-domainhigh lift problem posed by NASA-Langley center for inter-ested researchers to validate their CFD codes against avail-able experimental data for various take-off and landing con-figurations for a simplified high-lift wing with leading- andtrailing-edge devices.

The amount of validation that has been carried out in thepast for 3D high lift flows is limited. The reasons given byBussoletti et al. [1] for it include lack of sufficient 3D exper-imental high-lift data. Also the simulations that have beencarried out are on simple 3D geometries.

Previous high-lift CFD simulations in three dimensions in-clude those of Mathias et al. [2] and Jones et al. [3] whostudied a simple wing with half-span flap. Cao et al. [4]computed flow over a simplified Boeing 747 highlift config-uration. Mavriplis [5] [6] and Nash and Rogers [7] computedflow over the same NASA Trapezoidal Wing used in the cur-rent work.

Email addresses: abhishek@crlindia.com (Abhishek Khare),kishor@crlindia.com (Kishor Nikam)

For the current CFD analysis, performed under acooperative research agreement between the BoeingCompany and Computational Research Laboratories,full span landing configuration (configuration 1 aslisted on NASA Trapezoidal Wing website - http://db-www.larc.nasa.gov/trapwing/Archive/) has been taken asexperimental base and commercial code CFD++ has beenused on supercomputer Eka to perform various simulations.The work presented here describes the importance of gener-ating a grid with adequate resolution to capture the complexviscous phenomena. It is found that grid refinement at somecritical locations drive the prediction of CL at higher angleof attack. Apart from the grid refinement study, variousturbulence models have been used and comparative resultshave been documented.

2. GEOMETRY AND EXPERIMENTAL SETUP

The NASA trapezoidal wing is a three elements high-liftconfiguration having a single slotted flap and slat. The wingis mounted on a simple body-pod. This model is developedand tested by NASA to provide an experimental database ofa high-lift system to the global CFD community. The modelhas been tested on two different wind tunnels, NASA Ames12-Foot Pressurized Wind Tunnel (PWT) and NASA Lang-ley 14 X 22 Subsonic Wind Tunnel (SWT). Test data wasgenerated for the trap wing with three basic configurations,full span flap take off configuration, full span flap landingconfiguration and part span flap landing configuration. Thecurrent simulation utilized the full-span flap landing config-uration. Flap brackets have not been included in the modeledgeometry. Figure (1) shows the actual picture of the trap wing

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experimental setup and figure (2) shows the CAD model usedin the present simulation.

The test was carried at Mach number of 0.20 for aReynolds number of 4.3 million based on mean aerodynamicchord. The mean aerodynamic chord (c) of the trap wing is39.6 inches and the model semi-span is 85 inches.

The current computed results are obtained for a landingconfiguration with slat deflection of 30 degrees and flap de-flection of 25 degrees, a slat gap of 0.015c, slat overhang of0.015c, flap gap of 0.015c and a flap overhang of 0.005c.

Figure 1: Trapezoidal Wing in 12-Foot test section, NASA Ames

Figure 2: CAD model of the NASA Trap Wing

3. GRID GENERATION

The grid used in the present work has been generatedby using Boeing’s Modular Aerodynamic Design Compu-tational Analysis Process (MADCAP) and Advancing FrontLocal Reconnection (AFLR3) grid generator. MADCAP isa surface grid generator which takes surfaces in various for-mats like STL, IGES etc. Geometry pre-processing and sur-face parameterization prior to input to MADCAP were ac-complished using Boeing’s System for Low-Speed Unstruc-

tured Grid Generation (SLUGG) software system. AFLR3is a volume grid generator which takes triangulated surfacegrid in UGRID format and generates volume grid on that.AFLR3 generates the volume grid in two steps. In the firststep it generates the viscous grid with prisms elements. Sizeand number of layers of prisms can be controlled by inputparameters given to AFLR3. In second step of volume gridgeneration AFLR3 uses advancing front algorithm to fill theremaining domain with tetrahedral elements.

Surface grid at various critical regions has been refined tocapture the various flow features involved. After finding outthe critical regions and refining those adequately, stretchingratio (SR) has been varied to capture the wake generated fromvarious elements and its interactions with the boundary layersof other elements. Variable normal spacing on the surface hasbeen used in conjunction with the thickened boundary layer.

Table (1) shows the detail of the various grids used in thesimulation.

Grid Surface elements Volume elements Stretchingtype RatioA 375,680 15,860,599 1.23B 509,089 26,612,694 1.23C 596,872 28,143,372 1.18D 766,841 41,730,699 1.14E 1,036,314 69,633,564 1.10

Table 1: Grid details

4. SIMULATION METHODOLOGY

A compressible Reynolds Average Navier Stokes solver,CFD++ has been used in simulation. CFD++ uses cell cen-tered, finite volume, implicit/explicit algorithms to solve theNavier Stokes equations on unstructured/structured grids. InCFD++ various topography-parameter-free models are usedto capture turbulent flow features. The nonlinear subset ofthese models accounts for Reynolds stress anisotropy andstreamline curvature. All turbulence models can be inte-grated directly to the wall or with a sophisticated wall func-tion which accounts for compressibility as well. A rectangu-lar domain of size 100 times the body length in all the threedirections has been taken for simulations. Freestream pres-sure and velocity are imposed at the boundaries. Solve-to-wall approach has been used as the grids have been resolvedto very small Y+(less than 1). Steady state simulations havebeen performed for all the cases. Minmod flux limiter is en-abled to limit the interpolation slope in second order scheme.Convergence of the simulation depends on the turbulencemodel used and the angle of attack. Each simulation takesaround 16 hours of wall time to complete 1000 implicit it-erations on a grid size of around 28 million grid cells with128 processors. Convergence histories of both residuals andforces were monitored.

The simulations have been performed on Eka super-computer, situated at Computational Research Laboratories,

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Abhishek Khare, Raashid Baig, Rajesh Ranjan, Stimit Shah, S Pavithran, Kishor Nikam, Anutosh Moitra

Pune, India. Eka is a cluster of high-end compute nodesconnected with high speed communications networks. With1800 nodes, the system has a peak compute capacity of 172teraflops and has achieved sustained compute capacity of132.8 teraflops for the LINPACK benchmark.

5. RESULTS AND DISCUSSIONS

5.1. Turbulence ModelsA baseline grid with 16 millions cells has been generated

on the trap wing with a SR of 1.23 (Grid A). Simulations forangle of attack (α) ranging from 0 to 35 in steps of 5 degrees,have been performed.

Figure 3: CL Vs α for baseline, 16 million cells grid

Figure 4: CD Vs α for baseline, 16 million cells grid

The computations in the current work utilized variousturbulence models (Spalart-Allmaras, KERT, SST) with theflow assumed to be fully turbulent. All baseline simulationsutilized low Mach number preconditioning and were startedfrom free-stream initial conditions. Figures (3) and (4) show

Figure 5: Grid for baseline case

the CL and CD vs α for the baseline case. It can be seen thatsimulated values of CL, CD as well as CLmax are far below theexperimental values. Results are expected to improve withbetter grid resolution. Viscous grid for baseline case is shownin figure (5). Separation on the flap and near the wing bodyjunction can be seen from the surface restricted streamlinesplot shown in figure (6).

Figure 6: Surface restricted streamlines for baseline case

5.2. Effect of turbulence viscosity levels at the inletSpecified inflow conditions for turbulence eddy viscosity

for the Spalart-Allmaras model have been varied and its effecton the solution is observed. µt for the two cases is taken as5 times µ and 100 times µ. No appreciable change has beenobserved in the results.

5.3. Surface grid density effectsFor validation of any CFD simulation, study of conver-

gence of the computed solution with increasing grid densityis very important. To improve the accuracy of the computedsolution, surface grid at critical locations like wing bodyjunction, wing, flap, slat and the gaps between the elements.The resulting grid (B) is generated with the same SR 1.23

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as grid A. The consequence of refining the grid at locationsmentioned above is reflected in the simulation results. Thiscan be seen from the CL − α curve in figure (7). Surface gridrefinement resulted in improvement of the linear range of theCL − α curve. The effect of grid refinement on CD is shownin figure (8). The difference between experimental and sim-ulation values of CD is probably because of brackets presenton the experimental geometry. Figure (9) shows the surfacerestricted streamlines for this case. It can be seen that flowis attached on majority of the wing as compared to baselinecase.

The number of cells after surface grid refinement is 26 mil-lion.

Figure 7: Comparison of CL Vs α curves of baseline grid A with grid B

Figure 8: Comparison of CD Vs α curves of baseline grid A with grid B

5.4. Pre-conditioning Effects

For the regions where the flow-field is characterized byvery low speeds, compressible flow solvers require special

Figure 9: Surface restricted streamlines for case with grid B

treatment to account for the high artificial dissipation at nu-merical flux. CFD++ has a general implementation of time-derivative pre-conditioning, which involves pre-multiplyingthe time-derivative term in the governing differential equa-tions by a matrix which alters the rate of evolution of thephysical problem. This approach arguably leads to two ad-vantages - improved convergence rates as a result of the re-duced stiffness and improved accuracy as a result of the re-duced dissipation. The CFD++ user is given a choice to turnpre-conditioning ON or OFF, or turn it ON from a particulartime step.

Figure 10: Pre-conditioning effects for SA model

The current case has been run with both pre-conditioningON and OFF. As expected, no significant difference is ob-served between the pre-conditioned and non-pre-conditionedcases.

5.5. Effect of volume stretching ratio and variable nor-mal spacing on surface

The interaction of the wakes and boundary layers controlthe physics of high lift systems. Resolution of wakes andboundary layers of varying thicknesses over geometry com-ponents of widely varying sizes is of great importance in pre-diction of maximum lift. The first normal distance is scaled

Proceedings of ICEAE 2009

Abhishek Khare, Raashid Baig, Rajesh Ranjan, Stimit Shah, S Pavithran, Kishor Nikam, Anutosh Moitra

Figure 11: Pre-conditioning effects for KERT model

with the location and local Reynolds number to better resolvethe boundary layer. Also the boundary layer grid is thickenedto capture the wake as shown in figure (12).

Grid attributes such as normal spacing near the surface,grid density in wake regions and grid stretching ratio havelarge effect on the accuracy of the computed solution forcomplex high-lift flows. Grid stretching ratio was reducedin steps from 1.23 to 1.10 (number of cells varying from 21million upto 70 million). These grids has been labeled asA,C,D and E as given in table (1).

Results for CL − α and CD − α for the various grids havebeen shown in figures (14),(15),(16) and (17). It can be seenthat there is not much improvement in the results for valuesof SR less than 1.18 (Table (2)). Results on grid C are nowable to predict the linear as well as stall behavior with 2%of accuracy. In general the simulated lift curve closely re-sembles the experimental lift curve to engineering accuracy.Figure (13) shows surface restricted streamlines for grid Ccase.

It can also be observed from the results that SA turbulencemodel performs better compared to KERT and SST models.

Angle of Attack 10◦ 20◦ 25◦ 32◦Experimental CL 1.8240 2.4997 2.7986 3.0242Grid A (SR 1.23) 1.8069 2.4635 2.7200 2.9078Grid C (SR 1.18) 1.8160 2.4690 2.7220 2.9380Grid D (SR 1.14) 1.8205 2.4725 2.7272 2.9290Grid E (SR 1.10) 1.8253 2.4779 2.7309 2.9353

Experimental CD 0.3063 0.5557 0.6976 0.8546Grid A (SR 1.23) 0.2719 0.4843 0.5995 0.7480Grid C (SR 1.18) 0.2728 0.4848 0.5985 0.7529Grid D (SR 1.14) 0.2740 0.4860 0.6001 0.7534Grid E (SR 1.10) 0.2747 0.4867 0.5997 0.7534

Table 2: Experimental and Simulation CL and CD values for SA model

Figure 12: Grid for case with grid C

Figure 13: Surface restricted streamlines for case with grid C

6. SCALE-UP STUDY

Scale-up study has also been carried out for grid C (28million cells). The efficiency of parallel implementation andspeed-up have been shown in the figures (18) and (19). Thecode scales upto 192 cores as can be seen. Time requiredfor 10 implicit iterations on grid C having 28 million cells isgiven in table (3).

Number of Cores Time (in seconds)64 53396 364

128 299160 281192 274224 279256 363

Table 3: Time required for 10 iterations on grid C

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Figure 14: CL Vs α curves for different stretching ratios, SA model

Figure 15: CL Vs α curves for different stretching ratios, KERT model

7. CONCLUSIONS

Computational simulation of high-lift NASA trap wing hasbeen carried out using CFD++ on unstructured grids. CLmax

prediction has been achieved to engineering accuracy. A sys-tematic surface and volume grid refinement is done to capturethe complex flow encountered in the high-lift system.

Various critical regions on elements have been identifiedfor grid refinement to improve lift prediction. Grids withvariable normal spacing on the surfaces have been used withdifferent volumetric stretching ratio to capture the wakes andinteractions of these wakes with the boundary layers. Resultswith a grid having stretching ratio of 1.18 and 28 million cellsshows good match with the experimental data. Further re-duction in the stretching ratio rapidly increases the numberof cells without any significant improvement in the CL - αcurve. It can be concluded that 28 million cells with SR 1.18is sufficient if grid characteristics are right.

Although all the three turbulence models SA, KERT andSST perform well in the linear range of CL - α curve, it has

Figure 16: CD Vs α curves for different stretching ratios, SA model

Figure 17: CD Vs α curves for different stretching ratios, KERT model

been observed that the SA turbulence model performs bettercompared to KERT and SST models in the stall range of CL

- α curve. To further improve the simulation results unsteadysimulations can be performed. Also modeling of the bracketscan possibly help to improve the simulation results becauseof a closer match between the computational and experimen-tal geometries.

8. ACKNOWLEDGEMENTS

Authors gratefully acknowledge Metacomp Technologiesfor their valuable support.

REFERENCES

[1] Bussoletti, J., Johnson, P., Jones, K., Roth, K., Slotnick, J. P., Ying,S., and Rogers, S. E., June 1996, The Role of Applied CFD within theAST/IWD Program High-Lift Subelement: Applications and Require-ments, AST/IWD Program Report

Proceedings of ICEAE 2009

Abhishek Khare, Raashid Baig, Rajesh Ranjan, Stimit Shah, S Pavithran, Kishor Nikam, Anutosh Moitra

Figure 18: Efficiency of parallel implementation

Figure 19: Scale-up study on grid C (28 million cells)

[2] Mathias, D. L., Roth, K., Ross, J. C., Rogers, S. E., Cummings, R.M., Jan 1995, Navier-Stokes Analysis of the Flow about a Flap-Edge.AIAA; 95-0185

[3] Jones, K. M., Biedron, R. T., Whitlock, M., Jun 1995, Applicationof Navier-Stokes Solver to the Analysis of Multielement Airfoils andWings Using Multizonal Grid Techniques. Jun 1995, AIAA; 95-1855

[4] Cao, H. V., Rogers, S. E., Su, T. Y., Navier-Stokes Analyses of a 747High-Lift Configuration. Jun 1998, AIAA; 98-2623

[5] Mavriplis, D. J., Large Scale Parallel Unstructured Mesh Computa-tions for 3D High-Lift Analysis. Jan 1999, AIAA; 99-0537

[6] Mavriplis, D. J., Three Dimensional Viscous Flow Analysis for High-Lift Configurations Using a Parallel Unstructured Multigrid Solver.Oct 1999, SAE; 1999-01-5558

[7] Rogers, S.E., Roth, K., Nash, S., Aug 2000, CFD Validation of High-Lift flows with significant wind-tunnel effects. AIAA; 2000-4218

[8] Moitra, A., Jun 2001, Validation of an Automated CFD Tool for 2-DHigh-Lift Analysis, AIAA; 2001-2401

[9] Nash, S., Rogers, S.E., Numerical Study of a Trapezoidal Wing High-Lift Configurations. SAE; 1999-01-5559

[10] Johnson, P. L., Jones, K. M., Madson, M. D., Experimental Investiga-tion of A Simplified 3D High Lift Configuration in Support of CFDValidation. AIAA; 2000-4217

[11] Chaffin, M. S., Pirzadeh S., Unstructured Navier-Stokes High-LiftComputations on a Trapezoidal Wing, AIAA; 2005-5084

Abhishek Khare had the Masters of Technol-ogy in Department of Aerospace Engineering atIndian Institute of Technology Mumbai, Indiaand has been working as a member of techni-cal staff at Computational Research Laborato-

ries Ltd. Pune. His current interests are external aerodynam-ics, turbulence and high performance computing.

Raashid Baig had the Masters of Technologyin Department of Aerospace Engineering at In-dian Institute of Technology Mumbai, India andhas been working as a member of technical staff

at Computational Research Laboratories Ltd.Pune. His current interests are Turbo-machinery, Paralleldata visualization

Rajesh Ranjan had the Masters of Engineer-ing in Department of Aerospace Engineeringat Indian Institute of Science, Bangalore andhas been working as Member of Technical Staff

at Computational Research Laboratories, Pune,India. His current interests are external aerodynamics, paral-lel computing and benchmarking, and combustion.

Stimit Shah had Master of Engineering in De-partment of Aerospace Engineering at the In-dian Institute of Science, Bangalore, and hasbeen working as a Member of Technical Staff

at Computational Research Laboratories, Pune,India. His current interests are aerodynamics and turbulence.

S Pavithran got his degrees from IIT Madras, University ofMinnesota and University of Southern California. Followingthe post-doc at Monash University and Principal Engineerposition at Fluent India, he decided to return to academia andbecame a Professor at Vishwakarma Institute of Technology,Pune. He is a consultant for Computational Research Lab-oratories, is undertaking sponsored/consultancy projects andguiding doctoral candidates.

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Kishor S. Nikam joined Computational Re-search Laboratories (CRL) in Jan. 2007. He iscurrently working as a CFD Team Lead and pro-viding HPC-CFD consulting services to leadingcompanies in Aerospace, Automotive, Power

and Energy and Chemicals. Prior to join CRL he was work-ing with Intel Technologies, Applied Thermal Technologiesand Flowmaster. He has earned his bachelors degree inChemical Engineering and M. Tech. (Chemical Engineer-ing) from Indian Institute of Technology, Bombay. His areasof interest are CFD, Electronics Cooling, Thermal Manage-ment and HPC

Anutosh Moitra, Ph.D. is a Boeing Associate Technical Fel-low in the Enabling Technology & Research orgnization. Hiscurrent interests include complexities of high-lift airplaneaerodynamics and their prediction by CFD analysis.

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