Comparison of Numerical Simulation of the Flowaround an Airfoil in High Lift Configuration withPIV Experimental Results

D. Tran

DASSAULT AVIATION, 78 quai Marcel Dassault, 92552 Saint Cloud, France

Abstract

Airplane high lift systems allow to obtain aerodynamic characteristics required fortake-off and landing stages. In order to optimize such systems, it is necessary toimprove the understanding of the complex flow phenomena in high lift conditionsand to develop numerical methods capable to predict this flow with high accuracy.In the framework of the Europiv2 project, velocity fields provided by PIV for theONERA RA16SC1 three component airfoil in high lift configuration offer an op-portunity to acquire flow characteristics, to assess and validate numerical tools. Inthis paper, 2D steady k-ε Navier-Stokes results are presented for 2 angles of attackand compared to averaged PIV data.

For the slat, a good prediction of the stagnation point and the separated zone onthe windward side is observed.

Concerning the main body, computations as well as experiments show an in-crease of the boundary layer thickness and a delayed merging of the boundarylayer and the wake if the angle of attack becomes higher; but as expected for onepoint turbulence closures, this mixing is slower in the case of computations.

Over the flap, a separated region although more limited in comparison with ex-periment, is observed in the numerical simulation for the lowest angle of attackconsidered.

1 Introduction

Airplane high lift systems provide aerodynamic characteristics required duringtake-off and landing stages (Fig. 1). An improved efficiency of such systems al-lows to increase airplane performance in terms of approach speed, landing andtake off lengths and loads, safety, noise. But, the analysis of the flow field arounda high lift configuration reveals a complexity with the coincidence of a variety offlow phenomena such as separation, transition, interaction between wakes andboundary layer (Fig. 2). In order to optimize such systems, it is necessary to wellunderstand the flow physics in high lift conditions and to develop numerical toolscapable to predict this flow with high accuracy.

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Fig. 1. Airplane in high lift configuration.

Fig. 2. Flow around an airfoil in high lift conditions.

Within Europiv1 and Europiv2, flowfield velocity data obtained by means ofthe PIV technique offer opportunities on the one hand to study flow characteristicsand on the other hand to assess and validate numerical tools for high lift configu-rations. In Europiv1, the success of DLR PIV measurements in the AIRBUS Bre-men wind tunnel (LSWT) for the ONERA RA16SC1 two element airfoil, hasdemonstrated the applicability of this technique in industrial conditions and hasallowed to get a data base which was used for the validation of numerical simula-tion [1]. In Europiv2, the considered geometry is the RA16SC1 airfoil in landingconfiguration with slat and flap deployed respectively at the positions of 30° and40°. In addition to the main phenomena observed with a two component airfoil(slat lower side separation and interaction between the slat wake and the mainbody boundary layer), the presence of the flap generates other interesting phenom-ena such as :

- interaction between the wakes coming from the slat and the main bodywith the flap boundary layer

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- for low and medium angles of attack, separation on the flap.For this configuration, steady and unsteady velocity data fields provided by

PIV measurements allow to analyze the complex flow around a representativehigh lift configuration and complement the Navier-Stokes code validation of Das-sault Aviation.

In this paper, 2D steady k-ε Navier-Stokes results are presented and comparedto Europiv2 PIV data.

2 Steady Navier-Stokes Aether code

The main features of Dassault Aviation's steady Navier-Stokes Aether code are

GridsThe code can handle the unstructured mixture of numerous types of elements (tri-angles and quadrilaterals in 2D; tetrahedral, bricks and prisms in 3D).

Mean Flow transport EquationsDassault Aviation's Navier-Stodes code solves the 2D, axisymmetric and 3-Dcompressible Navier-Stokes equations.

Space discretisationA finite element approach, based on a symmetric form of the equations is writtenin terms of entropy variables. The advantages of this change of variables are nu-merous : in addition to the strong mathematical and numerical coherence theyprovide (dimensionally correct dot product, symmetric operators with positivityproperties, efficient preconditioning), entropy variables yield further improve-ments over the usual conservation variables, in particular in the context of chemi-cally reacting flows [2], [3].

IntegrationThe Galerkin/least squares (GLS) formulation introduced by Hughes and Johnson,is a full space-time finite element technique, employing the discontinuousGalerkin method in time [4]. The least square operator ensures good stabilitycharacteristics while retaining a high level of accuracy. The local control of thesolution in the vicinity of sharp gradients is further enhanced by use of a non-linear discontinuity capturing operator [4].

AccelerationConvergence to steady state of the compressible Navier-Stokes equations isachieved through a fully-implicit iterative time-marching procedure based onGMRES algorithm with nodal block-diagonal preconditioning [5]. A low-storageextension based solely on residual evaluations was also introduced [6]. It is par-ticularly well adapted to parallel processing, where the linear solver often consti-tutes a painful bottleneck. This algorithm has proven extremely efficient on manyscalar or vector architectures [7, 8].

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Turbulence ModelsDue to lack of universality of any turbulence model, several models are imple-mented in the Navier-Stokes code to cover the whole envelope of numericalsimulations. The models available today are the one equation Spalart-Almaras andtwo-equations models such as k-ε SST wall functions, k-ε SST two layer, k-l, k-ωSST, EARSM. In the k-ε SST two-layer formulation [9] used in this work, the tur-bulence kinetic energy equation and the mean flow equations are solved in the vi-cinity of the wall. The eddy viscosity and the turbulence dissipation are evaluatedusing algebraic length scales. This option requires the distance to the wall to beevaluated before the computation.

Turbulence model ImplementationIn the Navier-Stokes code, all the turbulence models use the "eddy viscosity "concept. The turbulent stresses and fluxes are modeled by analogy to molecularstresses and fluxes. In this approach, generally referred to as the Boussinesq ap-proximation, the effect of turbulence on the mean flow can be expressed in termsof an eddy viscosity function µt and a turbulent Prandtl number assumed to beconstant (Pn= 0.9 for turbulent boundary layers). The eddy viscosity function µt iscomputed with a turbulence model.

Coupling with the Navier-Stokes EquationsThe discretized mean flow equations and the turbulence equations are integratedusing a splitting method. At a current time step, we solve the Navier-Stokes equa-tions using turbulence data evaluated at the previous time while the turbulenceequations are solved using the flow variables computed at the current time step.

3 Geometry and wind tunnel tests in EUROPIV2

The studied geometry is the supercritical ONERA RA16SC1 airfoil in landingconfiguration (Fig. 3); it is characterized by a slat and a flap having deflection an-gles of 30° and 40°.

RA16flap40 degrees; slat 30 degrees

Fig. 3. RA16SC1 Airfoil.

The wind tunnel model with a span equal to 2 m and a chord equal to 0.5 m,was designed and manufactured by ONERA-IMFL with aerodynamic loads pro-

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vided by Dassault Aviation's computations. Experiments were carried out in theLSWT wind tunnel by AIRBUS BREMEN and PIV measurements were per-formed by DLR. During this test campaign, pressure distributions were obtainedalong the line of pressure taps located near the center line of the model for 20 an-gles of attack in the range between 0° and 19.5°. Because of a wind tunnel wallseparation which increased with angle of attack and which contaminated com-pletely the wing for angles higher than 20°, the investigation was limited to 19.5°.Concerning PIV measurements, they were performed for 3 angles of attack : 12°,17.5° and 19°. In order to support these wind tunnel tests, Dassault Aviation hadprovided two kinds of computational results :- The first one was obtained with a pre-design level code based on an inviscid

panel method coupled with a viscous integral method; in the multi-componentairfoil case, this code also takes into account the mixing boundary layer andwakes. As output, it provides in a very short time the global aerodynamic coef-ficients (Lift coefficient, Drag coefficient and Pitching moment) as a functionof the angle of attack. This code is a very useful and efficient tool during thedesign loop of a project. Results obtained for the studied geometry have beensent to ONERA for a strength analysis in order to prepare the model for windtunnel tests.

- The second part of the results was provided by 2D steady turbulent Navier-Stokes computations for the support of the test matrix definition and more pre-cisely for the definition of 3 angles of attack of interest : 12°, 17.5° and 22°(one in the linear part of the polar, one near maximum lift and one beyond themaximum).

Perhaps, due to a more important blockage effect with the presence of the flap,a strong separation not visible in Europiv1 experiments, appeared this time at thewind tunnel walls which hold the model, leading to more 3D flow. Hence, duringthe tests, it was observed that an important correction of the angle of attack wasnecessary for the comparison between computed pressure distributions and ex-perimental results. This correction can be obtained by using a strategy which willbe presented in the next chapter.

4 Computations

The upstream conditions are as follows :

V = 54 m/s Reynolds number = 1.8 106 based on the chord length C = 0.5 m.

The flow is supposed to be fully turbulent and free stream conditions were used(no confinement). In these conditions, 2D k-ε SST steady Navier-Stokes compu-tations have been performed for several angles of attack. The mesh used is un-structured; it contains 47,000 nodes. Fig. 4 shows an important concentration ofnodes near the wall.

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RA16SC1 slat 30 deg. flap 40 deg.

Fig. 4. Mesh.

4.1 Pressure coefficient

As mentioned above, because of a separation on the wind tunnel walls where therewas no boundary layer suction device, the flow became three dimensional for this2D geometry. Hence, a correction of the angle of attack is necessary for compari-son between 2D computation and 3D experiment.

This correction can be based on the same slat lift coefficient for both 2D com-putation and 3D experiment.

Fig. 5 shows that the correction is -2° for αexp equal to 6° and for αexp equal to12°, 17.5° and 19° for which PIV measurements were performed, this correction isequal to -4°.

Fig. 5. Slat lift coefficient.

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The equivalence between 3D experiment angles of attack and 2D numericalsimulation ones are given in table 1:

Table 1. Difference in angle of attack between experiments and computations3D experiment 2D computation

6° 4°12° 8°

17.5° 13°.519° 15°

Fig. 6 presents the comparison between computed pressure coefficient and ex-perimental results with the consideration of the angle of attack correction. For theslat, a good agreement is observed. On the lower side of this element, a regionwithout pressure gradient is visible; it is due to a separation which will be put inlight clearly with the velocity field analysis in the next chapter. Concerning themain body, a very good prediction of pressure is obtained. Also, the decrease ofthe pressure at the suction peak is observed if α increases. Regarding the flap,numerical simulation gives results very comparable to the experiments, except forαexp = 17.5° and 19° where computations overestimate slightly the pressure at thepeak suction.

Fig. 6. Pressure coefficient. Comparison between computations and measurements.

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In the light of this comparison, the strategy which consists in using an angle ofattack correction based on the same slat lift coefficient for both computation andexperiment, seems to be adequate.

4.2 Comparison between Computations and PIV Data

PIV measurements were performed for the angles of attack equal to 12°, 17.5° and19°.

The analysis of pressure distributions in Fig. 6 shows that the results corre-sponding to the angles of attack equal to 17.5° and 19° are close to each other.Hence, for comparison between 2D steady Navier-Stokes results and PIV data,only the experimental angles of attack equal to 12° and 19° were considered.

Fig. 7 shows windows corresponding to different set-ups where instantaneousand averaged velocity fields were measured by PIV [10]. For comparison betweensteady Navier-Stokes results and PIV data, averaged experimental velocities givenin these windows were used.

Fig. 7. PIV windows for different set-ups.

4.2.1 Velocity field

Fig. 8 gives the comparison between computation (continuous lines) and PIVresults (dashed lines) for αexp equal to 12°. Several flow phenomena mentionedabove for a 3 component airfoil in high lift configuration can be seen (separationon the slat lower side, slat wake and main body boundary layer interaction, mainbody cove separation, slat wake-main body wake and flap boundary layer interac-tion,..).

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Fig. 8. Mean velocity modulus. Comparison between computation and PIV data for α =12°.

In Fig. 9, velocity modulus is shown for the slat with PIV data represented bydashed lines and computed velocities by solid lines. A good prediction of the stag-nation point on the slat can be observed; with increasing angle of attack, this pointmoves towards the slat edge. Under this element of the geometry, a separationbubble is visible; its shape and its reverse flow are also correctly reproduced bynumerical simulations. As expected, the bubble size decreases if the angle of at-tack increases. In the gap between the slat and the main body, the flow is correctlypredicted and no blockage effect is observed.

(a) (b)Fig. 9. Mean velocity modulus under the slat for α = 12° (a) and 19° (b). Comparison be-tween computations and PIV data.

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Over the forward part (Fig. 10) and the rear part (Fig. 11) of the main body, adecelerated flow also visible with pressure analysis in Fig. 6, is disturbed by theslat wake. Comparison between numerical prediction and experiment shows apretty good agreement for the flow above the wake for 2 angles of attack. Con-cerning the boundary layer and the slat wake, an analysis in detail will be per-formed with the study of extracted velocity profiles in Fig. 15. Also, one can seethe PIV data dispersion in the overlapping region of the windows D and E wherethe data in window D are a little bit different from those in window E. For thewindow G (Fig. 11) where experimental results are obtained from 3 set-ups, asmall dispersion is also observed.

(a) (b)Fig. 10. Mean velocity modulus over the forward part of the main body for α = 12° (a) and19° (b). Comparison between computations and PIV data.

(a) (b)Fig. 11. Mean velocity modulus over the rear part of the main body for α = 12° (a) and 19°(b). Comparison between computations and PIV data.

In Fig. 12 corresponding to window K, the flow given by computations in theseparated region of the main body cove, is close to experiments. On the flap, thestagnation point is correctly predicted. In the gap between the main body and theflap, no blockage effect is observed.

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(a) (b)Fig. 12. Mean velocity modulus under the rear part of the main body for α = 12° (a) and19° (b). Comparison between computations and PIV data.

Fig. 13 presents results over the flap. We can observe the disturbances generatedby the slat wake and the main body wake in the decelerated flow. If the angle ofattack increases, the slat and main body wakes become more pronounced for bothcomputed and experimental results.

Regarding the main body wake region, the flow is decelerated up to a regionwhere the velocity value is very low. This area observed over the flap trailingedge, is located farther downstream in the case of experiments.

(a) (b)Fig. 13. Mean velocity modulus over the flap for α = 12° (a) and 19° (b). Comparison be-tween computations and PIV data.

4.2.2 Velocity profiles

Fig. 14 presents the locations where velocity profiles are extracted: 3 profiles overthe main body and 2 profiles over the flap.

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Fig. 14. Locations of extracted velocity profiles.

In Fig. 15, the velocity profiles at stations 1, 2 and 3 located over the main bodyare displayed. We can see that the prediction is close to experiment in the bound-ary layer at stations 2 and 3 and for the flow above the slat wake.

As it was observed in Europiv1 [1], the mixing between the slat wake and themain body boundary layer is slow in the case of computations. This discrepancywith experiment can be explained by the hypothesis used for one point turbulenceclosures that kinetic turbulent energy spectrum is in equilibrium; which is not thecase for this wake fed by a large separated zone under the slat.

If α increases, both experiments and computations show the effects such as:- an increase of the boundary layer thickness- a more pronounced wake- a delayed merging of the boundary layer and the slat wake.

(a) (b)Fig. 15. Velocity profiles for α = 12° (a) and 19° (b). Comparison between computationsand PIV data.

Fig. 16 displays the velocity profiles at station 4 located at mid-chord of theflap. We can observe a correct prediction of the boundary layer for α = 19° andthe minimal value of the main body wake velocity for 2 angles of attack. If α in-

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creases, the wakes become more pronounced for both computations and experi-ments.

(a) (b)Fig. 16. Velocity profiles for α = 12° (a) and 19° (b). Comparison between computationsand PIV data (station 4).

Concerning the velocity profile at station 5 located over the flap trailing edge,computed results are very different from PIV data for α = 12° (Fig. 17). The dis-crepancy is due to the presence of a separation bubble which is important with ex-periment but very thin in the case of computation as we can observe with stream-line analysis (Fig. 18, Fig. 19 and Fig. 20).

For the case of α = 19°, the minimal value of the main body wake velocity ispredicted correctly.

(a) (b)Fig. 17. Velocity profiles for α = 12° (a) and 19° (b). Comparison between computationsand PIV data (station 5).

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4.2.3 Streamlines

Fig. 18 displays over the flap streamlines obtained with experimental velocityfields. At α = 12°, the flow is separated on the last third part of the flap but re-mains attached for the case of α = 19°.

(a) (b)Fig. 18. PIV streamlines for α = 12° (a) and 19° (b).

In Fig. 19, no separation can be seen with computed streamlines for 2 an-gles of attack. But a close-view near the flap trailing edge wall shows a

separation for α = 12° but more limited in comparison with the experiment(Fig. 20). These results are confirmed by the analysis of the skin friction

which is negative at the flap trailing edge for this angle of attack (Fig. 21). It would be interesting to know whether the difference between com-

putation and experiment, concerning the separated area size, is due to the turbu-lence model or to the three-dimensionality of experimental flow.

(a) (b)Fig. 19. Computed streamlines for α (experiment) = 12° (a) and 19° (b).

In Fig. 19, another result can be observed : at α = 19°, the steady computationdisplays a strong deformation of streamlines over the flap trailing edge. This phe-

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nomenon which is also shown by several PIV snapshots based on instantaneousvelocity fields (Fig. 22), is not visible with averaged experimental results (Fig. 18).

(a) (b)Fig. 20. Computed streamlines near the flap wall for α (experiment) = 12° (left) and 19°

(right).

Fig. 21. Computed skin friction coefficient.

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5 Conclusions

2D Steady Navier-Stokes computations using the k-ε SST turbulence model forthe RA16SC1 airfoil in landing configuration have been carried out with the un-structured Aether code.

Due to a wind tunnel wall separation leading to a 3D flow for this 2D geome-try, an angle of attack correction was necessary for comparison of 2D numericalsimulation with PIV data. This correction obtained by considering the same slatlift coefficient for both computation and experiment, has allowed to observe agood agreement in wall pressure distribution between 2D computation and 3D ex-periment.

(a) (b)Fig. 22. Streamlines obtained with instantaneous PIV results (run 537 images n°16 (a) andn°34 (b)).

Within the flow field, the comparison of computations with PIV data has shownin the slat region a good prediction of the stagnation point location, the lower sideseparation and the flow in the gap between the slat and the main body.

Concerning the main body, the comparison with experiment is correct for theflow in the boundary layer and above the wake. With increasing angle of attack,computations as well as experiments show an increase of the boundary layerthickness and a delayed merging of the boundary layer and the wake. But, as ex-pected for one point turbulence closures, this mixing is slower in the case of com-putations.

On the flap, the change from a separated flow to an attached one if the angle ofattack increases, is predicted by CFD. But, the separated area observed at low an-gle of attack is more limited in the case of numerical simulation.

Note that the quality of the previous comparison is submitted to several sourcesof uncertainties such as :

- transition locations which were not measured during tests and whichshould be taken into account in computations instead of fully turbulent cal-culations

- three-dimensionality of experimental flow due to wind tunnel wall separa-tion.

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In conclusion, owing to velocity fields provided by PIV, a detailed study offlow characteristics has been possible. This analysis allows to improve the under-standing of physics of the complex flow surrounding typical high lift configura-tions and therefore contributes to enhance our capability to predict this kind offlow.

As far as code validation is concerned, a pretty good agreement is observedbetween averaged PIV data and 2D steady computations (RANS), using the k-εSST turbulence model. Such results are achieved despite the weakness of onepoint turbulence closure and the sources of uncertainties mentioned above (three-dimensionality of experimental flow and transition locations).

Currently, unsteady computations are under way and comparison with instanta-neous velocity fields provided by PIV, will be performed.

In the long term, the experimental data base obtained within EUROPIV2 willbe used for additional numerical investigations in order to improve turbulencemodels and validate LES and DES codes.

Acknowledgement

This work has been performed under the EUROPIV 2 project: EUROPIV 2 (AJoint Program to Improve PIV Performance for Industry and Research) is a col-laboration between LML URA CNRS 1441, Dassault Aviation, DASA, ITAP,CIRA, DLR, ISL, NLR, ONERA, DNW and the universities of Delft, Madrid,Oldenburg, Rome, Rouen (CORIA URA CNRS 230), St Etienne (TSI URACNRS 842) and Zaragoza. The project is managed by LML URA CNRS 1441and is funded by the CEC under the IMT initiative (contract no: GRD1-1999-10835).

We would like to acknowledge the good cooperation with all the partners in-volved in Task 3.1 and Task 3.2. We also wish to thank Mr. J.C. Courty and F.Chalot of Dassault Aviation for their fruitful discussions.

References

[1] J.C. Courty, Tran Dac, J.D. Marion, N. Getin, N. Pleindoux, N. Chabée, "Numericalsimulation of the flow around a high lift configuration. Comparisons with PIV".EUROPIV contract N°: BR.PR-CT95-0118, Report n° 37PT03.

[2] F. Chalot, M. Mallet, M. Ravachol, "A comprehensive Finite Element Navier-StokesSolver for Low and High-speed Aircraft Design". AIAA 94-0814, January 10-13,1994/ Reno, NV.

[3] F. Chalot and T.J.R. Hughes, "A consistent equilibrium chemistry algorithm for hyper-sonic flows". Computing Systems in Engineering, vol. 112, pp. 25-40, 1994.

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[4] F. Shakib, T.J.R. Hughes and Z. Johan, "A new finite element formulation for computa-tional fluid dynamics: X. The compressible Euler and Navier-Stokes equations". Com-puter Methods in Applied Mechanics and Engineering, vol. 89, pp. 141-219, 1991.

[5] F. Shakib, T.J.R. Hughes and Z. Johan, "A multi-element group preconditioned GMRSalgorithm for nonsymmetric systems arising in finite element analysis". ComputerMethods in Applied Mechanics and Engineering, vol. 75, pp. 415-456, 1989.

[6] F. Shakib, T.J.R. Hughes and Z. Johan, "A globally convergent matrix-free algorithmfor implicit time-marching schemes arising in finite element analysis in fluids". Com-puter Methods in Applied Mechanics and Engineering, vol. 87, pp. 281-304, 1991.

[7] Z. Johan, "Data Parallel finite Element Techniques for Large-scale Computational FluidDynamics". Ph. D. Thesis, Stanford University, 1992.

[8] F. Chalot, Q.V. Dinh, M. Mallet, A. Naïm, and M. Ravachol, "A multi-platform sharedor distributed-memory Navier-Stokes code". Parallel CFD 97, Manchester, UK, May19-21, 1997.

[9] Kasbarian C., Lebigre O., Mantel B., Mallet M., Ravachol M. et Tentillier M., "Devel-opment of finite element Navier-Stokes solver using unstructured adapted grids, appli-cation to turbulent flows". Computational Fluid Dynamics 92, Vol. 1, Ch. Hirsch et al.(Editors), 1992.

[10] J. Agocs, A. Arnott, B. Sammler, G. Schneider, A. Schröder, DLR, "Report on the PIVexperiments around a high-lift configuration for Work Package 3.1 DLR Göttingen".EUROPIV2 contract n° G4RD-CT-2000-00190, Report D3.5, 2002.