NUMERICAL SIMULATIONS OF TURBULENT FLOWS OVERTHE ONERA-M6 AND DLR-F6 CONFIGURATIONS

Ricardo Galdino da Silva∗ , João Luiz F. Azevedo∗∗ Instituto de Aeronáutica e Espaço, DCTA/IAE/ALA, São José dos Campos, SP, Brazil

Keywords: CFD, Drag prediction, Turbulence modeling, Mesh refinement

Abstract

The flow around the ONERA-M6 wing, one ofthe most known experimental aerodynamic case,is a good test case for a code validation pro-cess, since geometry and pressure coefficient dis-tributions at several stations along the wing areavailable. This test case will be used as a firststep of an ongoing validation process of an in-house developed Computational Fluid Dynamics(CFD) code, named BRU3D, for aeronautic ap-plications. Three refinement levels of a hybridmesh composed of prism layers in a region nearthe wing surface, with y+ around 1, and the restof the domain filled by tetrahedral elements aregenerated. The simulations use these meshes inconjunction with three different turbulence mod-els, namely SA, SST and BSL-EARSM. Thecomparison between pressure coefficient distri-butions from numerical and experimental resultswill give us the opportunity to find out the meshrefinement effect and the effect of turbulencemodels on a final solution, and hence assess dis-crepancies arising from such effects. The sec-ond test case is the DLR-F6 geometry, whichhas wind tunnel results and also numerical resultsavailable from the 2nd AIAA CFD Drag Pre-diction Workshop (DPW-II). The paper presentscomparisons of drag polar with and without en-gines obtained from our numerical results andexperimental data. Most of all results obtainedshow satisfactory agreement with experimentalresults, with the exception of the data obtainedwith the hybrid coarse mesh for both configura-tions with and without pylon and nacelle.

1 Introduction

Aerospaces and aeronautics cases usually hap-pen at high Reynolds number and also at highMach number, especially the aerospace applica-tions. These types of flows are within the inter-ests of Instituto de Aeronáutica e Espaço (IAE).Since, most of interest applications occur at highReynolds number an adequate turbulence model-ing is necessary. Moreover, flow features such asdetachment due to the presence of adverse pres-sure gradient, interaction between shock wavesand boundary layer, confluence of boundary layerand wakes, and wing tip vortex are also present inour typical flow simulation. Therefore, a success-ful simulation will only occur if the Computa-tional Fluid Dynamics (CFD) solver is been ableto deal with such flow features.

The present work mainly focuses on aero-nautics applications and all the results shownhere is just a first step. Once, our final goal isto have a CFD solver that is capable of gener-ated reliable aerodynamic results in a robust way.This achievement is possible through a processof validation and improving of the CFD solver,and at the end of this process it is possible to asolver that can be used in daily work. There-fore, the first test case selected to start the processof validation and enhancement of our in-houseCFD solver (BRU3D) is ONERA-M6 configura-tion, since its geometry and experimental data areavailable [1]. Moreover, this flow case presentsa couple of physics features mentioned earlier,such as boundary layer/shock wave interactionsand wing tip vortex, for instance. A numeri-

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RICARDO GALDINO DA SILVA , JOÃO LUIZ F. AZEVEDO

cal simulation of the flow around ONERA-M6wing was performed with three different meshrefinement levels, second-order spatial Roe flux-difference scheme, an implicit Euler scheme isused to march the complete set of equations,and SA (Spalart-Allmaras), SST (Shear StressTransport) and BSL-EARSM (BaSeLine - Ex-plicit Algebraic Reynolds Stress Models) turbu-lence models. The pressure coefficient distribu-tions were extracted from numerical solution andcompared to experimental data for certain posi-tions along the ONERA-M6 span.

Another important feature is to be able to pre-dict the variations on aerodynamic coefficientscaused by a modification on geometries and alsomodification on the configurations. For instance,the CFD solver should be able to predict the ef-fects caused by the installation of under wing en-gines. For this part of the investigation, the cho-sen test case is the DLR-F6, which are a publicdomain geometry and also was used at 2nd AIAACFD Drag Prediction Workshop (DPW-II). In ad-dition, there are wind tunnel data available forflow conditions of Reynolds number equal to 3million and Mach equal to 0.75 for configura-tions with (WBPN) and without engine (WB).A drag polar for each model configuration (WBand WBPN) is calculated from the simulation re-sults and compare to experimental data. Threedifferent levels of mesh refinement for hybrid(prismatic + tetrahedral + pyramidal mesh ele-ment) and hexahedral mesh, which can be ob-tained from DPW-II website. Moreover, as men-tioned, there are results at hand for DLF-F6 con-figuration with and without pylon and nacelle.Three hybrid meshes with different refinementlevels are generated in order to measure the meshrefinement effect on drag polar. In addition, threehexahedral (multiblock) meshes with differentlevels of refinement are also used, these meshesare obtained from the DPW-II website. All thesimulations are performed here with the Spalart-Allmaras (SA) turbulence model.

The present article is divided into five sec-tions: Introduction, Theoretical and NumericalFormulation, Mesh, Results and Concluding Re-marks. The first section, which is the current sec-

tion highlights the motivations and the objectiveof this effort. The second presents a brief descrip-tion of a theoretical and numerical formulationimplemented in our CFD code. In the third sec-tion, we present the meshes used for simulationsand a brief description of procedure used to gen-erate all the mesh refinement levels. In the sec-tion 4 the results for simulations of ONERA-M6,DLR-F6 WB configuration and DLR-F6 WBPNconfiguration are presented and also comparedwith experimental results for each configuration.Finally, in the fourth section, all the results ob-tained are presented. In the last section, conclud-ing remarks end this paper.

2 Theoretical and Numerical Formulation

In this section, not only, a brief description of atheoretical and numerical formulation, But also, alist of turbulence models and numerical schemesthat are available at BRU3D will be given. Thissection is mainly based on Ref. [2].

The flows considered in the present paper aregoverned by the 3-D compressible Reynolds av-eraged Navier-Stokes (RANS) equations and it isassumed to be fully turbulent. These equations inits dimensions form, are given by

∂Q∂t

+∇ · (Ee −Eν) = 0 (1)

on which Q is given by

Q = [ρ ρu ρv ρw ρτ1 ρτ2 ]T (2)

and the inviscid (Ee) and viscous (Eν) flux vectorsare given by

Ee =

ρvρuv+ pixρvv+ piyρwv+ piz(e+ p)v

τ1vτ2v

Eν =

0(τl

x j + τtx j

)i j(

τly j + τt

y j

)i j(

τlz j + τt

z j

)i j

β j i j

µdi f f1τ1, j i j

µdi f f2τ2, j i j

(3)

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TURBULENT FLOWS OVER THE ONERA-M6 AND DLR-F6 CONFIGURATIONS

The shear-stress tensor is defined as

τli j = µl

(∂ui

∂x j+

∂u j

∂xi− 2

3∂um

∂xmδi j

)(4)

on which ui is velocity component, and xi refersto the coordinate the system. The dynamic vis-cosity µl is determined by Sutherland’s law. Theunknown Favre-averaged Reynolds stress tensor,τt , is modeled within BRU3D via linear and non-linear edge-viscosity models (EVM). The linearEVM options available in BRU3D that is goingto be used in the present paper are the SA turbu-lence model, shown at Ref. [3], and the SST tur-bulence model, developed by Ref. [4]. The non-linear EVM is the BSL-EARSM model presentedin Refs. [5] and [6].

The RANS equations (Eq. 1) and the turbu-lence model equations according to finite volumemethod are given by

Vi∂Qi

∂t=−

n f

∑k=1

(Eek −Eνk) ·Sk =−RHS (5)

on which the subscript k stands for propertiescomputed in the k-th face, and n f representsthe number of faces, which form the i-th con-trol volume. In order to obtain Eq. 5, one as-sumes constant fluxes through volume faces andalso constant Qi proprieties inside the volumefaces. The first assumption is a sufficient approx-imation to obtaining 2nd-order accuracy in spacethe currently available flux computation schemes.In the convective flux computation, a Roe flux-difference splitting scheme [7] is assumed. Toachieve 2nd-order accuracy in space, primitiveproperties are linearly reconstructed at volumefaces with the MUSCL algorithm from Ref. [8] inconjugation with a limiter function, such as min-mod, van Albada or superbee limiters [9] that arecurrently available in BRU3D. The present effortuses the van Albada limiter function. The dif-fusion terms are discretized using a method thatcomputes non-oscillatory, highly accurate deriva-tives at the face, as described in Ref. [10].

A 1st-order backward Euler implicit non-linear scheme for Eq. 5 is given by

Vi∆Qn

i∆t

=−RHS(Qn+1

i)

(6)

Here, ∆Qni = Qn+1

i −Qni . The linearisation use an

expansion of RHS(Qn+1

i)

about ∆Qni as in

RHS(Qn+1

i)= RHS (Qn

i )

+∂RHS (Qn

i )

∂Qni

∆Qni +O(∆Qn

i )2 (7)

and leads to the 1st order accurate implicitscheme:

Vi∆Qn

i∆t

+∂RHS (Qn

i )

∂Qni

∆Qni =−RHS (Qn

i ) (8)

More detail on how to calculate the residue

(RHS (Qni )) , the Jacobian matrix

[∂RHS(Qn

i )∂Qn

i

],

and fluxes can be found in Ref. [2].

3 Mesh Generation

The numerical simulations will emulate a freefight condition. Hence, it is not necessary toinclude the wind tunnel walls in the numeri-cal domain. However, all the experimental datawere acquired from wind tunnel runs that alwayspresent wall effects. To eliminate these effects acorrect methodology had been applied to the ex-perimental data. Therefore, all the comparisons,which are going to be presented in section 4 ,between experimental data and numerical resultswere done within compatible conditions.

The numerical domain consists of a semi-sphere placed at a distance equal to two hun-dred Mean Aerodynamic Chord (MAC) from theONERA-M6 wing surface and also two hundredMAC of DPW-II WB and WBPN configurationsfor hybrid meshes. This quit a large distance isused to try to avoid any effect of boundaries con-ditions on near field flow solution. The semi-spherical outside part of the numeric domain iscalled Far Field and the characteristic equationsimposed as a boundary condition. Moreover, ano slip condition imposed to the wing surface.

This description is valid just for hybridmeshes, once these were generated by the au-thors. The hexahedral mesh of DLR-F6 WBconfiguration and DLR-F6 WBPN configurationwere taken from DPW-II web site [11] and the

3

RICARDO GALDINO DA SILVA , JOÃO LUIZ F. AZEVEDO

far field seems to be even more distant than 200times the MAC. In addition, the far field has arectangular shape.

Both meshes types hybrid and hexahedral forall configurations ( ONERA-M6, DLR-F6 WBand DLR-F6 WBPN) are divided in three levelsof refinement. The generation mesh process isreported just for the hybrid meshes and we limitourselves just to make analyses above hexahidralmeshes by comparing those between them and bycomparison with hybrid meshes. More details onhexahidral meshes can be found at DPW-II website [11]. It worth to mention that the mesh re-finement level is classified as fine, medium andcoarse, whereas in our case we just change thenomenclature from medium to baseline. Thus,the meshes in the present study are classified asfine, baseline and coarse.

Figure 1 shows all three surface mesh that isgenerated to evaluate the mesh effect on the so-lution. The trailing edge and wing tip has differ-ent levels of refinement when it is compared withthe rest of the wing surface. At the trailing edge,this refinement is not only because of the surfacecurvature, but also, because it is expected a highvariation of the pressure. The wing tip refinementis mainly to improve the space and volume refine-ment to have a better representation of the wingtip vortex. In spite of its wing tip refinement, thefine mesh surface do not present a difference insurface mesh refinement. This fact occurs as aconsequence of the element size set to wing sur-face, which is smaller than the imposed size to tipwing region.

(a) Coarse (b) Baseline (c) Fine

Fig. 1 Surface mesh according to each mesh re-finement level.

Figure 2 highlights the difference on the vol-umetric mesh due to the refinement process. The

tetrahedral growth ratio is the same for all threemeshes, consequently all the volumetric refine-ment is directly related to the surface mesh re-finement. On the other hand, not is the prim layerheight ratio identical for all meshes, once we usethe number of elements inside of the prism layeras a control parameter for mesh refinement.

(a) Coarse (b) Baseline (c) Fine

Fig. 2 Cut section of volumetric mesh localizedat wing midspan position.

Figure 3 shows hybrid surface meshes andhexahedral surface meshes that are generated toevaluate the mesh effect on the engine installationdrag. From that figure is possible to observe thatthe hybrid surface mesh is more refined than hex-ahedral surface mesh for each level (Fine, Base-line and Coarse) of mesh refinement. Our pro-cess of hybrid mesh generation starts from thefine mesh of WBPN configuration and a factor oftwo is applied once to obtain the baseline meshand twice to obtain the coarse mesh. Moreover, itis noticeable from Fig. 3 that the refinement fac-tor for hexahedral meshes are less than 2. In orderto maintain the same mesh surface refinement be-tween WBPN and WB meshes, each level of sur-face mesh refinement of WBPN configuration isused to generate its respective WB surface mesh.It is achieved by removing the pylon and nacellesurface mesh, this process leaves a hole at lowersurface located where the plane was fixed. At theend, this hole is closed and the WB surface meshis obtained.

The trailing edge and wing tip has differentlevels of refinement when it is compared with therest of the wing surface. At the trailing edge,this refinement is not only because of the surfacecurvature, but also, because it is expected a high

4

TURBULENT FLOWS OVER THE ONERA-M6 AND DLR-F6 CONFIGURATIONS

(a) F. Hyb. (b) B. Hyb. (c) C. Hyb.

(d) F. Hex. (e) B. Hex. (f) C. Hex.

Fig. 3 Three level of hybrid surface mesh forWBPN and WB configuation. On which, F.stands for Fine, B. stands for Baseline, C. standsfor Coarse, Hex. stands for Hexahedral mesh andHyb. stands for Hybrid mesh.

variation of the pressure. Close to the wing tip thevolumetric mesh refinement is mainly improvedby adding by selecting a region around the wingtip, inside this region the element size is fixed, inour case this volumetric element size is equal toits respective surface element size. This approachis used to try to improve the resolution of wing tipvortex. A similar approach is used in regions nearto the wing trailing edge and wing leading edge.

Figure 4 consists of a cut of volumetricmeshes (hybrid and hexahedral) at a certain po-sition on the wing span that is identical tothe nacelle center position related to the wingspan. This figure highlights the difference onthe volumetric mesh due to the refinement pro-cess and also shows differences from hexahedraland hybrid volumetric refinement. The tetrahe-dral growth ratio is the same for all three meshes,consequently all the volumetric refinement is di-rectly related to the surface mesh refinement. Onthe other hand, not is the prismatic layer heightratio identical for all meshes, once we use thenumber of elements inside of the prismatic layer

as a control parameter for mesh refinement. Asa consequence, this definition, the coarse meshseems to not have enough refinement in prismaticlayer, which is direct linked to the level of reso-lution of the boundary layer. Thus, it is expecteda result somewhat worse for coarse hybrid meshthan the results for the other meshes. Despite thefact with the coarse prismatic layer, all the volu-metric meshes seem to have a smooth growth ofits volumetric elements.

(a) F. Hex. (b) B. Hex. (c) C. Hex.

(d) F. Hyb. (e) B. Hyb. (f) C. Hyb.

Fig. 4 Three level of hexahedral surface mesh forWBPN configuration and WB configuration. Onwhich, F. stands for Fine, B. stands for Baseline,C. stands for Coarse, Hex. stands for Hexahedralmesh and Hyb. stands for Hybrid mesh.

4 Results

In this section, the numerical results obtainedwith BRU3D code will compared with experi-mental data available.The test case are ONERA-M6 wing and DLR-F6 WB configuration andDLR-F6 WBPN configuration, as mentioned ear-lier. This section will be divided in two subsec-tions related to each geometry type (ONERA-M6

5

RICARDO GALDINO DA SILVA , JOÃO LUIZ F. AZEVEDO

and DLR-F6). The subsection for 4.1 shows acomparison between numerical and experimentalresult of Cp distribution at some wing span loca-tions. In addition, the subsection 4.2 presents thenumerical and experimental drag polar for WBand WBPN configurations.

4.1 ONERA-M6 Wing

For this test case, the free-stream flow condi-tions are Mach number equal to 0.84, angle ofattack (AoA) of 3.06 degrees, and Reynolds num-ber, based on MAC length, around 11.72 mil-lion. These conditions match the conditions ofwind tunnel test reported in Ref. [1]. The ex-perimental data correspond to pressure coeffi-cients along the wingspan direction. For com-parisons between experimental and numerical re-sults, we select three position which correspondto η = 0.44, η = 0.80 and η = 0.99, on which η

of the wingspan.The numerical solution for all turbulence

model was considered to be converged, once eachRHS curve reached a certain constant level ofRHS after a given number of iterations, which isless than 2000 iteration for all results.

The flow conditions, which was mentionedearlier, together with the geometry of theONERA-M6 wing are responsible for the forma-tion of a λ shock over its upper surface. The pres-ence of double shock wave on the suction side istypical for λ shock, on experimental data the dou-ble shock formation is present from section withη = 0.20 to section with η = 0.80. The distancebetween the two shock waves keeps reducing un-til both shocks merges into single shock, that hap-pens somewhere between η = 0.80 and η = 0.90.All combinations of turbulence model (SA, SSTand BSL-EARSM) and refinement levels predictsthe presence of the λ shock. However, the loca-tion where the double shocks merge is not pre-dicted well for numerical results. The numeri-cal results indicate the shock waves merge loca-tion somewhere between η = 0.65 and η = 0.80.Figures 5(a) and 5(b) show the Cp distributionsuperimposes over the ONERA-M6 wing uppersurface and the isosurfaces of Mach number, re-

spectively. The upstream isosurface is formedwith Mack number equal to 1.4, and the down-stream isosurface is formed with Mach numberequal to 1.12. From those figures, it is noticeablethe formation of the λ shock wave over the uppersurface. These figures were constructed from thenumerical results obtained with fine mesh and SAturbulence model.

(a) Cp distribution.

(b) Iso-surfaces of Mach number equal to 1.40 andMach number equal to 1.12.

Fig. 5 Pressure coefficient distribution (Cp) andIso-surface of Mach number equal to 1.40 and1.12 extracted from numerical simulation ob-tained with fine mesh and SA turbulence model.

Figure 6 shows the comparison of pressurecoefficient (Cp) between the numerical results ofthe SA, SST and BSL-EARSM turbulence mod-els and experimental results. In general, thesecomparisons show good agreement between bothnumerical and experimental results. However,the only exception is section η = 0.80, in whichthe numerical solution is unable to predict thedouble shock formation.

The numerical results present a variation onCp results in the first sections as result of meshrefinement.The mesh refinement moves the shock

6

TURBULENT FLOWS OVER THE ONERA-M6 AND DLR-F6 CONFIGURATIONS

position predicted by numerical solution down-stream. The mesh refinement seems to improvethe prediction of shock position, which meansthat the numerical results are becoming moreclosely to experimental results as the refinementlevel increase. Indeed, at sections η = 0.80 andη = 0.99 the prediction of shock position is un-changing with the mesh refinement. The last sec-tion shows dependence on mesh refinement, atlist for locations with x/C (ratio between posi-tion in the x direction and the local profile chord)greater than 0.60. In summary, in regions wherethe double shock is present on the numerical so-lution, the mesh refinement exhibits a perceptibleeffect on the numerical solution. These observa-tions are similar for all turbulence models.

Figures 6(a), 6(b) and 6(c) present the numer-ical results of SA turbulence model. In addition,Figs. 6(d), 6(e) and 6(f) show the comparisonbetween experimental results and numerical re-sults of SST turbulence model for three levelsof mesh refinement. Moreover, Figs. 6(g), 6(h)and 6(i) presents a similar comparison for BLS-EARSM turbulence model. Both, the numeri-cal results of SST and BSL-EARSM turbulencemodels present behavior similar to those pre-sented by SA results. When the Cp results of SSTand BSL-EARSM are confronted, it is possible tofigure out that those results are pretty much alike.Besides, the SST turbulence model is based onthe linear eddy-viscosity, which means that theReynolds stress tensor are modelled based inBoussinesq assumption, and for BSL-EARSMthe Boussinesq assumption is altered to includeadditional nonlinear terms. That fact does notmake a significant difference on Cp solutions ob-tained from both turbulence models.

The mesh refinement is responsible for themajor changes in the numerical results, which ingeneral lead to diminish the discrepancy betweennumerical results and experimental results. Thewing leading edge mesh refinement increases itslocal acceleration and as a consequence the min-imum pressure coefficient Cp decreases.

All numerical solutions at section η = 0.80exhibit the worst result, since the double shock,which is present in experimental data, is not pre-

dicted. None of numerical settings were ableto give a corrected representation of the doubleshock formation, which are exposed in Fig. 6(b)for SA turbulence model, in Fig. 6(e) for SST tur-bulence model and in Fig. 6(h) for BSL-EARSMturbulence model show.

Finally, at section η= 0.99, there are discrep-ancies that grows downstream from 0.60 of thelocal chord. The mesh refinement tends to de-crease this discrepancy. On the other hand, al-most no effect is observed due to modificationson the turbulence model. Both, the mesh refine-ment effect and turbulence model are presented atFig. 6(c), 6(e) and 6(h). This could be interpretedas indication that we are not able to predict the tipwing vortex with the mesh refinement levels andturbulence models used in the present effort.

4.2 DLR-F6 Configuration

All the calculations have been performed atReynolds number equal to 3 × 106 and Machnumber equal to 0.75. The turbulence model SAavailable in BRU3D does not have a capabilityto predict the boundary layer transition, thus allsimulations are full turbulent. Moreover, the CFLis equal to 10 and the number of solver iterationsis limited to 3000, and after a 1500 iteration thevan Albada limiter is frozen. This approach wasable to make the RHS residual drops more than 7orders for all equations.

Figure 7 presents examples of Cp (pressurecoefficient) over upper and lower wing surface ofconfiguration WB and WBPN at AOA equal to0 degree. By means of comparison between theWB Cp distribution and WBPN Cp distribution, aqualitative analysis of the effect of the pylon andnacelle installation is possible. From that com-parison, it is noticeable the effect of the pylon andnacelle on the wing upper surface. Figure 7(a)shows a the inboard part. On the other hand, it isnot so clear the effect on the wing lower surfaceof this qualitative analysis. Figure 7(a) shows thatfor WB configuration the negative peaks of CPare distributed over the wing span, however forWBPN configuration (Fig. 7(c)) the Cp negativepeaks are limited to the inboard part of the wing.

7

RICARDO GALDINO DA SILVA , JOÃO LUIZ F. AZEVEDO

(a) SA - η = 0.44 (b) SA - η = 0.80 (c) SA - η = 0.99

(d) SST - η = 0.44 (e) SST - η = 0.80 (f) SST - η = 0.99

(g) BSL-EARSM η = 0.44 (h) BSL-EARSM η = 0.80 (i) BSL-EARSM η = 0.99

Fig. 6 Comparison of CFD results obtained with the SA, SST and BSL-EARSM turbulence models andexperimental results of pressure coefficient (Cp) distribution along the chord of three sections along thewingspan direction.

Figure 8 presents the comparison of the com-puted drag polar and lift curve for the all threerefinements levels of hexahedral mesh and alsohybrid mesh with experimental. It added and sub-tracted 50 drag counts from experimental dragvalues in order to stipulate a range of variation,in which all numerical results should be inside.These upper and lower limits will be shown in alldrag polars that are the presented in present study.The comparison between experimental and nu-merical drag polar shown in Figs. 8(a) and 8(b)revel a good agreement for all mesh refinementlevels.

Figure 8(a) shows the polar drag and the liftcurve obtained from a WB configuration withhexahedral mesh. All points of numerical dragpolars obtained falls within the range of variationof ±50 counts drag from the experimental polar

drag.The coarse hybrid mesh of both WBPN

configuration and WB configuration present theworse the results. All results for this mesh typeand refinement fall outside of the drag polarrange, which can be seen in Figs. 8(a) for WBconfiguration and 8(b) for WBPN configuration.This is a indication that this mesh is not appropri-ate for drag prediction. However, it is capable toshows the increase on drag due to engines instal-lations. The results that were obtained with oth-ers hybrid mesh refinement levels (baseline meshand fine mesh) fall within the variation range as-sumed for experimental drag polar. The results ofWBPN configuration with hybrid fine mesh arethe best of all simulations performed for DLR-F6 geometry, since the numerical results are veryclose to the results obtained from the wind tunnel

8

TURBULENT FLOWS OVER THE ONERA-M6 AND DLR-F6 CONFIGURATIONS

(a) WB - Upper surface. (b) WB - Lower surface.

(c) WBPN - Upper surface. (d) WBPN - Lower surface.

Fig. 7 Pressure coefficient (Cp) distribution overa DLR-F6 with and without pylon and nacelle.The solutions presented in this figure was ob-tained with hexahedral and AOA equal to 0 degree

test, Fig. 8(b) shows the plot used to verify theproximity between numerical results and experi-mental results. However, this behaviour was notobserved for WB configuration (Fig. 8(a)). TheCD final results for this case is higher than thewind tunnel values.

5 Concluding Remarks

The overall behavior of the ONERA-M6 wingnumerical results is in good agreement with ex-perimental data, since all numerical simulationspredict the formation of λ shock over the uppersurface of the ONERA-M6 wing, and the nu-merical pressure coefficient distribution presentonly small discrepancies from experimental Cpdistributions. In spite of that, the numerical re-sults for sections η = 0.80 and η = 0.99 presentdifferences from experimental data, mainly be-cause the present calculations have not been ableto capture the wing tip vortex. None of the nu-merical settings selected, namely, mesh refine-ment and choice of turbulence model, were ableto predict the correct spanwise location of the

(a) WB Drag Polar

(b) WBPN Drag Polar

Fig. 8 Comparison between experimental andnumerical results for DLR-F6 WB and WBPNconfigurations at Reynolds number equal to 3×106 and Mach number equal to 0.75. The abbre-viations Hex. and Hyb. in the legends stand forhexahedral and hybrid meshes, respectively.

double shock merging. The numerical resultswith the linear eddy-viscosity models, namely,SA and SST turbulence model, and those withthe nonlinear eddy-viscosity BSL-EARSM tur-bulence model were not able to capture the cor-rect position of the shock merging.

Most of the present results for the DLR-F6configuration, both with and without the pylonand nacelle elements, fall within a ±50 dragcount range around the experimental data. Theexception to this statement refers to the drag po-lar prediction for DLR-F6 configuration obtainedwith the hybrid coarse mesh. This result is prob-ably linked to the fact that these meshes do not

9

RICARDO GALDINO DA SILVA , JOÃO LUIZ F. AZEVEDO

have enough refinement in the boundary layer re-gion. The results with baseline hybrid mesh andfine hybrid mesh present an improvement on thedrag polar predictions. Such improvement is di-rectly related to the increase of mesh refinement,which not only increases the number of elementsinside the boundary layer, but also provides forsubstantial more refinement along the surface ofthe configuration. The authors feel, however, thatadditional studies would be necessary in order todefine which of these refinements is more signif-icant. The results obtained with the hexahedralmesh fall inside the assumed drag polar range,i.e., ±50 drag counts around the experimentaldrag polar.

Acknowledgments

The authors gratefully acknowledge the sup-port for the present research provided by Con-selho Nacional de Desenvolvimento Científico eTecnológico, CNPq, under the Research GrantsNo. 309985/2013-7, No. 400844/2014-1 and No.443839/2014-0. The work is also supported byFundação de Amparo à Pesquisa do Estado deSão Paulo, FAPESP, under the Research GrantsNo. 2008/57866-1 and No. 2013/07375-0.

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