advanced numerical simulations on structured grids …

ICAS 2002 CONGRESS

253.1

Abstract

This paper presents the most recent simulationsmade at Airbus France, using advancedstructured grids techniques available in the newgeneration CFD solver elsA. Three aircraftapplications have been carried out in order toshow the potentiality of the new functionalitiesapplied on complex configurations. First, aChimera calculation was performed in order toassess ground effect prediction as an alternativeto the panel method currently used today. Then,a Multigrid Adaptive Mesh Refinement strategywas applied on an isolated swept wing toevaluate accuracy improvements on shock waveprediction. Finally, recent improvementsachieved in the wall law function were tested ona Navier-Stokes engine/airframe configurationand compared to a classical low Reynoldsturbulence modeling approach.

Nomenclature

ρ densityα angle-of-attackMo free stream Mach numberhlanding minimum height of aircraft gravity

center at landingh height of aircraft gravity centerH h- hlanding :: relative ground effect

heightCLo, CDo lift and drag coefficients at free-

stream conditionsb half wing spanB total wing spany+1 first wall cell size in wall units

1 Introduction

Numerical methods are now widely usedthroughout the aircraft design process. Inparticular, Airbus intensively uses CFD withinthe scope of its responsibilities in all projectsand programs for the design and optimization ofaerodynamic shapes.

Moreover, as a complement to wind-tunneltests and semi-empirical methods, CFD is moreand more used in the assessment ofaerodynamic data for performance, loads andhandling qualities.

Today, most of our Euler and Navier-Stokes calculations are carried out on coincidentstructured meshes. In order to optimize designcycles and to fulfil the new needs andconstraints relative to aerodynamic datageneration, new numerical methods have beeninvestigated:• Chimera technique to reduce time spent in

mesh generation and to allow geometricalparametric studies without creating newmeshes.

• Multigrid Adaptive Mesh Refinement toimprove result accuracy withoutdowngrading computing performance.

• Turbulence wall law models to improvecomputing performances and convergencerate without downgrading accuracy.

ADVANCED NUMERICAL SIMULATIONS ONSTRUCTURED GRIDS FOR TRANSPORT AIRCRAFT,USING AN EFFICIENT OBJECT ORIENTED SOLVER.

L. BARRERA - Airbus France, Fr ,Ch. BENOIT, M.-C. LE PAPE, R. HOUDEVILLE, J. PETER - ONERA, Fr ,

J.-C. JOUHAUD - CERFACS, Fr

Keywords: Navier-Stokes, Object-Oriented, Chimera, AMR, Wall laws, Ground effect

L. BARRERA

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2 elsA solver

With the objective of federating allnational research teams and taking advantage ofolder functionalities implemented in separateCFD codes, ONERA has been developing a newgeneration solver called elsA since 1996, in co-operation with CERFACS. It has been designedaccording to an Object Oriented design methodand it is mainly coded with C++ language,thought the most CPU-expensive loops arecoded with Fortran language for betternumerical efficiency. This innovative approachleads to more upgradeable and inter-operableaerodynamic functions, and thus contributes tobetter integration of different development [1].

The main features and numerical functionsof elsA are listed below:• cell centered code dealing with structured

meshes.• no ghost-cell to ensure the connection

between domains (connecting data aretemporary)

• classical central and upwind fluxes for Eulermodel (centered flux with scalar or matrixdissipation, Van Leer flux, Roe flux)

• viscous flux computed from cell -centeredevaluations of velocity and temperaturegradients

• classical algebraic and transport equationsturbulence models (all of them followingBoussinesq’s assumption). Similardiscretization for the terms of the turbulencemodels and those from the mean flowsystem.

• three classical mechanical formulations(absolute variable/absolute or relative frame,relative variable/relative frame).

• Runge-Kutta or backward-Euler timeintegration for steady flows, dual time-stepping for unsteady flows.

• various multi-domain/ convergenceacceleration strategies : global multi-grid,local multi-grid and adaptive meshrefinement and chimera.

• mesh deformation• low-speed formulation

We describe below more precisely the veryrecent developments, which were used in thisstudy for aircraft applications.

2.1 Chimera gr ids

2.1.1 Chimera principleThe Chimera method is based on an

overlapping grid technique [2]. Its principle is tomesh independently different bodies and then totake into account interactions between thedifferent components by interpolations. Moreprecisely, on the one hand the mesh areasoverlapped by bodies are not computed by thesolver and body influence comes from a cellcrown around the body; on the other hand,domain influence goes through outflowboundaries. This technique allows the body tobe meshed quite independently, meshes mustonly sufficiently overlap to enableinterpolations. Meshes can also be re-used fordifferent relative positions. In elsA, theinterpolation is piecewise linear by tetrahedron,each cell being divided into 24 tetrahedrons.Bodies are modeled by a great number ofparallelepipeds. Interpolation cell researchbecomes efficient by using a preconditionedcartesian grid and other acceleration techniquesto find the interpolation tetrahedron [3],[4]. Inorder to reduce overlapping constraints andprevent some points from becoming orphan,extrapolation from neighbor cells is allowed; thenumerical scheme is also degenerated onoverlapping boundaries and around bodies, theninterpolation crown and boundaries have awidth of one cell [5].

2.1.2 Implementation in the elsA softwareIn the elsA software, using Chimera

consists in defining overlap boundaries andbody surfaces. Our implementation can be usedfor steady and unsteady flows (even withmoving bodies) and with various turbulencemodels. However, using it in conjunction withthe Multigrid acceleration technique is not yetavailable.

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ADVANCED NUM ERICAL SIM ULATIONS ON STRUCTURED GRIDS FORTRANSPORT AIRCRAFT, USING AN EFFICIENT OBJECT ORIENTED SOLVER.

2.2 Adaptive Mesh Refinement

2.2.1 Hierarchical Grid StructureThe Multigrid AMR algorithm consists in a

sequence of integration on different grid levels( maxll0 ≤≤ ). A grid lG is required to beunion of sub-blocks in which the samediscretization procedure is applied:

k,lkl GG ∪= , where k,lG are elementary

sub-blocks.The hierarchical grid structure respects the

“properly nested property” [6] which is basedon the following three rules:

(1) maxll0l ≤≤∀ , 1ll GG −⊂ , inclusion ofunderlying grids ;(2) =∩ hlkl GG ,, ∅ if hk ≠ , no overlapping ;

(3) adjacent cells of lG must only belong to thelevel 1l − , except for external or wallboundaries.

The first rule ensures the successive gridsnesting, i.e. the gradual basic mesh enrichmentwith finer and finer meshes. It means (with thethird rule) the recursiveness of the method.

The second rule is a standard choice, whichprevents overlapping, which is very expensivein computation time and memory storage.

The third rule enforces a strict inclusionand leads to a gradual distribution of refinementzones from the coarsest to the finest. However,it permits a finer and finer refinement near thesolid boundary.

2.2.2 Combining AMR and multi-grid methodsThe classical AMR method, i.e. the method

developed by Berger & Collela [7] is valid onlyfor unsteady flows. Indeed, it is no longer validfor steady flows because convergence on thehierarchical mesh is not guaranteed.

Here, we have developed a local 3D multi-grid algorithm for embedded meshes calledMultigrid AMR. Based on the multi-gridapproach, this technique [8] not only couplesthe different levels of grid but also acceleratesthe convergence to steady state.

It is based on a local forcing function,which allow a local formulation of Jameson’sFull Approximation Scheme [9]. This local

forcing function modifies coarse block residualsby constructing so-called composite residuals.

2.2.3 Automatic Grid AdaptationOnce the aerodynamic solver is able to

treat local refined meshes, it is important todevelop a specific tool for an automaticcalculation of sub-block location, based onaerodynamic user criteria. Since 1994, Airbushas been developing such a tool called MBREF.It is interfaced with our in-house data baseenvironment DAMAS (DAta for Meshes andAerodynamic Solvers) and can be divided intothe following stages:• compute a sensor (between 0 and 1) on the

all volume cells. Today, two Euler sensorsrespectively based on simplified density andpressure gradients are available.

( )( )

( ).....,min

,,,,,max

max

1

1

ii

iii

kkjjiiijk

ijkdoms

ijk

s

s

ss

ρρρρ

ρ

ρρρρρρ

+

++

−+−+−+

−=∆

∆∆∆∆∆∆=

=

• flag the cells satisfying a criteria, usually

thresholdss≥• compute sub-block locations according to

the "Grouping/Clustering" algorithm definedby Quirk [6]. A constraint on minimumflagged cells in a sub-block is defined bymeans of a creation ratio.

flagtotal

lsflaggedcel CN

N≥��

�

��

�

• create sub-blocks in the data base takingcare to project the new surface points ontothe CAD shape (stored in data base).

In practice, the user can manage therefinement strategy:• increasing the flag threshold value sthreshold to

be more selective about regions to refine.• increasing the creation ratio Cflag to obtain a

larger set of sub-blocks fitting the flaggedstructures well

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2.3 Wall laws

In a turbulent boundary layer, the meshmust be extremely refined at the wall in order tocorrectly simulate the strong velocity gradientsin the wall region, as well as the skin frictioncoefficient and other turbulent variables. Moreprecisely, the height y+

1 of the first cell on thewall (in wall units) is usually fixed around 0.3-1.0 depending on the turbulence model. Such aconstraint leads to large mesh sizes, low timesteps and large aspect ratio of the cells near thewall, which are damaging for accuracy andconvergence of the numerical scheme. A veryefficient way of improving consists in applyingthe wall law on the first cell the size of whichcan be much larger than y+

1 =1.At the walls, a no-slip condition is still

used. As the sizes of the adjacent cells are large,in the order of 50 to 100 in wall units, the shearstress τ and the heat flux q representing thediffusive flux densities must be obtained using aparticular treatment. The velocity profile in the

wall region )( ++= yfu is assumed constant,

with f a combination of linear and logarithmic

functions. +

u is the Van Driest transformedvelocity taking the compressibility effects intoaccount. Instead of using an explicit temperatureprofile in the wall region, a temperature-velocityrelationship is preferred. It is deduced from theintegration of the total enthalpy equation byneglecting the advection terms.The wall treatment is straightforward. Knowingthe velocity from the Navier-Stokes solution,

+u is obtained from the Van Driesttransformation and the velocity-temperaturerelationship. The velocity wall law gives theshear stress, which is assumed constant in thedirection normal to the wall. To extend the walltreatment to separated and 3D flows, the walllaw is expressed in a reference frame defined bythe velocity direction in the cells adjacent to thewalls. Such a treatment is not in contradictionwith the fact that the log law does not exist inseparated regions. Actually, in these regions τw

remains small and therefore y+ also, leading tothe use of the linear part of the velocity profile.This is equivalent to computing the velocity

gradient over two points instead of three for theordinary cells.As far as the transport equations of theturbulence models are concerned, k is imposedat the center of the cells adjacent to the wallsusing the Bradshaw hypothesis. The secondturbulent variable is deduced from analyticalrelation and is also imposed in the cells adjacentto the walls. For the k-ω model, thecharacteristic length scale of the Chen model[10] is used for the specific dissipation ω. Forthe k-l model, l is proportional to the walldistance. For the Spalart-Allmaras model, ν~ isimposed by using the closure relations of themodel, the velocity profile and a mixing-lengthformulation for the eddy viscosity [11].

3 Aircraft applications

3.1 Ground effect prediction using Chimeragr ids

3.1.1 IntroductionWhen an aircraft comes near the ground,

its aerodynamic characteristics are modified.Ground effect especially influences longitudinalcoefficients: lift, drag and pitching coefficients.Consequently, aerodynamic coefficientvariations must be correctly assessed beforeintegrating them in the control laws modeling,especially for automatic landings.

Ground effects are usually broken downinto 2 contributions: aircraft without tails andtails contributions. The current study is limitedto drag and lift variations on an aircraft withouttails.

When the aircraft comes down to aminimum "landing" height hlanding, experimentalmeasurements as well as numericalcomputations show:• a decrease of induced drag• an increase of lift in most cases. However,

the trend can be reversed at low heights, athigh angle-of-attack and in high liftconfiguration

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The induced drag reduction can beexplained by the influence of the "symmetric"wing tip vortex, which turns in a directioncontrary that the basic plane vortex, dampingthe original vortex. The magnitude of thereduction mainly depends on the full aircraftspan B and the absolute wing height.

Among many drag reduction factormodelizations for simplified unswept wings,Laitone suggested a correction of MacCormickformulation, which gives better values for lowheight [12]:

( )( )2

2

)/16(1

)/16()/2(1

Bh

Bh

C

C

Di

Di

πππ

++−

==Φ∞

(1)

The ground effect on lift results from twoopposite effects:• for low angle of attack and high height, the

presence of "symmetric" wing vortexinduces an upstream perturbation speed andvertical perturbation speed at trailing edge.Considering the small disturbancesapproach, it can be shown that lift increases.

• for high angle of attack and low height, theground reduces the effective angle of attack(channeling air flow). Flow is accelerated inthe convergent duct generated by wing andground, and so the wing is suckeddownward : the lift decreases

The second effect explains a suddendecrease of lift for low height and high angle-of-attack, sometimes leading to negative liftvariations. Moreover, it was shown that thisphenomenon is all the more visible as the highlift devices are deployed [15]. Similar behaviorwas also shown on a cambered single elementwing, as regards the variation of the downforce(in the racing car context) as a function ofheight and angle-of-attack [12].

3.1.2 Panel methodToday, the most commonly used numerical

method at Airbus for ground effect prediction isbased on a source/vortex panel method,completed with a vortex sheet balancing

algorithm. An "envelope" shape (no slot effects)approximates wing geometry and no viscouseffects are taken into account [14].

This method is very efficient (with respectto CPU time) and useful because:• surface meshes are generated rapidly• there is no need to generate multiple meshes

for different aircraft heights. Horizontalsymmetry plane condition is only introducedin the influence matrix coefficients.

• the calculation itself is very quick (half anhour on a CRAY J916)

• during the post-processing stage, induceddrag can be directly computed from vortexvalues given by the solver.

Calculations were performed on thesimplified Airbus fuselage/ envelope wingconfiguration at Mo=0.3. A parametric studywas conducted varying both the angle-of-attack(4°, 7° and 10°) and undimensionned height(H/B=0%, 5%, 10%…. 100%), where

landinghhH −= is the relative height with

respect to landing height (full ground effect).Figure 1 shows a general view of theconfiguration with the initial and final balancedwakes. The mesh contains 6000 panels (4000 onskin, 2000 on skeletons and wakes)

Figure 1 - Panel method on Airbus configurationM =0,30 - αααα=10 °H/B= 0%

3.1.3 Chimera method using elsAEven though panel method is very

efficient, it has many drawbacks for futureapplications. Wing geometry has to be

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simplified because real multi element airfoilscannot be correctly simulated by inviscidmethods, even by coupled methods. Moreover,in the presence of tails, there are strong viscousinteractions with rear fuselage and wing wake.

Therefore, it was natural to simulate thisconfiguration with Euler and RANS solvers.Unfortunately, within a classical multi-blockapproach, the mesh had to be generated forevery height and every angle-of-attack. In orderto avoid this repetitive mesh generation, aChimera simulation can be carried out in whichthe classical aircraft mesh moves into a"ground" mesh (cartesian grid) at differentheights and angles-of-attack.

ElsA calculations are performed with theEuler model on the same fuselage/wingconfiguration studied with the panel method.The goal of this study is to show that theChimera model is able to simulate the sameground effect as the panel method, and preparethe way for Navier-Stokes calculations on multielement wing configurations.

Figure 2 shows a general view of theEuler mesh used for the Chimera simulation.The original aircraft mesh is made up of 24structured blocks (960 000 nodes). It isimmersed in a single ground block (30 000nodes) as illustrated in the y- symmetry plane

Figure 2 - Chimera method on Airbus configurationM =0,30 - αααα=10 °H/B= 0%

3.1.4 Numerical resultsA qualitative comparison of Figure 1

and Figure 2 shows a similarity betweenpressure fields on wing and fuselage.

Due to low values of the lift variationswe are looking for, the convergence of Chimeracalculations must be carried far enough, untilcomplete stabilization of the lift coefficient. Foreach couple of height and angle-of-attack, 4000implicit cycles were necessary, because theassociation with multigrid acceleration is not yetavailable.

Lift and drag coefficients werecomputed in the same way for the twocalculation methods, by integrating pressurecoefficients on the aircraft skin. All the resultsare summarized in Figure 3. Lift and dragvariations are non-dimensioned with respect tovalues obtained without ground effect. ChimeraEuler results are plotted using filled symbolswhile the curves refer to panel the methodparametric study.

Ground effect on lift has three differentbehaviors depending on angle-of-attack:• at α=4°, lift always increases when height

decreases.• at α=7°, lift begins to increase when height

decreases, then it decreases near the groundwhile remaining positive

• at α=10°, lift begins to increase slightlywhen height decreases, then it stronglydecreases near the ground even becomingnegativeChimera calculations were only performed

at 2 heights for each angle-of-attack (full groundeffect and 10% of total span height). The EulerChimera results are in accordance with the 3different behaviors as regards the lift, even ifabsolute values slightly differ from panelmethod results.

Ground effect on drag has the samebehavior for the three angles of attack. Chimeraresults are very close to the panel results. Due tolow speed conditions and assuming that theground has no effect on viscous drag, the

253.7


decrease only affects the induced drag. Thepanel method post processing confirms thisassumption insofar as same drag ground effectwas found using near field approach (pressureintegration) and far field approach (Trefftz planemethod based on wake vortex values)

Figure 3 - Ground effect on lift and drag

As an indication, the ground effectmodelization from (1) has been also plotted,even if the wing has a sweep and dihedralangles. The minimum height h/B correspondingto landing was chosen considering the wing tipheight, where the strongest wake vortexappears.

3.2 Improving drag breakdown accuracyusing Multigr id Adaptive Mesh Refinement

3.2.1 IntroductionThe correct prediction of the wing shock

wave pattern is of the utmost importance fordrag prediction. With current methods,coincident meshes have to be considerablyrefined before obtaining mesh convergence withrespect to wave drag.

In order to improve accuracy whilekeeping reasonable mesh size, there are twoapproaches to adapt structured meshes andrefine them around flow patterns. The firstmethod simply moves nodes keeping the sameblocks topology, while the second methodintroduce new blocks for local mesh refinement.

The second approach was tested in thecurrent study. Starting from a coarse mesh,different levels of sub-blocks (locally refinedblocks) were automatically computed andintroduced using the MBREF tool.

3.2.2 Configuration descriptionTo illustrate this potential gain, a

simulation was carried out with the Euler modelon a swept wing configuration at Mo=0,80 andα=2,2°. At this flow condition, a swept shockwave appears along the wing, and a smoothsupersonic compression appears in the innerwing creating a "lambda" pattern (see Figure 4).A reference fine mesh containing 1,6.106 nodeswas unrefined along each direction, to generateboth a medium mesh (1 node out of 2: 210.000nodes) and a coarse mesh (1 node out of 4:28.000 nodes). The fine mesh is illustrated inFigure 4 : two blocks are arranged around thewing using a C-O topology.

Figure 4 - AS28 wing - Euler M esh - M =0,80 αααα=2,2°

The goal of this study is to obtain anequivalent accuracy to fine mesh, on a localrefined mesh obtained by introducing 2 levels ofrefined blocks on the coarse mesh.

As mentioned in paragraph 2.2.2, MBREFmainly depends on 3 main user parameters: the

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sensor, the creation ratio and the flag thresholdIn the present study the first two parameterswere fixed: density sensor and Cflag. Then, westudied the influence of flag threshold on theautomatic introduction of two sub-blocks.

3.2.3 Numerical resultsStarting from the coarse mesh, two

different mesh refinements were studied,varying the flag threshold involved in automaticintroduction of two levels of sub-blocks:• Refinement A : flag thresholds used for the

two levels are identical: slim1=5% slim2=5%• Refinement B : level1 flag threshold is

lower than level2: slim1=2% slim2=8%Refinement A creates 2 sub-blocks at

level1 and 5 sub-blocks at level2. The refinedmeshes are shown on Figure 5.

Figure 5 - Two level refined topology A

Pressure distributions are plotted on Figure6 along sections illustrated in Figure 4, andcompared to results obtained on fine mesh.Pressure peaks at leading edge and shock wavesharpness are equivalent to fine mesh, but theshock wave is located slightly upstream. Thisdifference is probably induced by an insufficientextension of the first refinement level.

In order to verify this assumption, a secondrefinement B was tested, trying to be lessselective at level1 and more selective at level2,to obtain roughly the same mesh size. It creates2 sub-blocks at level1 and 6 sub-blocks atlevel2. The refined meshes are shown in theFigure 7.

Figure 6 - Wing pressure distr ibution

Figure 7 - Two level refined topology B

With this new refinement, the shockwave is now located very close to the fineresults (see Figure 6). However, pressurecomparison matching is often an insufficientargument for accuracy comparison, especially ifdesigner study focuses on drag breakdown.

Thus, drag breakdown post processingwas carried out on all fine, medium, coarse andlocally refined calculations, using the FFD40

253.9


tool which was developed by ONERA in co-operation with Airbus France [16]-[17]. Aspecific development was necessary, so as notto take the masked cells on coarse and mediummeshes into account during drag integration. Asillustrated in Figure 8, the first refinement isinsufficient to predict shock wave drag (~ 4 dragcount error) while the second refinementprovides an error less than 1 drag count.

This application shows that anequivalent accuracy can be obtained using alocally refined mesh, compared to a fine meshroughly three times as big. Thus, the CPU timeand memory efficiencies can be reduced by athird, insofar as AMR treatment cost isnegligible compared to computation cost.

Figure 8 - Wave drag for initial meshes and localrefined meshes

3.3 Efficient engine/air frame integrationusing wall laws for Navier-Stokes simulations

3.3.1 IntroductionTurbulent Navier-Stokes simulations

around complex geometries, such as powerplant /airframe configurations are now widelyused at Airbus for the design and optimizationof pylon and nacelle shapes. Unfortunately, thecurrent meshing approach leads to big meshesand expensive calculations due to the severeboundary layer refinement near the wall, whichis necessary for the most usual low Reynoldsturbulence models. For this reason, somegeometries such as flap track fairing and wing

tip fences are often not taken into account inNavier-Stokes calculations.

In addition to the increase of the mesh size,the extreme refinement in the vicinity of thewall around wing, pylon and nacelle bodies hasother drawbacks:• it spreads out over the whole domain

calculation, unnecessarily covering someregions with low flow gradients

• the convergence rate can be slowed downdue to small time steps

• it induces other refinements on neighboringdomains in order to ensure cell sizecontinuity (rear surfaces on thick trailingedges)

• some precision problems may be foundduring mesh generation, and when meshesare modified during shape optimizationcycles or structure coupling cycles. The successful validation of wall laws on

3D configurations, even in the presence ofseparated flow, has been shown recently [11]with four popular turbulence models (k-ω, k-ε,k-l and Spalart Allmaras). The use of a wall lawturbulence model allows a considerabledecrease of the mesh size (about 1/3), thanks toa larger wall cell size y+

1=50, instead ofclassical value y+

1=1. Moreover, the increase inthe wall cell size often leads to a betterconvergence rate.

The aim of this application consists incomputing a complex power plant/airframeconfiguration using both low Reynoldsturbulence model and wall law model, in orderto show that Navier-Stokes calculations can becarried out at lower cost, with the sameaccuracy.

3.3.2 Configuration descriptionThe configuration is composed of a swept

wing section between two vertical walls,equipped with a pylon and a powered nacelle.

The original mesh is made up of 27coincident structured blocks. The mesh used forthe wall law calculation is then derived bymerging the first 9 cells near the wall, accordingto recommendations specified by ONERA. Inthis way, mesh size decreases from 2,25.106

nodes to 1,64.106 nodes.

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Figure 9 - S3Ch powerplant configuration

The calculations were made usingexperimental corrected values Mo=0,82 -α=1,56° - Re1=12,4.106 (per unit length) andignoring upper and lower wind tunnel walls.Engine TPS (Turbine Powered Simulator)operating conditions are simulated by thefollowing numerical boundary conditions:• subsonic injection at fan and core exit :

Ptfan/Pto=1,49,Ttfan/Tto=1,16,Ptcore/Pto=1,78, Ttcore/Tto=0,64

• constant pressure at fan face: pfan/po=1,43

3.3.3 Wall law boundary condition effectThe Wilcox k-ω turbulence model has been

used in the wall law calculation associated withthe Jameson scheme for the RANS system(κ2/κ4=0,5/0,016) and a second order Roescheme for the turbulence equations. Timeintegration uses a backward Euler schemecoupled with LU implicit and multigridacceleration techniques on 2 grid levels.

The Residual convergence history inFigure 10 shows that both calculations usingwall law mesh and refined boundary layer meshconverge in 1000-1500 cycles, with four ordersof magnitude reduction on the density residualand complete stabilization of aerodynamiccoefficients. The residuals were divided by theinitial values and the final values weresubtracted from the aerodynamic coefficients.The aerodynamic coefficients in the wall lawcalculation are stabilize faster even if theresiduals have higher values. Running on fourprocessors in parallel mode, the calculation

takes approximately 6 hours on Fujitsu VPP700for the fine mesh.

Figure 10 - Compared residuals convergence

Once the calculation is done, it is importantto check that the first cell size verifies20<y+1<200 as recommended by ONERA [11].Figure 11 illustrates this surface field on thewing and we can check that the constraint issatisfied correctly.

Figure 11 - Wing sections on S3Ch model - wall y+1

size

Computed pressure coefficients wereplotted in Figure 12 on the four wing sectionsillustrated in Figure 11 in order to visualize

Section C

Section F

Section G

Section I

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wing-pylon interactions. The wall law resultsare very close to those obtained on the refinedboundary layer mesh. All physical phenomenasuch as shock waves and flow accelerations arecaptured with the same accuracy, specially thestrong supersonic acceleration created by pyloninteraction on the wing lower surface at inboardpylon side (section F).

Figure 12 - Wing Cp distr ibution

Wall law boundary condition treatment hasa very slight impact on memory and CPU timeconsumption. Consequently, an immediate gaincan be obtained by the mesh size reduction, thatis to say around 25% for the current test case.

3.3.4 Turbulence model effectExperimental data is available from tests

performed in the ONERA S3-Chalais windtunnel in 1996. Pressure coefficients areavailable on the four wing sections defined inFigure 11.

Numerical results previously obtained withthe k-ω turbulence model (with wall laws) areroughly close to the experimental results butthere are two main defects (see Figure 13):• the shock is located downstream from the

experimental position, but it is a well knownbehavior of the k-ω turbulence model.

• the pressure coefficient peaks on the leadingedge upper surface are underestimated.For these reasons, a new mesh was

generated with finer mesh at the leading edge,and new calculations were performed with k-land Spalart Allmaras turbulence models. Asillustrated on Figure 13:• all turbulence models correctly predict the

double compression on the upper surface aswell as the strong supersonic acceleration onthe pylon inboard side

• shock wave location on the upper surface isvery similar between k-l and S.A.calculations and it is now much closer thanexperimental values.

• leading edge refinement causes a localizedflow acceleration on the upper surface, inaccordance with experimental trends insections C and F. However, a discrepancyremains on the level of flow acceleration onthe upper surface before the shockcompression. This may be explained bywind-tunnel test corrections, which provideequivalent free stream conditions on Machnumber and angle-of-attack. A completecalculation should be carried out on the realconfiguration with upper and lower walls.

Figure 13 - Turbulence model effect - Exper imentaldata

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Conclusion

Through these three industrialapplications, we have demonstrated that theelsA code is able to deal efficiently withcomplex configurations while using advancedfunctionalities on structured meshes such asChimera, wall laws and adaptive refinementtechniques. Considering the current knowledge,an efficient association of these functionalitiescan be foreseen in the short term.

The Chimera technique will allow thestructured mesh generation time, which is todaya real bottleneck in the global CFD process, tobe reduced considerably. Wall laws andadaptive refined meshes will allow accurateresults to be obtained using much smallermeshes. All in all, it will become easier andfaster to study the influence of geometry deviceson a reference aircraft (wing tip devices, flaptrack fairing, strakes…)

In this way we hope to considerablyimprove the global CFD process efficiency inorder to emphasize the use of CFD in theassessment of aerodynamic data.

Acknowledgements

The authors wish to acknowledge the AirbusMethod and Tools teams for their technicalsupport on tools, from the mesh generation topost processing stages. The authors would liketo thank A. Roure for his participation to thecoding of the AMR method.

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