zonal rans les coupling simulation of a transitional and separated flow around an airfoil near stall

8/7/2019 Zonal RANS LES Coupling Simulation of a Transitional and Separated Flow Around an Airfoil Near Stall

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Theor. Comput. Fluid Dyn. (2008) 22: 305315DOI 10.1007/s00162-007-0068-8

O R I G I N A L A R T I C LE

F. Richez I. Mary V. Gleize C. Basdevant

Zonal RANS/LES coupling simulation of a transitionaland separated flow around an airfoil near stall

Received: 3 May 2006 / Accepted: 7 August 2007 / Published online: 1 November 2007 Springer-Verlag 2007

Abstract The objective of the current study is to examine the course of events leading to stall just beforeits occurrence. The stall mechanisms are very sensitive to the transition that the boundary layer undergoesnear the leading edge of the profile by a so-called laminar separation bubble (LSB). In order to provide help-ful insights into this complex flow, a zonal Reynolds-averaged NavierStokes (RANS)/large-eddy simulation(LES) simulation of the flow around an airfoil near stall has been achieved and its results are presented andanalyzed in this paper. LSB has already been numerically studied by direct numerical simulation (DNS) orLES, but for a flat plate with an adverse pressure gradient only. We intend, in this paper, to achieve a detailedanalysis of the transition process by a LSB in more realistic conditions. The comparison with a linear instabilityanalysis has shown that the numerical instability mechanism in the LSB provides the expected frequency ofthe perturbations. Furthermore, the right order of magnitude for the turbulence intensities at the reattachmentpoint is found.

Keywords Stall Transition Laminar separation bubblePACS 47.27.Cn

1 Introduction

Thanks to the Reynolds-averaged NavierStokes (RANS) approach, the calculation of flows around a wholeaircraft is nowadays possible. However many studies seem to prove that this approach is not mature for theprediction of complex flow phenomena. For example, the numerical simulation of the flow around an airfoilat static and dynamic stall is still a very challenging task for computation fluid dynamics (CFD). The dynamicstall flow phenomenon concerns the delay in the stalling characteristics of airfoils that are rapidly pitchedbeyond the static angle. Dynamic stall has serious implications in terms of achievable performance, whichneed to be predicted accurately as soon as possible in the airfoil design cycle. The account of this phenome-

non is important for the design of many industrial domains as helicopter rotor blades (retreating blade) or jetengines (rotating stall). This phenomenon is characterized by a massive unsteady flow separation and by theformation of large-scale vortical structures leading to hysteresis effects. As a result, the maximum values oflift and pitching moment highly exceed their static values. Hence, because of the manufacturing interest, the

Communicated by R.D. Moser

F. Richez (B) I. Mary V. GleizeDepartment of Computational Fluid Dynamics and Aeroacoustics, ONERA,29 Avenue de la Division Leclerc, BP 72, 92322 Chtillon, FranceE-mail: [email protected]

C. BasdevantLaboratoire dAnalyse, Gomtrie et Applications, CNRS, Universit Paris-Nord, 93430 Villetaneuse, France


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306 F. Richez et al.

Fig. 1 Zonal RANS/LES coupling mesh

unsteady RANS (URANS) equations have been widely used to compute dynamic stall flow, but the results arefar from being totally reliable for predicting the dynamic stall behavior of airfoils [17]; moreover, they have alarge computational cost. In this context, some researchers have chosen to start from scratch by consideringstatic stall. They have proven that the solution shows grid and turbulent model dependency [4]. And even inthe simpler case of static stall, RANS simulation does not correctly predict the stall angle of attack and themaximum lift. Other studies [14,18] have shown that this phenomenon is very sensitive to the transition of theboundary layer at the leading edge. This may be one of the reasons why the RANS approach, which has notbeen developed to treat transition, fails to predict stall occurrence. As large-eddy simulation (LES) providesan effective tool for tackling such flow condition, we have decided, in this study, to use a zonal RANS/LEScoupling method [11] in order to gain a more physical description of the transitional and separated flows.A first coupling simulation of the flow around an airfoil near stall with an LES domain including the wholesuction-side boundary layer and the wake zone, has been performed, so that it could be almost considered a

full LES. Moreover, we have paid particular attention to the mesh resolution in the transitional zone in orderto obtain an accurate description of the flow in this area. The numerical method, the flow, and the computa-tion parameters are presented in the two first sections. Then, the results of this calculation are presented andanalyzed in the third section. In particular, a detailed account of the transition, numerically obtained at theleading edge by an LSB, is given. To prove that the transition scenario observed numerically has a physicalmeaning, a linear stability analysis of the mean flow in the transitional zone is presented in the last section. Thisstudy confirms that the flow is highly unstable in this area and that the numerical oscillations observed in theLES and which lead to transition result, as expected, from a two-dimensional (2D) inviscid KelvinHelmholtzinstability mechanism.

2 Numerical method

The compressible NavierStokes equations are solvedin a multiblock structured solverbased on a finite volumemethod.OverlappingRANS andLES domains are used (see Fig. 1).In the RANS domain, the SpalartAllmarasmodel is used in order to take into account the pressure-side turbulent boundary layer. The selective mixed-scalemodel is used to model the subgrid-scale terms [6]. At each time step, the values of the conservative variablesin the RANS domain of the overlapping zone are computed by averaging the LES variables in the cell volumeof the RANS domain. Moreover these conservative variables are used to transport the turbulent viscosity ofthe SpalartAllmaras model. The information transfer between the RANS and the LES domains requires someboundary conditions. These are obtained by the use of ghost cells and an enrichment procedure [11].

The viscous fluxes are discretized by a second-order-accurate centered scheme. For efficiency reasons, animplicit time integration is employed to deal with the very small grid size encountered near the wall. Thena three-level backward differentiation formula is used to approximate the temporal derivative, leading to asecond-order accuracy. An approximate Newton method is used to solve the nonlinear problem. At each iter-ation of the inner process, the resolution of the linear system relies on the lowerupper symmetric GaussSeidel


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Zonal RANS/LES coupling simulation 307

(LU-SGS) implicit method. Usually LES requires a high-order centered scheme for the Euler fluxesdiscretization in order to minimize dispersive and dissipative numerical errors. However such a scheme cannotbe applied easily in complex geometry. Therefore, a variant of the AUSM+(P) scheme, whose dissipationis proportional to the local fluid velocity, is employed [9]. The original AUSM+(P) scheme proposed by

Edwards and Liou has been modified to be well adapted to low-Mach-number boundary layer simulations.These numerical methods, developed at the Office National dEtudes et Recherches Arospatiales (ONERA,The French Aerospace Lab) in the FLU3M code, have been validated in several applied computations [5].

3 Flow and computation parameters

The computation presented in this paper has been achieved for an OA209 profile, which is an helicopter fanblade profile, with a chord of 0.5 m. The Reynolds number is 1.8 million and the inflow Mach number is0.16. The angle of attack is 15 which is, according to experimental study achieved by the ONERA [12],

just prior to stall occurrence. The 2D RANS domain is a C-grid composed of 1 , 153 101 points while thethree-dimensional (3D) LES domain is composed of 9.5 million points in the suction-side boundary layer andby 1.6 million points in the wake zone. Compared to the RANS domain, the LES grid is more highly refinedin the streamwise direction and keeps the same resolution in the wall-normal direction (see Fig. 1). In order to

reduce the computational cost, the LES domain is decomposed into several subdomains, which differ in theirspanwise extent and spanwise resolution. The spanwise extent has been chosen in order to be greater than theboundary layer thickness along the profile [11]. At the interface between these domains, the shorter domainin the spanwise direction imposes flow periodicity, since its information is duplicated in the ghost cell of thelarger domain. As the scale of the turbulent vortices varies significantly in the streamwise and the wall-normaldirections, local mesh refinement in the spanwise direction is used and an enrichment procedure is performedbetween the LES blocks. Hence, the LES domains are designed in order to satisfy all along the suction sideof the boundary layer these resolution conditions expressed in wall unit in the streamwise, wall normal, andspanwise directions, respectively: x+ 50, y+ 2, and z+ 15. According to earlier studies, thisgrid resolution and the spanwise size should be sufficient to resolve the vortices of the turbulent boundarylayer. The code is parallelized using a domain decomposition technique based on the openMP directive. Thetime step used in this simulation is t= 1.3 107s. With four inner iterations in the Newton process, largertime steps have been found to give rise to numerically unstable behavior. The computation has been running at

13 Gflops for 5000 total central processing unit (CPU) hours on a four-processor NEC SX5 to ensure that theunsteady solution fluctuates around a stationary averaged state. The statistical variables presented thereafterhave been computed during the last six periods of the vortex shedding that occurs at the trailing edge.

4 Numerical results

4.1 Aerodynamic characteristics

Figure 2 shows the lift and drag coefficients calculated by the LES and compared to experimental data [12]and two RANS simulations using k Wilcox and SpalartAllmaras models. These RANS simulations havebeen computed with the same RANS grid as shown in Fig. 1 and the same modified AUSM+(P) scheme hasbeen employed. The lift and drag coefficients have also been computed for stall angles of attack, with the

two RANS models, in order to show the inability of the fully turbulent RANS approach to predict the stallphenomenon accurately. Looking at the values obtained at the 15 angle of attack (Table 1), one can see thatthe RANS simulations overestimate the experimental lift and underestimate the drag, while the LES has thequite opposite effect. The history of the LES lift and drag coefficients is shown in Fig. 3. Some oscillationsappear on these curves, due to vortex shedding at the trailing edge. The frequency f of this phenomenon can beeasily calculated and corresponds to a Strouhal number (based on the freestream velocity U0 and the boundarylayer thickness at the trailing edge ) ofSt = f/U0 = 0.21 as expected. During the last five periods of thevortex shedding, the lift seems to oscillate around a constant value, which means the solution has statisticallyconverged. The variation of the lift coefficient is about 6% of its averaged value. The variation of the dragcoefficient is however more important and represents 60% of its averaged value.

LES and RANS pressure distributions are almost identical and in good general agreement with the experi-mental data (see Fig. 4). Some differences appear at the leading edge. The LES simulation provides a flattenedshape of the pressure distribution, which is characteristic of a separated flow. Let us notice that no such shape is


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Angle of attack (degrees)

Liftcoe

ffic

ien

t

0 5 10 15-0.5

0

0.5

1

1.5

ExperimentRANS k-WilcoxRANS SALES

Angle of attack (degrees)

Dragcoeff

icien

t

0 5 10 150

0.01

0.02

0.03

0.04

0.05

ExperimentExperimentRANS k-WilcoxRANS SA

LES

Fig. 2 Experimental and numerical lift and drag coefficients as a function of the angle of attack

Table 1 Experimental and numerical lift and drag coefficients

Experiment LES RANS SA RANS k-

Lift 1.416 1.366 1.487 1.490Drag 0.029 0.039 0.023 0.021

observed for the fully turbulent RANS simulations because the premature increase of the turbulent viscosity atthe leading edge prevents the flow from separating. Looking at the experimental measurements, no conclusionabout the presence, location, and size of the LSB can be drawn. Indeed, the distance between two consecutivemeasurement points has the same order of magnitude as the LSB length. Furthermore, the size of the LSB isvery sensitive to the freestream turbulence intensity and to the surface roughness [7,13]. It seems likely that

t (s)

Dragcoe

fficient

0 0.02 0.04 0.06

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08LES

RANS k-

RANS SAExperiment

t (s)

Liftcoe

fficient

0 0.02 0.04 0.06

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

LES

RANS k-

RANS SAExperiment

Fig. 3 Lift and drag coefficients history compared to RANS and experimental values

x/c

Cp

0.25 0.75

-10

-8

-6

-4

-2

0

x/c

Cp

-0.01 0.01 0.03 0.05

-10

-8

-6

-4

Experiment

LES

RANS k-

RANS SA

Fig. 4 Pressure distribution


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x/c

Cf

0 0.2 0.4 0.6 0.8 1

0

0.02

0.04

0.06

LES M2RANS k-RANS SA

x/c

Cf

0.6 0.8 1-0.001

0

0.001

0.002

x/c

Cf

- 0. 01 0 0. 01 0 .0 2 0 . 03 0 .0 4 0 . 05

-0.02

0

0.02

0.04

0.06

Fig. 5 Skin friction distribution across the whole upper surface of the airfoil

the LSB size will differ between experiment and LES, as long as these effects are not considered. However,the sudden decrease of the experimental lift curve (see Fig. 2) leads one to suppose that the LSB is present inthe real flow. Indeed, it is now known that a steep drop of lift at stall is very likely due to the breakdown of theLSB from the leading edge [3,10,13]. Even if the freestream turbulence intensity and the surface roughnessreduces the LSB length, the instability mechanisms responsible for the transition must be the same in theexperiment and in the LES. Therefore, although the LSB size might be overestimated by the LES, the effectsof this transition type on the downstream turbulent boundary layer should be comparable to the experiment.Indeed, the presence of the LSB near the leading edge increases the thickness of the downstream turbulentboundary layer, which might lead to a larger turbulent separation at the trailing edge. This may explain thelarge discrepancy in the skin friction between RANS (which does not capture the LSB) and LES all along thesurface (see Fig. 5). The skin friction at the trailing edge shows that both RANS and LES provide a small

separated turbulent flow, which lies on more than 20% of chord for LES and between 12 and 14% for theRANS simulations. The larger turbulent separated zone of the LES may be a reason for the lower value ofthe lift. At the leading edge, the LSB, obtained with LES, is followed by the transition of the boundary layer,as indicated by the steep slope of the skin friction. Many studies tend to prove that this transition mechanismis a crucial parameter in stall occurrence [14,18]. Nevertheless, the transition mechanisms in a LSB are verycomplex and are not easy to capture in a numerical simulation, all the more so in an applied configuration suchas a pitched airfoil. Then, in order to see the capabilities of LES to give an accurate description of the LSB,a more detailed analysis of the flow in this area has been carried out. In this following analysis, we make anattempt to provide helpful insights into the numerical and physical origins of what is observed in this LES.

4.2 Analysis of the transition

The analysis of the mean flow reveals that the laminar boundary layer separates at 0.4% of the chord from theleading edge. Moreover, the averaged length and height of the LSB are, for this simulation, 1.3 and 0.03% ofthe chord, respectively (see Fig. 6). Even if this structure is very small, detailed attention has been paid to themesh resolution in this area: within the LSB region, there are about 180 points in the streamwise direction and40 points in the wall-normal direction. Figure 7 represents, for three different times, the streamwise evolutionof the three components of the instantaneous velocity at a constant distance from the wall. The streamwisedirection is made nondimensional with respect to the length of the LSB. The analysis of these instantaneousdata shows that the boundary layer is laminar and two dimensional at the separation point. The flow becomesunsteady and three dimensional between 25 and 75% of the bubble length. At the reattachment point the flowis highly unsteady and three dimensional. Furthermore, the study of the temporal evolution of the skin frictionshows that the instantaneous separation point does not move with time, but the instantaneous reattachmentpoint fluctuates greatly as the flow transitions and becomes highly unsteady. Its seems that the flapping of thereattachment point leads to vortex shedding that spreads rearward and is quickly dissipated in the turbulent


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x/c

y/c

0.005 0.01 0.015

0.01

0.015

0.02

Lb/c=1.3%

Hb/c=0.03%

Fig. 6 Mean flow streamlines in the LSB

x/Lb

u/U

0

0 0.5 1

-0.5

0

0.5

1

1.5

2at t

1

t2

t3

(a)

x/Lb

v/U

0

0 0.5 1

-0.5

0

0.5

1

1.5

2

2.5 at t1

t2

t3

(b)

x/Lb

w/

U0

0 0.5 1

-0.5

0

0.5

1 at t1

t2

t3

(c)

Fig. 7 Instantaneous streamwise (a), wall normal (b), and spanwise (c) velocity components at 3% of the bubble length fromboundary, as a function of the streamwise coordinate, at three different times

boundary layer. Looking at the instantaneous Q criteria isosurface (see Fig. 8), one can see two-dimensionalvortex structures that appear in the second half of the bubble. It seems that a specific wavenumber is selectedbefore the flow becomes three dimensional at the reattachment point. A more detailed study presented hereafterwill confirm this assumption.


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Fig. 8 Instantaneous Q criteria isosurface near the transitional bubble colored by the streamwise velocity component

urms

/U0

d/c

0 .0 2 5 0 . 0 5 0 .0 7 5 0 .1

0

0.0008

0.0016

(a)

urms/U0

d/c

0.25 0.5

0

0.0015

0.003

(b)

urms/U0

d/c

0 . 15 0 . 3 0 .4 5 0 .6

0

0.0015

0.003

(c)

urms/U

0

d/c

0 .0 5 0 .1 0 .1 5 0 .2

0

0.005

0.01

0.015(d)

urms/U0

d/c

0.0250.05 0.075 0.1 0.125

0

0.02

0.04

0.06

(e)

Fig. 9 Root-mean-square streamwise velocity profiles urms at the separation point (a), in the middle of the LSB (b), at thereattachment point (c), at 10% of the chord (d), and at 50% of the chord (e)

Figures 9 and 10 represent the root-mean-square (rms) streamwise and wall-normal velocity fluctuationprofiles in the local frame, in the LSB, and much further into the turbulent boundary layer. This confirms thatthe flow is still laminar at the separation point. The maximum fluctuations occur at the reattachment point whereurms attains 70% of the freestream velocity as can be seen from Fig. 9c. According to previous works [19] forthe LSB obtained on a flat plate with a semicircular leading edge, these maximum values seem to be stronglyoverestimated. This is due to the fact that the velocity fluctuations are made nondimensional with respect to thefreestream velocityU0 while the flow is accelerated up to 3 U0 in this area (see Fig. 11). Hence, consideringthe edge velocity as a reference, one can find a maximum streamwise rms fluctuation of 23%, which is veryclose to the value found by Yang et al. [19]. Alam and Sandham [1] found a maximum streamwise fluctuation

intensity of 16%. However, in their DNS, the transition results from the growth and stretching of -vortices,which is a different mechanism from the 2D mode observed in the present LES. The experimental studies ofLSB usually give a maximum of streamwise fluctuations between 15 and 20%, depending on the flow parame-ters. Hence, in this LES, the steep variation of the streamwise turbulence intensity near the reattachment pointis indicative of a quick transition, which is expected because of the highly unstable inflexional mean velocityprofile. Moreover, the turbulence intensity peak value at the reattachment point of the LSB seems to have theright order of magnitude. Then, further downstream, the turbulence intensity reduces and reaches a typicalturbulent boundary layer level between 10 and 15% (see Figs. 9e and 10e). Note that the double-peaked shapeof the urms and vrms profiles in the bubble (Figs. 9b, 10b) resembles a TollmienSchichting wave in a transi-tional separated flow [2], and is different from the single-peaked profile described by Spalart and Strelets [16],which might result from an absolute instability mechanism as suggested by Alam and Sandham [1].

To study the instability mechanism of the flow in the LSB more accurately, a Fourier transform of thepressure signals at different locations along the bubble has been calculated. Figure 11 shows the mean velocity


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vrms

/U0

d/c

0.025 0.05 0.075 0.10

0.0008

0.0016

(a)

vrms

/U0

d/c

0.25 0.5

0

0.0015

0.003

(b)

vrms

/U0

d/c

0.15 0.3 0.45 0.6

0

0.0015

0.003

(c)

vrms

/U0

d/c

0.0250.05 0.075 0.1 0.125

0

0.02

0.04

0.06

(e)

vrms

/U0

d/c

0 .0 5 0 .1 0 .1 5 0 .2

0

0.005

0.01

0.015(d)

Fig. 10 Root-mean-square wall-normal velocity profiles vrms at the separation point (a), in the middle of the LSB (b), at thereattachment point (c), at 10% of the chord (d), and at 50% of the chord (e)

U/U0

y/c

0 5 10 15

0.0004

0.0012

x/Lb=0 x/Lb=0.42x/Lb=0.24 x/Lb=077x/Lb=0.59 x/Lb=1

Fig. 11 Mean velocity profiles in the local frame at six stages in the LSB

f (Hz)

SPL(dB)

104

105

106

20

40

60

80

100

120

f = 90000 Hz

x/Lb=0

0


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5 Temporal instability analysis of the transition

To ensure that this computation gives a physical description of the transition, a local linear inviscid stabil-ity analysis [15] was carried out. This study should allow one to compare the calculated frequency of the

most highly amplified waves in the LSB simulation with the theoretical frequency of the most linearly unstablewavesthat the mean flow undergoes. To perform this analysis, the continuityand incompressible NavierStokesequations are considered as follows:

divu

= 0 (1)

tu + divu u

=

1

grad p +

1

div

(2)

with =

grad u + tgrad u

.

The flow solution variables are then expressed as a superposition of the basic flow Q = (U0, V0,W0, p0)

and the disturbance quantities qp =up, vp, wp, pp

. The basic flow is assumed to be parallel:

Q = (U0(y), 0, 0, p0(y)) .

This assumption may appear to be very strong in the case of separated flow, but the wavelength is small enoughcompared to the bubble length to consider the flow as locally parallel. Furthermore, this hypothesis greatlysimplifies the formulation and the resolution of this theoretical analysis.

Then, considering this basic flow Q solution of Eqs. (1) and (2), linearizing the NavierStokes system atQ, and omitting the viscous terms, we can obtained the disturbances equations:

xup + yvp = 0 (3)

tup +U0 xup + vp yU0 = x pp (4)

tvp +U0 xvp = y pp (5)

According to Eq. (3), a stream function of the disturbances can be introduced as follows:

up

= y

vp = x

Then, the system (35) can be reduced to the following equation:

(t+U0x) U0 x = 0 (6)

where a prime () denotes a y-derivative.Using normal modes:

(x, y) = (y)ei(kxt)

we obtain an equation known as the Rayleigh equation:

(U0 c)(

k2) U0 = 0 (7)

where c = k

is the phase velocity.The modes are discretized using the Chebyshev collocation. The matrix-eigenvalue problem is then solved

numerically for the dispersion relation D(, k) = 0.The three mean velocity profiles, represented with squares, triangles, and circles in Fig. 11, have been

considered as basic flows. Then, a temporal analysis has been performed for each mean velocity profile. Forthis type of analysis, a spatial disturbance characterized by its wavenumber is introduced into the flow, andthe temporal growth rate = Imaginary() and corresponding frequency f = Real()/2 are computed.The results obtained for different values of the real wavenumber k are plotted in Fig. 13. We can see that, asexpected, the inflectional mean velocity profile in the bubble is unstable via an inviscid KelvinHelmholtzinstability mechanism, because of the positive value of the temporal growth rate. Moreover, the most unstablefrequency for the three basic flows is around 90,000 Hz, which is in good agreement with the LES. Therefore,the scenario of the numerically observed transition seems to be realistic. Indeed, it has already been shown


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f (Hz)

(s-1)

50000 150000

10000

30000

f = 90000 Hz

Fig. 13 Temporal growth rate of a disturbance as a function of its frequency for three different mean velocities

that the transition in a LSB is dominated by two-dimensional KelvinHelmholtz waves even if three-dimen-sional disturbances can exist and play an important role [2]. Let us also notice that the initial amplitude of theperturbations is not controlled here, although Augustin et al. have shown this has a strong effect on the overallsize of the LSB.

This linear stability analysis has revealed that the wavelength of the most unstable mode has an order ofmagnitude of 1/8 Lb. This shows the LSB is long enough to consider the parallel assumption of the linearstability analysis as satisfactory. Furthermore, the grid resolution in the LSB is fine enough to have 20 gridpoints by wavelength of the unstable mode. Hence, the grid resolution seems to be sufficient to resolve thegrowth of this unstable mode accurately.

The question of the convective or absolute nature of this instability mechanism is not treated here, but

no low-frequency fluctuations coexisting with the high-frequency oscillations studied above have been founddespite the fact that they have been observed in other LSB simulations [8]. The reason may be that the reversedflow in the bubble does not exceed 10%, which should make the flow only convectively unstable.

6 Conclusion

An LES of the flow around an airfoil profile at a high angle of attack and for a realistic Reynolds number hasbeen achieved. This simulation shows that the transition of the suction-side boundary layer via an LSB nearthe leading edge can be captured by LES. Moreover, knowing that this structure plays an important role in thestall phenomenon, particular attention can be paid to the resolution of the mesh in this area. Good agreementof the calculated aerodynamic characteristics with available experimental and RANS data has been obtained.Furthermore, we have also successfully compared the numerical results of the transition with a linear inviscidinstability theory. Hence, this simulation will be considered as a reference solution for ongoing simulations.

Subsequent studies will consist of reducing the LES domain to the transitional zone, first investigatingthe influence of the LES domain size on the transitional flow and then studying the influence of the turbu-lence model in the RANS domain in order to find out whether some turbulence models are more suitablethan the SpalartAllmaras model for the coupling. Once the most well adapted turbulence model is found, theRANS/LES coupling method will be applied to a stalled configuration.

Acknowledgments The authors would like to acknowledge Michel Costes from the ONERA Applied Aerodynamics depart-ment for his advice and knowledge concerning stall phenomenon. We would also like to thank Lutz Lesshafft from the ONERACFD Department and Daniel Arnal and his team for enlightening discussions about instability mechanisms. We wish to thankGuillaume Desquesnes from the ONERA CFD department, who has been helpful in the development of the instability analysiscode.


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zonal rans les coupling simulation of a transitional and separated flow around an airfoil near stall

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