RANS-LES inlet boundary condition for aerodynamic and aero-acoustic. acoustic applications. Fabrice Mathey Davor Cokljat Fluent Inc.

Transcription

1 RANS-LES inlet boundary condition for aerodynamic and aero-acoustic acoustic applications Fabrice Mathey Davor Cokljat Fluent Inc. Presented by Fredrik Carlsson Fluent Sweden

2 ZONAL MULTI-DOMAIN RANS/LES Motivation / Challenge: accurate prediction of separated flows acoustics FSI Enrichment procedure? RANS/LES interfaces? U RANS LES

3 ZONAL MULTI-DOMAIN RANS/LES Fluent 6.2: general purpose CFD solver Enrichment procedure: LES Turbulent Inlet boundary conditions: Vortex Method (Sergent 2002) Enrichment procedure LES

4 WALE Model (Nicoud, Ducros, 1999) Wall-Adapting Local Eddy-Viscosity model Algebraic (0-equation) model retains the simplicity of Smagorinsky s model SGS ( Cs ) ν = 2 ( d d S ) ij Sij 5/2 3/2 ( ) ( d d SS ) ij ij + SS ij ij 5/4 The WALE SGS model adapts to local near-wall flow structure. Wall damping effects are accounted for without using the damping function explicitly. Correct asymptotic behavior of ν t

5 Numerics 2 nd (O) Implicit time advancement scheme Non-Iterative Time-Advancement (NITA) schemes Fractional-step method Kim et al. (2002, Int. J. Numer. Meth. Fluids., 38) PISO (Non Iterative PISO) Spatial discretization: Momentum 2 nd CD or BCD for complex geometries Energy, Species, Scalars: QUICK

6 Bounded Central Differencing Motivation Central differencing (CD) is an ideal (nondissipative) scheme for LES due to its nondissipative nature. Yet, CD often produces unphysical wiggles. Aggravated by small physical diffusivity with LES and coarse meshes Unphysical wiggles from CD

7 Bounded Central Differencing Idea of Bounding SOU FOU Normalized variable φ ~ f 1 CD ~ φ φ φu = φ φ D U? β =? 1 φ ~ C Normalized-Variable Diagram (NVD) U C f D i 1 i i + 1 i i + 2 % φ =Γ % φ + Γ % φ ( 1 ) * CD * SOU f f f

8 Bounded Central Differencing (cont d) CD BCD

9 LES Inlet Boundary Conditions Turbulent Inlet Boundary conditions : ( x, ) = ( x) + { ( x, ) ui t Ui ui t 123 mean velcocity field turbulent fluctuations Precursor domain, recycling (Lund et al. 1998) Realistic inlet turbulence Cpu cost not universal Vortex Method (Sergent at al. 2002) Spatial correlation simple implementation

10 VORTEX METHOD Based on Sergent (2003) Consider the 2D vorticity transport equation: A particle discretization ( vortex point transported by the flow) is considered : r N r r ω( x,t)= Γi( t)η( x xi, t) With Γ(k,ε) given by: and η(k,ε): ω r + ( u. ) = t With k,ε in the inlet plan, σ vortex size and S the inlet surface. i=1 π Sk(, x y) Γ i(, xy) = 4 3 N 2ln(3) 3ln(2) ( ) r 2 r 2 x x 2 2 2σ 2σ r 1 η ( x) = 2e 1 e 2 2πσ 2 ω ν ω

11 VORTEX METHOD Use Biot-Savart law for velocity field: r u x ( ) 1 = 2π r r r' r ( x x) ω ( x ). z r r r dx ' 2 x x r r r r x x N r r r r r 1 ( xi x) z u( x) = Γ i 1 e r r e 2 2π i= 1 x x i 2 2 i x xi 2 2 2σ 2σ ' Local vortex size: σ 3/2 ~ k / ε Characteristic time scale: τ ~ k / ε Typical vortex number ( )

12 Vortex Method: for unstructured grid in fluent 6.2 (Mathey et al. 2003) U

13 Validation: Vortex Method at Inlet Periodic ref. Case Mellen et al Change periodic condition with VM and outflow Inlet + Vortex Method Outflow U Re=10595 Computational Domain

14 Validation: Vortex Method at Inlet Periodic LES predictions of the reattachment point by different methods Periodic VM Random xr 5. H 5.2 h 7.7 h VM Random

15 Validation: Vortex Method at Inlet Periodic LES predictions of the reattachment point by different methods Periodic VM Random xr 5. H 5.2 h 7.7 h VM Random

16 Validation: Vortex Method at Inlet Vortex Method Simulation VM Random Noise

17 25 Ahmed Body : challenging case RANS simulation: RANS predicted Fully attached/separated flow Unsteady wake LES simulation: Hinterberger at al :Fully separated flows - use of wall functions - need to resolve boundary layers? Krajnovic et al. 2005: low RE DES: (Kapadia & Roy, 2004) Fully separated flow Scattering in experimental results Ahmed et al. (1984) / Lienhart & Becker (2003)

18 Zonal LES/RANS coupling: Ahmed Body RANS/LES: Two separate simulations Full RANS (V2F) 4 M cells(prism+tetra) Slant and Wake: LES (WALE) 1.6 M cells (hexa) + Vortex Method RANS: V2F RANS/LES interface: RANS profiles +VM Y+ ~1 to 5 LES: WALE Y+ ~1 to 5

19 Vortex Method & Two Steps Zonal Hybrid RANS/LES: Ahmed Body Ahmed Body 25 : Challenging for RANS Challenging: Separation / reattachment above the slant Unsteady wake Expensive with full LES (high Re case) Full RANS (V2F)

20 Vortex Method & Zonal Hybrid RANS/LES Zonal LES/RANS coupling : Ahmed Body 25

21 Vortex Method & Zonal Hybrid RANS/LES Zonal LES/RANS: Ahmed Body

22 Ahmed Body Slant y (mm) U y (mm) U rms

23 Ahmed Body Wake y (mm) ,00E+02 U 4,50E+02 4,00E+02 3,50E+02 3,00E+02 y (mm) 2,50E+02 2,00E+02 1,50E+02 1,00E+02 5,00E+01 0,00E+00 u-rms

24 Ahmed Body Slant RANS RANS/LES LES RANS

25 Vortex Method & Zonal Hybrid RANS/LES TABLE 1: DRAG FORCE AND FORCE COMPONENT RANS LES/RANS Exp Exp (Ahmed) (Lienhart et al.) Cs Cb Cf Cd

26 Vortex Method & Zonal Hybrid RANS/LES Zonal LES/RANS coupling: Ahmed Body

27 Conclusion & future work: Embedded LES RANS/LES interface conditions: «RANS domain» Virtual body force in Filtered NS equations to drive the velocity Field to perturbed velocity field with the VM enrichment procedure Airfoil LES/RANS LES/RANS interface: k,ε boundary conditions based on correlations? Quéméré & sagaut (2004) RANS/LES «LES box»

28 Embedded LES: Trailing Edge Acoustics Prediction RANS: attached boundary layers U Ffowcs Williams: radiated sound δs Trailing Edge Noise Prediction - Re C = Exp. Data from C. Kunze (2004) University of Notre Dame LES box: acoustics source

29 RANS/LES coupling Mesh: 1.5 M cells RANS/LES Non conformal interfaces

30 RANS/LES coupling

31 RANS/LES coupling RANS LES U m U m u rms