Optimizing calculation costs of tubulent flows with RANS/LES methods

Size: px

Start display at page:

Download "Optimizing calculation costs of tubulent flows with RANS/LES methods"

Alisha Hood
5 years ago
Views:

1 Optimizing calculation costs of tubulent flows with RANS/LES methods Investigation in separated flows C. Friess, R. Manceau Dpt. Fluid Flow, Heat Transfer, Combustion Institute PPrime, CNRS University of Poitiers ENSMA, Poitiers, France Present address : Lab. Mechanics, Modelling and Clean Processes CNRS Aix-Marseille University, Marseille, France Spring Festival ERCOFTAC, Toulon, 2013/4/9

2 INTRODUCTION Motivation In recent years: Numerous continuous hybrid RANS-LES methods Friess, Manceau HYBRID RANS/LES METHODS 1

3 INTRODUCTION Motivation In recent years: Numerous continuous hybrid RANS-LES methods Common feature: ambiguous definition of the resolved variables RANS regions: Reynolds (statistical) averaging LES regions: spatial filter Friess, Manceau HYBRID RANS/LES METHODS 1

4 INTRODUCTION Motivation In recent years: Numerous continuous hybrid RANS-LES methods Common feature: ambiguous definition of the resolved variables RANS regions: Reynolds (statistical) averaging LES regions: spatial filter Matching in homogeneous turbulence: Spatial filter spatial average when Statistical average = spatial average Friess, Manceau HYBRID RANS/LES METHODS 1

5 INTRODUCTION Motivation In recent years: Numerous continuous hybrid RANS-LES methods Common feature: ambiguous definition of the resolved variables RANS regions: Reynolds (statistical) averaging LES regions: spatial filter Matching in homogeneous turbulence: Spatial filter spatial average when Statistical average = spatial average Usual configurations: inhomogeneous fundamental inconsistency Friess, Manceau HYBRID RANS/LES METHODS 1

6 INTRODUCTION Motivation In recent years: Numerous continuous hybrid RANS-LES methods Common feature: ambiguous definition of the resolved variables RANS regions: Reynolds (statistical) averaging LES regions: spatial filter Matching in homogeneous turbulence: Spatial filter spatial average when Statistical average = spatial average Usual configurations: inhomogeneous fundamental inconsistency For inhomogeneous, stationary flows (statistical average independent of t): consistency issue addressed in the frame of temporal filtering Hybrid Temporal LES/RANS (Fadai-Ghotbi, Friess, Manceau, Gatski, and Borée, 2010) Friess, Manceau HYBRID RANS/LES METHODS 1

7 FORMALISM Temporal filtering approach within the LES formalism: TLES (Pruett, 2000; Pruett, Gatski, Grosch, and Thacker, 2003) ũ(x,t) = 0 G T (τ) u(x,t+τ) dτ ũ i t + ũ iũ j x j = 1 ρ P ũ i x i Re x 2 j τ ijsfs x j E T (ω) Ĝ T Ĝ T E T (ω) ω Friess, Manceau HYBRID RANS/LES METHODS 2

8 FORMALISM Temporal filtering approach within the LES formalism: TLES (Pruett, 2000; Pruett, Gatski, Grosch, and Thacker, 2003) ũ(x,t) = 0 G T (τ) u(x,t+τ) dτ ũ i t + ũ iũ j x j = 1 ρ P ũ i x i Re x 2 j τ ijsfs x j Subfilter stresses τ ijsfs : Dτ ijsfs Dt = P ij +φ ij +D T ij +D ν ij ε ij RANS and TLES equations are form-invariant provides a consistent basis for RANS-TLES hybridization E T (ω) Ĝ T Ĝ T E T (ω) ω Friess, Manceau HYBRID RANS/LES METHODS 2

9 FORMALISM Temporal filtering approach within the LES formalism: TLES (Pruett, 2000; Pruett, Gatski, Grosch, and Thacker, 2003) ũ(x,t) = 0 G T (τ) u(x,t+τ) dτ ũ i t + ũ iũ j x j = 1 ρ P ũ i x i Re x 2 j τ ijsfs x j Subfilter stresses τ ijsfs : Dτ ijsfs Dt = P ij +φ ij +D T ij +D ν ij ε ij RANS and TLES equations are form-invariant provides a consistent basis for RANS-TLES hybridization E T (ω) Ĝ T Ĝ T E T (ω) ω c ω Friess, Manceau HYBRID RANS/LES METHODS 2

10 FORMALISM Temporal filtering approach within the LES formalism: TLES (Pruett, 2000; Pruett, Gatski, Grosch, and Thacker, 2003) ũ(x,t) = 0 G T (τ) u(x,t+τ) dτ ũ i t + ũ iũ j x j = 1 ρ P ũ i x i Re x 2 j τ ijsfs x j Subfilter stresses τ ijsfs : Dτ ijsfs Dt = P ij +φ ij +D T ij +D ν ij ε ij RANS and TLES equations are form-invariant provides a consistent basis for RANS-TLES hybridization E T (ω) Ĝ T Ĝ T E T (ω) ω c 0: SFS stresses tend to Reynolds stresses 10-4 RANS equations recovered ω c ω Friess, Manceau HYBRID RANS/LES METHODS 2

11 FORMALISM Temporal filtering approach within the LES formalism: TLES (Pruett, 2000; Pruett, Gatski, Grosch, and Thacker, 2003) ũ(x,t) = 0 G T (τ) u(x,t+τ) dτ ũ i t + ũ iũ j x j = 1 ρ P ũ i x i Re x 2 j τ ijsfs x j Subfilter stresses τ ijsfs : Dτ ijsfs Dt = P ij +φ ij +D T ij +D ν ij ε ij RANS and TLES equations are form-invariant provides a consistent basis for RANS-TLES hybridization E T (ω) Ĝ T Ĝ T E T (ω) ω c 0: SFS stresses tend to Reynolds stresses 10-4 RANS equations recovered ω c 0 ω c ω Friess, Manceau HYBRID RANS/LES METHODS 2

12 FORMALISM Temporal filtering approach within the LES formalism: TLES (Pruett, 2000; Pruett, Gatski, Grosch, and Thacker, 2003) ũ(x,t) = 0 G T (τ) u(x,t+τ) dτ ũ i t + ũ iũ j x j = 1 ρ P ũ i x i Re x 2 j τ ijsfs x j Subfilter stresses τ ijsfs : Dτ ijsfs Dt = P ij +φ ij +D T ij +D ν ij ε ij RANS and TLES equations are form-invariant provides a consistent basis for RANS-TLES hybridization E T (ω) Ĝ T Ĝ T E T (ω) ω c 0: SFS stresses tend to Reynolds stresses 10-4 RANS equations recovered ω c 0 ω c ω c : SFS stresses vanish ω Navier-Stokes equations recovered Friess, Manceau HYBRID RANS/LES METHODS 2

13 CONTROL OF THE RANS LES TRANSITION T-PITM method (Fadai-Ghotbi et al., 2010) Temporal version of the PITM (Chaouat and Schiestel, 2005) Friess, Manceau HYBRID RANS/LES METHODS 3

14 CONTROL OF THE RANS LES TRANSITION T-PITM method (Fadai-Ghotbi et al., 2010) Temporal version of the PITM (Chaouat and Schiestel, 2005) Three spectral zones [0,ω c ], [ω c,ω d ], [ω d, ] Friess, Manceau HYBRID RANS/LES METHODS 3

15 CONTROL OF THE RANS LES TRANSITION T-PITM method (Fadai-Ghotbi et al., 2010) Temporal version of the PITM (Chaouat and Schiestel, 2005) Three spectral zones [0,ω c ], [ω c,ω d ], [ω d, ] Partial integration over each zone of the transport equation for E T (x,ω) Dk m Dt Dε Dt = P m ε m +D m [ ] ε = C ε1 P m C ε1 +r(c ε2 C ε1 ) k m } {{ } Cε 2 (ω c ) ε 2 k m +D ε Friess, Manceau HYBRID RANS/LES METHODS 3

16 CONTROL OF THE RANS LES TRANSITION T-PITM method (Fadai-Ghotbi et al., 2010) Temporal version of the PITM (Chaouat and Schiestel, 2005) Three spectral zones [0,ω c ], [ω c,ω d ], [ω d, ] Partial integration over each zone of the transport equation for E T (x,ω) Dk m Dt Dε Dt = P m ε m +D m [ ] ε = C ε1 P m C ε1 +r(c ε2 C ε1 ) k m } {{ } Cε 2 (ω c ) ε 2 k m +D ε Fundamental parameter: r = k m k m +k r k m = modelled k r = resolved = measure of the energy partition among resolved and subfilter scales Friess, Manceau HYBRID RANS/LES METHODS 3

17 CONTROL OF THE RANS LES TRANSITION T-PITM method (Fadai-Ghotbi et al., 2010) Temporal version of the PITM (Chaouat and Schiestel, 2005) Three spectral zones [0,ω c ], [ω c,ω d ], [ω d, ] Partial integration over each zone of the transport equation for E T (x,ω) Dk m Dt Dε Dt = P m ε m +D m [ ] ε = C ε1 P m C ε1 +r(c ε2 C ε1 ) k m } {{ } Cε 2 (ω c ) ε 2 k m +D ε Fundamental parameter: r = k m k m +k r k m = modelled k r = resolved = measure of the energy partition among resolved and subfilter scales r = 1 RANS Friess, Manceau HYBRID RANS/LES METHODS 3

18 CONTROL OF THE RANS LES TRANSITION T-PITM method (Fadai-Ghotbi et al., 2010) Temporal version of the PITM (Chaouat and Schiestel, 2005) Three spectral zones [0,ω c ], [ω c,ω d ], [ω d, ] Partial integration over each zone of the transport equation for E T (x,ω) Dk m Dt Dε Dt = P m ε m +D m [ ] ε = C ε1 P m C ε1 +r(c ε2 C ε1 ) k m } {{ } Cε 2 (ω c ) ε 2 k m +D ε Fundamental parameter: r = k m k m +k r k m = modelled k r = resolved = measure of the energy partition among resolved and subfilter scales r = 1 RANS r = 0 DNS Friess, Manceau HYBRID RANS/LES METHODS 3

19 CONTROL OF THE RANS LES TRANSITION T-PITM method (Fadai-Ghotbi et al., 2010) Temporal version of the PITM (Chaouat and Schiestel, 2005) Three spectral zones [0,ω c ], [ω c,ω d ], [ω d, ] Partial integration over each zone of the transport equation for E T (x,ω) Dk m Dt Dε Dt = P m ε m +D m [ ] ε = C ε1 P m C ε1 +r(c ε2 C ε1 ) k m } {{ } Cε 2 (ω c ) ε 2 k m +D ε Fundamental parameter: r = k m k m +k r k m = modelled k r = resolved = measure of the energy partition among resolved and subfilter scales r = 1 RANS In between TLES r = 0 DNS Friess, Manceau HYBRID RANS/LES METHODS 3

20 DERIVATION OF AN EQUIVALENT DES T-PITM: difficulties to reach the expected energy partition Modify the form of the system of equations Friess, Manceau HYBRID RANS/LES METHODS 4

21 DERIVATION OF AN EQUIVALENT DES T-PITM: difficulties to reach the expected energy partition Modify the form of the system of equations T-PITM Equivalent DES dk m dt = P m ε+d m dk m dt dε dt = C ε ε1 P m C k ε2(ω c ) ε2 D ε m k m = P m ψ(ω c )ε+d m dε dt = C ε ε 2 ε1 P m C ε2 D ε k m k m C ε2(ω c ) = C ε1 +r(ω c )(C ε2 C ε1 ) ψ(ω c ) = k3/2 m /ε L(ω c ) Friess, Manceau HYBRID RANS/LES METHODS 4

22 DERIVATION OF AN EQUIVALENT DES T-PITM: difficulties to reach the expected energy partition Modify the form of the system of equations T-PITM Equivalent DES dk m dt = P m ε+d m dk m dt = P m ψ(ω c )ε+d m dε dt = C ε ε1 P m C k ε2(ω c ) ε2 D ε m k m dε dt = C ε ε 2 ε1 P m C ε2 D ε k m k m C ε2(ω c ) = C ε1 +r(ω c )(C ε2 C ε1 ) ψ(ω c ) = k3/2 m /ε L(ω c ) Equivalence (Manceau et al., 2010): ψ function that gives the same energy partition as the C ε2 function? Friess, Manceau HYBRID RANS/LES METHODS 4

23 DERIVATION OF AN EQUIVALENT DES Procedure T-PITM H-TLES dk m dt dε dt = C ε1 = P m ε+d m dk m dt ε k m P m C ε2 ε 2 k m D ε = P m ψε+d m dε dt = C ε ε 2 ε1 P m C ε2 D ε k m k m Friess, Manceau HYBRID RANS/LES METHODS 5

24 DERIVATION OF AN EQUIVALENT DES Procedure T-PITM H-TLES dk m dt dε dt = C ε1 = P m ε+d m dk m dt ε k m P m C ε2 ε 2 k m D ε = P m ψε+d m dε dt = C ε ε 2 ε1 P m C ε2 D ε k m k m Starting from the RANS system: C ε2 = C ε2 and ψ = 1 same equations same partition (r = 1) Friess, Manceau HYBRID RANS/LES METHODS 5

25 DERIVATION OF AN EQUIVALENT DES Procedure T-PITM H-TLES dk m dt dε dt = C ε1 = P m ε+d m dk m dt ε k m P m C ε2 ε 2 k m D ε = P m ψε+d m dε dt = C ε ε 2 ε1 P m C ε2 D ε k m k m Starting from the RANS system: C ε2 = C ε2 and ψ = 1 same equations same partition (r = 1) Introducing infinitesimal variations δc ε2 and δψ (perturbation analysis) Friess, Manceau HYBRID RANS/LES METHODS 5

26 DERIVATION OF AN EQUIVALENT DES Procedure T-PITM H-TLES dk m dt dε dt = C ε1 = P m ε+d m dk m dt ε k m P m C ε2 ε 2 k m D ε = P m ψε+d m dε dt = C ε ε 2 ε1 P m C ε2 D ε k m k m Starting from the RANS system: C ε2 = C ε2 and ψ = 1 same equations same partition (r = 1) Introducing infinitesimal variations δc ε2 and δψ (perturbation analysis) Same variation of the partition of energy if 1 C ε2 C ε1 ψ δψ = 1 ( C C ε2 ε1 C ε1 1 )δc ε2 Friess, Manceau HYBRID RANS/LES METHODS 5

27 DERIVATION OF AN EQUIVALENT DES Procedure dk m dt dε dt = C ε1 T-PITM = P m ε+d m dk m dt ε k m P m C ε2 ε 2 k m D ε H-TLES = P m ψε+d m dε dt = C ε ε 2 ε1 P m C ε2 D ε k m k m Starting from the RANS system: C ε2 = C ε2 and ψ = 1 same equations same partition (r = 1) Introducing infinitesimal variations δc ε2 and δψ (perturbation analysis) 1 Same variation of the partition of energy if C ε2 C ε1 ψ δψ = 1 ( C C ε2 ε1 C ε1 1 ( ) Cε2 ( ) By integration: Equivalence ψ = r C ε1 C ε2 C ε1 )δc ε2 Friess, Manceau HYBRID RANS/LES METHODS 5

28 DERIVATION OF AN EQUIVALENT DES Link with the cutoff frequency ψ = k3/2 m /ε L L = 1+ r 3/2 ( )L C ε2 C ε1 1 )(1 r C ε1 int where L int = k3/2 C ε2 ε Friess, Manceau HYBRID RANS/LES METHODS 6

29 DERIVATION OF AN EQUIVALENT DES Link with the cutoff frequency ψ = k3/2 m /ε L L = 1+ r 3/2 ( )L C ε2 C ε1 1 )(1 r C ε1 int where L int = k3/2 C ε2 ε Evaluation of r as a function of ω c r = k m k = 1 k ω c E T (ω)dω E T (ω) = Eulerian frequency spectrum Friess, Manceau HYBRID RANS/LES METHODS 6

30 DERIVATION OF AN EQUIVALENT DES Link with the cutoff frequency ψ = k3/2 m /ε L L = 1+ r 3/2 ( )L C ε2 C ε1 1 )(1 r C ε1 int where L int = k3/2 C ε2 ε Evaluation of r as a function of ω c r = k m k = 1 k E T (ω)dω ω c r = 1 β E T (ω) = Eulerian frequency spectrum ( ) 2/3 ( ) 2/3 Us k ω c k ε U s = U 2 +γk is the sweeping velocity (Tennekes, 1975) Friess, Manceau HYBRID RANS/LES METHODS 6

31 DERIVATION OF AN EQUIVALENT DES Link with the cutoff frequency ψ = k3/2 m /ε L L = 1+ r 3/2 ( )L C ε2 C ε1 1 )(1 r C ε1 int where L int = k3/2 C ε2 ε Evaluation of r as a function of ω c r = k m k = 1 k E T (ω)dω ω c r = 1 β E T (ω) = Eulerian frequency spectrum ( ) 2/3 ( ) 2/3 Us k ω c k ε U s = U 2 +γk is the sweeping velocity (Tennekes, 1975) Cutoff frequency = maximum observable frequency ω c = min ( π dt ; U ) sπ Friess, Manceau HYBRID RANS/LES METHODS 6

32 DERIVATION OF AN EQUIVALENT DES Subfilter stress model Friess, Manceau HYBRID RANS/LES METHODS 7

33 DERIVATION OF AN EQUIVALENT DES Subfilter stress model EB RSM (Manceau and Hanjalić, 2002) : a single scalar α accounting for wall effects α+l 2 2 α = 1 φ ij ε ij = α 3 (φ ij ε ij) w +(1 α 3 )(φ ij ε ij) h Friess, Manceau HYBRID RANS/LES METHODS 7

34 DERIVATION OF AN EQUIVALENT DES Subfilter stress model EB RSM (Manceau and Hanjalić, 2002) : a single scalar α accounting for wall effects α+l 2 2 α = 1 φ ij ε ij = α 3 (φ ij ε ij) w +(1 α 3 )(φ ij ε ij) h Modified EB RSM model Friess, Manceau HYBRID RANS/LES METHODS 7

35 DERIVATION OF AN EQUIVALENT DES Subfilter stress model EB RSM (Manceau and Hanjalić, 2002) : a single scalar α accounting for wall effects α+l 2 2 α = 1 φ ij ε ij = α 3 (φ ij ε ij) w +(1 α 3 )(φ ij ε ij) h Modified EB RSM model H-TLES : dt dε sfs dt dτ ijsfs = P ijsfs +φ ijsfs +D T ijsfs +D ν ijsfs k3/2 sfs ε ijsfs Lε sfs = standard Friess, Manceau HYBRID RANS/LES METHODS 7

36 DERIVATION OF AN EQUIVALENT DES Subfilter stress model EB RSM (Manceau and Hanjalić, 2002) : a single scalar α accounting for wall effects α+l 2 2 α = 1 φ ij ε ij = α 3 (φ ij ε ij) w +(1 α 3 )(φ ij ε ij) h Modified EB RSM model H-TLES : dt dε sfs dt dτ ijsfs = P ijsfs +φ ijsfs +D T ijsfs +D ν ijsfs k3/2 sfs ε ijsfs Lε sfs = standard T-PITM : dτ ijsfs dt dε sfs dt = standard P sfs ε sfs = C ε1 C ε 2 sfs ε2 +Diff. k SFS k SFS Friess, Manceau HYBRID RANS/LES METHODS 7

37 FLOW OVER A PERIODIC HILL Configuration and numerics Periodically constricted channel Friess, Manceau HYBRID RANS/LES METHODS 8

38 FLOW OVER A PERIODIC HILL Configuration and numerics Periodically constricted channel Re b = U b h/ν = meshes Friess, Manceau HYBRID RANS/LES METHODS 8

39 FLOW OVER A PERIODIC HILL Configuration and numerics Periodically constricted channel Re b = U b h/ν = meshes Comparison with a 2D RANS & ref LES from (Breuer et al., 2009) Friess, Manceau HYBRID RANS/LES METHODS 8

40 FLOW OVER A PERIODIC HILL Configuration and numerics Periodically constricted channel Re b = U b h/ν = meshes Comparison with a 2D RANS & ref LES from (Breuer et al., 2009) Numerics Code Saturne: open source finite volume solver developed by EDF CDS convection scheme for resolved momentum + UDS for sfsquantities Friess, Manceau HYBRID RANS/LES METHODS 8

41 FLOW OVER A PERIODIC HILL Effects of grid refining T-PITM results for a coarse and a fine grid, vs 2D RANS and LES 4 3 LES fine TPITM coarse TPITM 2D RANS 4 3 LES Breuer fine TPITM coarse TPITM 2D RANS y/h 2 y/h x/h + 2 U/U b 0,03 0, LES fine TPITM coarse TPITM 2D RANS x/h + 12 k/u 2 b Cf 0, Streamwise velocity, total kinetic energy & friction coefficient x/h Friess, Manceau HYBRID RANS/LES METHODS 9

42 FLOW OVER A PERIODIC HILL Effects of grid refining Separation / reattachment Cas Maillage N x N y Nz(x/h) sep (x/h) reatt RANS T-PITM T-PITM LES (Breuer et al.) LES (Fröhlich et al.) Friess, Manceau HYBRID RANS/LES METHODS 10

43 FLOW OVER A PERIODIC HILL Isocontours of zero-q criterion : coarse & fine grid refining the grid allows resolving more structures Friess, Manceau HYBRID RANS/LES METHODS 11

44 CONCLUSIONS Temporal filtering : a consistent formalism for hybrid RANS/(T)LES modelling Friess, Manceau HYBRID RANS/LES METHODS 12

45 CONCLUSIONS Temporal filtering : a consistent formalism for hybrid RANS/(T)LES modelling Equivalent DES Friess, Manceau HYBRID RANS/LES METHODS 12

46 CONCLUSIONS Temporal filtering : a consistent formalism for hybrid RANS/(T)LES modelling Equivalent DES as for DES, based on a length-scale modification in the subfilter stress equations k3/2 sfs L(r) vs. k 3/2 sfs C DES DES temporal filtering Friess, Manceau HYBRID RANS/LES METHODS 12

47 CONCLUSIONS Temporal filtering : a consistent formalism for hybrid RANS/(T)LES modelling Equivalent DES as for DES, based on a length-scale modification in the subfilter stress equations k3/2 sfs L(r) vs. k 3/2 sfs C DES DES temporal filtering equivalence with T-PITM demonstrated analytically for equilibrium flows (Manceau et al., 2010) Friess, Manceau HYBRID RANS/LES METHODS 12

48 CONCLUSIONS Temporal filtering : a consistent formalism for hybrid RANS/(T)LES modelling Equivalent DES as for DES, based on a length-scale modification in the subfilter stress equations k3/2 sfs L(r) vs. k 3/2 sfs C DES DES temporal filtering equivalence with T-PITM demonstrated analytically for equilibrium flows (Manceau et al., 2010) more convenient than T-PITM Friess, Manceau HYBRID RANS/LES METHODS 12

49 CONCLUSIONS Temporal filtering : a consistent formalism for hybrid RANS/(T)LES modelling Equivalent DES as for DES, based on a length-scale modification in the subfilter stress equations k3/2 sfs L(r) vs. k 3/2 sfs C DES DES temporal filtering equivalence with T-PITM demonstrated analytically for equilibrium flows (Manceau et al., 2010) more convenient than T-PITM main parameter : subfilter to total energy ratio r, can be related to cutoff frequency ω c Friess, Manceau HYBRID RANS/LES METHODS 12

50 CONCLUSIONS Temporal filtering : a consistent formalism for hybrid RANS/(T)LES modelling Equivalent DES as for DES, based on a length-scale modification in the subfilter stress equations k3/2 sfs L(r) vs. k 3/2 sfs C DES DES temporal filtering equivalence with T-PITM demonstrated analytically for equilibrium flows (Manceau et al., 2010) more convenient than T-PITM main parameter : subfilter to total energy ratio r, can be related to cutoff frequency ω c Application to massively separated flows Friess, Manceau HYBRID RANS/LES METHODS 12

51 CONCLUSIONS Temporal filtering : a consistent formalism for hybrid RANS/(T)LES modelling Equivalent DES as for DES, based on a length-scale modification in the subfilter stress equations k3/2 sfs L(r) vs. k 3/2 sfs C DES DES temporal filtering equivalence with T-PITM demonstrated analytically for equilibrium flows (Manceau et al., 2010) more convenient than T-PITM main parameter : subfilter to total energy ratio r, can be related to cutoff frequency ω c Application to massively separated flows Satisfactory results : RANS << hybrid LES Friess, Manceau HYBRID RANS/LES METHODS 12

52 REFERENCES Bentaleb, Y., Manceau, R., A hybrid Temporal LES/RANS formulation based on a two-equation subfilter model. In: Proc. 7th Int. Symp. Turb. Shear Flow Phenomena, Ottawa, Canada. Breuer, M., Peller, N., Rapp, C., Manhart, M., Flow over periodic hills - Numerical and experimental study in a wide range of Reynolds numbers. Comput. Fluids 38 (2), Chaouat, B., Schiestel, R., A new partially integrated transport model for subgrid-scale stresses and dissipation rate for turbulent developing flows. Phys. Fluids 17 (065106), Fadai-Ghotbi, A., Friess, C., Manceau, R., Gatski, T., Borée, J., Temporal filtering: a consistent formalism for seamless hybrid RANS-LES modeling in inhomogeneous turbulence. Int. J. Heat Fluid Fl. 31 (3). Friess, Manceau HYBRID RANS/LES METHODS 13

53 REFERENCES Manceau, R., Friess, C., Gatski, T., Of the interpretation of DES as a Hybrid RANS/Temporal LES method. In: Proc. 8th ERCOFTAC Int. Symp. on Eng. Turb. Modelling and Measurements, Marseille, France. Manceau, R., Hanjalić, K., Elliptic Blending Model: A New Near-Wall Reynolds-Stress Turbulence Closure. Phys. Fluids 14 (2), Pruett, C. D., Eulerian time-domain filtering for spatial large-eddy simulation. AIAA journal 38 (9), Pruett, C. D., Gatski, T. B., Grosch, C. E., Thacker, W. D., The temporally filtered Navier-Stokes equations: Properties of the residual stress. Phys. Fluids 15 (8), Tennekes, H., Eulerian and Lagrangian time microscales in isotropic turbulence. J. Fluid Mech. 67, Friess, Manceau HYBRID RANS/LES METHODS 14

54 Temporal filtering and cutoff frequency Contours of U S dt/ : coarse & fine mesh convective time scale governs temporal filtering Friess, Manceau HYBRID RANS/LES METHODS 15

Toward an equivalence criterion for Hybrid RANS/LES methods

Toward an equivalence criterion for Hybrid / methods Christophe Friess, R. Manceau, T.B. Gatski To cite this version: Christophe Friess, R. Manceau, T.B. Gatski. Toward an equivalence criterion for Hybrid