Downloaded 590 times
![Original
source
codes
for
SGS
model
$ src
$ cd
turbulenceModels/incompressible/LES/
$ ls
1. Check
the
original
source
code
for
SGS
model.
2. Glance
the
codes
of
Smagorinsky
model.
$ gedit
Smagorinsky/Smagorinsky.*
3. In
this
exercise,
we
look
the
codes
of
dynamic
models.
$ ls
*[Dd]yn*
4. Compare
the
structures
and
statements
of
the
related
codes
(*.C
and
*.H).](https://image.slidesharecdn.com/lescustomizationen-150615153813-lva1-app6892/85/Customization-of-LES-turbulence-model-in-OpenFOAM-34-320.jpg)
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Customization of LES turbulence model in OpenFOAM
- 1. Customiza*on of LES turbulence model in OpenFOAM yotakagi77 Open CAE Local User Groups in Japan @Kansai June 13, 2015, Osaka University
- 2. Agenda • Basic informa*on on turbulence model • Tensor mathema*cs • Exercise 1: Compiling and execu*on of WALE model • Exercise 2: Implementa*on of coherent structure Smagorisky model • Addi*onal works
- 3. Basic informa*on on turbulence model
- 4. Turbulent flow simula*on DNS LES RANS Modeling No Subgrid scale Reynolds average Accuracy ◎ ○ △ Cost × ○ ◎ Vortex (eddy) field Reynolds average 4
- 5. Turbulent flow simula*on DNS LES RANS Modeling No Subgrid scale Reynolds average Accuracy ◎ ○ △ Cost × ○ ◎ DNS grid, u Reynolds average 5
- 6. Turbulent flow simula*on DNS LES RANS Modeling No Subgrid scale Reynolds average Accuracy ◎ ○ △ Cost × ○ ◎ LES grid, u = u – u’ Reynolds average 6
- 7. Turbulent flow simula*on DNS LES RANS Modeling No Subgrid scale Reynolds average Accuracy ◎ ○ △ Cost × ○ ◎ Filtering approach Reynolds average 7
- 8. Detached-‐eddy simula*on (DES) • P. R. Spalart (1997): – We name the new approach “Detached-‐Eddy Simula8on” (DES) to emphasize its dis8nct treatments of a?ached and separated regions. Super-‐Region Region Euler (ER) RANS (RR) Viscous (VR) Outer (OR) LES (LR) Viscous (VR) Focus (FR) Departure (DR) 8 Spalart (2001)
- 9. Detached-‐eddy simula*on (DES) • P. R. Spalart (1997): – We name the new approach “Detached-‐Eddy Simula8on” (DES) to emphasize its dis8nct treatments of a?ached and separated regions. Super-‐Region Region Euler (ER) RANS (RR) Viscous (VR) Outer (OR) LES (LR) Viscous (VR) Focus (FR) Departure (DR) Spalart (2001) 9
- 10. Coupling with momentum equa*on through viscosity • RANS • LES ∂U ∂t + ∇⋅ UU( )− ∇⋅ ν+ νt( ) ∇U + (∇U)T ( )( )= ∇p ∂U ∂t + ∇⋅ UU( )− ∇⋅ ν+ νSGS( ) ∇U + (∇U)T ( )( )= ∇p Turbulent viscosity Sub-grid scale viscosity Only change viscosity! 10
- 11. Significant problem: difference of filtering (average) approaches LES Filtering Reynolds average Spa*al Temporal Inconsistency at the interface between LES and RANS regions 11
- 12. Standard SGS model in OpenFOAM Library name Note Smagorinksy Smagorinsky model Smagorinksy2 Smagorinsky model with 3-‐D filter homogeneousDynSmagor insky Homogeneous dynamic Smagorinsky model dynLagragian Lagrangian two equa*on eddy-‐viscosity model scaleSimilarity Scale similarity model mixedSmagorinsky Mixed Smagorinsky / scale similarity model homogeneousDynOneEqE ddy One Equa*on Eddy Viscosity Model for incompressible flows laminar Simply returns laminar proper*es kOmegaSSTSAS k-‐ω SST scale adap*ve simula*on (SAS) model
- 13. Standard SGS model in OpenFOAM Library name Note oneEqEddy k-‐equa*on eddy-‐viscosity model dynOneEqEddy Dynamic k-‐equa*on eddy-‐viscosity model spectEddyVisc Spectral eddy viscosity model LRDDiffStress LRR differen*al stress model DeardorffDiffStress Deardorff differen*al stress model SpalartAllmaras Spalart-‐Allmaras model SpalartAllmarasDDES Spalart-‐Allmaras delayed detached eddy simula*on (DDES) model SpalartAllmarasIDDES Spalart-‐Allmaras improved DDES (IDDES) model vanDriestDelta Simple cube-‐root of cell volume delta used in incompressible LES models
- 14.
- 15. Tensor • Rank 0: ‘scalar’, e.g. volume V, pressure p. • Rank 1: ‘vector’, e.g. velocity vector u, surface vector S. Descrip*on: a = ai = (a1, a2, a3). • Rank 2: ‘tensor’, e.g. strain rate tensor Sij, rota*on tensor Ωij. Descrip*on: T = Tij = T11 T12 T13 T21 T22 T23 T31 T32 T33 ! " # # # $ % & & &
- 16. Symmetric/an*symmetric tensor • Velocity gradient tensor is decomposed into strain rate tensor (symmetric) and vor*city tensor (an*symmetric, skew). • In turbulence modeling, Sij and Ωij are usually used. Dij = ∂ui ∂xj , Sij = 1 2 ∂ui ∂xj + ∂uj ∂xi " # $$ % & '', Ωij = 1 2 ∂ui ∂xj − ∂uj ∂xi " # $$ % & '' Dij = Sij +Ωij
- 17. Opera*ons exclusive to tensors of rank 2 T = 1 2 (T+ TT )+ 1 2 (T− TT ) = symmT+skewT, trT = T11 +T22 +T33, diagT = (T11,T22,T33), T = T− 1 3 (trT)I+ 1 3 (trT)I = devT+ hydT, detT = T11 T12 T13 T21 T22 T23 T31 T32 T33
- 18. OpenFOAM tensor classes Opera2on Mathema2cal Class Addi*on a + b a + b Subtrac*on a – b a – b Scalar mul*plica*on sa s * a Scalar division a / s a / s Outer product a b a * b Inner product a ·∙ b a & b Double inner product a : b a && b Cross product a × b a ^ b Square a2 sqr(a) Magnitude squared |a|2 magSqr(a) Magnitude |a| mag(a) Power an pow(a, n)
- 19. OpenFOAM tensor classes Opera2on Mathema2cal Class Transpose TT T.T() Diagonal diag T diag(T) Trace tr T tr(T) Deviatoric component dev T dev(T) Symmetric component symm T symm(T) Skew-‐symmetric component skew T skew(T) Determinant det T det(T) Cofactors cof T cof(T) Inverse inv T inv(T)
- 20. Exercise 1: Compiling and execu*on of WALE model
- 21. Governing equa*on for incompressible LES • Filtered con*nuity and Navier-‐Stokes equa*ons where ∂ui ∂xi = 0, ∂ui ∂t +uj ∂ui ∂xj = − 1 ρ ∂p ∂xi + ∂ ∂xi (−τij + 2νSij ) τij = uiuj −uiuj
- 22. SGS eddy viscosity model • Decomposi*on of kine*c energy • Conserva*on of GS energy kGS • Conserva*on of SGS energy kSGS ∂kGS ∂t +uj ∂kGS ∂xj = τijSij −εGS + ∂ ∂xi −uiτij − puj ρ +ν ∂kGS ∂xj # $ %% & ' (( k = 1 2 ukuk = 1 2 ukuk + 1 2 (ukuk −ukuk ) kGS kSGS ∂kSGS ∂t +uj ∂kSGS ∂xj = −τijSij −εSGS + ∂ ∂xi uiτij − 1 2 (uiuiuj +uj uiui )− puj − puj ρ +ν ∂kSGS ∂xj # $ % % & ' ( (
- 23. Smagorinsky model • Local equilibrium between SGS produc*on rate and SGS energy dissipa*on: • Eddy viscosity approxima*on: • Aper dimensional analysis and scaling, εSGS ≡ν ∂ui ∂xj ∂ui ∂uj −ν ∂ui ∂xj ∂ui ∂xj $ % && ' ( )) = −τijSij τij a = −2vSGS Sij νSGS = (CS Δ)2 | S |, | S |= 2SijSij , CS : Smagorinsky constant
- 24. WALE model • Traceless symmetric part of the square of the velocity gradient tensor: • Eddy viscosity of WALE model: Sij d = 1 2 (Dij 2 + Dji 2 )− 1 3 δijDkk 2 = SikSkj +ΩikΩkj − 1 3 δij SmnSmn −ΩmnΩmn #$ %& Sij d Sij d = 1 6 (S2 S2 +Ω2 Ω2 )+ 2 3 S2 Ω2 + 2IVSΩ, S2 = SijSij, Ω2 = ΩijΩij, IVSΩ = SikSkjΩjlΩli νSGS = (CwΔ)2 (Sij d Sij d )3/ 2 (SijSij )5/ 2 + (Sij d Sij d )5/ 4 (Nicoud and Ducros, 1999)
- 25. Model parameters of WALE model Field a Field b Field c Field d Field e Field f Cw 2/Cs 2 10.81 10.52 10.84 10.55 10.70 11.27 If CS = 0.18, 0.55 ≤ CW ≤ 0.6. If CS = 0.1, 0.32 ≤ CW ≤ 0.34. Model parameter Cw is dependent on Smagorinsky constant CS. (Nicoud and Ducros, 1999)
- 26. Source code of WALE model • V&V working group, Open CAE Society of Japan hsps://github.com/opencae/VandV/tree/master/ OpenFOAM/2.2.x/src/libraries/incompressibleWALE • OpenFOAM-‐dev hsps://github.com/OpenFOAM/OpenFOAM-‐dev/tree/ master/src/TurbulenceModels/turbulenceModels/LES/WALE
- 27. Download and compile $ mkdir –p $FOAM_RUN $ cd $ git clone https://github.com/opencae/VandV $ cd VandV/OpenFOAM/OpenFOAM-‐BenchmarkTest/ channelReTau110 $ cp –r src $FOAM_RUN/.. $ run $ cd ../src/libraries/incompressibleWALE $ wmake libso $ ls $FOAM_USER_LIBBIN 1. Download the source code of WALE model from the V&V repository, and compile the WALE model library.
- 28. Simula*on of channel flow $ run $ cp –r $FOAM_TUTORIALS/incompressible/pimpleFoam/ channel395/ ./ReTau395WALE $ cd ReTau395WALE 2. The standard tutorial case of channel flow at Reτ = 395: copy the tutorial case file into your run directory. 3. Edit constant/LESProper*es and system/controlDict $ gedit constant/LESProperties LESModel WALE; printCoeffs on; delta cubeRootVol; ...
- 29. Simula*on of channel flow $ gedit system/controlDict ... libs ("libincompressibleWALE.so"); This line is necessary to call the new WALE library in solver. $ ./Allrun 4. Aper checking other numerical condi*ons and parameter, run the solver. 5. If the solver calcula*on is normally finished, you check the logs and visualize the flow field with ParaView, and plot the fields profile generated by postChannel.
- 30. Simula*on of channel flow at Reτ = 110 $ run $ cp –r ~/VandV/OpenFOAM/OpenFOAM-‐BenchmarkTest/ channelReTau110/template $FOAM_RUN/ReTau110WALE $ cd ReTau110WALE $ gedit caseSettings 6. If you use the test case of channel flow supplied in the V&V repository, copy the template case and edit the seung. controlDict { deltaT 0.002; endTime 0.022; libs "libincompressibleWALE.so"; }
- 31. Simula*on of channel flow at Reτ = 110 turbulenceProperties { simulationType LESModel; } LESProperties { LESModel WALE; delta cubeRootVol; } The original caseSeungs is for DNS simula*on on large parallel machine. You had beser to change other parameters in blockMeshDict and decomposeParDict.
- 32. Simula*on of channel flow at Reτ = 110 $ ./Allrun 7. Aper checking other numerical condi*ons and parameter, run the solver. 8. If the solver calcula*on is normally finished, you check the logs and visualize the flow field with ParaView. If the integra*on *me is not sufficient for the flow field to become fully developed state, run longer simula*ons.
- 33. Exercise 2: Implementa*on of coherent structure Smagorisky model
- 34. Original source codes for SGS model $ src $ cd turbulenceModels/incompressible/LES/ $ ls 1. Check the original source code for SGS model. 2. Glance the codes of Smagorinsky model. $ gedit Smagorinsky/Smagorinsky.* 3. In this exercise, we look the codes of dynamic models. $ ls *[Dd]yn* 4. Compare the structures and statements of the related codes (*.C and *.H).
- 35. Private member func*ons: updateSubGridScaleFields void Smagorinsky::updateSubGridScaleFields (const volTensorField& gradU) { nuSgs_ = ck_*delta()*sqrt(k(gradU)); nuSgs_.correctBoundaryConditions(); } void dynLagrangian::updateSubGridScaleFields (const tmp<volTensorField>& gradU) { nuSgs_ = (flm_/fmm_)*sqr(delta())*mag(dev(symm(gradU))); nuSgs_.correctBoundaryConditions(); } void dynOneEqEddy::updateSubGridScaleFields ( const volSymmTensorField& D, const volScalarField& KK ) { nuSgs_ = ck(D, KK)*sqrt(k_)*delta(); nuSgs_.correctBoundaryConditions(); } In Smagorinsky.C In dynLagrangian.C In dynOneEqEddy.C
- 36. Understanding formula*on with codes • What calcula*on, mathema*cal opera*on, and variable are necessary for coherent structure Smagosinsky model (CSM)? Compare the formula*on of models with the related source codes. • In CSM, the second invariant of velocity gradient is used: where € Q = 1 2 ΩijΩij − SijSij( )= − 1 2 ∂uj ∂xi ∂ui ∂xj Sij = 1 2 ∂ui ∂xj + ∂uj ∂xi # $ %% & ' ((, Ωij = 1 2 ∂ui ∂xj − ∂uj ∂xi # $ %% & ' ((
- 37. Coherent structure Smagorinsky model for non-‐ rota*ng flow (NRCSM) • Smagorinsky model (SM) based on an eddy-‐viscosity, • The model parameter C is determined as follows: with where NRCSM model is invalid for rota*ng flow. € C = C1 | FCS |3/ 2 € C1 = 1 20 , FCS = Q E € τij a = −2CΔ2 | S | Sij (τij a = −2νt Sij, νt = CΔ2 | S |) E = 1 2 ΩijΩij + SijSij( )= 1 2 ∂ui ∂xj $ % && ' ( )) 2
- 38. Coherent structure Smagorinsky model (CSM) • Smagorinsky model (SM) based on an eddy-‐viscosity, • The model parameter C is determined as follows: with where Improved CSM model is valid for rota*ng flow. € C = C2 | FCS |3/ 2 FΩ € C2 = 1 22 , FCS = Q E , FΩ =1− FCS € τij a = −2CΔ2 | S | Sij (τij a = −2νt Sij, νt = CΔ2 | S |) E = 1 2 ΩijΩij + SijSij( )= 1 2 ∂ui ∂xj $ % && ' ( )) 2
- 39. Seung for making new library $ run $ cd ../src/libraries $ cp -‐r incompressibleWALE/WALE/ ./NRCSM $ cp –r incompressibleWALE/Make ./NRCSM $ cd NRCSM $ rename WALE NRCSM * $ rm –r NRCSM.dep $ rm –rf Make/linux64Gcc47DPOpt $ gedit Make/files 1. Copy the source code of WALE model. Compile them. NRCSM.C LIB = $(FOAM_USER_LIBBIN)/libNRCSM $ sed –i ‘s/WALE/NRCSM/g’ NRCSM.C $ sed –i ‘s/WALE/NRCSM/g’ NRCSM.H
- 40. Seung for making new library $ wmake libso $ ls $FOAM_USER_LIBBIN If you find the renamed and recompiled library (libNRCSM.so), you are ready to make a new library for the NRCSM. 2. You can easily learn the codes for calcula*ng the Q and E terms from the postProcessing u*li*es. There are two ways of calcula*ng Q, that is, with velocity gradient tensor and with SS and ΩΩ terms. $ util $ cd postProcessing/velocityField/Q $ gedit Q.C &
- 41. Introducing model coefficient C1 $ run $ cd ../src/libraries/NRCSM/ $ gedit NRCSM.C NRCSM.H 3. Replace all ‘cw’ with ‘c1’ (gedit or sed), and change the value to 0.05. c1_ ( dimensioned<scalar>::lookupOrAddToDict ( "c1", coeffDict_, 0.05 ) ) NRCSM.C $ wmake libso
- 42. Q and E calcula*ons 4. In NRCSM.C, insert the calcula*on of Q and E. Copy&Paste the corresponding sec*on from Q.C. Save and Compile them. volScalarField Q ( 0.5*(sqr(tr(gradU)) -‐ tr(((gradU)&(gradU)))) ); volScalarField E ( 0.5*(gradU && gradU) ); NRCSM.C $ gedit NRCSM.C $ wmake libso
- 43. FCS and C calcula*ons 5. In NRCSM.C, insert the calcula*on of FCS and C (coefficient of eddy viscosity model). Save and Compile them. volScalarField Fcs ( Q/ max(E,dimensionedScalar("SMALL",E.dimensions(),SMALL)) ); volScalarField ccsm_ ( c1_*pow(mag(Fcs),1.5) ); NRCSM.C $ gedit NRCSM.C $ wmake libso
- 44. νSGS calcula*on 6. In NRCSM.C, modify the nuSGS_ calcula*on. Look the other updateSubGridScaleFields func*ons in the dynamic models. nuSgs_ = ccsm_*sqr(delta())*mag(dev(symm(gradU))); NRCSM.C Save and compile them. $ wmake libso 7. Finally, comment out or delete unnecessary statements (the calcula*ons for WALE model). Save and compile them. $ wmake libso $ gedit NRCSM.C
- 45. kSGS calcula*on //-‐ Return SGS kinetic energy // calculated from the given velocity gradient tmp<volScalarField> k(const tmp<volTensorField>& gradU) const { return (2.0*c1_/ce_)*sqr(delta())*magSqr(dev(symm(gradU))); } NRCSM.H 8. The calcula*on of kSGS is invalid, but the value of kSGS is not actually used in LES with NRCSM model. If you requires a proper kSGS, consult the paper of Kobayashi (PoF, 2005).
- 46. Valida*on with channel flow $ run $ cp –r $FOAM_TUTORIALS/incompressible/pimpleFoam/ channel395/ ./ReTau395NRCSM $ cd ReTau395NRCSM 9. The standard tutorial case of channel flow at Reτ = 395: copy the tutorial case file into your run directory. 10. Edit constant/LESProper*es and system/controlDict $ gedit constant/LESProperties LESModel NRCSM; printCoeffs on; delta cubeRootVol; ...
- 47. Valida*on with channel flow $ gedit system/controlDict ... libs ("libNRCSM.so"); This line is necessary to call the new NRCSM library in solver. $ ./Allrun 11. Aper checking other numerical condi*ons and parameter, run the solver. 12. If the solver calcula*on is normally finished, you check the logs and visualize the flow field with ParaView, and plot the fields profile generated by postChannel.
- 48. Addi*onal works 1. Compile and test the WALE model supplied from openfoam-‐dev. Prepare a Make directory by yourself. 2. Implementa*on of CSM model. Add FΩ term and C2 coefficient. 3. Calcula*on of Q and E terms with SS and ΩΩ terms. Compare the results with the solu*on of Exercise 2. 4. Valida*on of customized model with other flow fields such pipe, backstep, cylinder, and rota*ng flow.
- 49. References • OpenFOAM User Guide • OpenFOAM Programmer’s Guide • 梶島, 乱流の数値シミュレーション 改訂版, 養賢堂 (2014). • P. R. Spalart et al., “Comments on the Feasibility of LES for Wings, and on a Hybrid RANS/LES Approach”, 1st ASOSR CONFERENCE on DNS/LES (1997). • P. R. Spalart, “Young-‐Person’s Guide to Detached-‐Eddy Simula*on Grids”, NASA CR-‐2001-‐211032 (2001). • F. Nicoud and F. Ducros, “Subgrid-‐scale modelling based on the square of velocity gradient tensor”, Flow, Turbulence and Combus*on, 62, pp.183-‐200 (1999).
- 50. References • 小林, “乱流構造に基づくサブグリッドスケールモデルの開 発”, ながれ, 29, pp.157-‐160 (2010). • H. Kobayashi, “The subgrid-‐scale models based on coherent structures for rota*ng homogeneous turbulence and turbulent channel flow”, Phys. Fluids, 17, 045104 (2005). • H. Kobayashi, F. Ham and X. Wu, “Applica*on of a local SGS model based on coherent structures to complex geometries”, Int. J. Heat Fluid Flow, 29, pp.640-‐653 (2008).