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Customization of LES turbulence model in OpenFOAM

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Customization of LES turbulence model in OpenFOAM

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This slide is the distribution material on the seminar, "Customization of LES turbulence model in OpenFOAM". (June 13 2015 "OpenCAE Local User Group @ Kansai")
http://ofbkansai.sakura.ne.jp/

This slide is the distribution material on the seminar, "Customization of LES turbulence model in OpenFOAM". (June 13 2015 "OpenCAE Local User Group @ Kansai")
http://ofbkansai.sakura.ne.jp/

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Customization of LES turbulence model in OpenFOAM

  1. 1. Customiza*on  of  LES  turbulence    model   in  OpenFOAM yotakagi77   Open  CAE  Local  User  Groups  in  Japan   @Kansai   June  13,  2015,  Osaka  University
  2. 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. 3. Basic  informa*on  on  turbulence  model  
  4. 4. Turbulent  flow  simula*on DNS LES RANS Modeling No Subgrid  scale Reynolds  average Accuracy ◎ ○ △ Cost × ○ ◎ Vortex  (eddy)  field Reynolds  average 4
  5. 5. Turbulent  flow  simula*on DNS LES RANS Modeling No Subgrid  scale Reynolds  average Accuracy ◎ ○ △ Cost × ○ ◎ DNS  grid,  u Reynolds  average 5
  6. 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. 7. Turbulent  flow  simula*on DNS LES RANS Modeling No Subgrid  scale Reynolds  average Accuracy ◎ ○ △ Cost × ○ ◎ Filtering  approach Reynolds  average 7
  8. 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. 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. 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. 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. 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. 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. 14. Tensor  mathema*cs
  15. 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. 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. 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. 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. 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. 20. Exercise  1:  Compiling  and  execu*on  of   WALE  model  
  21. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 33. Exercise  2:  Implementa*on  of  coherent   structure  Smagorisky  model
  34. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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).  

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