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Setting and Usage of OpenFOAM multiphase solver (S-CLSVOF)

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Setting and Usage of OpenFOAM multiphase solver (S-CLSVOF)

  1. 1. Setting  and  Usage  of   OpenFOAM  multiphase   solver(S-‐‑‒CLSVOF) Graduate  school  of  Engineering  Science   Osaka  Univ.   D1 Takuya  Yamamoto 30th  OpenCAE  study  mee2ng  @  Kansai,  Japan   2014/05/31 Ver.  3   updated  in  2015/7/20
  2. 2. •  Improved  solver  of  OpenFOAM  interFoam(VOF)   •  Improved  surface  tension  model(CSF  model)  by   using  re-­‐ini2aliza2on  equa2on  (Level-­‐Set  func2on)   •  Please  refer  the  previous  presenta2on  (In   Japanese)   25th  OpenCAE  study  mee2ng  @  Kansai,  Japan 26th  OpenCAE  study  mee2ng  @  Kansai,  Japan J. U. Brackbill, D. B. Kothe, C. Zemach, J. Comput. Phys. 100 (1992) 335–354. CSF  model VOF C. W. Hirt, B. D. Nichols, J. Comput. Phys. 39 (1981) 201–225. S-­‐CLSVOF(Simple  Coupled  Volume  Of  Fluid  with  Level  Set)  method What  is  S-‐‑‒CLSVOF  solver   (sclsVOFFoam)?
  3. 3. Generally Level-­‐Set  method   •  low  volume  preserva2ve  quality   •  Normal  unit  vector  (high  accuracy) VOF  method   •  high  volume  preserva2ve  quality   •  Normal  unit  vector  (low  accuracy)   M. Sussman, P. Smereka, S. Osher, J. Comput. Phys. 114 (1994) 146–159. CLSVOF(Coupled  Volume  Of  Fluid  with  Level  Set)  method S-­‐CLSVOF(Simple  Coupled  Volume  Of  Fluid  with  Level  Set)  method Simple  coupling High  accuracy,  however,  slightly-­‐low  volume  preserva2ve  quality BeYer  than  VOF  method,  High  volume  preserving  quality What  is  S-‐‑‒CLSVOF  solver   (sclsVOFFoam)?
  4. 4. Specifically     In  A.  Albadawi  et  al.,  Int.  J.   Mul2phase  Flow,  53,  11-­‐28  (2013).   Implemented  the  S-­‐CLSVOF  method   What  is  S-‐‑‒CLSVOF  solver   (sclsVOFFoam)?
  5. 5. 0 0 0 0 0 0 0 0 0.1 0.3 0 0 0.5 0.95 1.0 0 0.4 1.0 1.0 1.0 0 0.7 1.0 1.0 1.0 VOF What  is  S-‐‑‒CLSVOF  solver   (sclsVOFFoam)? re-­‐ini2aliza2on  Eq. Level-­‐Set  func2on
  6. 6. Version  in  OpenFOAM •  OpenFOAM-‐‑‒2.0.x •  OpenFOAM-‐‑‒2.1.1 •  OpenFOAM-‐‑‒2.1.x Validated  only  above  versions Released  site  (solver  and  tutorials) hYps://bitbucket.org/nunuma/public/src
  7. 7. Usage  (Solver  compilation) 1.  Copy  sclsVOFFoam  solver  to  applica2ons/ solvers  (cp  -­‐r  sclsVOFFoam  applica2ons/ solvers)   2.  Change  directory  to  sclsVOFFoam  (cd   sclsVOFFoam)   3.  Compile(wmake)   4.  Finish  solver  compila2on Please  type  sclsVOFFoam
  8. 8. Usage  (dam  break) cp  -­‐r  $FOAM_TUTORIALS/mul2phase/interFoam/laminar/damBreak  . copy  damBreak  folder edit  damBreak  folder 1.  Edit  constant/transportProper2es   Add  the  following  commnts  in  transportProper2es   deltaX                    deltaX  [  0  0  0  0  0  0  0  ]  0.01;     2.  Add  psi(Level-­‐Set  func2on)  in  0  folder  (ini2al  condi2on)   (Based  on  alpha1)   cp  -­‐r  0/alpha1  0/psi         3.  Execute  sclsVOFFoam (deltaX  value  is  the  cell  width   near  interface  posi2on) Edit  psi(Non-­‐dimension,  Boundary  condi2ons  are  zeroGradient)
  9. 9. Usage  (dam  break) Change  based  on  interFoam  tutorial  case   1.  In  transportProper2es,  you  must  write  grid  spacing   (DeltaX).   2.  You  must  define  ini2al  condi2ons  and  boundary   condi2ons  of  Level-­‐Set  func2on(psi). Cau;on   •  Boundary  condi2on  for  Level-­‐Set  func2on  have  not   been  implemented.   (You  can’t  use  fixed  contact  angle.  )   •  You  can  use  only  zero  gradient  for  level  set  func2on.  
  10. 10. Summary •  Advance  boundary  conditions  of  Level-‐‑‒ Set  function  have  not  been   implemented. •  By  changing  a  tutorial  of  interFoam,   one  can  easily  execute  the  solver.
  11. 11. • If  there  are  something   wrong,  please  send  e-‐‑‒mail   to  me. • Please  correct  my  English!!   • Please  teach  me!! tak_1031@hotmail.co.jp E-­‐mail  address
  12. 12. References 1.  G. Tryggvason, R. Scardovelli and S. Zaleski, Direct Numerical Simulations of Gas-Liquid Multiphase Flows, Cambridge University Press, Cambridge 2011. 2.  C. W. Hirt, B. D. Nichols, J. Comput. Phys. 39 (1981) 201– 225. 3.  J. U. Brackbill, D. B. Kothe and C. Zemach, J. Comput. Phys. 100 (1992) 335–354. 4.  A. Albadawi et al., Int. J. Multiphase Flow 53 (2013) 11-28. 5.  M. Sussman, P. Smereka and S. Osher, J. Comput. Phys. 114 (1994) 146–159.
  13. 13. Support   Documentation
  14. 14. •  Governing  Equations Navier-‐‑‒Stokes  Eq. Advection  of  α interFoam  (VOF) sk gP t δσ ρν σ σ nF Fvvv v = ++∇+−∇=∇⋅+ ∂ ∂ 2 ::  liquid  phase   ::  interface   ::  gas  phase 1=α 0=α 10 <<α Fluid  phase     Gas  phase ( ) 0=⋅∇+ ∂ ∂ l t vα α ( ) 0=⋅∇+ ∂ ∂ vα α t ( )( ) 01 =−⋅∇+ ∂ ∂ g t vα α Subscripts  l,  g  represent  liquid  and  gas  phase ( ) glr gl vvv vvv −= −+= αα 1 Defini;on ρ =αρl +(1−α)ρg µ =αµl +(1−α)µg ( ) 0=⋅∇+ ∂ ∂ vα α t CSF  model
  15. 15. sk gP t δσ ρν σ σ nF Fvvv v = ++∇+−∇=∇⋅+ ∂ ∂ 2 ::  liquid  phase   ::  interface   ::  gas  phase 1=α 0=α 10 <<α ( ) ( )( ) 01 =−⋅∇+⋅∇+ ∂ ∂ r t vv ααα α In  alphaEqn.H,  the  defini2on  is   wriYen.   ∂α ∂t + ∇⋅ αv( )= 0 This  term  works  only  interface  area   because  (1-­‐α)α is  included. ρ =αρl +(1−α)ρg µ =αµl +(1−α)µg interFoam  (VOF) •  Governing  Equations Navier-‐‑‒Stokes  Eq. Advection  of  α
  16. 16. S-‐‑‒CLSVOF  method ∂v ∂t +v⋅∇v = −∇P +ν∇2 v + Fσ + ρg ::  liquid  phase   ::  interface   ::  gas  phase 1=α 0=α 10 <<α Level-­‐Set  func2on  φ φ0 = (2α −1)⋅Γ Γ  ;  non-­‐dimension  number Γ = 0.75Δx Δx  ;  non-­‐dimension  number ∂φ ∂τ = S(φ0 ) 1− ∇φ( ) φ x,0( )= φ0 x( ) Re-­‐ini2aliza2on  equa2on ∂α ∂t + ∇⋅ αv( )= 0 ∇φ Itera2on  number  φcorr φcorr = ε Δτ ε =1.5Δx Interface  width  ε ρ =αρl +(1−α)ρg µ =αµl +(1−α)µg α∇ Schema2c •  Governing  Equations Navier-‐‑‒Stokes  Eq. Advection  of  α
  17. 17. ∂v ∂t +v⋅∇v = −∇P +ν∇2 v + Fσ + ρg ::  liquid  phase   ::  interface   ::  gas  phase 1=α 0=α 10 <<α Fσ =σkδ∇φ CSF  model k = −∇⋅nf = −∇⋅ ∇φ( )f ∇φ( )f +δs $ % & & ' ( ) ) ∂α ∂t + ∇⋅ αv( )= 0 Dirac  func;on  δ δ φ( )= 0 δ φ( )= 1 2ε 1+cos πφ ε ! " # $ % & ! " # $ % & φ >ε φ ≤ε Heaviside  func;on  H H φ( )= 0 H φ( )= 1 2 1+ φ ε + 1 π sin πφ ε ! " # $ % & ! " # $ % & H φ( )=1 Curvature ρ =αρl +(1−α)ρg µ =αµl +(1−α)µg •  Governing  Equations Navier-‐‑‒Stokes  Eq. Advection  of  α S-‐‑‒CLSVOF  method
  18. 18. •  Governing  Equations Navier-‐‑‒Stokes  Eq. Advection  of  α ∂v ∂t +v⋅∇v = −∇P +ν∇2 v + Fσ + ρg ::  liquid  phase   ::  interface   ::  gas  phase 1=α 0=α 10 <<α ∂α ∂t + ∇⋅ αv( )= 0 H φ( )= 0 H φ( )= 1 2 1+ φ ε + 1 π sin πφ ε ! " # $ % & ! " # $ % & H φ( )=1 ρ =αρl +(1−α)ρg µ =αµl +(1−α)µg ρ = Hρl +(1− H)ρg µ = Hµl +(1− H)µg In  A. Albadawi et al. (2013), no  physical  property  is  updated. φ < −ε φ ≤ ε φ > ε Heaviside  func;on  H S-‐‑‒CLSVOF  method
  19. 19. Ex.1(Bubble  in  Cavity) 0.1  m 0.1  m 0.5  m/s 0.02  m liquid  1 liquid  2 Physical  Proper;es   Dynamic  viscosity 1.0  x  10-­‐3  m2/s   Surface  tension  10  mN/m  Purpose   Deforma2on  by  shear  stress   (No  Buoyancy  flow   Same  physical  proper2es  area  used  in  both     liquid  1  and  liquid  2) Calc.1   interFoam  (VOF)   Calc.  2   sclsVOFFoam(S-­‐CLSVOF) Numerical  Grid   200  x  200  (x,  y  direc2on) x y
  20. 20. Calc.1(Bubble  in  Cavity) VOF S-­‐CLSVOF Ini;al  condi;on
  21. 21. Calc.1(Bubble  in  Cavity) VOF S-­‐CLSVOF
  22. 22. Calc.  2(Dam  Break) 0.584  m 0.584  m 0.048  m 0.292  m 0.292  m 0.1461  m phase  1   Dynamic  viscosity 1  x  10-­‐6  m2/s   Density  1000  kg/m3 phase  1 phase  2 phase  2   Dynamic  viscosity 1.48  x  10-­‐5  m2/s   Density  1  kg/m3 Surface  tension 70  mN/m  
  23. 23. VOF S-­‐CLSVOF Calc.  Time  about  1.3  2mes  longer  in  S-­‐CLSVOF Calc.  2(Dam  Break)
  24. 24. VOF S-­‐CLSVOF 0.2  s 0.2  s 0.3  s 0.3  s 0.4  s 0.4  s 0.5  s 0.5  s Calc.  2(Dam  Break)
  25. 25. Laplace  Pressure •  Verification (A. Albadawi et al.(2013)) Laplace  Pressure Laplace  Pressure  is  shown  as  following   equation. Δp =γ 1 R + 1 R' ! " # $ % & Δp = p0 in − p∞ out p0 in p∞ out Pressure  in  bubble Pressure  at  outside  of  bubble Compare  the  numerical  and  analy2cal  pressures M. M. Francois et al., J. Comput. Phys., 213, 141-173 (2006).
  26. 26. Verification  problem  1 •  Numerical  domain Δpexact =γ 1 R + 1 R' ! " # $ % & = 2 Δp = p0 in − p∞ out p0 in p∞ out Pressure  at  the  bubble  center Pressure  at  wall uniform  spacing  grid   DX  =  0.001  m  (Fine)              =  0.0005  m  (Coarse) 0.05  m 0.05  m 0.01  m Laplace  pressure(Theory) Physical  Proper;es   γ  0.01  N/m   Laplace  pressure  (Calc.) ρg  1  kg/m3   µg  10-­‐5  kg/(ms)   ρl  1000  kg/m3   µl  10-­‐3  kg/(ms)   gas liquid zero  gravity  condi;on   calc.  ;me   0.1  sec.     (Δt  =  1x10-­‐5  sec.  (Coarse))   (Δt  =  5x10-­‐6  sec.  (Fine))   rela;ve  pressure  error  E0   E0 = Δp− Δpexact Δpexact
  27. 27. Laplace  Pressure  (VOF)   •  Result  (VOF(Coarse)) black  line  (alpha  =  0.5)
  28. 28. •  Result  (VOF(Fine)) Laplace  Pressure  (VOF)   black  line  (alpha  =  0.5)
  29. 29. Results  (E0,  VOF) CAlpha 0 1 2 VOF  (Coarse) 25.17 25.23 25.38 VOF  (Fine) 19.34 19.29 19.05 Δpexact =γ 1 R + 1 R' ! " # $ % & = 2 Δp = p0 in − p∞ out p0 in p∞ out E0 = Δp− Δpexact Δpexact E0  depending  on  CAlpha Laplace  pressure(Theory) Laplace  pressure  (Calc.) Pressure  at  the  bubble  center Pressure  at  wall rela;ve  pressure  error  E0  
  30. 30. •  Result  (SCLSVOF(Coarse)) Laplace  Pressure  (S-‐‑‒CLSVOF)   black  line  (alpha  =  0.5)
  31. 31. •  Result  (SCLSVOF(Fine)) Laplace  Pressure  (S-‐‑‒CLSVOF)   black  line  (alpha  =  0.5)
  32. 32. Results  (E0,  S-‐‑‒CLSVOF) E0  depending  on  CAlpha CAalpha 0 1 2 VOF  (Coarse) 25.17 25.23 25.38 VOF  (Fine) 19.34 19.29 19.05 SCLSVOF  (Coarse) 1.557 0.1749 1.752 SCLSVOF  (Fine) 1.496 1.210 0.9390 Δpexact =γ 1 R + 1 R' ! " # $ % & = 2 Δp = p0 in − p∞ out p0 in p∞ out E0 = Δp− Δpexact Δpexact Laplace  pressure(Theory) Laplace  pressure  (Calc.) Pressure  at  the  bubble  center Pressure  at  wall rela;ve  pressure  error  E0  

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