- 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. • 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. 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. 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. 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. 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. 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. 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. 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. 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. • 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. 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.
- 15. • 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
- 16. 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
- 17. 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
- 18. ∂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
- 19. • 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
- 20. 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
- 21. Calc.１（Bubble in Cavity） VOF S-‐CLSVOF Ini;al condi;on
- 22. Calc.１（Bubble in Cavity） VOF S-‐CLSVOF
- 23. 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
- 24. VOF S-‐CLSVOF Calc. Time about 1.3 2mes longer in S-‐CLSVOF Calc. 2（Dam Break）
- 25. 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）
- 26. 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).
- 27. 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
- 28. Laplace Pressure (VOF) • Result (VOF(Coarse)) black line (alpha = 0.5)
- 29. • Result (VOF(Fine)) Laplace Pressure (VOF) black line (alpha = 0.5)
- 30. 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
- 31. • Result (SCLSVOF(Coarse)) Laplace Pressure (S-‐‑‒CLSVOF) black line (alpha = 0.5)
- 32. • Result (SCLSVOF(Fine)) Laplace Pressure (S-‐‑‒CLSVOF) black line (alpha = 0.5)
- 33. 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