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

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

Graduate school of Engineering Science Osaka Univ.

D1Takuya Yamamoto

30th OpenCAE study mee2ng @ Kansai, Japan 2014/05/31

•  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)?

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

BeWer than VOF method, High volume preserving quality


Specifically

In A. Albadawi et al., Int. J. Mul2phase Flow, 53, 11-‐28 (2013). Implemented the S-‐CLSVOF method


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


re-‐ini2aliza2on Eq. Level-‐Set func2on

Version in OpenFOAM

•  OpenFOAM-‐‑‒2.0.x•  OpenFOAM-‐‑‒2.1.1•  OpenFOAM-‐‑‒2.1.x

Validated only above versions

Released site (solver) hWp://o^kansai.sakura.ne.jp/data/sclsVOFFoam21.tar.gz

Released site (tutorial case) hWp://o^kansai.sakura.ne.jp/data/sta2c_VOF.tar.gz

hWp://o^kansai.sakura.ne.jp/data/sta2c_SCLSVOF.tar.gz

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

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)

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.

Summary

•  Advance boundary conditions of Level-‐‑‒Set function have not been implemented.

•  By changing a tutorial of interFoam, one can easily execute the solver.

•  If there are something wrong, please send e-‐‑‒mail to me.• Please correct my English!! • Please teach me!!

[email protected]

E-‐mail address

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.

Support Documentation

•  Governing EquationsNavier-‐‑‒Stokes Eq.

Advection of α

interFoam (VOF)

sk

gPt

δσ

ρν

σ

σ

nF

Fvvvv

=

++∇+−∇=∇⋅+∂

∂ 2

:: liquid phase :: interface :: gas phase

1=α

0=α10 <<α

Fluid phase Gas phase

( ) 0=⋅∇+∂

∂ltvαα

( ) 0=⋅∇+∂

∂ vααt

( )( ) 01 =−⋅∇+∂

∂gtvα

α

Subscripts l, g represent liquid and gas phase

( )

glr

gl

vvv

vvv

−=

−+= αα 1Defini;on

ρ =αρl + (1−α)ρgµ =αµl + (1−α)µg

( ) 0=⋅∇+∂

∂ vααt

CSF model

sk

gPt

δσ

ρν

σ

σ

nF

Fvvvv

=

++∇+−∇=∇⋅+∂

∂ 2


1=α

0=α10 <<α

( ) ( )( ) 01 =−⋅∇+⋅∇+∂

∂rtvv ααα

α

In alphaEqn.H, the defini2on is wriWen.

∂α∂t

+∇⋅ αv( ) = 0 This term works only interface area because (1-‐α)α is included.


interFoam (VOF)


Advection of α

S-‐‑‒CLSVOF method

∂v∂t+v ⋅∇v = −∇P +ν∇2v +Fσ + ρg


1=α

0=α10 <<α

Level-‐Set func2on φ φ0 = (2α −1) ⋅ΓΓ ; non-‐dimension number

Γ = 0.75ΔxΔx ; 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 =

εΔτ

ε =1.5ΔxInterface width ε


α∇

Schema2c


Advection of α

∂v∂t+v ⋅∇v = −∇P +ν∇2v +Fσ + ρg


1=α

0=α10 <<α

Fσ =σ kδ∇φCSF model

k = −∇⋅n f = −∇⋅∇φ( ) f

∇φ( ) f +δ

$

%&&

'

())

∂α∂t

+∇⋅ αv( ) = 0

Dirac func;on δ

δ φ( ) = 0

δ φ( ) = 12ε

1+ cos πφε

!

"#

$

%&

!

"#

$

%&

φ > ε

φ ≤ ε

Heaviside func;on H H φ( ) = 0

H φ( ) = 121+ φ

ε+1πsin πφ

ε

!

"#

$

%&

!

"#

$

%&

H φ( ) =1

Curvature



Advection of α



Advection of α

∂v∂t+v ⋅∇v = −∇P +ν∇2v +Fσ + ρg


1=α

0=α10 <<α

∂α∂t

+∇⋅ αv( ) = 0

H φ( ) = 0

H φ( ) = 121+ φ

ε+1πsin πφ

ε

!

"#

$

%&

!

"#

$

%&

H φ( ) =1


ρ = Hρl + (1−H )ρgµ = Hµl + (1−H )µg

In A. Albadawi et al. (2013), no physical proper2es are updated.

φ < −ε

φ ≤ ε

φ > ε

Heaviside func;on H


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

Calc.１（Bubble in Cavity）

VOF S-‐CLSVOF Ini;al condi;on

Calc.１（Bubble in Cavity）VOF S-‐CLSVOF

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

VOF S-‐CLSVOF

Calc. Time about 1.3 2mes longer in S-‐CLSVOF

Calc. 2（Dam Break）

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）

Laplace Pressure

•  Verification (A. Albadawi et al.(2013))

Laplace PressureLaplace Pressure is shown as following equation.

Δp = γ 1R+1R '

!

"#

$

%&

Δp = p0in − p∞

out p0in

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).

Verification problem 1

•  Numerical domain

Δpexact = γ1R+1R '

!

"#

$

%&= 2

Δp = p0in − p∞

out

p0in

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−ΔpexactΔpexact

Laplace Pressure (VOF)

•  Result (VOF(Coarse))

black line (alpha = 0.5)

•  Result (VOF(Fine))

Laplace Pressure (VOF)


Results (E0, VOF)

CAlpha 0 1 2

VOF (Coarse) 25.17 25.23 25.38

VOF (Fine) 19.34 19.29 19.05


!

"#

$

%&= 2

Δp = p0in − p∞

out

p0in

p∞out


E0 depending on CAlpha




Pressure at wall


•  Result (SCLSVOF(Coarse))

Laplace Pressure (S-‐‑‒CLSVOF)


•  Result (SCLSVOF(Fine))

Laplace Pressure (S-‐‑‒CLSVOF)


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


!

"#

$

%&= 2

Δp = p0in − p∞

out

p0in

p∞out





Pressure at wall


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

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