coupling level-set with volume of fluid - openfoam version...

Coupling Level-Set with Volume ofFluid

OpenFOAM version 2.3.x

Sankar Menon

Chalmers University of Technology

OpenFOAM course 2015January 15, 2016

Outline for section

Motivation

Theoretical BackgroundNavier-Stokes and continuityVolume Of Fluid advective

ImplementationCase folderInitialisingHeader filesSurface tension correctionsclsVOFFoam

Test Case

Motivation Sankar Menon OFv2.3.x 2/23

Motivation

• Representation of sharp interfaces to capture phenomena atthe interface

• Application of a Surface Capturing method - coupling theVolume of Fluid(VOF) and Level Set(LS).

• VOF is mass conservative and bounded, while LS is thesharper interface capturing but not mass conservative.

• Two solvers developed, sclsVOFFoamsf and sclsVOFFoam.

Working on the OpenFOAM version 2.3.x environment

Motivation Sankar Menon OFv2.3.x 3/23

Outline for section

Motivation



Test Case

Theoretical Background Sankar Menon OFv2.3.x 4/23

NS and continuity equation

∂vi∂xi

= 0,

∂vi∂t

+∂vivj∂xj

= −1

ρ

∂p

∂xj+ ν

∂2vi∂xj∂xj

+ gi + Fσ

where v is the velocity in the tensor from, ν is the kinematicviscosity, Fσ is the volumetric surface tension force, gi is thegravitational acceleration, ρ is the density and p is the pressure.

Theoretical Background — Navier-Stokes and continuity Sankar Menon OFv2.3.x 5/23

Volume Of Fluid advective equation

∂α

∂t+∂αvj∂xj

= 0

water : α = 1

air : α = 0

interface : 0 < α < 1

Bringing in the counter gradient compressive term

∂α

∂t+∂αvj∂xj

+∂vcjαβ

∂xj= 0.

where vc ensures compression (vc = vl − vg, l and g stands forliquid and gas, respectively), while the ∂/∂xj guaranteesconservation and αβ guarantees boundedness (β = 1− α).

Theoretical Background — Volume Of Fluid advective Sankar Menon OFv2.3.x 6/23

Level Set function and coupling

φ0 = (2α− 1)Γ

where Γ = 0.75∆x and ∆x meshcell size.Re-initialisation equation

∂φ∂τ = S(φ0)(1−∇φ)

φ(x, 0) = φ(x)

Iteration number, φcorr = ε/∆τInterface width, ε = 1.5∆x

the surface tension will be calculatedas :

Fσ = σκ(φ)δ(φ)∇φ

where σ is the surface tensioncoefficient and δ is the Diracfunction to limit the influence ofsurface tension within the interface.

The physical properties can be calculated using the Heaviside function

H(φ) =

0, ifφ < ε12 [1 + φ

ε + 1π sin(πφε )] if φ ≥ 1

1, ifφ > ε


Density and viscosity correction,VOF method :

ρ = αρl + (1− α)ρg

µ = αµl + (1− α)µg

CLSVOF method :

ρ = Hρl + (1−H)ρg

µ = Hµl + (1−H)µg

where l is the liquid and g is the gas.


Mesh

0.00

0.00

0.00

0.00

0.00

0.00

0.03

0.05

0.30

0.30

0.00

0.25

0.80

0.90

1.00

0.05

0.80

0.90

0.90

1.00

1.00

1.00

1.00

1.00

1.00

VOF

1 2 3 4 5

1

2

3

4

5

-0.75

-0.75

-0.75

-0.75

-0.75

-0.75

-0.70

-0.68

-0.30

-0.30

-0.75

-0.38

0.45

0.60

0.75

-0.68

0.45

0.60

0.60

0.75

0.75

0.75

0.75

0.75

0.75

psi0

1 2 3 4 5

1

2

3

4

5

-3.75

-3.58

-3.47

-2.06

-2.06

-3.75

-3.05

-1.50

-1.22

-0.94

-3.61

-1.58

1.36

2.06

1.78

-0.94

1.64

3.19

3.47

3.75

-1.59

2.62

3.19

3.19

3.75

psi

1 2 3 4 5

1

2

3

4

5

0.00

0.00

0.00

0.02

0.02

0.00

0.00

0.09

0.14

0.21

0.00

0.08

0.88

0.98

0.95

0.21

0.93

1.00

1.00

1.00

0.08

1.00

1.00

1.00

1.00

H

1 2 3 4 5

1

2

3

4

5


Numerical Algorithm

Initialize velocity, pressure and liquid volumefraction, and update density and viscosity fields

Constructing φ from α

Start time

PIMPLE loop

Advection of volume fraction (α)

Update density and viscosity withnew liquid volume fraction value

reconstructing φ from α

Velocity equation / momentum predictor equation

Pressure correction / PISO

Continue for a new time step?

Finish

Initialize variables withprevious time step values

CLSVOFsf CLSVOFor

Yes

Yes

No

No


Outline for section

Motivation



Test Case

Implementation Sankar Menon OFv2.3.x 11/23

createFields.H

New variables areinitialised in createFields.H.H heavisidedelta, δ Dirac functionpsi, φ LS functionC curvatureand constants aredeltaX, ∆x mesh cell size,gamma, γ small non-dimensional number

of initialising LS,epsilon, ε interface thickness,deltaTau, ∆τ artificial time step,dimChange for phi reinitialisation fraction,sigma, σ recalled since the surface tension

is calculated with LS.nu1 ν1 and nu2, ν2 recalled for viscosity correction

for CLSVOF

Implementation — Initialising Sankar Menon OFv2.3.x 13/23

Solver header files

mappingPsi.H

• Initialise the LS function φ

solveLSFunction.H

• Re-initialise the LS, φ

• Calculate the Dirac function, δ

• Calculate the heaviside function, H

calcNewCurvature.H

• Calculate the interface normal

• Calculate the curvature of surface tension

updateFlux.H

• Update the convective flux in NS equation.

Implementation — Header files Sankar Menon OFv2.3.x 14/23

Surface tension correction

In UEqn.H, the new surface tension force is computed.

UEqn

==

fvc::reconstruct

(

(

// mixture.surfaceTensionForce()

sigma*fvc::snGrad(psi)*fvc::interpolate(C)*fvc::interpolate(delta)

- ghf*fvc::snGrad(rho)

- fvc::snGrad(p_rgh)

) * mesh.magSf()

)

And also in pEqn.H.

surfaceScalarField phig

(

(

// mixture.surfaceTensionForce()

sigma*fvc::snGrad(psi)*fvc::interpolate(C)*fvc::interpolate(delta)

- ghf*fvc::snGrad(rho)

)*rAUf*mesh.magSf()

);

This concludes the sclsVOFFoamsf solver!

Implementation — Surface tension correction Sankar Menon OFv2.3.x 15/23

sclsVOFFoam

Now we move to the sclsVOFFoam, where the viscosity anddensity are corrected.DensityThe density is recomputed by adding the below code at the end ofsolveLSFunction.H.

const volScalarField limitedH

(

"limitedH",

min(max(H, scalar(0)), scalar(1))

);

rho == limitedH*rho1 + (1.0 - limitedH)*rho2;

Implementation — sclsVOFFoam Sankar Menon OFv2.3.x 16/23

sclsVOFFoam

Viscosity Also, the viscosity is recomputed by adding the followingin the end of solveLSFunction.H.

volScalarField& nuTemp = const_cast<volScalarField&>(mixture.nu()());

nuTemp == limitedH*nu1 + (1.0 - limitedH)*nu2;

Limiting H The heaviside is kept in the limited region of0 < H < 1 by addingH == limitedH;

in solveLSFunction.H.


sclsVOFFoamConvective Flux

surfaceScalarField phiH

(

fvc::flux

(

phi,

H,

alphaScheme

)

+ fvc::flux

(

-fvc::flux(-phir, scalar(1) - H, alpharScheme),

H,

alpharScheme

)

);

MULES::explicitSolve(H, phi, phiH, 1, 0);

rhoPhiH = phiH*(rho1 - rho2) + phi*rho2;

}

Thus rhoPhiH is computed instead of rhoPhi. This rhoPhiH is then fed into the

UEqn.H


sclsVOFFoam

Overwriting Alpha

// reInitialise the alpha equation

if (runTime.outputTime())

{

Info<<"Overwriting alpha" << nl << endl;

alpha1 = H;

volScalarField& alpha10 = const_cast<volScalarField&>(alpha1.oldTime());

alpha10 = H.oldTime();

}


Outline for section

Motivation



Test Case

Test Case Sankar Menon OFv2.3.x 20/23

Bubble column

Figure : Initial configuration and boundaryconditions for the test case.

Initial configurationand boundaryconditions for the testcase


Running the case

Download the tar package to the path -$WM_PROJECT_USER_DIR/applications/solvers/multiphase/.

tar -zxvf sclsVOFFoam.tar.gz

cd sclsVOFFoam

wmake

Extract the case file that is downloaded from the portal.

tar -zxvf bubblecol.tar.gz

cd bubblecol


Results


coupling level-set with volume of fluid - openfoam version...

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