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Equation Solving in Multiphase Flow

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Old   May 21, 2013, 05:14
Default Equation Solving in Multiphase Flow
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Dear foamers,

I would like to know how are the Navier-Stokes equations solved in a multiphase flow.

Let's consider a liquid/air flow. When a mesh is full of liquid or air, the equation resolution is similar to a monophasic fluid flow.

But when a cell is partially filled with liquid and gas, are the equations solved for each phase fraction? Maybe the density and other parameters are averaged for each cell?

Thank you for your time,
Andreas
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Old   May 21, 2013, 07:22
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Hi Andreas,

Ive been working with the interFoam solver many times.

For the density you are creating a averaged density in that cell for the beginning:

Code:
00037     const dimensionedScalar& rho1 = twoPhaseProperties.rho1();
00038     const dimensionedScalar& rho2 = twoPhaseProperties.rho2();
00039 
00040 
00041     // Need to store rho for ddt(rho, U)
00042     volScalarField rho
00043     (
00044         IOobject
00045         (
00046             "rho",
00047             runTime.timeName(),
00048             mesh,
00049             IOobject::READ_IF_PRESENT
00050         ),
00051         alpha1*rho1 + (scalar(1) - alpha1)*rho2,
00052         alpha1.boundaryField().types()
00053     );
00054     rho.oldTime();
First you extract the value of the density for phase1 and phase2 out of the properties file and then creating a averaged density:

Code:
alpha1*rho1 + (scalar(1) - alpha1)*rho2

After that every time step execute the following line:
Code:
00082         twoPhaseProperties.correct();
In that function (object=twoPhaseProperties; function=correct()) you should find the calculation of the thermophysical variables depending on Phase1 and Phase2.

Hope that is helpful.

Tobi
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Old   May 21, 2013, 14:01
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Hello Tobi, and thank you for your answer.

I am working on interFoam as well!

What you are saying is that the density is averaged on each cell automatically?
What about other parameters? Is pressure averaged as well?

And finally, are the Navier-Stokes solved for these averaged values? Or maybe for each phase fraction on each cell.

Thank you,
Andreas
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Old   May 21, 2013, 14:13
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Hi,

first
Code:
p == p_rgh + rho*gh;
So you can see that p is calculated with the averaged density.

and p_rgh is calculated as:
Code:
        fvScalarMatrix p_rghEqn
        (
            fvm::laplacian(rAUf, p_rgh) == fvc::div(phiHbyA)
        );
The variables rAUf, phiHbyA is calculated in pEqn.H befor.
I am familiar with the code of standard solvers for compressible and incompressible flows but not for multiphase.

For that I can not give you an exact answer.


For the velocity:
Code:
    fvVectorMatrix UEqn
    (
        fvm::ddt(rho, U)
      + fvm::div(rhoPhi, U)
      + turbulence->divDevRhoReff(rho, U)
    );

    UEqn.relax();
As you can see there are the averaged values again.

But the averages are just in those cells with 0 < alpha < 1
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