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phase-fraction equation in multiphase model

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Old   March 23, 2017, 05:11
Default phase-fraction equation in multiphase model
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zzj
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zhengzongji
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hi, Dear foamers

I have just learned phase-fraction equation in two-phase model
It is ez to understand: ∂(alpha)+∇·(U·alpha) = 0

but when it turns to multiphase model, I can hardly figure out what the equation will change into.

Could anybody gives me some suggestions or gives some links related to this?

thanks

zzj
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Old   March 23, 2017, 12:41
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I think it is the same for each of the i phases:
∂(alpha_i)+∇·(U·alpha_i) = 0
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Old   March 24, 2017, 05:00
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Quote:
Originally Posted by zzj View Post
hi, Dear foamers

I have just learned phase-fraction equation in two-phase model
It is ez to understand: ∂(alpha)+∇·(U·alpha) = 0

but when it turns to multiphase model, I can hardly figure out what the equation will change into.

Could anybody gives me some suggestions or gives some links related to this?

thanks

zzj
you can refer to Chapter 4 of Dr. Henrik Rusche's Thesis on Computational Fluid Dynamics of Dispersed Two-Phase Flows at High Phase Fractions
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Old   March 27, 2017, 02:17
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Quote:
Originally Posted by decah View Post
I think it is the same for each of the i phases:
∂(alpha_i)+∇·(U·alpha_i) = 0

Dear decah,thanks for your replying.

In fact,the code shows that in multiphase mixture model we need to solve a variable named "alphaPhiCorr".

but "alphaPhiCorr" need all the phases to solve.
(It means we can not solve fraction equation phase by phase)

And the fraction equation is:
∂(alpha)+∇·(alphaPhiCorr) = 0.(I get the equation from multiphaseMixture.c)

MULES::limit
(
1.0/mesh_.time().deltaT().value(),
geometricOneField(),
alpha,
phi_,
alphaPhiCorr,
zeroField(),
zeroField(),
1,
0,
true
);

And alphaPhiCorr is solved by each phase,following is the code:
alphaPhiCorrs.set
(
phasei,
new surfaceScalarField
(
"phi" + alpha.name() + "Corr",
fvc::flux
(
phi_,
alpha,
alphaScheme
)
)
);

surfaceScalarField& alphaPhiCorr = alphaPhiCorrs[phasei];

forAllIter(PtrDictionary<phase>, phases_, iter2)
{
phase& alpha2 = iter2();

if (&alpha2 == &alpha) continue;

surfaceScalarField phir(phic*nHatf(alpha, alpha2));

alphaPhiCorr += fvc::flux
(
-fvc::flux(-phir, alpha2, alpharScheme),
alpha,
alpharScheme
);
}

I do not know what does the alphaPhiCorr mean.

May be a mathematical formula can help easier understanding.

Last edited by zzj; March 27, 2017 at 03:22.
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Old   March 27, 2017, 02:22
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Dear kera,thanks for your help.

I am reading the essay.

I will reply after reading.

thanks again.
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Old   March 27, 2017, 03:18
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Quote:
Originally Posted by kera View Post
you can refer to Chapter 4 of Dr. Henrik Rusche's Thesis on Computational Fluid Dynamics of Dispersed Two-Phase Flows at High Phase Fractions
Hi,kera

I have finished reading.

Unfortunately,The paper only gives the equation of two phases model,
I can hardly figure out the equation in multiphase model.
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Old   April 5, 2017, 04:33
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Finally,I figure out the equations

In fact, Decah's idea is right, we just need to solve each phase.
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