# phase-fraction equation in multiphase model

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 March 23, 2017, 05:11 phase-fraction equation in multiphase model #1 New Member   zhengzongji Join Date: Feb 2017 Posts: 9 Rep Power: 2 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

 March 23, 2017, 12:41 #2 Member   Declan Join Date: Oct 2016 Location: Ireland Posts: 32 Rep Power: 2 I think it is the same for each of the i phases: ∂(alpha_i)+∇·(U·alpha_i) = 0

March 24, 2017, 05:00
#3
Member

Ricky
Join Date: Jul 2014
Location: Germany
Posts: 40
Rep Power: 4
Quote:
 Originally Posted by zzj 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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March 27, 2017, 02:17
#4
New Member

zhengzongji
Join Date: Feb 2017
Posts: 9
Rep Power: 2
Quote:
 Originally Posted by decah I think it is the same for each of the i phases: ∂(alpha_i)+∇·(U·alpha_i) = 0

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.

 March 27, 2017, 02:22 #5 New Member   zhengzongji Join Date: Feb 2017 Posts: 9 Rep Power: 2 Dear kera,thanks for your help. I am reading the essay. I will reply after reading. thanks again.

March 27, 2017, 03:18
#6
New Member

zhengzongji
Join Date: Feb 2017
Posts: 9
Rep Power: 2
Quote:
 Originally Posted by kera 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

Unfortunately,The paper only gives the equation of two phases model,
I can hardly figure out the equation in multiphase model.

 April 5, 2017, 04:33 #7 New Member   zhengzongji Join Date: Feb 2017 Posts: 9 Rep Power: 2 Finally,I figure out the equations In fact, Decah's idea is right, we just need to solve each phase.

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