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how to calculate the interface normal between mulitphase

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Old   October 19, 2018, 23:31
Question how to calculate the interface normal between mulitphase
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Lei Zhou
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Hello everyone:
I feel confused about the calculation of interface normal between mulitphase.
It's the source code in line 1150-1171 at https://www.openfoam.com/documentati...8C_source.html
/************************************************** *******************/
Foam::tmp<Foam::surfaceVectorField> Foam:haseSystem::nHatfv
(
const volScalarField& alpha1,
const volScalarField& alpha2
) const
{

surfaceVectorField gradAlphaf
(
fvc::interpolate(alpha2)*fvc::interpolate(fvc::gra d(alpha1))
- fvc::interpolate(alpha1)*fvc::interpolate(fvc::gra d(alpha2))
);

const dimensionedScalar deltaN
(
"deltaN",
1e-8/pow(average(mesh_.V()), 1.0/3.0)
);

// Face unit interface normal
return gradAlphaf/(mag(gradAlphaf) + deltaN);
}
/************************************************** **/
What's the meaning behind the code?
My understanding is that the grad(alpha1) and -grad(alpha2) both are approximation of interface normal from phase1 to phase2. Then, the linear combination of grad(alpha1) and -grad(alpha2) is still a approximation of interface normal from phase1 to phase2. So the premultiply factors( alpha2, alpha1) are weighted factor.
Is my understanding right?
Is there any other explanation?

Last edited by joe1949; October 20, 2018 at 10:21.
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Old   December 9, 2018, 08:13
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Lei Zhou
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Self answering :

Both grad(alpha1)/alpha1 and -grad(alpha2)/alpha2 are the normal from alpha1 to alpha2. Then their sum grad(alpha1)/alpha1 + ( -grad(alpha2)/alpha2 ) are the interface normal.
considering that the division operation is time-comsuming. So we can use alpha1*alpha2 to times ( grad(alpha1)/alpha1 + ( -grad(alpha2)/alpha2 ) ) to eliminate the denominator, because the magnitude of the normal can be uniformization. The result is alpha2*fvc::grad(alpha1) - alpha1*fvc::grad(alpha2)
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Old   October 29, 2021, 05:09
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JungHoon Lee
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Quote:
Originally Posted by joe1949 View Post
Self answering :

Both grad(alpha1)/alpha1 and -grad(alpha2)/alpha2 are the normal from alpha1 to alpha2. Then their sum grad(alpha1)/alpha1 + ( -grad(alpha2)/alpha2 ) are the interface normal.
considering that the division operation is time-comsuming. So we can use alpha1*alpha2 to times ( grad(alpha1)/alpha1 + ( -grad(alpha2)/alpha2 ) ) to eliminate the denominator, because the magnitude of the normal can be uniformization. The result is alpha2*fvc::grad(alpha1) - alpha1*fvc::grad(alpha2)



Dear Lei Zhou,


thank you so much for great information. I know this post seem quite old but I would like to ask you wehre did you get this equation? Could you please refer a literature for this?


Thanks so much in advance!
JungHoon
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