# discretizing void fraction transport equation

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 September 9, 2013, 11:40 discretizing void fraction transport equation #1 New Member   Join Date: Sep 2010 Location: Windsor, Ontario Posts: 17 Rep Power: 9 Hi everybody, I am having a really hard time for discretizing the transport equation for void fraction in OpenFOAM. The equation is as following: d(alpha)/dt+U.Δ(alpha)=Δ.J and J is a function of alpha. I appreciate it if you help me to write it in OpenFOAM format. Thanks.

 September 10, 2013, 02:23 #2 Senior Member   Bernhard Join Date: Sep 2009 Location: Delft Posts: 790 Rep Power: 15 What did you try up until now? Where are you stuck exactly? Have a look at \$FOAM_SOLVERS/basic/scalarTransportFoam

 September 10, 2013, 13:25 #3 New Member   Join Date: Sep 2010 Location: Windsor, Ontario Posts: 17 Rep Power: 9 Thanks for your response. I describe for you the whole story. The equation that I have put in my first post d(alpha)/dt+U.Δ(alpha)=Δ.J is the governing equation for the transport of particles in a suspension due to normal stresses (Δ is the divergence operator here). The normal stress is the J term in the right hand side. The process that I have done to reach the J equation is: SP=-etha0*gamma*ethaN*Q Here, etha0 and ethaN are viscosity, gamma is the magnitude of the strain rate and Q is a tensor. In OpenFOAM format it is : volTensorField SP = -1.0*etha0*sqrt(magSqr(symm(fvc::grad(U))))*ethan*Q To find J, i have done: volVectorField divSP = fvc::div(SP); volVectorField J= (-2.0*aa*aa/9.0/etha0)*fphi*divSP; As you see J is a vector which is calculated based on a divergence process on a tensor field. I do not know if the divergence calculation is correct or not. Having the J vector field, I have written the transport equation of void fraction: fvScalarMatrix alphaEqn ( fvm::ddt(alpha) + fvm::div(phic, alpha, scheme) - fvc::div(J) ); As you see another divergence is applied to J. So now I do not know first: if the two divergence process that I have done are written correctly in OpenFOAM format or not, second: is my transport equation which is the discretized form of the equation presented in my first post correct or not? I appreciate if any body can help me.

 September 11, 2013, 08:27 #4 New Member   Join Date: Sep 2010 Location: Windsor, Ontario Posts: 17 Rep Power: 9 any answer?!

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