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What is solid volume fraction correction equation

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Old   June 20, 2016, 03:30
Question What is solid volume fraction correction equation
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I would like to use Matlab to simulate gas-solid fluidized bed, thus, there would be four variables including the gas phase velocity, solid phase velocity, gas phase pressure and solid volume fraction. I used guessed pressure and solid volume fraction in both phase momentum equations to solve for gas velocity and solid velocity, respectively. And then use continuity equation to correct the pressure (just as SIMPLE algorithm suggested). But I don't know how to correct the solid volume fraction. Do anybody have any ideas for that?
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Old   June 22, 2016, 01:22
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Solids volume fraction is problematic field because the solids pressure is a severely nonlinear function as the solids fractions approaches the packing limit. The logic follows that solid mass transport (say, face fluxes of solid) leads to new solids volume fraction which leads to new solids pressure which should lead to correction of the mass transport. You can build a solids pressure (correction) equation much like the gas pressure equation. Or you can transform it into a solids fraction equation (assuming that your solids state relation is invertible). I can tell you from experience that if you have dense regions where the solids pressure is high, there is no easy way to solve this problem.

MFIX uses a solids fraction correction equation with some nonlinear relaxation scheme to try to stabilize the implicit calculation. And it also uses adaptive time stepping to reduce the time step when it encounters convergence problems. This can (and often does) include problems arising from solids packing. I refer you to for full details.

OpenFOAM (I believe) uses a somewhat artificial mechanism to limit solids volume fraction using the MULES limiting scheme. I will admit to not having investigated it fully, but the source code is readily available to review.

Here is how Ansys Fluent implements it:
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gas-solid fluidizd bed, matlab, solid volume fraction

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