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Need Confirmation - Eulerian solver for tiny particules

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Old   August 29, 2012, 11:26
Wink Need Confirmation - Eulerian solver for tiny particules
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HECKMANN Frédéric
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Hi everyone, it would be nice if somebody can give me some confirmations on the general aspect of my algorithm and the "code" that follows (especially the translation of the equations). I want to setup an unsteady Eulerian solver to compute the behavior of tiny particles in a fluid (only the fluid impact the particules motion through the drag).

Nomenclature :
- \alpha volume fraction of the particles
- \vec{u} velocity of the particles
- f(Re) function of the relative Reynolds number
- \tau time respond of the particle
- \vec{V} velocity of the fluid


Continuity equation :
\frac{\partial \alpha}{\partial t} + {\nabla \alpha \vec{u}} = 0

Momentum equation
\frac{\partial \alpha \vec{u}}{\partial t} + {\nabla \alpha \vec{u} \vec{u}} = \frac{f(Re)}{\tau } \alpha (\vec{V} -\vec{u})

The algorithm I have in mind :
1) setup a "phi_alpha" flux equal to \alpha \vec{u}
2) initialize this flux in the createfield with:
Code:
"linearInterpolate(alpha)*linearInterpolate(u) & mesh.Sf()"
3) solve the continuity equation using the following code:
Code:
fvScalarMatrix cEqn
(
fvm::ddt(alpha)
+ fvc::div(alpha_phi)
);
cEqn.solve()
4) update the flux phi_alpha with:
Code:
alpha_phi -= cEqn.flux();
5) compute the relative Reynolds number, the function f(Re) and \tau
6) solve the momentum equation using:
Code:
fvVectorMatrix uEqn
(
fvm::ddt(alpha, u)
+ fvm::div(alpha_phi, u)
==
fRe / Tau * alpa * (V – u)
);
uEqn.solve()
My questions are:
i) I'm not sure of the step 4... I kind of reproduce the simpleFoam code. Is there any documentation somewhere about the command ".flux" ?
ii) I'm not sure of the translation of the momentum equation step 6. Do I need to use a specific formulation for the source term ? Does the solver identify the last "u" by itself ?

Thank you in advance for reading this.

Last edited by fredo490; August 29, 2012 at 11:28. Reason: Tiny corrections
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Old   September 13, 2012, 03:24
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Gerhard Holzinger
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have a look into twoPhaseEulerFoam or bubbleFoam and the thesis of H. Rusche. They all deal with a Eulerian formulation of two-phase fluid flows.

I would recommend to get into bubbleFoam or twoPhaseEulerFoam and remove everything you don't need. Particles with constant diameter and only drag as momentum exchange should not be a big problem.

Last edited by GerhardHolzinger; September 13, 2012 at 03:27. Reason: added clarifiaction
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