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August 29, 2012, 10:26 
Need Confirmation  Eulerian solver for tiny particules

#1 
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HECKMANN Frédéric
Join Date: Jul 2010
Posts: 236
Rep Power: 8 
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 :  volume fraction of the particles  velocity of the particles  function of the relative Reynolds number  time respond of the particle  velocity of the fluid Continuity equation : Momentum equation The algorithm I have in mind : 1) setup a "phi_alpha" flux equal to 2) initialize this flux in the createfield with: Code:
"linearInterpolate(alpha)*linearInterpolate(u) & mesh.Sf()" Code:
fvScalarMatrix cEqn ( fvm::ddt(alpha) + fvc::div(alpha_phi) ); cEqn.solve() Code:
alpha_phi = cEqn.flux(); 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() 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 10:28. Reason: Tiny corrections 

September 13, 2012, 02:24 

#2 
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Gerhard Holzinger
Join Date: Feb 2012
Location: Austria
Posts: 178
Rep Power: 16 
have a look into twoPhaseEulerFoam or bubbleFoam and the thesis of H. Rusche. They all deal with a Eulerian formulation of twophase 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 02:27. Reason: added clarifiaction 

Tags 
equations, euler, particles 
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