Dear colleagues,
what are the minimal grid requirements regarding cell size and particle diameter? I have a grid with average cell volume greater then particle volume in a Eulerian-Lagragian model. However, close to the impeller (MRF rotating zone), the cell size are much smaller for correctly resolving the Boundary Layer. In this case, the particle (volume) occupies the volume of 2 or more cells. What are the implications in the continuity and momentum equaion (2-way-coupoling)? Is there a problem? How do I solve the problem? Does anyone know any study in this regard?
Thank you in advance.
Best wishes,
Jose
Hi Jose,
As far as I know, if you want to fully resolve the particles; then, more cells which cover the particle are able to resolve better interface. However, if you have many particles it's pointless to resolve the entire system (computationally not possible). Therefore, it's better to model them, the ideal size of the cell would fit 10 particles inside (of course it depends on size of the particle).Then instead of Eulerian-Lagrangian, it's better to use Eulerian-Eulerian. The other option would be Hybrid Eulerian-Eulerian DPM (can somwhow handle 4-way couppling as well). which is a bit tricky to impelement.
Hi Jose,
As far as I know, the typical models for Lagrangian Particle Tracking, like drag force model, etc (that are widely used in literature) are based on the assumption that the particle diameter is considerably smaller than the cell size, say dp < cellSize/10.
This assumption is sometimes called "undisturbed fluid velocity".
When you can not use larger grid cells (due to limitations in the boundary layer, for example) you may use some possible solutions. One way is to use a multigrid technique; I mean a coarse grid for Lagrangian part and a fine grid for the Eulerian one.
You can take a look at this paper:
http://refhub.elsevier.com/S0142-727X(16)30448-9/sbref0010
I think the size of cells should be bigger than the particles, I did my modeling like that. but my particles were too small so I haven't any problem in BC. On the other hand, it depends on your particle tracking algorithm. maybe you can consider only the center of particle and its location in the mesh.
Dear all, I appreciate your insights, thank you for the discussion.
Azadeh, I've done that. However I still need to validate with an experiment that cost quite a lot. Therefore I would like be somehow near to the solution before heading to the experiment.
Reza, I'm now particularly interesting in particle tracking. I'll later use the Euler-Euler model. The final model will have a broad range of particle size varying from 50 to 2000 microns, which might not be a problem for the Eu-Eu model. My question is how does the conservation equations are solved in the two different scenarios: particle smaller than the grid cell size (far away from the impeller) or particle much bigger than grid cell size ( vicinity of the BL)?
Lopez, Ebrahim just clarified my point.
Ebrahim, this is exactly what I was in mind when posted this question here. I will study the paper you sent and the terms you mentioned deeper now.
Fatemeh, that could be a potential solution. Do you know any method able to do that?
Thank you all for the comments.
It depends on how you calculate the interfacial pressure. If you use just one cell value then the mesh has to be bigger than the particle. If you integrate the interfacial pressure over the meshes that contain the surface then you should use a mesh that is as fine as needed to obtain convergence.
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