I am simulating periodic co-current immiscible two-phase flow in a 2D channel, the wetting phase flows along the upper

and lower plate while non-wetting phase flows in the center region by imposing a body force using SC model using palabos-v0.7r2.

I input the same LB kinematic viscosity \nu_{lb} for both fluids (the value is 1/6) and the density of wetting and nonwetting fluids are 1 and 0.1, respectively. Fluid distribution is symmetric with respect to the main flow direction (x-direction) and fluid-fluid interfaces are flat.

My objective is to verify my model with the results of:

" Shan-and-Chen-type multiphase lattice Boltzmann study of viscous coupling effects for two-phase flow in porous media"

by Haibo Huang?, Zhitao Li, Shuaishuai Liu and Xi-yun Lu

Theoretically, there should be no velocity in a direction perpendicular to the main flow direction (main flow is in x-direction). However, in my simulation results, I see velocity peaks in y-direction at the interface between to fluids!!!

My guess is that this accounts for fluid-fluid interaction force F_{f-f} at the interface.

Could please help me solve this problem?

Hello Mr. Ali,

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You are probably already aware of the existence of spurious currents when the Shan-Chen method is used (well, not only the Shan-Chen method... almost every diffused interface multiphase model suffer for this pathology). However, if I understand well, you have a planar interface between the two fluids (spurious currents are non-zero only when we have to deal with curved interfaces).
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In this case, if the velocity is calculated correctly, the spurious velocity should disappear at the interface after some time iterations.

When I talk about “correct velocity”, I’m thinking of the average velocity for the two fluid (that as you can understand is critical at the interface because of the inter-particle forces and have to be properly calculated).

Look at Shan and Doolen 1995 or Martys and. Chen, 1996.

Have a nice day

Andrea

Hi Andrea,

Thanks for your answer. The articles that you mentioned were very useful and you are right about the “correct velocity”; the overall velocity perpendicular to the planar interface in the channel flow is almost zero in my simulation results (velocity in different phases has the same value but an opposite direction).

I am planning to calculate phase (relative) permeability values ( phase permeability is a fluid and medium parameter (tensor) that describes the relationship between the phase flow velocity and the pressure gradient ). In this case, I am dealing with non-planar and planning to calculate the average velocity of each phase ( which is affected by the high velocities of each phase near the interface with another fluid and gives erroneous results!).

Do you know any solution for decreasing the spurious velocity effects?

Ali

Hello,

a possible answer to your question can be found in:

Sbragaglia, M., Benzi, R., Biferale, L., Succi, S., Sugiyama, K. &

Toschi, F. 2007 Generalized lattice Boltzmann method with multirange pseudopotential.

Phys. Rev. E 75, 026702.

I have tried the extended neighborhood solution only. A lot of numerical work for a decrease of the spurious velocities

of an order of magnitude only. But maybe it can help…

Good luck

Andrea