# Equilibrium thru Interface

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April 23, 2018, 08:40
#21
Member

Peng Liang
Join Date: Mar 2014
Posts: 59
Rep Power: 12
Quote:
 Originally Posted by Cyp I can explain it to you through a simple example. Consider only the diffusion between two phases (beta and gamma for instance) : In the beta-phase you have and in the gamma-phase Both phases are connected through a flux continuity at the interface and the thermodynamic equilibrium condition reads: What you look for is an partial differential equation that govern where is the phase indicator provided from the VOF solution. With such a formulation, C is defined on the whole domain. In the same manner, you can defined a diffusion field as Now you express the derivative of C : multiplying this relation by D and applying the divergence operator, you get : Just keep in mind that according to the distribution theory you have : . Consequently, the previous equation reduces to: This additional term represents the interfacial jump condition. If there is a continuity, you can get rid of it. However, if you have a partitioning relation, you have to consider it. At the interface, we have . Consequently, more over, So So your diffusion equation becomes : With such a formulation, you will automaticly have a jump condition at the interface between beta and gamma. You can also optimised the solution with I let you adapt this exemple to the advection-diffusion equation. Best regards, Cyp
Thans a lot Cyp, then what does nß mean in your equation? Do you think that I should use interfoam to start for my plasma-liquid interaction? I see a lot of other standard multiphase solvers in Openfoam and I am quite confused as to which one to choose.

Bests,

Peng

April 23, 2018, 08:49
#22
Senior Member

Cyprien
Join Date: Feb 2010
Location: Stanford University
Posts: 299
Rep Power: 18
Quote:
 Originally Posted by tjliang Thans a lot Cyp, then what does nß mean in your equation? Do you think that I should use interfoam to start for my plasma-liquid interaction? I see a lot of other standard multiphase solvers in Openfoam and I am quite confused as to which one to choose. Bests, Peng

is the normal vector to the gas/liquid interface. In your problem, I will say it depends. If you have an immiscible interface between your two fluids. Yes, you can go for a Volume of Fluid solver as a starting point.

 July 2, 2018, 14:29 #23 New Member   Rajesh Singh Join Date: Jun 2010 Posts: 15 Rep Power: 16 Dear FOAMer, I have imported StarCCM+ mesh to openfoam 5.0 and quality of mesh was also good. The CCM mesh is trimmed mesh with polyhedral cells. The flow simulation for interFoam with species transport equation (Haroun formulation)diverges after some iterations. Below is report of the checkMesh. Help for resolving this issue would be appreciated. Thanks in advance ******************************* Create time Create polyMesh for time = 0 Time = 0 Mesh stats points: 2709670 faces: 7273254 internal faces: 6550582 cells: 2217107 faces per cell: 6.23508 boundary patches: 10 point zones: 0 face zones: 1 cell zones: 1 Overall number of cells of each type: hexahedra: 1558763 prisms: 17795 wedges: 1051 pyramids: 73 tet wedges: 51 tetrahedra: 184093 polyhedra: 455281 Breakdown of polyhedra by number of faces: faces number of cells 4 4 5 43 6 76272 7 247451 8 4264 9 70800 10 3318 11 356 12 16481 13 700 14 204 15 35328 16 60 Checking topology... Boundary definition OK. Cell to face addressing OK. Point usage OK. Upper triangular ordering OK. Face vertices OK. Number of regions: 1 (OK). Checking patch topology for multiply connected surfaces... Patch Faces Points Surface topology floweriod1 110302 113851 ok (non-closed singly connected) flow:sheet1 229147 166554 ok (non-closed singly connected) flow:sheet2 228457 166118 ok (non-closed singly connected) flowutg 9532 9665 ok (non-closed singly connected) flow:wallt 9576 9998 ok (non-closed singly connected) floweriod2 110292 113851 ok (non-closed singly connected) flow:inl 5071 5594 ok (non-closed singly connected) flow:wallb 10551 11107 ok (non-closed singly connected) flowutl 5792 6040 ok (non-closed singly connected) flow:ing 3952 4069 ok (non-closed singly connected) Checking geometry... Overall domain bounding box (-0.0133625 -0.013 -0.0851) (0.0133628 0.013 0.007) Mesh (non-empty, non-wedge) directions (1 1 1) Mesh (non-empty) directions (1 1 1) Boundary openness (4.18881e-14 -2.88815e-15 1.82866e-17) OK. Max cell openness = 2.78469e-16 OK. Max aspect ratio = 9.20971 OK. Minimum face area = 1.10391e-11. Maximum face area = 6.4e-07. Face area magnitudes OK. Min volume = 5.01959e-16. Max volume = 5.12e-10. Total volume = 3.4427e-05. Cell volumes OK. Mesh non-orthogonality Max: 57.8894 average: 11.7876 Non-orthogonality check OK. Face pyramids OK. Max skewness = 3.2775 OK. Coupled point location match (average 0) OK. Mesh OK. End

June 7, 2022, 07:55
#24
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Join Date: Feb 2021
Location: Austria
Posts: 39
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Quote:
 Originally Posted by Cyp @Article{Haroun2010, Title = {Volume of fluid method for interfacial reactive mass transfer: Application to stable liquid film }, Author = {Y. Haroun and D. Legendre and L. Raynal}, Journal = {Chemical Engineering Science }, Year = {2010}, Number = {10}, Pages = {2896 - 2909}, Volume = {65}, Abstract = {A volume of fluid method is developed in order to simulate reactive mass transfer in two-phase flows and is applied to study reactive laminar liquid film. The thermodynamic equilibrium of chemical species at the interface is considered using Henry's law. The chemical species concentration equation is solved using primitive variables and local fluxes are locally directly calculated at the interface. The present treatment of jump discontinuity of chemical concentration is consistent with a volume of fluid approach and the difficulty to calculate accurate local mass flux across interface is overcome. For plane interface, the precision of the numerical simulation is found to be very satisfactory while for curved interface a special procedure has been developed to reduce the development of spurious fluxes at the interface. The algorithm is validated for different cases by comparison with available solutions. The method is then applied to study non-reactive and reactive mass transfer in a falling liquid film. The results show that the liquid side mass transfer is well predicted by the Higbie (1935) theory when the transfer is controlled by the film advection provided that adequate parameters are considered, i.e. the actual velocity at interface and not the average liquid film velocity. For situations controlled by diffusion, the Sherwood number tends to a constant value characteristic of purely diffusive situations. For the reactive mass transfer, first and second order irreversible chemical reactions in the liquid phase are considered. The numerical results are compared respectively, with Danckwerts (1970) and Brian et al. (1961) solutions and good agreement is observed. The proposed Volume of Fluid method is shown to be well adapted to deal with interfacial reactive mass transfer problems. }, DOI = {http://dx.doi.org/10.1016/j.ces.2010.01.012}, File = {Haroun2010.pdf:ARTICLES/Haroun2010.pdf:PDF}, ISSN = {0009-2509}, Keywords = {\{CFD\}}, URL = {http://www.sciencedirect.com/science/article/pii/S0009250910000291} } Cheers,

Hello Cyp,

I am trying to simulate a single bubble movement in a solution of water and sugar with interIsoFoam solver, OF2112. I modified the solver and coupled the density, surface tension and viscosity of solution to the concentration of sugar which is different in various parts of the domain. In order to solve the distribution of sugar (a passive scalar) in the geometry, I added a new equation to the solver as below:

fvScalarMatrix CEqn
(
fvm::ddt(C)
+ fvm::div(phi, C)
- fvm::laplacian(dc,C)
==
fvOptions(C)
);

CEqn.relax();
fvOptions.constrain(CEqn);
CEqn.solve();
fvOptions.correct(C);

Now, the problem is, sugar concentration penetrates inside the bubble which is not correct. I would like to know how can I prevent sugar entering the bubble? I would be more than happy if you share your opinion with me.

June 7, 2022, 07:57
a question
#25
Member

Join Date: Feb 2021
Location: Austria
Posts: 39
Rep Power: 5
Quote:

Hello Astrodan,

I am trying to simulate a single bubble movement in a solution of water and sugar with interIsoFoam solver, OF2112. I modified the solver and coupled the density, surface tension and viscosity of solution to the concentration of sugar which is different in various parts of the domain. In order to solve the distribution of sugar (a passive scalar) in the geometry, I added a new equation to the solver as below:

fvScalarMatrix CEqn
(
fvm::ddt(C)
+ fvm::div(phi, C)
- fvm::laplacian(dc,C)
==
fvOptions(C)
);

CEqn.relax();
fvOptions.constrain(CEqn);
CEqn.solve();
fvOptions.correct(C);

Now, the problem is, sugar concentration penetrates inside the bubble which is not correct. I would like to know how can I prevent sugar entering the bubble? I would be more than happy if you share your opinion with me.

 Tags drop, interface position, interfoam, openfoam