Bharat, what numerical model do you use to describe two-phase flow (VOF, level-set, etc)? What are the flow characteristics (immiscible/miscible gas-liquid flows? compressible/incompressible)? For example, if you work with immiscible flows, your boundary condition at the wall should correctly describe contact angle. 

Dear Andrey

I am working on mixture model by solving a scalar transport equation for liquid saturation. As far my understanding goes the wall b.c you mentioned is applicable for VOF/LS model only. Please tell if it is not so. I am looking for conservation of convective flux conservation across interface and at wall B.c like Flux correct Transport(FCT) scheme for two-phase flows.

Thanks,

Dear Bharat

As i understand, you are using a diffuse interface model for two phase fluid modeling. In diffuse interface i suggest you to use harmonic interpolation for approximation of the properties, i.e., density or viscosity. Patankar Book have a bright discussion for this. Go to the attached Link:

http://bookzz.org/book/2350124/21d0a9

Dear Bharat

It would be helpful to know the type of the transport model and the scheme you are using, but generally I would recommend to consider the following points:

1. As the convection term is nonlinear, it should be noticed to use conservative form of the equations to handle the large gradients.

2. If the density variation along the boundary is large, instabilities may occur handling large gradients for the adjacent cells. To overcome this it would be helpful to know whether you are solving the convection-diffusion equation together or separately.

3. The variation of viscosity along the boundary will not affect the convection as it only appears in the diffusion part of the transport equation.

4. For the interface boundaries if you apply the kinematic boundary condition on the interface it might be ok. If the mesh is distorted along the boundary you may need to fulfil the kinematic boundary condition along the liquid column.

Hopefully, the so called moving mesh methods would help you. 

http://www.sciencedirect.com/science/article/pii/S0021999109000126

Article An efficient moving mesh spectral method for the phase-field...

Dear All ,

Thanks for your responses. 

I will briefly outline my problem and various schemes I am using for solving this problem.

Please have a look at the RG-Q.jpg file I have  attached here for domain and boundary conditions.

1). I am modeling Two-Phase Flow in Porous Media using Two-Phase Multiphase Mixture(TPMM) Model developed by Prof. C.Y. Wang(Penn State Univ.) in 1994. I am doing this using UDFs over the Single-Phase solver of FLUENT. I have written UDF for density, viscosity, scalar convective flux and scalar diffusion term.

2). Steady state problem.

3). Using first order upwind for momentum and scalar transport equation.

4). For pressure interpolation I am using PRESTO scheme in FLUENT.

5). Density is variable but not a function of pressure. Rather it is a function of scalar quantity (s) itself using mixture rule.

6). Lambda(λ(s) ) varies form 0 over the AB B.C to 1 across liquid-vapor interface and is also a function of  scalar (s).

7). I am already using Harmonic interpolation for diffusivity coefficient at cell faces.

Problem = When I specify AB boundary as a velocity inlet, advection of interface takes place very well with minor false diffusion at the edges.(I have checked this by switching off diffusion term in scalar transport equation). But scalar values are bounded and UDS is converging in fine manner.

 But Whenever I make AB boundary as a wall boundary condition while retaining same scalar boundary condition, the scalar term becomes unbounded and diverges after some iterations.

I have checked this to be due to small value of λ(s) and due to rapid change in density.

CAN SOMEONE SUGGEST ME HOW TO TACKEL THIS inconsistency in convective flux near AB boundary and at interface ?????

Please I need to solve this really. It is very very important. ANy help/suggestion/related links are MOST WELCOME.

Looking forward to some useful hints and direction.

Bharat

Respected Borisyuk,

I appreciate your answer. I feel you have understood my query very well. Because the density and viscosity terms are dependent on scalar quantity itself, therefore in the domain (attached in my above previous response) there is a inhomogeniety in the flow field. 

Also in addition to that Lambda(λ(s) ) varies form 0 over the AB B.C to 1 across liquid-vapor interface and is also a function of scalar (s).

Can you suggest me some practical solution on how should I tackel this problem ??

I know CFD persons must be aware of these issues and it is not a big problme as well but I have not much experience and thus I am seeking some direction.

Thanks,

With Regards

Bharat

Dear Bharat,

The velocity boundary works as an initial value problem. The scalar quantity adapts itself to the inner conditions as it flows inside. The wall boundary resembles a boundary value problem and dictates a very low value at each time-step where it meets much higher values of the adjacent cells and of course a large gradient of the scalar quantity occurs which the model cannot handle. If you are solving a steady state problem I would suggest to try to define a time-dependent wall boundary condition, so that you cold lessen the scalar quantity over a period of time to the desired value, to let the model adapt itself to new values by smaller gradients over a suitable time to reach the steady state.

Well Thanks for such an insightful reply Kourosh. I really appreaciate and am benefitting form your deep understanding of numerics.

      I think I have solved the problem by initialising the velocity field over the whole domain. Right now after proper initialisation wall boundary condition is giving good convergence.

Well please tell me :  Which book did you referred to learn these details ? I would like to learn CFD in very detailed manner.

Thanks & Regards,

Bharat

Dear Bharat,

Good to hear you have solved the problem. Thanks for your kind words. There are quite a few books in CFD. Some deal with more general aspects and some are in more detail. I have listed a few of them you could perhaps have a look. The order is only a recommendation to start with more general ones.

Regards and all the best.

Versteeg, H.K., and Malalasekera, W.,1995, "An Introduction to Computational Fluid Dynamics, The Finite Volume Method", Longman, England.

Hoffmann, K.A., and Chiang, S.T.,1993, "Computational Fluid Dynamics for Engineers", Vol. I, Engineering Education System, USA.

Tannehill, J.C., Anderson, D.A., and Pletcher, R.H.,1997, "Computational Fluid Mechanics and Heat Transfer", 2nd ed., Taylor & Francis, Washington, DC.

Patankar, S.V.,1980, "Numerical Heat Transfer and Fluid Flow", McGraw-Hill Book Company, New York.

Hirsch, C.,1988, "Numerical Computation of Internal and External Flows; Volume 1, Fundamentals of Numerical Discretisation", John Wiley & Sons, Chichester, UK.

Hirsch, C.,1990, "Numerical Computation of Internal and External Flows; Volume 2, Computational Methods for Inviscid and Viscous Flows", John Wiley & Sons, Chichester, UK.

Abbott, M.B., and Basco, D.R.,1989, "Computational Fluid Dynamics, An Introduction for Engineers", Longman Scientific & Technical, Essex, England.

Abbott, M.B.,1979, "Computational Hydraulics, Elements of the Theory of Free Surface Flows", Pitman, London.

Roache, P.J.,1972, "Computational Fluid Dynamics", Hermosa Publishers, Albuquerque, New Mexico.

Thanks for your reply. I have 1st, 3rd and 4th books but not others. I will study them successively.

With Regards,

Bharat

Hi all,

      Recently I properly initialised the whole velocity flow field and saw that saturation was not that much diverging and out-of-bound. SO I thought problem solved. Bingo !!!

 But No I was wrong. I need help. Can someone give me link to suitable literature for nonlinear cnvective term ?? 

Thanks & Regards,

Bharat