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July 20, 2012, 07:53 
Info on Volume of Fluid Algorithum

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Junaid Ahmad Khan
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I am trying to write a code on VOF Model in C++ using Finite Volume Method. Previously i used FVM and success fully write a code for Lid Driven Cavity and Natural Convection now i want to write it for 2D Dam Breaking like openFoam. Now i am trying it for some time but i am not getting the logic behind VOF. Please give you suggestions, recommend books, or paper, and most importantly governing equations and algorithm. My brain is not moving in any direction on that problem. Please Help. Junaid 

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July 24, 2012, 02:26 

#2 
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Ren/Xingyue
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Dear Junaid,
I wrote a VOf code based on CICSAM (Ubbink, you could find his doctoral thesis online). This is an easy method based on original DA VOF method, similar with FACVOF. There are some other VOF methods like PLICVOF, which are different in surface Reconstruction. Maybe you can find something you need in a review (Volumeoffluid interface tracking with smoothed surface stress methods for threedimensional flows) written by Denis Gueyffier. Ren 

July 25, 2012, 14:12 

#3 
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Junaid Ahmad Khan
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Hi, Thanks for your reply.
I have lots of questions for you. First is, as mentioned in the thesis that First solve "alpha" equation. and then momentum equation. As i have mentioned in my post that i have code the lid driven cavity. in that i did not use densities. kindly tell me how to handle density in momentum equation. Problem i am working on is vertical column of water, so the source term is gravity, give me some tips to solve momentum eq and tips for the boundary conditions of volume fraction (alpha) equation. Regards, Junaid 

July 25, 2012, 16:03 

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Quote:
Then you have to solve alpha equation, which is I guess the volume fraction. One you got the distribution of alpha, ro=alpha*ro1 + (1alpha)* ro2 where ro1 is the density of the first fluid, ro2 is the density of the second fluid Do the same with the viscosity Then solve your navierstokes equation with new ro and new viscosity. once you got your velocity distribution you can advect alpha for the next time step, and so on... Quote:


July 26, 2012, 01:51 

#5  
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Ren/Xingyue
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Quote:
In my code I use a smoothed matrix to smooth the VOF function to make sure the density calculated from VOF function as smoothed as possible according to a master thesis.That is a good thesis can give you a quick understand of numerical method for two phase flow named'' A navier stokes solver for single and two phase flow'' by Kim Motoyoshi Kalland and you could find a source code used by the author in that thesis. hope that can help you. Ren 

July 26, 2012, 09:05 

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Thanx Ren for this interesting reference ! It will definitely help


July 29, 2012, 04:44 

#7 
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Junaid Ahmad Khan
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Thanks guys,
how can we handle the boundary condition regarding Atmospheric pressure in a simple vertical column of water or dam break problem. Domain is surrounded with three walls and an open surface. at the wall can we use dp/dx or dp/dy equal to zero. by using p[0,j]=p[1,j] where j=0 to ny for zero wall gradiant. and similarly u and v both equal to zero at walls. now the question is what would be the condition at the open surface for both pressure and velocity. and most importantly what would be the boundary condition for the volumn fraction (alpha ) on walls and the open surface. Kindly correct me if i am wrong. because when i run the simulation the volumn fraction or the phase contours shows that water phase disappears or sometimes it blows up when it disappears it moves downwards not sidewise. please comment. 

July 29, 2012, 05:09 

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Quote:
For velocity BC instead of no slip use rather free slip. Quote:
Quote:
First verify your NavierStokes solver in a pure monophase case, but with a given distribution of density and viscosity. Then check your solver for the transport equation of the mass fraction alone with a constant velocity field. Then couple the both 

July 29, 2012, 06:06 

#9  
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Ren/Xingyue
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I don't know what kind of VOF you used. When the water phase disappeared, you should check your volume convection equation. for example in one dimensional problem, inside the water phase (not the surface) Ap*Fp(n+1)=b0*Fp(n)+Ae*Fe+Aw*Fw, if Ap>b0+Ae+Aw then the water phase will disappear quickly. 

August 3, 2012, 04:21 

#10 
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Junaid Ahmad Khan
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Hi Guys,
As leflix suggested to use it for mono phase . So i use it on lid driven cavity. Now the eq i used is dF/dt+d(uF)/dx+d(vF)/dy=0 discritize Form fn[col][row]=f[col][row](ue*(f[col+1][row]+f[col][row])uw*(f[col1][row]+f[col][row])+vnn*(f[col][row1]+f[col][row])vs*(f[col][row]+f[col][row+1]))/apo where apo=(dx*dy)/dt i am using uniform grid 5 x 5 i started with initializing the fn field by 0 1 2 3 4 5  0 0 0 0 0 0 0 1 00 0 0 0 0 2 01 1 0 0 0 3 01 1 0 0 0 4 01 1 0 0 0 5 0 0 0 0 0 0 the outer nodes are the ghost nodes. the above discretize form is solved using explict formulation only for the internal nodes. Now the problem is that the total volume with in the cavity reduces and become negtive. for the above grid the total volume is 6. as i iteration increase the total volume decrease. So any suggestion to solve this problem. (The problem is that the mass with in the system is not conserved. is it due to some boundary condition or anything else. the code i am using for lid driven cavity is working fine and the velocity profiles are compared with ghia et al. for this problem i am using 81 x 81 grid). 

August 3, 2012, 04:28 

#11 
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Junaid Ahmad Khan
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Hi Guys,
As leflix suggested to use it for mono phase . So i use it on lid driven cavity. Now the eq i used is dF/dt+d(uF)/dx+d(vF)/dy=0 discritize Form fn[col][row]=f[col][row](ue*(f[col+1][row]+f[col][row])/2uw*(f[col1][row]+f[col][row])/2+vnn*(f[col][row1]+f[col][row])/2vs*(f[col][row]+f[col][row+1])/2)/apo ue =u velocity at east face uw =u velocity at west face vnn =v velocity at north face vs =v velocity at south face where apo=(dx*dy)/dt i am using uniform grid i started with initializing the "f" (volume fraction) field by let say we have grid 5 x 5 0 1 2 3 4 5  0 0 0 0 0 0 0 1 00 0 0 0 0 2 01 1 0 0 0 3 01 1 0 0 0 4 01 1 0 0 0 5 0 0 0 0 0 0 the outer nodes are the ghost nodes. the above discretize form is solved using explict formulation only for the internal nodes i.e. from 1 to 4 in this case and calculate new f field and copy new field in the old field by copying the values. Now the problem is that the total volume with in the cavity reduces and become negtive. for the above grid the total volume is 6. as iteration increases the total volume decreases. So any suggestion to solve this problem. (The problem is that the mass with in the system is not conserved. is it due to some boundary condition or anything else. the code i am using for lid driven cavity is working fine and the velocity profiles are compared with ghia et al. for this problem i am using 81 x 81 grid). Last edited by JunaidAhmad; August 3, 2012 at 04:49. 

August 8, 2012, 03:50 

#12 
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Junaid Ahmad Khan
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Will some body give some input.


August 9, 2012, 08:46 

#13  
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Ren/Xingyue
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Quote:
You can't discretize the volume convection in this form. VOF method is not easy like that. 

August 9, 2012, 14:51 

#14 
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Junaid Ahmad Khan
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any recommendation for papers?


Tags 
multiphase flow, vof model 
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