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November 1, 2013, 16:46 
Laminar steady flow between parallel plates using Fortran

#1 
New Member
saeb
Join Date: Mar 2013
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Hello,
I have developed a code to solve momentum and energy equations in a lid driven cavity using QUICK scheme to interpolate the convective terms and MMIM1 method to avoid checker board pressure field problem (since collocated grids have been employed) and my results were compatible with the benchmark. Now I am going to solve laminar steady flow between two parallel plates including the entrance length. We have uniform velocity at the entrance. To solve the momentum equation, I changed the near boundary source terms at the outlet and the boundary values at the inlet and outlet boundaries. Since my outlet is at fully developed region, the velocity gradient has set to be zero at this boundary and for inlet boundary I used dirihlet boundary conditions. The problem is that the axial velocity vanishes in the axial direction and it will be zero after a specific length. I was wondering if any of you has experienced the same problem before or has any idea to help me. I appreciate if you help me in this regard. Thanks in advance, 

November 1, 2013, 17:38 

#2  
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Filippo Maria Denaro
Join Date: Jul 2010
Posts: 1,645
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Quote:
Are you solving a compressible flow problem? Actually, for incompressible flows you cannot have that the flow rate changes along the axis. As very simple check, I suggest to set inflow and outflow to Dirichlet BC for laminar flow, that is the parabolic velocity profile. Check if you get a steady Poiseuille solution. Then, if everything works fine, set the outlet with Neumann condition and see what happens. 

November 2, 2013, 10:20 

#3 
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saeb
Join Date: Mar 2013
Posts: 11
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Dear Filippo,
Thank you very much for the idea, it helped me in a way. I tried the Poiseuille flow profile at both the inlet and outlet boundaries. The result I achieved still have a serious problem as you see in following link: export.jpg It tells me that the problem in my code was not at the boundaries. It seems to be in momentum equation solution itself. But what I can not understand is if something is wrong with momentum solution why I got an accurate answer in lid driven cavity problem? Sincerely, 

November 2, 2013, 10:27 

#4  
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Filippo Maria Denaro
Join Date: Jul 2010
Posts: 1,645
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Quote:
I cannot see the attachment... I suggest to work still on the Poiseuille case, try to initialise with the analytical solution and check if the divergencefree constraint is fulfilled. Use a low Re number 

November 2, 2013, 10:39 

#5 
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saeb
Join Date: Mar 2013
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Thanks for the help, sure I will try to do that.
Sorry, I edited the attachment link. 

November 2, 2013, 10:47 

#6  
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Filippo Maria Denaro
Join Date: Jul 2010
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Quote:
There is for sure an error in the code, I see the inflow and outflow that simply diffuse the parabolic profile in the interior. It seems that the pressure gradient does not enter into the solution 

November 3, 2013, 09:23 

#7 
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saeb
Join Date: Mar 2013
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I have tried to check the code with different relaxation factors and different grid numbers. I have been bewildered by the result. The result is completely different for different relaxation factors and different grid numbers.
I don't understand why I should get completely different results when I only change the number of grids?! Is this normal? 

November 14, 2013, 16:35 

#8 
New Member
saeb
Join Date: Mar 2013
Posts: 11
Rep Power: 4 
Hello,
I am still dealing with two problems in my code: 1 my solution is sensitive to the grid number 2 The velocity oscillates at a few entrance nodes I believe the problem can be from outlet boundary pressure . I have been using a two point extrapolation to find the outlet pressure but I recently found an article which said: "The outlet pressure is set equal to the sum of the pressure of upstream nodes and a uniform bulk pressure correction." But I can't find anything about the term "uniform bulk pressure correction" in the literature. Appreciate if you share any information about the outlet pressure boundary condition. Sincerely Last edited by saaghi; November 15, 2013 at 04:54. 

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