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October 10, 2005, 05:23 
pressure outlet BC for incompressible flow

#1 
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Hi: I have implemented the SIMPLE method by Patankar (1980) to compute incompressible flow. To correct the pressure field, the socalled PressureCorrection Equation has been employed.
I am in the midst of searching the correct implementation of BC at the boundaries (inlet, outlet, wall) for pressure correction terms (p'). At outlet faces, Constant pressure (p) has been used and thus the p' is set to 0 while extrapolating the 3 velocity components; for other boundaries, p and p' are extrapolated.. Unfortunately, the solution diverges !! Is my treatment correctly implemented? Could anyone help to advise on the correct implementation of pressure outlet BCs (fixing the P) for SIMPLE algorithm?? I have tried to scale the mass flow rate at outlet boundary. It works; however, this method needs prior knowledge of the outlet mass flow rate; which I think it is impractical for unsteady flow..What you guys think?? khai ching 

October 10, 2005, 05:41 
Re: pressure outlet BC for incompressible flow

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hi,
maybe u can try using underrelaxation mtds for your pressure & maybe velocities as well. this should prevent divergence. recommended values from fluent are 0.3 & 0.7 respectively. hope it helps 

October 10, 2005, 05:49 
Re: pressure outlet BC for incompressible flow

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Thanks for the reply..
I have implemented 2 methods to treat the outlet BCs (1) Pressure outlet: fixing the pressure (p' = 0) and extrapolate the velocities.. I have tried to reduce the u/relaxation factor to about 0.05 for pressure and 0.10 for velocities; However, it fails... (2) mass scaling at outlet: scale the velocity vectors at outlet as accordance to the expected mass flow rate.. This works..I have extrapolated p' and P at all boundaries.. I am wondering whether the Pressure Correction Equation can be implemented together with the pressure outlet BC.. From Davidson (1996), he has extrapolated p' and P at ALL boundaries.. khai ching 

October 10, 2005, 15:00 
Re: pressure outlet BC for incompressible flow

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>> I have tried to scale the mass flow rate at outlet boundary. It works; however, this method needs prior knowledge of the outlet mass flow rate; which I think it is impractical for unsteady flow
If I understand you correctly, you extrapolate your velocities to the boundaries and then scale them using conservation of mass. The extrapolation is probably ok (there really is no good exit boundary condition, without having to make some sort of simplification/assumption). My response is particularly related to the scaling issue. There is nothing wrong with scaling, and indeed you may have to do it anyway to make sure you conserve mass. Your concern about the need to know the mass flow rate in advance seems unjustified since you're dealing with incompressible flow. Therefore, unsteady or not, you already know the exist mass flow rate based on your inlet (and wall) boundary conditions. Adrin Gharakhani 

October 13, 2005, 22:48 
Re: pressure outlet BC for incompressible flow

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Dear Adrin: Does that mean I must scale the mass flow rate at outlet even I impose the constant Pressure BC at outlet?
I am using the Pressure Equation right now instead of the pressure correction equations. I am still in the midst of verifying my implementation.. Please advise. khai ching 

October 14, 2005, 14:42 
Re: pressure outlet BC for incompressible flow

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Just want to make myself clear what I mean by scaling: you have an input mass flow rate m_i, and you get a solution that has an exit velocity distribution u_e. Now if you multiply u_e by the local density and crosssectional area, chances are you'll get an exit mass flow rate m_e, which is not exactly equal to m_i. (hopefully the two are not too far off; if so, then you have an error some place). Then you want to scale your u_e such that m_e=m_i. This "scaling" has nothing to do with your BC type; it is there to make sure that you don't have source accumulation/depletion (by violating continuity)
I don't know the details of your approach, but make sure you don't over/underspecify your boundary conditions (i.e., have more BCs imposed than is necessary as dictated by the pde) Adrin Gharakhani 

October 15, 2005, 02:58 
Re: pressure outlet BC for incompressible flow

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thanks..
My code works right now with the pressure outlet BC implemented and continuity is satisfied using the Pressure Equation..(Thanks to Dr Hrvoje Jasak) I still have some doubts about the implementation of Pressure Correction Equations(PCE). Anyone has used the PCE in concert with the constant pressure outlet BC? What will be the boundary conditions (p') at the boundary faces? So far, I have extrapolated p' at all boundaries while fixing p'=0 at outlet(since I fix P_out). This method dint work unless I extrapolated p' and P at outlet as well. By doing that, I have to scale the mass flow rate at outlet to ensure global mass conservation.. khai ching 

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