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April 5, 2006, 23:07 
compressible boundary conditions

#1 
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Hi everybody, I am writing a finite volume code for unsteady 2D laminar flow. It uses for numerical simulations of resonant oscillations in a tube which has one inflow and three walls(no outflow).The boundary conditions that I use is prescribed velocity u=u0*sin(wt) at the inlet. It is like fluid entering a closed end box. The tube is filled with air under normal circumstances (T0=291.789,P0=101325pa).The density can be get from the equation of state. The pressure at the boundary is extrapolated. My code follows the SIMPLE method for compressible flow. The mass residual and total residual do not converge at one time step(dt=0.000027). I don't know how to set pressure boundary conditions in this problem. In SIMPLE method, only relative pressure is not enough. The absolute pressure is needed.Because the density is got from the equation of state P/(Rc*T). How can I know the absolute pressure? What boundary conditions should I use for this problem? And the SIMPLE method can solve this kind of problems ? Any message from you is appreciated. Thank you!


April 7, 2006, 04:36 
Re: compressible boundary conditions

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Sorry for the delay. In the pressure correction subroutine you do not have a reference pressure.That means that the pressure is calculated as follws: P=P+URFP*P' and not P=P+URFP*(P'P'(REF)) as in incompressible flows. This is the reason that you can use the equation of state to calculate density without having a reference density as well. Hope that I have helped you a bit.If you have any more questions,feel free.


April 9, 2006, 11:29 
Re: compressible boundary conditions

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Hi George, thank you for your reply. You mean the absolute pressure can be calculated as P=P+URFP*P'. How is UREP defined? In my pressure correction subroutine, the pressure is calculated as follows: P=P+ (P'P'(REF)). Because the pressure correction equation has the Neumann boundary condition in SIMPLE methods. Only relative pressure variety (P'P'(REF)) can be got. How can the absolute pressure variety P' be calculated? Does any special pressure boundary condition be needed besides velocity inlet boundary condition? Does the P'(REF) be needed to calculate first, then the P'= (P'P'(REF)) + P'(REF)? Or other method is used. And the velocity u=u0*sin (wt) can be used at the inlet as boundary condition, right? Thank you !


April 10, 2006, 05:06 
Re: compressible boundary conditions

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URFP is the underrelaxation factor for the pressure correction.You should set the P(REF)=0.0 , because in compressible flows the pressure as you say is the absolute one.That is why you calculate pressure with the formula: P=P+URFP*P' . As long as the velocity boundary condition is concerned,the answer is yes,you can use it,no problem!


April 10, 2006, 08:50 
Re: compressible boundary conditions

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When I set the P'(REF)=0.0, I have to find this reference point at which the value of absolute pressure should be known. Which point is chosen to be the reference point is the difficulty for me. My problem has the resemblance to your internal combustion engine problem. How did you find the reference point in your problem? I think not all the points in the calculation region can be chosen as the reference point (be set P'(REF)=0.0). Can you give me some advice about my problem? Thanks a lot!


April 10, 2006, 09:43 
Re: compressible boundary conditions

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You do not need the reference point if you calculate the absolute pressure.The only thing you need is to specify the absolute pressure at the inflow or/and at the outflow,for example Pin=101325 Pa and Pout=99000 Pa


April 11, 2006, 23:47 
Re: compressible boundary conditions

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Hi, George Pin and Pout are not known in my problem if I give the inlet velocity. I don't know how to specify the absolute pressure at the inflow or/and at the outflow if I use the inlet velocity boundary condition. Any message from you is appreciated. Thank you!


April 12, 2006, 16:53 
Re: compressible boundary conditions

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It should be known,otherwise you could not tell what the density of the incoming fluid would be.You can specify the pressure at the inlet,but this boundary condition is not what drives the fluid in the chamber,but the velocity condition that you have set


April 24, 2006, 06:23 
Re: compressible boundary conditions

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Hi, George ,I followed your advice and thought one way to specify the inlet pressure. I used the compressible boundary condition, prescribing the total pressure, the total pressure and the inlet flow direction.
I specified the static pressure Pin=P0+Pd*cos(wt) at the inlet and the inlet velocity Uin=u0*sin(wt).Then the total pressure is calculated from the static pressure and inlet velocity. The static temperature is known. The total temperature can be calculated. But I met two difficulties. First, in certain timestep, the residuals fluctuate dramatically. The code seemed not converge. In most timestep, it was OK. Second, when the inlet velocity specified Uin=u0*sin(wt), I think the velocity wave in the middle of the tube would be the sine wave. Now, in my code, the velocity wave was sine wave when the inlet velocity was positive. When the inlet velocity was negative (3.14+2*k*3.14< t <2*3.14+2*k*3.14,k=1,2,3…….), the velocity was nearly zero. Can you give me some advice about my pressure boundary condition and my difficulties? Thanks a lot! vivian 

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