In my recent computational practice, I found that mass conservation at every step is very important to the convergence for colocated grid. When mass flow boundary is applied, outlet velocity is corrected by the mass balance, and convergence is fast. However, When the pressure boundary is applied(mass balance for inlet and outlet isn't considered), there is very bad convergence. Has anybody has similiar experience? is it a bug or just like this? Thank you for your comments

Hi! I experienced the same.Sometimes for pressure boundaries,the code couldn't converge at all.Or it converged to quite large residuals (approximately 0.01). I do not know what this is all about and I do not know what one can do to avoid it.I think one way is to calculate from the pressure difference the mass flow,so that you always have mass flow boundary.

thank you for your response. When I try relaxation factor (alpha_P+alpha_V=1.0), the code smoothly converges, only slowly. When I use the small source term in the momentum eq., very good convergence can be obtained. Have you this experience? Welcome any comments. By the way, I think that pressure drop by mass flow boundary can't be used for the pressure boundary.

I can't understand what is the small source term in the momentum equation.As far as the alpha_P+alpha_V=1 is concerned,I think that this formula is not based on any theory,just in experience.The pressure drop can be used to obtain mass flow boundary,if you make an assumption and you suppose that the flow is isentropic and you correct the mass flow with a factor (C_d).This factor is about 0.6-0.8.But for a long time the pressure boundary troubles me, and I decided to follow the method that I told you.It is not completely correct,but the mistake is very small. One other thing that plays some part,and I do not know which, is the pressure gradient.If you set pressure boundary and also you set the pressure gradient at the boundary,strange things happen...I am working at it right now. Hope to have more comments.

When gas flow through the porous media,the source term should be considered in the momentum equation.

About your treatment,could you explain it more detail? When C_d is given as 0.6-0.8, how the mass flow boundary is guaranteed?

About the pressure gradient, what you metioned is the pressure gradient in the node to the boundary or ..? I think that you don't need to set pressure gradient at the boundary. By the way, how did you treat the pressure correction term P' in the boundary?

Hi Dalton,

I presume you are dealing with an incompressible flow. I don't understand your quote "mass balance at inlet". If you specify velocity at inlet (which you should in an incompressible flow according to the MOC), there's nothing to do there.

You are dealing with the classic problem. There have been conferences on outflow BC's for incompressible flow, though I don't remember the dates. It's not a trivial problem. Here are my random thoughts on this one:

Mass conservation boundary condition fails to perform for multiple inlets/outlets.

If you specify pressure at boundary node P' at that node is zero, simply because there is nothing to correct at that node.

Using mass conservation with Pressure specified is a bad idea.

As you may know according to Method of Characterstics (MOC) for incompressible flow one BC at outflow boundary must come from outside the domain. This is usually the exit pressure. If you specify exit pressure you cannot in principle specify exit velocity (or mass conservation) Other combinations are known to work but require special treatment.

Specifying exit velocity (or mass conservation) works good for single inlet & outlet if you have placed the boundary at correct location far away from the happening region in the flow, I guess you already know that

If you have single inlet & outlet & you specify consevation of mass at outflow you can also use zero pressure gradient at outflow. This combination had worked for me.

Hope this helps,

Abhijit.

Thank you, Abhijit.

I am simulating the incompressible flow in the bed with porous media. This is a case with single inlet and outlet. Because the outlet pressure must be given, so pressure boundary is appled. Outlet area is slope, here, velocity is nonuniformly distributed, but without reverse flow. As you said, if exit pressure is given, exit velocity or mass conservation can not be specified. From my experience, mass conservation really can be helpful for convergence. So the combination is important. But how to specify conservation of mass at outflow and use zero pressure gradient at outflow? Could you give some advice or relevant papers? Appreciate your help.

Hi Dalton,

Can you give more details about your problem, i.e. geometry, BC's & location of bc's etc...

unfortunately, I don't have any experience in porous media flows, but the basic principles should still apply.

The logic behind not specifying exit velocity or mass conservation when exit pressure is specified goes like this:

if you use mass conservation to correct exit plane velocity its like saying exit pressure no influence on the flow field. The two conditions will try to correct each other & you will end up with backflow or recirculation region at exit. I have observed this.

Here's how I did it for the incompressible flow over a backward facing step:

At each iteration I calculate ratio of inflow/outflow say lets call it "m" . "m" could be +ve/-ve. Then multiply the exit plane velocities with m. Then use dp/dn = 0 to set exit plane pressure. All this mumbo-jumbo has to be done at each iteration. Initially outflow=0 so you can set m =0 at first iteration. As you said, I observed good convergence with this BC. When my code converged, I got a nice laminar fully developed profile at exit...

Hope this helps.

Abhijit Tilak.

Thank you Abhijit,

My case is simply described here.

+++++++++++++++++++++++++++++++++++* + * + * + * + * +++++|||+++++++++++++++++++++++++++++++++++++*

Note: +, wall; *, outlet; |||,inlet

For porous media, only one more sink term in momentum eq. So just ignore it.

From your comments, dp/dn=0 at exit plane. That is to say normal pressure gradient is equal to zero. It means that the approach you adopted is typical mass flow boundary. Pressure can't be specified in advance. Welcome your further comments.

My case is simply described here.

+++++++++++++++++++++++++++++++++++* + * + * + * + * +++++|||+++++++++++++++++++++++++++++++++++++*

Note: +, wall; *, outlet; |||,inlet

Sorry for again,

My case is simply described here.

111111111111111111111111111111112 1 2 1 2 1 2 11111333111111111111111111111111111111111112

Note: 1, wall; 2, outlet; 3,inlet

I am surprised, Why "enter" key doesn't work? Abhijit, could you give me an email address? I can email to you. Anyway, outlet is a slope. Hope this following figure works.

wwwwwwwwwwwwwwww w o w o w o wwwwwiiwwwwwwwwwwwwwwwwo

Hi Dalton,

my email address is tilak_abhijeet@rediffmail.com maybe you can send me a graphical discription in MSWORD/PDF file, if thats good for you. Is this a 1-D problem ?

Abhijit