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Biga August 14, 2003 17:43

Specified mass-flow rate in an outlet
Hy there!

I'm currently trying to implement a boundary condition into a 3D Finite Volume method. This bc should handle an outlet in which the user know the mass-flow rate. The bc actually modifies the exit static pressure in each iteration in order to reach the prescribed mass-flow rate. I have a doubt, however: What's the equation that relates mass-flow rate and the pressure? Does any one now it? I know some commercial codes do it, but I couldn't have access to the proper formulation. Does anyone have any idea?

Thanx a lot in advance. Biga

Tom (the other one) August 15, 2003 04:40

Re: Specified mass-flow rate in an outlet
The equation you are looking for is the Navier-Stokes equation, relating velocity to pressure and therfore massflow to pressure.

Jonas Holdeman August 15, 2003 22:02

Re: Specified mass-flow rate in an outlet
In general the pressure gradient is given by irrotational part of (-u.grad(u) + 1/Re*del^2(u)) + conservative forces, which cannot be expressed in terms of flow.

For the special case of fully-developed internal flow, a relation of the form you described does exist. It is of the form: grad(p)=c_p/Re*phi, where phi is the net internal flow, Re the Reynolds number, and c_p is known as the "Poiseuille constant". c_p depends only on the flow geometry, and is 3 for flow in a 2D duct.

Biga August 17, 2003 21:02

Re: Specified mass-flow rate in an outlet
Thanks, Jonas

That's more "implementable"... =D However, that gradient would make it a bit harder... :\

I've been looking in the Fluent UDFs and found one equation, which is delta p = MFR_desired * delta MFR / (rho * area^2), where MFR = mass flow rate. Do you where this equation comes from??? :)

I've tried the implementaion with a pressure "driver" of my own, written as: delta p = p * delta MFR / MFR_desired, and it seems to work, what makes me think that I don't really need a physical equation but only a driver to the desired pressure.

Weel, thanks again anyway, Biga

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