Flow Between Parallel Plates With Parabolic Entrance Velocity
 

Dear Friends,

Previously I worked on the steady flow between parallel plates with uniform entrance velocity and I got satisfactory results. Since then I have been working on parabolic entrance velocity but I am not sure about the validity of the results.

The following plot is the centerline axial velocity when the mean axial velocity is Um=0.1004708 (which seems alright):

http://www.cfd-online.com/Forums/mem...cture534-1.jpg

but when I decrease the range of the vertical axis it seems that there is an error which I am not sure if this is an acceptable numerical error or not.
The following is the same plot with smaller range of vertical axis:

http://www.cfd-online.com/Forums/mem...cture535-2.jpg

As you see this error only shows itself in very small range of vertical axis.

what are your outlet boundary conditions?
It seems to be numerical errors. Parabolic velocity profile is the exact solution to this problem. but your solution is numerical and have some errors depending on your order of dicretization. So I suggest that you refine mesh in y direction. If the error decreases as you refine the mesh, be sure that it is just discretization error.

At the outlet we have fully developed boundary condition (zero gradient for velocity components).

Do you suggest to use a finer mesh in Y direction or axial direction(X)?

I don't think it is from the discretization scheme, because I checked the results with upwind, QUICK, and CUBISTA schemes and got almost the same results for all.

I think your flow is not fully developed at the outlet. increase the length of channel.
if you are using simple algorithm, check the global mass conservation. your mass flow rate is not equal to the integral of inlet parabolic profile.

Since the inlet velocity profile is parabolic, the channel length doesn't matter anymore, the flow is fully developed all along the length.

I am using the simple algorithm and I think the problem is in the mass conservation too.

Are you saying I have to check the corrections?

Implement boundary condition as follows:
at every time step calculate inlet and outlet mass flow rate (M_in , M_out)
then at the outlet use U(imax)=U(imax-1)*M_in/M_out instead of zero boundary condition
for pressure correction use zero gradient at the outlet
This will solve your problem

I have already done all these, but the problem should be somewhere else.
Thank you anyway.

in this case M_in is not equal to U_m*h
M_in=SUM(u_1j*Dy)
Have you considered this?

Yes, of course I did.