A question of Time
 

I have a question hopefully someone can answer.

I'm trying to grow a boundary layer where I have periodic boundaries at either end of my model. The question is which is quicker:

a) A short model (stream wise driection) where the flow will have to pass through, using the periodic boundaries, more times for the boundary layer to develop (but the model has fewer cells).

or

b) A longer model which the flow will take longer to pass through (more cells), however because the profile has longer to develop it shouldn't need to pass through the model as many times.

I'm just curious.

Cheers Bob

Re: A question of Time
 

Hi Bob,

Without a doubt, the short model. The code does not "track" the flow through a model. At a periodic interface, the control volume equations are simply assembled at the common node from element sectors on either side of the periodic.

Set up your model with a single cell in the streamwise direction. With very fine resolution of the boundary layer, you will still be on the order of 1000 nodes.

The flow will be fully developed, so the second order terms will go to zero, so your can run 1st Oder Upwind without losing accuracy.

You will have to add a momentum source to drive the fluid. The source should be uniform in the streamwise direction and equal to the desired pressure drop per unit length (i.e. dP/dx). The mass flow will then depend upon the solution.

Since diffusion will be the dominant timescale, use a very large timestep (10000 [s] should be good!). Convergence will be slow, because of the nature of this kind of problem. However, values of interest will converge within 80 to 100 timesteps (probably less than a minute). If you're patient, you could probably run it to round-off error (MAX Residual ~1e-6).

Regards, Robin

Re: A question of Time
 

Cheers Robin I thought it may be quicker that way. I'm supprised that you can get away with such a large time step. I'll give it a try Bob

Re: A question of Time
 

Hi Bob,

Maybe it is just a difference in terminoligy...but? I am not sure the suggested set-up is physical. What is a "fully developed boundary layer". In an internal flow, the fully developed flow occurs when the outer flow region shrinks to zero and the two boundary layers "meet" and the mean velocity profile is no-longer changing with the stream-wise coordinate...right? This is not actually a boundary layer flow in the "thin shear layer assumption" sense?

In an external flow, the simplest of which is flow over a flat plate...there never is a fully developed flow..the boundary layer thickness: delta continues to increase with the distance along the plate...right...remember the similarity variable solution...??

What are you really trying to do?

If it is fully developed internal flow...maybe you can get away with the one-element thick assumption...but I would really suggest double checking it as well!

Regards,

Bak_flow

Re: A question of Time
 

Good point. I was thinking in terms of an internal flow.

-Robin

Re: A question of Time
 

Hi Guys, I was thinking along the lines of atmpospheric boundary layers. Bob