The influence of the Blockage Ratio in the propoerties of the flow
 

Hi,

I am wondering what can be the influence of the blockage ratio (D/H) on the properties of the flow past a circular cylinder.

I am trying to similate the flow past a circular cylinder, and initially I was using the following dimensions for the domain (similar dimessions as used in the references): H=8D, L = 16D, D= 1 meter.
Cylinder located at x= 4D, y = 4D.
Inflow at the left wall of the domain.

The Strouhal number I was obtaining was an overestimation of the expected Strouhal number (at least 10% greater than expected: 0.18 vs 0.165 for Re=100).

After having read the following papers / references:
- Kumar, B.,Mittal, S., 2006. Effect of blockage on critical parameters for flow past a circular cylinder .International Journal for Numerical Methods in Fluids
50, 987–1001.
- Behr, M., Hastreiter, D.,Mittal, S.,Tezduyar, T.E., 1995. Incompressible flow past a circular cylinder: dependence of the computedf low field on the
location of the lateral boundaries. Computer Methods in Applied Mechanics and Engineering 123,309–316.
- Qu, Norberg, Davidson, Peng, 2013. Quantitative numerical analysis of flow past a circular cylinder at Reynolds number between 50 and 200. 39, 347-370

I decided to change the dimensions of the simulation domain: H=32, L=32. The location of the cylinder is at x=16, y=16.
Now all the fluid flow properties matches the expected values (indicated in several references):For example, now I am obtaining St=0.165 for Re=100. the error obtained for this transient simulation is less than 0.01%.

The type of boundary conditions used at the lateral walls of the domain (top and bottom walls) by me is the same as appearing in references:
Uy = 0.
d Ux / dy = 0

I have several questions about this:
- Do you think this makes sense? I mean, I would expect that location of the wall needs be far away from the cylinder, but so small ratio is it needed for this (D/H = 1/32 = 0.03125?
- The boundary conditions used by me are the same as in the literature. Assuming that I do not have an error in the implementation of the boundary conditions, the following questions arise: How have the references manage to obtain the expected values using a smaller domain? Why do I need a bigger domain?

Sorry for this long post.

If something is not clear enough let me know. I will try to provide more details / clarifications.

Best regards,
Hector.

That depends also on the low Re number. The field is much more influenced by the elliptic part of the momentum equation. Thus, you need to locate the walls far from the body

What you state makes sense. When simulating the flow for a higher Reynolds number (Re=200), the needed blockage ratio obtained by me is greater, which means that the walls can be located nearer.

This is aligned what you are describing. Since the elliptic part of the momentum equation (viscosity) is lower, then the walls can be nearer.

But, how did the references manage to obtain the same values using a nearer walls?
Did they use any other kind of B.C. although they describe they used another B.C. totally different?

Sorry but I don't know those papers and I cannot answer about the BC.s ...
However, I see that with your BC.s you consider tau_wall=0 so that you have slip at the wall. And I wonder why do you consider the wall... You could set free-stream conditions..

This is a quite interesting sugestion / idea.
How do you set free-stream condition?
I understand that what you mean is not setting any B.C. at all, and letting the flow to freely move/flow at that wall.
Is that what you mean?

Numerically you can set a condition that let the normal velocity to be different from zero, for example the normal derivative (or second derivative) equal to zero