Hi all! I'm quite new to this forum, but am actually looking for experimental or computational results pertaining to the classical case of flow past a square cylinder at low Reynolds number. I need to verify my own computational results with established ones, but could not seem to find any which contains stable recirculating wake region with NO vortex shedding (Re at 30 ?). Anyway, I got my results with no recirculation zones at Re 30, so I guess I must be wrong somewhere. Pls advise me.

Thx a lot!

Stiff

Go to http://www.featflow.de/

For a bluff body (such as the square) you should get an aft-end "recirculation" due to "separation", even at modest Re. You may not see this effect if you are in the Stokes flow regime where Re << 1! In the latter case, the streamlines (but not necessarily the complete physical picture) will look more like that of potential flow over the bluff body.

So, I'd suggest that you check your results for grid-independence. It appears to me that, if the code and its implementation are bug-free, you have substantial numerical diffusion; so much so that your Re is reduced from your desired value of 30 to the actual computational value of O(1)!

If you find evidence to the contrary please share your findings with us.

Adrin Gharakhani

How so, will I have numerical diffusion as to alter the Reynolds number to a much lower value? In fact, one of my worries was the implication of a higher kinematic viscosity, thus causing unnecessary "sluggishness". Please advise. Thx!

try the "Album of Fluid Mechanics" which has a lot of pictures of (very) low Re flows. You should be able to find a refeerence there. You should be able to get a non-shedding recirculation zone at some Re. What kind of scheme have you implemented in your code?

I'm actually doing a very prelimnary test for my algorithm, after which I'll need to use more complicated schemes and composite grids. Thus I need to get my algortihm correct first before I can continue. Now I'm using the Leapfrog(time)- Dufort Frankel explicit scheme.

(1). For algorithm and code development, there are several standard test cases to validate the solution. (2). These are: 2-D channel flow or fully developed channel flow, sudden expansion channel flow or flow over a back step, square cavity flow with a moving lid, flow over a 2-D cylinder. These cases have been studied over 25 years at least, so, you should be able to find the references quite easily.

If you are using a low order (diffusive) method with coarse grids, then you can reduce your effective Reynolds number substantially. There is no way to quantify it for me. Anyway, first do a grid-independence test, and I agree with John Chien, try the standard benchmark tests (the step channel problem is a very good one). Also, the problem you are solving is external flow, you'll have to make sure that your "outer" boundaries are far enough, as they have significant impact on your flow field. (On the other hand, you may be capturing the correct physics ) but you won't know it without good experiments and parametric test of convergence of your results)

Adrin Gharakhani