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zonexo March 29, 2006 04:37

Vortex shedding for square cylinder

I did a simulation for flow past square cylinder using my own NS 2d fractional code.

I kept on getting symmetrical result even after I increased Re beyond 100. There is no vortex shedding. I've run it for around physical time of 20s.

Has anyone experience this before?

Thank you

ganesh March 29, 2006 04:53

Re: Vortex shedding for square cylinder
Dear Zonexo,

It is not necessary to expect that the cylinder sheds at Re=100, unless you have definitive expeimental results for the same cylinder. In fact different bodies (geometries) shed at different Re, the critical Re for vortex shedding depends on the geometry(because it decides the presure grad. and then separtion etc...). But if you do have an experimental result that predicts vortex shedding, look for some bug in the code, and also at the time steps used.

Hope this helps



James Date March 29, 2006 08:32

Re: Vortex shedding for square cylinder
Also, you might find you need to introduce a little numerical instability into the solution in order to get the cylinder to shed. You could do this by making the flow non-symmetric (i.e inlet boundary condition at a slight angle) early on in the simulation then switching to symmetric when the shedding starts up. You might also find if you have a course mesh, you don't capture any unsteadiness; however, you need to be sure that vortex shedding does physically occur for this case as suggested by Ganesh.

ramp March 29, 2006 09:06

Re: Vortex shedding for square cylinder
There is something missing.

The reported literature suggests that the vortex shedding for square cylinder (unconfined flow) takes place at Reynolds number (based on the side of square cylinder) in between 45-50. Most of the phenomena, in laminar flow, are too close to the circular cylinder, only things differs in these two cases are the point of separation, which is almost fixed for square but not for circular.

You can read the following article and go through the references there in:

Heat and fluid flow across a square cylinder in the two-dimensional laminar flow regime, Sharma, A., Eswaran, V. Numerical Heat Transfer; Part A: Applications 45 (3), pp. 247-269 (2004).

Best regards.... Ramp

Jim_Park March 29, 2006 10:22

Re: Vortex shedding for square cylinder
There's also the possibility of numerical diffusion damping and smearing vortices. This depends on the accuracy of your differencing and the mesh resolution you're using.

zonexo March 30, 2006 00:53

Re: Vortex shedding for square cylinder
Thanks everyone,

I have been testing with my own codes. In fact, i've 2 codes - cartesian & structured, using the same fractional step scheme. They should be exactly the same, because the cartesian is actually a simplification of the structured one.

I found that after about 1500 time steps (t~18), the cartesian one still is symmetrical but the structured one has started showing some asymmetry. After 2500 (t~30), vortex shedding has started for the structured one, but not for the cartesian one.

Is this possible?

Moreover, from what James said, it seems that there is no definite time for the shedding to occur. Is this true?

I've used the method suggested by James and now there's shedding for the cartesian case ;-) after 1500 time step. So does this mean that the cartesian code is correct after all?

TITAN Algorithms, Staff March 30, 2006 08:23

Re: Vortex shedding for square cylinder
Dear Zonexo,

please review the link at the following:

The square clinder will shed voritices readily provided the mesh is not too coarse. The model shown at the above link demonstrates two mesh refinement cases. Both are solved at Re = 100. A link to the models is also provided. The smaller model will solve in the demo version of Hyperion-TFS.

kind regards,


Renato. March 30, 2006 09:22

Re: Vortex shedding for square cylinder
Is your mesh refined enough near to the cylinder?

How have you been applying the initial conditions? Your flow is being accelerated from a "stationary field" or you're giving a init. cond. previously computed with a slower flow. I'm asking it because if you're accelerating the flow from a stationary field you'll have to wait some time until your flow reach the velocity desired, then after this point you'll have to wait one more time to have the instability started.

I'm not used with structure or cartesian methods but, I guess, due the mesh symmetry, instabilities are harder to be obtained, in these cases, some numerical perturbation could help you.



ramp March 30, 2006 15:11

Re: Vortex shedding for square cylinder
Hi !!

I think there no fixed time at which vortex shedding would occur. It will depend on various things.

I could get your point about the structured & cartesian thing.. do u mean the grid is structured & unstructured while equations are in cartesian system in both the cases.

The reference [Sharma & Eswaran] has solved the problem using the structured grid and they have very fine grid near and on the cylinder surface...

The code might be correct... such type of method for disturbing the flow, not similar to what James has suggested, has also been used for the circular cylinder [Braza M, Chasaing P, Ha Minh H (1986) Numerical study and physical analysis of the pressure and velocity fields in the near wake of a circular cylinder. J Fluid Mech 165:79"130]

Regards.... Ramp

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