# stability

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 August 28, 2006, 09:57 stability #1 Bharathi Guest   Posts: n/a Hi, I am a second-year Phd student doing research in CFD. I am trying to generate the Von-Karman vortex street in a flow past circular cylinder. I chose half-cylinder domain so that the computations become simple. The Navier-Stokes equations are solved for stream function and vorticity inorder to find the instability of the flow. But for some reason, even around Reynolds number = 50, the flow is pretty much stable. Is it that by considering only half cylinder domain, the wake instability cannot be captured ? Regards, Bharathi.

 August 28, 2006, 12:07 Re: stability #2 ganesh Guest   Posts: n/a Dear Bharati, In considering the half cylinder domain, what boundary conditions do you prescribe on the bottom edges, apart from the cylinder. If you boundary condition is one of symmetry, it is wrong, as the flow is no longer symmetric and there is a periodic vortex shedding. You can try out with the full cylinder and see if the vortex shedding is initiated. In any case, Re=50 is just at the verge of initiation of vortex shedding, it is more appropraite to check out your code with Re=100 or 200. Regards, Ganesh

 August 28, 2006, 12:18 Re: stability #3 agg Guest   Posts: n/a Besides what ganesh suggested i would also try refining the grid if possible.

 August 28, 2006, 13:07 Re: stability #4 Mani Guest   Posts: n/a Bharathi, you surely must have seen pictures of Karman vortex streets before, and you know that they are not symmetric. Vortices are shed alternately on the upper and lower sides of the cylinder. You should use the full cylinder, not half of it. Ganesh is right in suggesting a higher Reynolds number. A good grid resolution for a second order scheme has roughly 400 cells around the cylinder circumference and a decent grid density in the wake region (this is to get "accurate" results; vortex-shedding can be observed on coarser grids as well). One more thing to consider: Depending on your initial sonditions, it may take a very long time before the instability develops. Try to start from a non-symmetric (non-zero angle of attack) steady-state solution to trigger vortex shedding. (of course, there is a way to make it work on a half cylinder, but for that you have to assume (or know) the vortex shedding frequency: you could use a time-lagged boundary condition on the cut. is this what you are trying to do?)

 August 29, 2006, 01:51 Re: stability #5 Bharathi Guest   Posts: n/a Hi, Thankyou very much for your suggestions. Infact, I did grid refinement and also calculated the flow for higher Reynolds number (upto 300). But they are of no use. Then came to the conclusion that either considering half domain could be incorrect or the boundary conditions could be wrong and these led me to put forward my questions in cfd-online. Actually, I am using linear stability analysis to find out the instability in the flow past cylinder. According to this, it is the sign of real part of eigenvalues which determines the stability of flow (if it is +ve, flow becomes unstable). Also, I am using conformal mapping used by Fornberg (JFM, 1991) to map half circular domain to upper half plane and then calculating the steady and unsteady flow. I have tried different lateral bottom boundary conditions to see if I could capture wake instability. Few of them are psi_yyy=0, psi_y=0 ; psi_y=0, omega_y=0 (here, x is streamwise direction and y is the direction normal to the flow, psi=stream function, omega=vorticity , psi_yyy means the third partial derivative of psi w.r.t y, psi_y means the first partial derivative of psi w.r.t y etc). When I used psi_yyy=0, psi_y=0, I found instability even for Re=20 which is absolutely wrong. On the other hand, I found that the flow to be stable even for Re=300 when I used psi_y=0, omega_y=0 as the boundary condition. Also, in few papers, I found that the eigen vectors (ie, perturbations of stream function and vorticity) to be symmetric w.r.t the stream line passing through the centre of the cylinder. This made me to think that probably using half circular cylinder domain could be correct. Based on this information, could you please suggest what has to be done to capture the wake instability ? Thanks, Bharathi.

 August 29, 2006, 04:29 Re: stability #6 Michael B Guest   Posts: n/a Hi Bharathi. I've done some CFD calculations withe regards to flow around a cylinder. As Mani said you need to create a full , but only 2D grid, around the cylinder. Often the von Karman street behind to cylinder takes a lot of time to develop. You can increase the performance by having to inlets, one on the upper side and one on the lower side, running with different inlet velocities. After some few iterations you can change your inlets to have the same speed and the vortex street should start automatically. Have a look at www.pbase.com/michaelbo/cfd Michael

 August 29, 2006, 07:43 Re: stability #7 Renato. Guest   Posts: n/a Just a doubt regarding your problem? Is your grid structured? I'm asking for that because the instability condition is easily reached in unstructured grids (full model) -- at least on the cases I've already ran with my code ;o). By the way, it would be interesting to see any instability comparison between cases ran with structured x unstructured grids. Regards Renato.

 August 30, 2006, 02:58 Re: stability #8 Michael B Guest   Posts: n/a unstructured. I've uploaded some pictures to www.pbase.com/michaelbo/cfd

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