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M. Rafique August 7, 1999 15:00

Wavy-vortex flow
Hi, I want to simulate Wavy-vortex flow in Taylor-Couette problem using Fluent (I have Taylor Vortex flow solution as Initial Conditions). Can some one guide me 1)How should I modify the Problem. 2)How can I incorporate the wavy nature of the solution.

All suggestions are welcome Regards

John C. Chien August 8, 1999 14:35

Re: Wavy-vortex flow
(1). That's a great idea. What I did was I typed "Taylor-Couette" into Yahoo web search, and I was very surprised that there were so many sites related to this simple flow problem between two cylinders. (2). So, it took me a while to visit some of these Taylor-Couette flow sites. There were sites with vortex pictures, with book reviews, with test set-up, with FEM simulation,....etc...(3). So, if you are tired of running the flow over a square cavity problem, this so-called Taylor-Couette flow is going to be very interesting. (4). When the gap between the two cylinders is equal to the height, you have a square cavity problem in cylindrical coordinates.(with the inner cyliner rotating). This has some applications in turbomachinery in terms of the cavity flows, flow through seals,etc. But I am not going to touch those problems right now. (5). When the height of the two cylinders is much larger than the gap, it becomes a Couette flow in cylindrical coordinates. And if the radii of the two cylinders become very very large, you have almost the 2-D couette flow, that is a moving flat plate over another stationary flat plate leaving a small gap in between. (6). With this background, the interesting thing is people think that there is a relationship between this rotating cylinder system and the real world cartesian system. The only problem is, in the real world cartesian system, the system is open, and the outlet is not looped back to the inlet. Otherwise, it has been used to study the possible cause of the flow transition and turbulence. (7). In the finite system like the two cylinder problem, there is not much one can do. You can only change the rotating speed of the inner cylinder, make it a function of time (oscillating cylinder), feed the flow through instead of two end walls. Anyway, these are things you can change. (8). Under the critical Taylor's number of ( I don't have the definition for it yet) 1708, the flow will be steady state. after that, it will take several states depending upon the rotating speed. And the flow will be 3-D transient laminar first, and eventually it will become turbulent. So, you could be getting into the LES or even DNS domain. (9). But this wavy-vortex (I strongly suggest that readers should visit the Taylor-Couette sites with pictures first) is the second stage of development. So, it is not yet in the turbulent domain. (10). My suggestion is that you must find out the exact range of this wavy-vortex stage in terms of RPM first, and try to do the simulation with the same rotating speed. Whether you can capture this stage depends on several factors, such as the time-step, the mesh density, the numerical scheme used. (If you can't get the answer, you should contact the vendor about the problem and get their opinion as to whether the code is suitable for this type of problem or not).

Patrick Godon August 9, 1999 09:38

Re: Wavy-vortex flow
Let me add a few details concerning the remarks of John.

Check the original paper by Coles, 1965, J. Fluid Mech., vol. 21, page 385. There are two kinds of transition to turbulence in the Couette flow - subcritical (due to a finite amplitude perturbation of the flow, non-linear stability) and supercritical (due to an infinitesimal perturbation of the flow, linear stability). I guess you are interested in the Linear stability only. The first onset of the instability is characterized by the Taylor vortices, where only a few modes are unstable.

See also The review of Saric, 1994, Annu. Rev. Fluid Mech., vol. 26, page 379, for the basic mechanism of the instability of the Couette flow and the Taylor vortices.

There are very good people in France working on these Couette flow problems.

Sorry I cannot help you with Fluent.

Bonne chance et bon courage!


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