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 Luiz Eduardo Bittencourt Sampaio June 7, 2001 17:36

Spinning Cylinder

Hi everyone, I need to know if a cylinder (2 meters diameter) spinning at 1000 rpm would be able to induce its wall speed to the adjacent layers of the fluid or if the turbulence effect will not allow this. I mean, analitically (and assuming laminar flow), this cylinder (assume first an infinit heigth) would create a field velocity such as v/r where v is the wall speed. But I dont know how those magic turbulence phenomenon would modify this formula. I tried to run some CFD codes, but I can never trust my results.

Does any one have an empirical or CFD data on this subject? Is there an analitic turbulent solution?

Best Regards, Luiz

 John C. Chien June 7, 2001 21:10

Re: Spinning Cylinder

(1). Because of the viscous effect, the surrounding flow will eventually become a solid body rotation.(assuming that the air around it is free to rotate.

 Luiz Eduardo Bittencourt Sampaio June 8, 2001 00:39

Re: Spinning Cylinder

Thank you Mr. Chien. You mean, the velocity will be something like v=wr (w being the angular speed of the cylinder) instead of v=wR^2/r (where R is the cylinder radi and r is the distance to the cylinder axis)? All beacause of turbulence??? (In laminar flow we would expect v=wR^2/r, rigth?) What is the domain validation for this behaviour since it cannot extend to infinity (otherwise, we would have a big - infinit - velocity far away from the cylinder, which is not phisically possible)?

Best regards and thank you again, Luiz

 John C. Chien June 8, 2001 00:48

Re: Spinning Cylinder

(1). I think it is like a plate moving at a constant speed. If the far field is not constraint, then eventually you will have constant velocity moving at the plate velocity. (2). If the far field is constraint, or fixed, then you will have the 2-D Couette flow. (linear velocity between the wall and the fixed outer boundary, for laminar flow. For turbulent flow, the velocity profile will be different.) (3). You can extend the 2-D case to the cylindrical case. (4). for finite length, you will have 3-D flows. I think, it has been discussed here, long time ago. There are many websites on this problem. You can do some Internet searches first.

 Dr Strangelove June 8, 2001 09:53

Re: Spinning Cylinder

If your cylinder is spinning in quiescent air, it sounds like the Reynolds number will be about 7e6, which is getting high enough that a transition to turbulence cannot be ruled out.

Critical Reynolds numbers, (Re_x), for flow past flat plates, have been measured between 3.5e5 and 1e6, for example.

Every geometry is different, so, as John Chien has suggested, you should research the literature for more information.

 Luiz Eduardo Bittencourt Sampaio June 8, 2001 10:25

Re: Spinning Cylinder

Thank you again, Mr.Chien, I ve been looking in the web for this. I looked in cfd-online, in CFD companies (sometimes they provide examples and movies), but I couldn'tfind any. Could you provide any pointers to this?

Best Regards, luiz

 John C. Chien June 9, 2001 01:21

Re: Spinning Cylinder

(1). Try to use the key words "rotating couette flow" or "Taylor couette flow" in the serach engine.

 Luiz Eduardo Bittencourt Sampaio June 9, 2001 10:22

Re: Spinning Cylinder

Thank you Mr. Chien, I was able to find very good web sites, with a lot of experimental data. All of them talk about Taylor vortices and velocities of the fluid, but no one mentioned about the pressures. Do you know what happens to the pressure behaviour when this kind of vortex appears? I mean, is the pressure gradient lower than when in laminar flows? Best Regards, Luiz

 John C. Chien June 10, 2001 00:45

Re: Spinning Cylinder

(1). If the dominating factor is the tangential velocity, then I think, the radial pressure distribution will have to be balanced by the centrifugal force.

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