Formulation of Flow generated by a cylinder

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The discussion focuses on calculating the frictional torque on a high-speed spindle where flow is generated by the cylinder's rotation. The user questions the validity of using a free vortex model, where tangential velocity (Vtheta) is inversely proportional to radius (1/r), at high rotation speeds. Concerns are raised about the implications of a negative derivative of Vtheta for shear stress calculations on the cylinder's surface. Additionally, the user seeks alternative formulations for this problem and resources for further reading. The conversation also touches on the relevance of this scenario to windage effects in permanent magnet generators (PMGs).
eaglemre
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Hi All;

I try to find the frictional torque on a high speed spindle. There is no flow past the cylinder, the flow is generated due the rotation of the cylinder.
I read book of Munson and it is written there that this kind of flow can be modeled by a free votex approach.
Is free vortex formulation where Vtheta is proportional to 1/r valid for high rotation speeds or do I need another model?
To calculate the shear stress on the surface of the cylinder the derivative of the Vteta is required and in this case it becomes negative.Does this cause any problem?
Are there any other simple formulation for these kind of problem?
I will be glad for your answers.I would be great if you can give some link or suggest a book for this very simple formulation.

Regards
 
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I have never had to look into something like this. However, in dealing with PMGs we do have to deal with windage in regards to the rotor. Would this be a similar situation?
 

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