Formulation of Flow generated by a cylinder

[eaglemre]

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

 

[FredGarvin]

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?

 

[ravenprp]

,

Thank you for your question. The formulation of flow generated by a cylinder is a well-studied problem in fluid mechanics. The flow generated by a rotating cylinder is commonly referred to as a "vortex flow" and can be modeled using various approaches. The free vortex formulation, where the tangential velocity (Vtheta) is inversely proportional to the radius (r), is a valid approach for high rotation speeds. However, it is important to note that this formulation assumes an inviscid flow, meaning there is no frictional force present. In reality, there will always be some level of viscosity present in the flow, so the results may not be entirely accurate.

To calculate the shear stress on the surface of the cylinder, the derivative of the tangential velocity is indeed required. In this case, the negative derivative simply indicates that the velocity decreases as the radius increases, which is expected in a vortex flow. This should not cause any problems in your calculations.

As for other simple formulations, the free vortex approach is one of the most commonly used for this type of problem. However, there are other approaches such as the forced vortex or the Rankine vortex model that may also be applicable in certain cases. I would recommend consulting a fluid mechanics textbook or doing some further research to determine which approach is most suitable for your specific problem.

I hope this helps answer your questions. Good luck with your research!