Formulation of Flow generated by a cylinder

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SUMMARY

The discussion focuses on determining the frictional torque on a high-speed spindle where flow is generated by the rotation of a cylinder, rather than external flow. The participant references Munson's book, which suggests modeling this flow using a free vortex approach, where the tangential velocity (Vθ) is inversely proportional to the radius (1/r). The participant questions the validity of this model at high rotation speeds and the implications of a negative derivative of Vθ on shear stress calculations. They seek alternative formulations and resources for better understanding this phenomenon.

PREREQUISITES
  • Understanding of fluid dynamics principles, particularly vortex flow.
  • Familiarity with shear stress calculations in rotating systems.
  • Knowledge of high-speed spindle mechanics and torque analysis.
  • Basic grasp of mathematical derivatives in the context of fluid velocity profiles.
NEXT STEPS
  • Research "Free Vortex Flow in Fluid Dynamics" for foundational concepts.
  • Study "Shear Stress Calculations in Rotating Cylinders" for practical applications.
  • Explore "High-Speed Spindle Design and Performance" for insights on torque analysis.
  • Read "Fluid Mechanics by Munson" for detailed explanations and examples related to vortex flow.
USEFUL FOR

Mechanical engineers, fluid dynamics researchers, and anyone involved in the design and analysis of high-speed rotating systems will benefit from this discussion.

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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