flow generated by a rotating cylinder 2

[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

 

[btrueblood]

Try the Theodorsen and Regier paper in the following link, it has a wealth of good data and a summary of analytical formulas. It will lead you to to the original analyst of this type of flow field, T. vonKarman. Note that the data and analyses presented are for cylinders rotating in large chambers (effect of nearby walls is assumed to be small). In the case of close-clearance shrouds and heat transfer (both by wall cooling and by direct injection of mass flow to the shroud cavity), the drag coefficient of rotors and shafts can vary quite a bit.

The report is Experiments on drag of revolving disks, cylinders, and streamline rods at high speeds,
Theodorsen, Theodore; Regier, Arthur, Report Number: NACA-TR-793

http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19930091870_1993091870.pdf

Beyond that, a lot of technical work has been done by the various large turbine engine manufacturers, some of which has been published in the ASME journal family. Probably the best current semi-public research (at least on rotating disks, but probably shafts as well) is being done at the U. of Bath in England, by professors M. Wilson and J. M. Owen.

Some other, later reports of somewhat less utility:
Heat Transfer by Laminar Flow from A Rotating Plate, Journal of Aeronautical Sciences, Millsaps, K., and Pohlhausen, K., vol. XX, Feb., 1952, pp. 120-126.

Compressible Laminar Flow and Heat Transfer About a Rotating Isothermal Disk, NACA Tech., Ostrach, S., and Thornton, P.R. Note 4320, Aug. 1958.

Mass Transfer, Flow and and Heat Transfer About A Rotating Disk, ASME, Sparrow, E.M. and Gregg, J.L., Paper 59-A-107, 1960.

 

[IRstuff]

How about:

http://en.wikipedia.org/wiki/Magnus_effect

TTFN

FAQ731-376

 

[eaglemre]

Dear btrueblood thanks for the links i will check the these.
Dear IRstuff I know Magnus effect,but it happens when there is uniform flow also in my case as i told flow is generated only by the cylinder.