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On rotationally symmetric flow above an infinite rotating disk

Published online by Cambridge University Press:  29 March 2006

R. J. Bodonyi
R. J. Bodonyi
Affiliation:
Department of Aeronautical and Astronautical Engineering, The Ohio State University, Columbust
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Abstract

The similarity equations for rotationally symmetric flow above an infinite counter–rotating disk are investigated both numerically and analytically. Numerical solutions are found when α, the ratio of the disk's angular speed to that of the rigidly rotating fluid far from it, is greater than −0.68795. It is deduced that there exists a critical value αcr, of α above which finite solutions are possible. The value of α and the limiting structure as α → αcr are found using the method of matched asymptotic expansions. The flow structure is found to consist of a thin viscous wall region above which lies a thick inviscid layer and yet another viscous transition layer. Furthermore, this structure is not unique: there can be any number of thick inviscid layers, each separated from the next by a viscous transition layer, before the outer boundary conditions on the solution are satisfied. However, comparison with the numerical solutions indicates that a single inviscid layer is preferred.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 67 , Issue 4 , 25 February 1975 , pp. 657 - 666
Copyright
© 1975 Cambridge University Press

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