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High Reynolds number flow between two inflnite rotating disks

Published online by Cambridge University Press:  09 April 2009

H. Rasmussen
H. Rasmussen
Affiliation:
Laboratory of Applied Mathematical Physics The Technical University of Denmark, Lyngby, Denmark
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In 1921 von Karman [1] showed that the Navier-Stokes equations for steady viscous axisymmetric flow can be reduced to a set of ordinary differential equations if it is assumed that the axial velocity component is independent of the radial distance from the axis of symmetry. He used these similarity equations to obtain a solution for the flow near an infinite rotating disk. Later Batchelor [2] and Stewartson [3] applied these equations to the problem of steady flow between two infinite disks rotating in parallel planes a finite distance apart.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 12 , Issue 4 , November 1971 , pp. 483 - 501
Copyright
Copyright © Australian Mathematical Society 1971

References

[1]Karman, T. v., ‘Über laminare und turbulente Reibung’, Z. Angew. Math. Mech. 1 (1921), 233–252.Google Scholar
[2]Batchelor, G. K., ‘Note on a class of solutions of the Navier-Stokes equations representing steady rotationally symmetric flow’, Quart. J. Mech. Appl. Math. Vol. IV (1951), 29–41.Google Scholar
[3]Stewartson, K., ‘On the flow between two rotating coaxial disks’, Proc. Cambridge Phil. Soc. 49 (1953), 333–341.Google Scholar
[4]Tam, K. K., On two singular perturbation problems in fluid mechanics (Unpublished Ph. D. thesis, University of Toronto, 1965).Google Scholar
[5]Mellor, G. L., Chapple, P. J. and Stokes, V. K., ‘On the flow between a rotating and stationary disk’, J. Fluid Mech. 31 (1968), 95–112.CrossRefGoogle Scholar
[6]Lance, G. N. and Rogers, M. H., ‘The axially symmetric flow of a viscous fluid between two infinite rotating disks’, Proc. Roy. Soc. Ser. A 266 (1962), 109–121.Google Scholar
[7]Pearson, C. E., ‘Numerical solutions for the time-dependent viscous flow between two rotating coaxial disks’, J. Fluid Mech. 21 (1965), 623–633.Google Scholar
[8]Picha, K. G. and Eckert, E. R., ‘Study of the air flow between coaxial disks rotating with arbitrary velocities in an open or enclosed space’, Proc. 3rd U. S. Nat. Cong. Applied Mechanics (1958), 791–798.Google Scholar
[9]Rogers, M. H. and Lance, G. N., ‘The rotationally symmetric flow of a viscous fluid in the presence of an infinite rotating disk’, J. Fluid Mech. 7 (1960), 617–631.Google Scholar
[10]Dyke, M. van, Perturbation methods in fluid mechanics (Academic Press, New York, 1964).Google Scholar
[11]Rott, N. and Lewellen, W. S., ‘Boundary layers and their interactions in rotating flows’, Progress in Aeronautical Sciences 7 (1966), 111–144.Google Scholar
[12]Rasmussen, H., Steady viscous axisymmetric flows associated with rotating disks (Unpublished Ph. D. thesis, University of Queensland, 1968).Google Scholar
[13]Fettis, H. E., ‘On the integration of a class of differential equations occurring in boundary layer and other hydrodynamical problems’, Proc. 4th midwest Conf. Fluid Mech., Purdue University, Sept., 1955 (1956), 93–114.Google Scholar