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High Reynolds number flow between torsionally oscillating disks
Published online by Cambridge University Press: 17 April 2009
Abstract
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In this paper the problem solved is that of unsteady flow of a viscous incompressible fluid between two parallel infinite disks, which are performing torsional oscillations about a common axis. The solution is restricted to high Reynolds numbers, and thus extends an earlier solution by Rosenblat for low Reynolds numbers.
The solution is obtained by the method of matched asymptotic expansions. In the main body of the fluid the flow is inviscid, but may be rotational, and in the boundary layers adjacent to the disks the non-linear convection terms are small. These two regions do not overlap, and it is found that in order to match the solutions a third region is required in which viscous diffusion is balanced by steady convection. The angular velocity is found to be non-zero only in the boundary layers adjacent to the disks.
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- Research Article
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- Copyright © Australian Mathematical Society 1970
References
[1]Rosenblat, S., “Flow between torsionally oscillating disks”, J. Fluid Mech. 8 (1960), 388–399.CrossRefGoogle Scholar
[2]Rosenblat, S., “Torsional oscillations of a plane in a viscous fluid”, J. Fluid Mech. 6 (1959), 206–220.CrossRefGoogle Scholar
[3]Benney, D.J., “The flow induced by a disk oscillating in its own plane”, J. Fluid Mech. 18 (1964), 385–391.CrossRefGoogle Scholar
[5]Rasmussen, H., “Steady viscous axisymmetric flows associated with rotating disks”, Ph.D. Thesis, Univ. of Queensland, 1968.Google Scholar
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