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Computing internal viscous flow problems for the circle by integral methods

Published online by Cambridge University Press:  11 April 2006

R. D. Mills
R. D. Mills
Affiliation:
Computing Science Department, Glasgow University, Scotland
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Abstract

Steady two-dimensional viscous motion within a circular cylinder generated by (a) the rotation of part of the cylinder wall and (b) fluid entering and leaving through slots in the wall is considered. Studied in particular are moving-surface problems with continuous and discontinuous surface speeds, simple inflow–outflow problems and the impinging-jet problem within a circle. The analytical solutions at zero Reynolds number are given for the last two types of problem. Numerical results are obtained at various Reynolds numbers from the integral representation of the solution. At zero Reynolds number this approach involves a quadrature around the circumference of the cylinder. At other Reynolds numbers it involves an iterative–integral technique based on the use of the ‘clamped-plate’ biharmonic Green's function.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 79 , Issue 3 , 9 March 1977 , pp. 609 - 624
Copyright
© 1977 Cambridge University Press

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