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Flow past an impulsively started circular cylinder

Published online by Cambridge University Press:  29 March 2006

W. M. Collins  and
S. C. R. Dennis
W. M. Collins
Affiliation:
Department of Applied Mathematics, University of Western Ontario
S. C. R. Dennis
Affiliation:
Department of Applied Mathematics, University of Western Ontario
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Abstract

An accurate method is described for integrating the Navier-Stokes equations numerically for the time-dependent flow past an impulsively started circular cylinder. Results of integrations over the range of Reynolds numbers, based on the diameter of the cylinder, from 5 to ∞ are presented and compared with previous numerical, theoretical and experimental results. In particular, the growth of the length of the separated wake behind the cylinder has been calculated for R = 40, 100 and 200 and is found to be in very good agreement with the results of recent experimental measurements. The calculated pressure distribution over the surface of the cylinder for R = 500 is also found to be in reasonable agreement with experimental measurements for the case R = 560.

For Reynolds numbers up to 100 the equations were integrated until most of the features of the flow showed a close approximation to steady-state conditions. The results obtained are in good agreement with previous calculations of the steady flow past a circular cylinder. For R > 100 the integrations were continued until the implicit method of integration broke down by reason of its failure to converge. A secondary vortex appeared on the surface of the cylinder in the case R = 500, but for higher Reynolds numbers, including the case R = ∞, the procedure broke down before the appearance of a secondary vortex. In all cases the flow was assumed to remain symmetrical.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 60 , Issue 1 , 21 August 1973 , pp. 105 - 127
Copyright
© 1973 Cambridge University Press

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