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Impulsively started flow around a circular cylinder by the vortex method

Published online by Cambridge University Press:  21 April 2006

P. A. Smith  and
P. K. Stansby
P. A. Smith
Affiliation:
Simon Engineering Laboratories, University of Manchester, M13 9PL, UK
P. K. Stansby
Affiliation:
Simon Engineering Laboratories, University of Manchester, M13 9PL, UK
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Abstract

Impulsively started, viscous, incompressible flows around a circular cylinder are simulated by a Lagrangian vortex solution of the vorticity equation using random walks for diffusion and the vortex-in-cell method for convection in a fractional-step scheme. Vortices are introduced around the surface at each timestep to satisfy the zero-slip condition. In the range of Reynolds numbers 2.5 × 102 to 105, comparisons with two analytical solutions, valid for small times (t < 1), show reasonable agreement. For somewhat longer times (t < 5), for a similar range of Reynolds numbers, comparisons are made with accurate Eulerian numerical solutions and with careful flow-visualization experiments. Agreement is good provided a sufficiently large number of vortices is introduced per timestep. The number required increases as Reynolds number increases. If too few are introduced, the vorticity in the wake tends to roll up too tightly. The vortex method remains stable, whereas Eulerian schemes have been reported to become eventually unstable unless upwind differencing is used, reducing accuracy.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 194 , September 1988 , pp. 45 - 77
Copyright
© 1988 Cambridge University Press

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