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A study of two-dimensional flow past regular polygons via conformal mapping

Published online by Cambridge University Press:  01 June 2009

ZHONG WEI TIAN  and
ZI NIU WU
ZHONG WEI TIAN
Affiliation:
Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
ZI NIU WU*
Affiliation:
Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
*
†Email address for correspondence: ziniuwu@tsinghua.edu.cn
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Abstract

In this paper we study two-dimensional flow around regular polygons with an arbitrary but even number of edges N and one apex pointing to the free stream, with comparison to circular-cylinder flow. Both inviscid flow and low-Reynolds-number viscous flow are addressed. For inviscid flow, we obtained the exact solution for pure potential flow through Schwarz–Christoffel transformation, with the emphasis on the role of edge number, N, on the flow details. We also studied the behaviour, stationary lines and stability of vortex pair and found new stationary lines compared to circular cylinder. For viscous flow we derived the equation of stream function in the mapped (circle) domain, based on which approximate expressions for the critical Reynolds numbers and Strouhal number, as functions of the edge number, are obtained. The Reynolds number is based on the diameter of the circumscribed circle. For the steady flow, the first critical Reynolds number is a monotonically decreasing function of N, while N → ∞ corresponds to that for circular cylinder. The bifurcation point is ahead of the bifurcation point for circular cylinder. For unsteady flow, the critical Reynolds number for vortex shedding and the Strouhal number are both monotonically decreasing functions of N.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 628 , 10 June 2009 , pp. 121 - 154
Copyright
Copyright © Cambridge University Press 2009

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