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The flow field due to a body in impulsive motion

Published online by Cambridge University Press:  26 April 2006

Renwei Mei  and
Christopher J. Lawrence
Renwei Mei
Affiliation:
Department of Aerospace Engineering, Mechanics and Engineering Science, University of Florida, Gainesville, FL 32611, USA e-mail: rwm@mozart.aero.ufl.edu
Christopher J. Lawrence
Affiliation:
Department of Chemical Engineering and Chemical Technology, Imperial College of Science, Techology and Medicine, London SW7 2BY, UK e-mail: c.lawrence@ic.ac.uk
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Abstract

An asymptotic analysis for the long-time unsteady laminar far wake of a bluff body due to a step change in its travelling velocity from U1 to U2 is presented. For U1 [ges ] 0 and U2 > 0, the laminar wake consists of a new wake of volume flux Q2 corresponding to the current velocity U2, an old wake of volume flux Q1 corresponding to the original velocity U1, and a transition zone that connects these two wakes. The transition zone acts as a sink (or a source) of volume flux (Q2 – Q1) and is moving away from the body at speed U2. Streamwise diffusion is negligible in the new and old wakes but a matched asymptotic expansion that retains the streamwise diffusion is required to determine the vorticity transport in the transition zone. A source of volume flux Q2 located near the body needs to be superposed on the unsteady wake to form the global flow field around the body. The asymptotic predictions for the unsteady wake velocity, unsteady wake vorticity, and the global flow field around the body agree well with finite difference solutions for flow over a sphere at finite Reynolds numbers. The long-time unsteady flow structures due to a sudden stop (U2 = 0) and an impulsive reverse (U1U2 < 0) of the body are analysed in detail based on the asymptotic solutions for the unsteady wakes and the finite difference solutions. The elucidation of the long-time behaviour of such unsteady flows provides a framework for understanding the long-time particle dynamics at finite Reynolds number.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 325 , 25 October 1996 , pp. 79 - 111
Copyright
© 1996 Cambridge University Press

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