An unsteady point vortex method for coupled fluid–solid problems
 Sébastien Michelin,
 Stefan G. Llewellyn Smith
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Abstract
A method is proposed for the study of the twodimensional coupled motion of a general sharpedged solid body and a surrounding inviscid flow. The formation of vorticity at the body’s edges is accounted for by the shedding at each corner of point vortices whose intensity is adjusted at each time step to satisfy the regularity condition on the flow at the generating corner. The irreversible nature of vortex shedding is included in the model by requiring the vortices’ intensity to vary monotonically in time. A conservation of linear momentum argument is provided for the equation of motion of these point vortices (Brown–Michael equation). The forces and torques applied on the solid body are computed as explicit functions of the solid body velocity and the vortices’ position and intensity, thereby providing an explicit formulation of the vortex–solid coupled problem as a set of nonlinear ordinary differential equations. The example of a falling card in a fluid initially at rest is then studied using this method. The stability of broadsideon fall is analysed and the shedding of vorticity from both plate edges is shown to destabilize this position, consistent with experimental studies and numerical simulations of this problem. The reducedorder representation of the fluid motion in terms of point vortices is used to understand the physical origin of this destabilization.
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 Title
 An unsteady point vortex method for coupled fluid–solid problems
 Open Access
 Available under Open Access This content is freely available online to anyone, anywhere at any time.
 Journal

Theoretical and Computational Fluid Dynamics
Volume 23, Issue 2 , pp 127153
 Cover Date
 20090601
 DOI
 10.1007/s0016200900967
 Print ISSN
 09354964
 Online ISSN
 14322250
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Fluid–solid interaction
 Point vortex
 Vortex shedding
 47.15.ki
 47.63.mc
 Industry Sectors
 Authors

 Sébastien Michelin ^{(1)} ^{(2)}
 Stefan G. Llewellyn Smith ^{(1)}
 Author Affiliations

 1. Department of Mechanical and Aerospace Engineering, Jacobs School of Engineering, UCSD, La Jolla, CA, 920930411, USA
 2. Ecole Nationale Supérieure des Mines de Paris, 6062 Boulevard Saint Michel, 75272, Paris Cedex 06, France