An Inviscid Model of Discrete-Vortex Shedding for Two-Dimensional Oscillating Flow around a Flat Plate

概要

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An observation of the flaw around the oscillating flat plate shows that the flow separates at the edge, and the vortices are shed into the fluid. The effect of the viscosity seems dominant only in shedding the vortices, so that such an unsteady problem may be tractable with the potential flow theory by assuming that (1) the fluid is incompressible and irrotational except a vortex sheet, and (2) the behavior of the vortex sheet can be approximated by that of a system of discrete vortices. In the frame work of the potential flow theory it is evident that the hydrodynamic force coefficient does not depend upon the frequency but upon the amplitude of the oscillation, which is consistent with the experimental facts. In this paper an attempt is made to utilize such assumptions in order to investigate the nonlinear characteristics of the hydrodynamic forces acting on the flat plate oscillating normally to its plane. A new method providing the mechanism of shedding and growth of the nascent vortices is proposed for the elimination of the disposable parameter which has usually been introduced for meeting to the uncertainty of the simultaneous determination both of the circulation and of the position of the new vortex born. The method is proved to be useful in the starting problem and in the oscillating problem with a rather small amplitude.
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