Simulation of the unsteady vortical flow of freely falling plates

Abstract

An inviscid vortex shedding model is numerically extended to simulate falling flat plates. The body and vortices separated from the edge of the body are described by vortex sheets. The vortex shedding model has computational limitations when the angle of incidence is small and the free vortex sheet approaches the body closely. These problems are overcome by using numerical procedures such as a method for a near-singular integral and the suppression of vortex shedding at the plate edge. The model is applied to a falling plate of flow regimes of various Froude numbers. For \(\text {Fr}=0.5\), the plate develops large-scale side-to-side oscillations. In the case of \(\text {Fr}=1\), the plate motion is a combination of side-to-side oscillations and tumbling and is identified as a chaotic type. For \(\text {Fr}=1.5\), the plate develops to autorotating motion. Comparisons with previous experimental results show good agreement for the falling pattern. The dependence of change in the vortex structure on the Froude number and its relation with the plate motion is also examined.