On the interaction of a collapsing cavity and a compliant wall

Abstract

The collapse of a spherical vapour cavity in the vicinity of a compliant boundary is examined numerically. The fluid is treated as a potential flow and a boundary-element method is used to solve Laplace's equation for the velocity potential. Full nonlinear boundary conditions are applied on the surface of the cavity. The compliant wall is modelled as a membrane with a spring foundation. At the interface between the fluid and the membrane, the pressure and vertical velocity in the flow are matched to the pressure and vertical velocity of the membrane using linearized conditions. The results of calculations are presented which show the effect of the parameters describing the flow (the initial cavity size and position, the fluid density and the pressure driving the collapse) and the parameters describing the compliant wall (the mass per unit area, membrane tension, spring constant and coating radius) on the interaction between the two. When the wall is rigid, the collapse of the cavity is characterized by the formation of a re-entrant jet that is directed toward the wall. However, if the properties of the compliant wall are chosen properly, the collapse can be made to occur spherically, as if the cavity were in an infinite fluid, or with the reentrant jet directed away from the wall, as if the cavity were adjacent to a free surface. This behaviour is in qualitative agreement with the experiments of Gibson & Blake (1982) and Shima, et al. (1989). Calculations of the transfer of energy between the flow and the coating are also presented.