The Dynamic Balances of Dissolved Air and Heat in Natural Cavity Flows

Abstract

In steady, fully developed and unventilated cavity flows occurring in practice, air (originally dissolved in the water) and heat are diffused through the fluid towards the interface providing a continuous supply of air and vapour to the cavity. This must be balanced by the rate of entrainment of volume of air and vapour away from the cavity in the wake. These equilibria which determine respectively the partial pressure of air within the cavity and the temperature differences involved in the flow are studied in this paper. The particular case of the cavitating flow past a spherical headform has been investigated in detail. Measurements indicate a near-linear relation between the partial pressure of air in the cavity and the total air content of the water. From a second set of experiments, designed to estimate the volume rates of entrainment under various conditions by employing artificial ventilation, it appears that this is a function only of tunnel speed and cavity size within the range of the experiments. A simplified theoretical approach involving the turbulent boundary layer on the surface of the cavity is then used to estimate the rates of diffusion into the cavity. The resulting air balance yields a partial pressure of air/air content relation compatible with experiment. The water vapour or heat balance suggests that the temperature differences involved are likely to be virtually undetectable experimentally.