On the scaling of air entrainment from a ventilated partial cavity

Abstract

AbstractThe behaviour of a nominally two-dimensional ventilated partial cavity was examined over a wide range of size scales and flow speeds to determine the influence of Froude, Reynolds, and Weber number on the cavity shape, dynamics, and gas entrainment rate. Two geometrically similar experiments were conducted with a 14:1 length scale ratio. The results were compared to a two-dimensional semi-analytical model of the cavity flow, and Froude scaling was found to be sufficient to match basic cavity shapes. However, the air flux required to maintain a stable cavity did not scale with Froude number alone, as the dynamics of the cavity closure changed with increasing Reynolds number. The required air flux differed over one order of magnitude between the lowest and highest Reynolds number flows. But, for sufficiently high Reynolds numbers, the rate of scaled entrainment appeared to approach Reynolds number independence. Modest changes in surface tension of the small-scale experiment suggested that the Weber number was important only at the lowest speeds and smaller length scale. Otherwise, the Weber numbers of the flows were sufficiently high to make the effects of interfacial tension negligible. We also observed that modest unsteadiness in the inflow to the large-scale cavity led to a significant increase in the required air flux needed to maintain a stable cavity, with the required excess gas flux nominally proportional to the flow’s perturbation amplitude. Finally, discussion is provided on how these results relate to model testing of partial cavity drag reduction (PCDR) systems for surface ships.