Stable–streamlined and helical cavities following the impact of Leidenfrost spheres

We report results from an experimental study on the formation of stable–streamlined and helical cavity wakes following the free-surface impact of Leidenfrost spheres. Similar to the observations of Mansoor et al. (J. Fluid Mech., vol. 743, 2014, pp. 295–326), we show that acoustic ripples form along the interface of elongated cavities entrained in the presence of wall effects as soon as the primary cavity pinch-off takes place. The crests of these ripples can act as favourable points for closure, producing multiple acoustic pinch-offs, which are found to occur in an acoustic pinch-off cascade. We show that these ripples pacify with time in the absence of physical contact between the sphere and the liquid, leading to extremely smooth cavity wake profiles. More importantly, the downward-facing jet at the apex of the cavity is continually suppressed due to a skin-friction drag effect at the colliding cavity-wall junction, which ultimately produces a stable–streamlined cavity wake. This streamlined configuration is found to experience drag coefficients an order of a magnitude lower than those acting on room-temperature spheres. A striking observation is the formation of helical cavities which occur for impact Reynolds numbers $Re_{0}\gtrsim 1.4\times 10^{5}$ and are characterized by multiple interfacial ridges, stemming from and rotating synchronously about an evident contact line around the sphere equator. The contact line is shown to result from the degeneration of Kelvin–Helmholtz billows into turbulence which are observed forming along the liquid–vapour interface around the bottom hemisphere of the sphere. Using sphere trajectory measurements, we show that this helical cavity wake configuration has 40 %–55 % smaller force coefficients than those obtained in the formation of stable cavity wakes.

On the scaling of air entrainment from a ventilated partial cavity

The 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.