A comparison of pre-impact gas cushioning and Wagner theory for liquid-solid impacts

Abstract

The normal impact of a symmetric rigid body with an initially quiescent liquid half-space is considered using both Wagner theory and a model of viscous gas pre-impact cushioning. The predictions of these two theories are compared for a range of different body shapes. Both theories assume that the impactor has small deadrise angle. Novel solutions of the Wagner normal impact problem for a symmetric body with a power-law shape are presented, which generalize the well-known results for a parabola and a wedge. For gas cushioned pre-impacts, it is shown that a pocket of gas is entrained even for body shapes with a cusp at the body minimum. A scaling law is developed that relates the dimensions of the trapped gas pocket to the slope of the body. For pre-impact gas cushioning, surface tension is shown to smooth the liquid free-surface and delay the instant of touchdown for a smooth parabolic body, while for a wedge, increasing surface tension initially delays touchdown, before hastening touchdown as the importance of surface tension is increased further. For a flat-bottomed wedge, gas entrainment is again predicted in the gas-cushioning model although the location of initial touchdown, either on the transition between the wedge and the flat bottom or along the side of the wedge, now depends upon the parameters of the body shape.

Gravity effect on water entry during an early stage

“…Note that the air-cushion effect is more difficult to account for and analyse because this effect changes the scenario of the impact. It is still unclear how to match the pre-impact stage with the air-cushion effect and the Wagner-type impact model; see recent papers by Ross & Hicks (2019) and Moore (2021). In the present study, we focus on the correction to the solution in the main flow region, which lacks both the jet-root region and the spray jet, caused by gravity.…”

Experimental investigation of wave tip variability of impacting waves

“…35,55 Prior to impact, gas cushioning (i.e., the increase in pressure in front of the wave tip) can also result in deformation of the wave tip. 49,56,57 The wave tip deflection is shown to depend on the density ratio and the scale of the experiment. 39,40 However, accurate measurements of the wave tip deflec-143 tion have up to now not been reported.…”

“…26,45 The global features of a wave impact on a vertical wall can be accurately represented by potential flow models. 4, [46][47][48][49] Apart from ignoring viscous effects, these simulations generally also ignore surface tension effects, as the impact is inertia dominated. 46 The irrotational flow assumption seems to be valid, as qualitative agreement between experimental and numerical impact pressures can be obtained.…”

“…50 Furthermore, the inertia of the wave tip is small and consequently it is pushed upward where it can eventually be blown off the wave crest. 46,49 Compressible multiphase simulations are required to capture this effect. 26, 51,52 However, the simulations are often not able to capture the development of instabilities on the wave crest.…”

Slamming Liquid Impact and the Mediating Role of Air

“…This is usually achieved by limiting the geometry of the impactor to a wedge with a deadrise angle that is large enough to avoid any air being trapped between itself and the liquid surface. Extensions to this model have also been made for impactor surface profiles such as convex surfaces [85,120,121,122,123]. However it can be shown using experiments (see for instance chapter 5) that having a small deadrise angle does not eliminate the effect of intervening air flow on the free surface (FS).…”