Air entrapment and its effect on pressure impulses in the slamming of a flat disc on water

Abstract

The presence of ambient air in liquid-slamming events plays a crucial role in influencing the shape of the liquid surface prior to the impact, and the distribution of loads created upon impact. We study the effect of trapped air on impact loads in a simplified geometry, by slamming a horizontal flat disc onto a stationary water bath at a well-controlled velocity. We show how air trapping influences pressure peaks at different radial locations on the disc, how the pressure impulses are affected and how local pressure impulses differ from those obtained from area-integrated (force) impulses at impact. More specifically, we find that the air layer causes a gradual buildup of the load before the peak value is reached, and show that this buildup follows inertial scaling. Further, the same localised pressure impulse at the disc centre is found to be lower than the corresponding (area-integrated) force impulse on the entire disc. While the (area-integrated) force impulses are close to the classical result of Batchelor (An Introduction to Fluid Dynamics, Cambridge University Press, 1967, § 6.10) and Glasheen & McMahon (Phys. Fluids, vol. 8, issue 8, 1996, pp. 2078–2083), the localised pressure impulses at the disc centre, where the trapped air layer is at its thickest, lie closer to the theoretical estimation by Peters et al. (J. Fluid Mech., vol. 724, 2013, pp. 553–580) for an air-cushioned impact.

Water entry of cups and disks

“…Furthermore, though we do not know the exact geometry of surface , we make the approximation . Applying these assumptions and expanding the left-hand side of (4.4) yields A first-order approximation for is made by assuming a linear variation in time from to of a disk at some time ; that is, (Jain, Vega-Martínez & Van Der Meer 2021 b ). As added mass is typically a function of normalized body submergence , we assume , where is a constant to be determined.…”

“…Similar to cups, disks have also been shown to trap an air layer on the nose due to the deformation of the pool surface caused by the approach of the disk (Jain et al. 2021 b ). Yet, as disks do not have the wedge-shaped walls to contain this air layer, we find that the splash and cavity behaviour of disk impact is highly sensitive to the inclination angle of the face, , relative to the flat free surface.…”

“…Typically, past studies on the vertical water entry of disks have either actively enforced that the disk face impacts truly flat to the surface (Peters, van der Meer & Gordillo 2013; Jain et al. 2021 a , b ) or have explicitly varied the inclination angle, but for values of (Bodily et al. 2014; Sun et al.…”

Comparison of Schlieren-based techniques for measurements of a turbulent and wavy free surface

“…To the authors' knowledge, this is the first study to compare the performance of multiple optical techniques for surface reconstruction. The TIR-D and M-G techniques, due to their recency, are featured in limited studies other than the original work (Jain et al, 2022;Jain, Gauthier, Lohse, et al, 2021;Jain, Vega-Martínez, et al, 2021;Kochkin et al, 2022;Mungalov & Derevyannikov, 2021;Rudenko et al, 2022). These techniques have also gone unnoticed in reviews of optical techniques for surface measurements such as a recent comprehensive review by Gomit et al (2022).…”

Total-internal-reflection deflectometry for measuring small deflections of a fluid surface

“…The gradient fields are then integrated using a suitable algorithm to obtain a full reconstruction of the imaged area. Even when a fully quantitative reconstruction cannot be obtained, a great deal of qualitative information can be learnt from mere visualisations of the free surface, as used by Fermigier et al (1992), Jain et al (2021b) and Chang et al (2013Chang et al ( , 2015. Non-intrusive acoustic techniques to measure the interface dynamics have also been developed (Horstmann et al 2019).…”