The water entry of a sphere in a jet

Abstract

The forces on an object impacting the water are extreme in the early moments of water entry and can cause structural damage to biological and man-made bodies alike. These early-time forces arise largely from added mass, peaking when the submergence is much less than one body length. We experimentally investigate a means of reducing impact forces on a rigid sphere by placing the sphere inside a jet of water so that the jet strikes the quiescent water surface prior to entry of the sphere into the pool. The water jet accelerates the pool liquid and forms a cavity into which a sphere falls. Through on-board accelerometer measurements and high-speed imaging, we quantify the force reduction compared to the case of a sphere entering a quiescent pool. Finally, we find the emergence of a critical jet volume required to maximize force reduction; the critical volume is rationalized using scaling arguments informed by near-surface particle image velocimetry (PIV) data.

Impact force reduction by consecutive water entry of spheres

“…Instead, it enters the water pool through a thick jet base and is enveloped by the jet to such extent that it resembles a sphere inside a thick jet entering the pool. Speirs et al (2019a) showed that, for a similar kind of water entry of a sphere , Mt = 2.67, and the upper sphere falls through a fully formed Worthington jet. The lower sphere diameter is 38 mm.…”

“…Shiffman & Spencer (1945) showed that, for large density ratios, the value of C d max can be taken as ∼1 during the initial moment of entry (when b ∼ 0.1-0.2 per discussion of (3.3)) of a single sphere into a quiescent pool. Speirs et al (2019a) argued that when a sphere enters the pool travelling within a jet, this C d max ∼ 1 value decreases, and (3.11) becomes, (3.12) where they reported α = 0.25, reducing the impact drag coefficient in sphere in a jet cases to C new d = 0.25C d max . Despite the opposing jet direction between Speirs et al (2019a) and the Worthington jets in this study, plotting the measured impact acceleration values as a function of Fr in figure 10 reveals a similar reduction in impact drag coefficient for the on jet cases, albeit only in the 1.43 ≤ Mt < 4 range.…”

“…(Kornhauser 1964;May 1975;Seddon & Moatamedi 2006;Guillet et al 2020). Previous studies have shown that impact forces can be reduced not only through object geometry (McGehee, Hathaway & Vaughan 1959;Thompson 1965;Li & Sigimura 1967;May 1970;Qi et al 2016;Sharker et al 2019;Güzel & Korkmaz 2020), but also by modifying the near-surface region via, for example, aeration (Elhimer et al 2017) or liquid jet-induced acceleration (Speirs et al 2019a). An interesting extension to the idea of free surface modification is to launch a precursory object to agitate the free surface before entry.…”

Water impact of a surface-patterned disk

“…2016; Speirs et al. 2019). In that the impulse refers to momentum loss by water impact, the dimensionless impulse is obtained by dividing the impulse by the momentum of the falling unit at impact, .…”

“…For a sphere placed inside a downward columnar jet of water, so that the sphere and water jet fall together into a quiescent pool of water, the impact force on the sphere is less than that of a sphere falling without a water jet (Speirs et al. 2019). The peak pressure on a plate impacting aerated water is much smaller than that impacting still water, because air bubbles extend the period over which shock loading is applied to the plate (Ma et al.…”