Water entry of grooved spheres: Effect of the number of grooves and impact velocity

Highlights

• The water entry of grooved spheres is experimentally investigated.

• The role of grooves on the air entrainment cavity formation is highlighted.

• The cavity dynamics is studied when the grooves number and impact velocity change.

• Effect of grooves number on sphere kinetics at some impact velocities is studied.

Abstract

In this paper, the results of an experimental investigation of the normal impact of grooved spheres on a calm water surface are presented. Particular attention is given to describe the air cavity formation when the number of grooves and the impact velocity change. All experimental tests are conducted in a constant surrounding fluid Bond number, Capillary length using grooved spheres with constant diameter but in various impact, Reynolds and Froude numbers, and the trajectory of spheres is visualized by a high-speed camera at $1\sim 2\text{kfps}$ frame rate. This study extends the recent paper (Mehri and Akbarzadeh, 2020) that first investigated the water entry of grooved spheres, by considering higher impact velocities. The study introduces the role of grooves in the air entrainment cavity formation and shows the dependence of the cavity characteristic such as upper and underlying cavity shape, vertical upward and downward reentrant jets, and splash curtain shape on the number of grooves and the impact velocity. Also, the effect of the number of grooves on and sphere kinetics like descent trajectory, velocity, and acceleration is discussed.

Introduction

The fluid mechanics of water entry of falling objects is of great importance in many military and industrial activities or processes. Some of them are water engineering structures, underwater moving vehicles, waterborne transport, navy applications (such as ship slamming and air-to-sea weapons), coating process, sprayed adhesives, paint aerosols, and inkjet printing (May and Hoover, 1963, Korobkin and Pukhnachov, 1988, Seddon and Moatamedi, 2006, Truscott et al., 2014, Sun et al., 2018). Therefore, this topic has been considered in many experimental and theoretical studies over the last few decades such as Von Karman, 1929, May, 1975, Abrate, 2011, Louf et al. (2018), and to name but a few.

The dynamics of the water-entry process is mainly influenced by hydrostatic pressure, gravity, water surface tension, and inertia. The growth and pinch-off of the air cavity (bubble separation) is a dynamic interaction between these main forces (Truscott et al., 2014, Louf et al., 2018). After the air cavity is created, the liquid/air interface is pushed radially inward by the liquid hydrostatic pressure, which finally causes the cavity to rupture. It results in a distinct pinch-off or the deep seal event (May, 1975). It should be noted that this is an air-entraining cavity formation mechanism, which belongs to the relatively low-velocity water entry cases. In contrast, for projectiles with large enough speed, cavitation may responsible for cavity formation (filled with an air/steam mixture) (Aristoff and Bush, 2009) which is not the subject of the present study.

Based on a known classification, the studies of the relative low-speed water entry dynamics are categorized into two main issues namely short-term and long-term cavity dynamics which are related to the “up to pinch-off” and “after pinch-off”, respectively. The first issue has been widely investigated regarding air-cavity shapes, perturbed fluid flows, and pinch-off characteristics. In these subjects, the reader can refer to many academic works like Abelson, 1970, Bergmann et al., 2006, Duclaux et al., 2007, Gekle et al., 2009, Truscott and Techet, 2009, Yan et al., 2009, Truscott et al., 2012, Bodily et al., 2014, Mansoor et al., 2014, Hurd et al., 2017, Watson et al., 2018, Kim and Park, 2019, Watson et al., 2020, and to name but a few. And in the second field, the readers can also review some experimental and theoretical works, the most important of which are references (Grumstrup et al., 2007, Gekle et al., 2008, La Foy et al., 2010, Bodily et al., 2014, Mansoor et al., 2014, Vakarelski I.V et al., 2017, Louf et al., 2018).

A review of the above-mentioned and other research works, like references (Aristoff and Bush, 2009, Di Mundo et al., 2018, Duclaux et al., 2007, Duez et al., 2007, Kiyama et al., 2019, Korkmaz and Güzel, 2017, Mansoor et al., 2014, Shentu et al., 2019; Speirs et al., Speirs et al. , 2019a, Speirs et al. , 2019b; Techet and Truscott, 2011, Ueda et al., 2011, Vakarelski et al., 2019, Worthington and Cole, 1900, Yang et al., 2019, Zhao et al., 2016) indicates that one of the important matters on cavity dynamics (both up to and after pinch-off) are the characteristics of the falling object surface. Their research comment and emphasize that altering the surface properties of a falling object such as wettability or roughness can affect the hydrodynamic properties of the object’s descent and its entrained air cavity. In this regards, for low impact velocities, a cavity forms if the impact capillary number (${\mathrm{Ca}}_I={\mu }_w{U}_I∕{\sigma }_w$) is higher than the critical value (${\mathrm{Ca}}_{cr}$) for the given surface wetting angle or static contact angle (${\theta }_c$) (Truscott et al., 2014). Truscott et al. (2014) illustrated that, the critical capillary number for hydrophilic surfaces (${\theta }_c<90$ degrees) is higher than 0.1. Instead, for hydrophobic materials, because of their low wettability characteristic (or ${\theta }_c>90$ degrees), a large air cavity may be entrained during the water entry (for more details refer to the works of Mansoor et al. (2014) and Aristoff and Bush (2009)). Concerning the surface properties of a falling projectile, Duclaux et al. (2007) proved that the hydrophobicity plays a role in the threshold of air entrainment. Duez et al. (2007) demonstrated visually that falling hydrophilic spheres require a larger impact velocity to produce an air-cavity than do their hydrophobic counterparts. Aristoff and Bush (2009) focused on dense hydrophobicity of objects’ surface to ensure air entrainment cavity creation even at low Weber numbers. Techet and Truscott (2011) examined experimentally the trajectories, forces, and cavity formation of the water entry of spinning hydrophobic and hydrophilic spheres. Mansoor et al. (2014) experimentally examined the cavity formation during the impact of super-hydrophobic spheres. The used hydrophobic coating was a roughness with a typical sub-micrometer (around 500 nm) peak-to-trough heights. Recently, Shentu et al. (2019) simulated numerically (based on the VOF method and boundary data immersion method) the water entry process of hydrophobic objects. They considered the effects of the density of the object, hydrophobicity, and impact velocity on the water crown, the air-cavity, and the flow pattern. Also, Vakarelski et al. (2019) studied experimentally the stable-streamlined cavities following the impact of non-superhydrophobic spheres on water. They showed that such streamlined cavities are attached just above the sphere’s equator instead of wrapping around it and this sphere with the attached cavity has near-zero drag.

Due to the important role of projectiles’ surface properties on the water-entry dynamics that was described, we performed recently an innovative experimental study to investigate the hydrodynamic characteristics of heated/no-heated of grooved/un-grooved spheres during free-surface water entry (Mehri and Akbarzadeh, 2020). In that work, we considered horizontal and vertical grooves on some steel spheres of diameter $20\mathrm{mm}$ and tested the water entry at a very small impact velocity ($0.3\mathrm{m}{\mathrm{s}}^{-1}$) but at various sphere temperatures ($25\sim 200°\mathrm{C}$). As an important result, we found that for an un-grooved sphere, the descent velocity increases with increasing body temperature, whereas the opposite is true for a grooved sphere. Also, we observed that increasing the number of horizontal grooves has a remarkable effect on descent performances so that the five-grooved sphere has the highest descent speed and acceleration due to the less upward resistance forces. To complete and develop this previous work, we carried out a new study. In this new study, the results of further experimental investigation of the normal impact of grooved spheres (only at room temperature of $24\sim 26°\mathrm{C}$) on a calm water surface, especially at higher impact velocity, are analyzed. The study particularly focuses on the air cavity formation both up to and after pinch-off and spheres kinetics when the number of horizontal grooves and the impact velocity change. All experimental tests are in a constant surrounding fluid Bond number ($\mathrm{Bo}=54.4$) and Capillary length (${\lambda }_c=2.71\mathrm{mm}$) using grooved spheres with a constant diameter (20 mm). The trajectory of spheres is visualized by a high-speed camera at 1$\sim$2 [kfps] frame rate. The study shows the dependence of the cavity characteristic such as cavity shape, vertical Worthington jets, and splash curtain shape on the number of grooves and the impact velocity. The paper is structured as follows. In Section 2, the details of the experimental set-up and the test protocols are introduced. The issue of conditions required for cavity formation and the influence of object surface grooves is discussed in Section 3. Qualitative and quantitative outcomes showing the stages in the cavity formation, sphere descent dynamics are provided in Section 4. And eventually, in Section 5, the main findings and conclusions are summarized.