Experimental investigation of oblique water entry of high-speed truncated cone projectiles: Cavity dynamics and impact load
Introduction
Water entry of objects has been investigated for more than a century (Worthington and Cole, 1897) because of its great importance in civil and military applications, such as slamming of coastal structures and vessels (Faltinsen et al., 2004, Abrate, 2011, Cheng et al., 2020), seaplane design (Von Karman, 1929, Cheng et al., 2019), space shuttle recycling (Seddon and Moatamedi, 2006), and torpedo or missile water entry (May, 1952, May, 1975). Both axisymmetric (Duez et al., 2007, Aristoff and Bush, 2009) and three-dimensional (Techet and Truscott, 2011, Sun et al., 2015, Sun et al., 2018) descriptions of water entry can be found in the literature. In some early studies, the vertical water entry of axisymmetric bodies was investigated in detail. The capillary number, wettability, and geometry determine whether a cavity can be generated (Duez et al., 2007). In practice, water entry phenomena are most often three-dimensional, with the fluid flow and the motion of the penetrating body being asymmetric, and the situation is more complicated than in the axisymmetric case (Mirzaei et al., 2020, Song et al., 2020, Chaudhry et al., 2020).
During water entry by a projectile, the water is pushed away from the projectile on impact, and a cavity is generated. A transient impact load of very high amplitude can be generated on the surface of the projectile, lasting for several milliseconds (Waugh and Stubstad, 1975, Vincent et al., 2018). This impact load may damage the structure of the projectile, so it is necessary to study the load of the projectiles during the impact. The load is determined by the fluid–structure interaction between the projectile and the water, and the cavity dynamics therefore plays a crucial role in water entry. The geometrical shape, inertial properties, wettability, impact angle, and linear and angular velocities of a projectile determine its water entry characteristics (Truscott et al., 2014, Truscott and Techet, 2009, Li et al., 2020). Bodily et al. (2014) presented results on impact load of slender projectiles with three kinds of head (cone, ogive, and flat). The results showed that different impact angles resulted in deflected trajectories and variations in drag. It was found that a flat-nosed projectile experienced 20 times more load than the other projectiles. Recently, Shi et al. (2019) carried out a detailed study of spherical ogive projectiles with different nose shape parameters entering water at several impact velocities and angles. Their results showed that, for the same nose shape (ogive), splashing, cavity shape, cavity pinch-off, and cavity ripple were strongly related to nose shape parameters.
However, in previous three-dimensional water entry studies, the effect of nose shape parameters has not been considered in a systematic manner. In addition, the motion of the body in the water, fluid–structure interactions, the nonstationary behavior of the cavity, and splashing also need to be taken into account. Owing to the existence of these nonlinear and unsteady phenomena, cavity growth and the associated loads on structures are far from being well understood, and it is not an easy task to establish a three-dimensional physical model to predict the process of oblique water entry. In this paper, we present systematic experiments on oblique water entry of truncated cone projectiles with different nose shapes. We focus mainly on the cavity dynamics and the transient loads on the truncated cone projectiles, and we found that the two are closely related. The relationship between the cavity dynamics and transient loads of the high-speed truncated cone projectiles has not discussed in detail in previous studies.
The impact velocity is a crucial factor in water entry. The cavity that is formed as a result of low-speed water entry is filled mainly with air. However, high impact velocities will cause cavitation of the water (Brennen, 2014), which will make an extra contribution to cavity formation (Truscott et al., 2014), and the cavity will be filled with a mixture of air and water vapor. When the cavity surrounds the whole projectile, only a small part of the projectile is in contact with the water and the frictional drag on it is decreased. This phenomenon, which is called supercavitation (May, 1975), is exploited for reducing drag on, for example, naval weapons (May, 1952, May, 1975, Hrubes, 2001) and surface ships (Matveev, 2003). Several high-speed projectile water entry experiments were undertaken to study the macroscopic evolution of natural supercavitation (Shi et al., 2000, Truscott et al., 2009, Yao et al., 2014, Zhao et al., 2016, Chen et al., 2018) and the stability of projectile trajectories (Truscott et al., 2009, Chen et al., 2019). Nevertheless, to date, there has been a lack of detailed research on initial cavity formation, which is important for the subsequent water entry characteristics (Weiland and Vlachos, 2012). In this paper, advanced imaging techniques are used to capture the initial evolution of the cavity. We present a series of clear pictures of the projectiles and associated cavities, as well as analyzing the relationship between cavity characteristics and nose shape parameters.
The kinetic and kinematic characteristics of high-speed projectiles have been investigated in a number of studies (Truscott et al., 2009, Guo et al., 2012, Zhao et al., 2016, Chen et al., 2018), which concluded that the physical properties of the projectiles and the ballistic parameters determined the changes in velocity, the acceleration, and the trajectory of the high-speed objects. However, in these studies, the accelerations of the projectiles were measured by high-speed imaging, and the load data had only limited accuracy. In Yan et al. (2018) and Chen et al. (2019), the loads on underwater vehicles during water entry were recorded by sensors inside these projectiles, but the cavity pictures that were obtained did not show a sufficient amount of detail. Here, with the help of a special acceleration measurement system, detailed load data during the projectile water entry are recorded. The generation of loads on projectiles with different nose shapes are analyzed by studying the fluid–structure interaction. The aim of this study is to simultaneously determine the load characteristics and the cavity dynamics during oblique water entry of high-speed truncated cone projectiles.
The remainder of the paper is organized as follows. First, we present our experimental setup in Section 2. The effects of two dimensionless parameters of the projectile nose on cavity dynamics are investigated in Section 3. In Section 4, we carry out a quantitative study to reveal the dependence of the load characteristics on the governing parameters. Finally, the results of the study are summarized and conclusions are drawn in Section 5.
Section snippets
Experimental setup
Fig. 1 demonstrates a schematic of the experimental setup. The system consists of a high-pressure gas gun, a water tank, an accelerometer, a velocity measurement system, a high-speed camera, data analysis software, and computers. The projectile is launched by the high-pressure gas gun, and the experiments are performed in a water-filled rectangular water tank 1.1 m 1.1 m 4.6 m. The water temperature is 25°C, and all the experiments are conducted under standard atmospheric pressure. The
Three typical impact conditions
For oblique water entry of a truncated cone projectile, we have found three distinct impact conditions that we will describe in turn. The positions of the projectile relative to the water surface in each condition are presented schematically in Fig. 4(a). The three conditions are defined by the relationship between the cone half-angle and the impact angle : (i) ; (ii) ; (iii) . In conditions (i), (ii), and (iii), the first impact of the projectile on the water surface is at
Load characteristics
The nose shape determines the cavity behavior and consequently affects the load characteristics. Understanding how the nose shape influences the acceleration of the projectiles can provide references for the design of the nose to reduce impact accelerations. In this section, the axial loads on projectiles are studied systematically. The axial load data are obtained from the acceleration acquisition system inside the projectiles.
Conclusions
In present work, we experimentally studied the oblique water entry of high-speed truncated cone projectiles with different nose parameters. We focused on the effects of two governing parameters, (in the range 2–25) and (in the range 7°–30°), on the early stage of the cavity behavior and the axial impact load of the projectile. A high-speed camera captured the cavity evolution process, including the cavity generation, two-cavity coalescence, cavity collapse, etc. The axial acceleration of
CRediT authorship contribution statement
Yu-Tong Sui: Experiment, Investigation, Writing - original draft. A-Man Zhang: Conceptualization, Resources, Data curation. Fu-Ren Ming: Investigation, Formal analysis. Shuai Li: Writing - review & editing, Supervision.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This work is supported by the National Natural Science Foundation of China (52088102, 51879053), and the Industrial Technology Development Program (JCKY2018604C010).
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