Water-entry Cavity Research Articles

Numerical simulations of series and parallel water entry of supersonic projectiles in compressible flow

This paper describes numerical simulations of the series and parallel water entry of supersonic projectiles with different head shapes, entry velocities, interval times, and interval distances. We focus on the cavity geometry and the drag force characteristics of the projectiles. For projectiles entering the water in series, no cavity is formed by the second projectile. This second projectile impacts and penetrates the water jet, and moves inside the cavity formed by the first projectile. Moreover, the impact drag force coefficient of the second projectile is significantly smaller than that of a single projectile entering the water with the same entry conditions. The cavitation drag force coefficient of the second projectile fluctuates. In the case of projectiles entering the water in parallel, the impact drag force coefficient is slightly smaller than that of single-projectile water entry. After the projectiles impact the water, the drag force coefficient declines sharply, increases again to form a small peak, and then reduces to an approximately constant value that is slightly larger than that of a single projectile entering the water. Additionally, although the outside boundary of the parallel water entry cavity shows a similar shape to that of single-projectile water entry, the blockage effect causes the inside boundary to form an approximately straight line.

The Numerical Simulation of the Vertical Water Entry Process of High Speed Projectile with Small Angle of Attack

Based on the numerical simulation method, the high speed vertical water entry process of projectile moving at 1000m/s with small angle of attack is studied. By analyzing the cavity configuration and hydrodynamic characteristics of the process, the influences of the small entry angle on the water entry stability process are obtained. The simulation results indicate that the projectile’s ballistic can achieve relative stable state when the water entry angle is less than 0.5°, otherwise the water entry cavity can be pierced by tail fin. The pierced size tend to increase with the increased water entry angle as well as the projectile’s ballistic become unstable. In addition, the rotation of the projectile owing to pitching moment has little effect on cavity configuration and water entry stability.

Numerical and experimental investigation on the oblique water entry of cylinder.

The study of water entry cavity and the analysis of load characteristics are hot topics in water entry research. The coupled Euler-Lagrange method is used to carry out simulation research on the water entry process of a cylinder. Aiming at the water vapor mixing phenomenon caused by structure slamming on the water at the initial time of water entry, the slamming load is further studied by correcting the sound speed in the water. The differences between the calculated results obtained by adjusting the number of units in the numerical simulation prove the convergence of the numerical method. Water entry experiments of a cylinder were carried out, and the results are in good agreement with the simulation data. The motion state simulation and analysis are carried out for the process of water entry with different initial speeds and angles. The changes in the structure's positions, air cavities, and slamming loads are obtained. The rule of slamming pressure with the water entry angle and the relationship between pressure and acceleration are determined.

Experimental study of the evolution of water-entry cavity bubbles behind a hydrophobic sphere

This paper describes an experimental investigation of the cavity evolution and shedding wake behind a hydrophobic sphere during the water-entry process. Two distinct shedding phenomena are confirmed by varying the impact velocity and sphere size: regular air-bubble shedding and unstable air-cloud shedding. Both of these modes are highly dependent on the Weber and Bond numbers. Under the air-bubble shedding mode, approximately periodic big bubble shedding and low-frequency oscillation signals are observed. The relationship between big bubble shedding events and the corresponding acoustic signals is derived, and an empirical method for predicting the shedding period is proposed. The in-phase relationship between small bubble shedding and cavity rippling is confirmed, and we refer to the cavity shedding phenomenon as “acoustic” shedding. Unlike the observations of air-bubble shedding, the air-cloud shedding mode produces a group of disordered small bubbles from the rear of the cavity. Moreover, the cavity seal type has a significant effect on the cavity shedding mode. A deep seal always promotes the onset of air-cloud shedding, whereas surface seals with relatively low Bond numbers result in the air-bubble shedding mode. A surface seal suppresses resonance in the cavity volume. By observing the cavity motion, we find that air-cloud shedding is always accompanied by severe cavity resonance and a rapid decrease in cavity length. Under the air-bubble shedding mode, the cavity motion exhibits relatively weak oscillations.

Mathematical modeling of the oblique water-entry of cylindrical projectiles

Water-entry is the process in which a moving body with an initial velocity impacts the free surface and enters the water from the air and has many important applications in different fields of science and engineering. In this paper, a new transient model of the cavity shape by the consideration of the memory effect of the cavity is developed to predict the shape of the water-entry cavity for circular cylinders and this model has been used to develop the complete model of the oblique water-entry of a cylindrical projectile. The proposed model could predict the impacts of the cavity on the cylinder body and it is tried to take into account all of the forces and moments which act on the projectile in order to develop an accurate model for the water-entry problem. The simulation results of several oblique water entry of cylindrical projectiles in different angles show that the new proposed model could predict the projectile attitude and the trajectory of the projectile with good accuracy relative to the experimental data of water-entry and in a relatively shorter time of simulations compared to the numerical studies.

Numerical study on the cavity characteristics and impact loads of AUV water entry

The high-speed water entry process of an autonomous underwater vehicle (AUV) has a strong impact nonlinearity, and a cavity formed by air and water will often be generated as part of the entry process. The shape of the water-entry cavity plays an important role in the load characteristics and stability of the water-entry trajectory. In this paper, a numerical model for describing the cavity and impact load characteristics of a high-speed water-entry AUV is established. The simulation results such as cavity shape and impact load are compared with experimental data. The good agreement between the numerical results and those of the experiments reveals the accuracy and capability of the numerical algorithm. Subsequently, the arbitrary Lagrange-Euler (ALE) numerical algorithm is used to simulate and analyse the variation laws of the cavity characteristics and impact loads with different head shapes, water-entry velocities, water-entry angles and angles of attack. The results obtained in this study can provide a good reference for the trajectory control and structural design of the AUV.

The influences of "gas" viscosity on water entry of hydrophobic spheres.

An extremely thin gas film was found between a sphere and a free surface when the sphere impacted onto a water pool. That might influence the generation and evolution of water entry cavity. However, it is quite difficult to be captured through normal numerical and experimental tests. In this work, by using a finite element method we investigate the water entry of a hydrophobic sphere with gas viscosity artificially increased. The air film rupture in the early stage, contact line dynamics on a curved solid surface, and air pocket formation are investigated. The numerical results reveal that the lifetime of the gas film can be predicted by a viscous squeezing flow model qualitatively well. That relates to the fact that the gas film is much thinner than the diameter of the sphere, even when the gas viscosity is 100 times as large as the liquid one. However, inviscid flow can be found in the most part of the liquid bulk. The free surface profile (or the gas film profile) is then determined by the impact speed, namely the Weber number. More importantly, after the "gas" film ruptures at the bottom of the sphere, a contact line is generated. The contact line retracts along the sphere's surface, and the retracting speed fulfils [Formula: see text] law generally. This implies that the retracting process of the gas film is dominated by the inertia-capillary balance, rather than simply by the visco-capillary.

Dynamic characteristics of parallel water-entry cavity based on potential flow theory

During the water-entry of the parallel axisymmetric bodies, the water-entry cavities are asymmetrical due to the mutual interference between the cavities. In the current study of the cavity dynamic models, the relatively perfect models of axially symmetric dynamic calculation of low speed single water entry have been established. These models mainly focus on the evolution of cavitation, and thus simplifying the flow pattern. However, due to the particularity of parallel water, the fluid forms a relative flow during the evolution of the cavitation in the inner region of the axisymmetric body axis. As a result, the flow is no longer axisymmetric but develops into a complex three-dimensional flow with strong nonlinearity, making the the theoretical model more difficult to establish. In order to analyze the evolution of the parallel cavities of the parallel axisymmetric body water-entry, the flow of the water-entry cavity interference region is simplified by the existing single water-entry calculation model based on the potential flow theory. The constraint of the relative flow to the cavity is simplified into a constraint potential, and the variation of cavity shape is analyzed. Based on the nonlinear hypothesis, the influence function is introduced to establish the calculation model of three-dimensional cavity and the three-dimensional evolution characteristics of parallel cavities are analyzed. The obtained results show that the velocity potential of the axisymmetric body water-entry can be regarded as the superposition of a point source and a line source located on the axis of the cavity. The expansion of the cavity is affected mainly by the point source, while the shrinkage of the cavity is influenced mainly by the line source. During the parallel water-entry of the axisymmetric body, the evolution of the parallel cavities in space is mirror symmetric and the mutual interference between cavities can be analyzed by introducing the potential wall surface. The potential wall has an inhibitory effect on the evolution of the cavities. The variation of the parallel water-entry cavity radius with the polar angle is related to the depth of the cavity cross section. In the inhibition evolution area near the closed point, the cavity radius decreases gradually with the increase of the polar angle, and the void section radius in the inhibition evolution region far from the closed point increases with the polar angle increasing, and is opposite to the radius law. In the shallower depth of the water-entry, the excessive evolution is formed in the expansion process of the cavity, and the excessive evolution will gradually weaken and disappear in the contraction process of the cavity.

Experimental and numerical investigation on the flow structure and instability of water-entry cavity by a semi-closed cylinder

The purpose of this present study is to address instability flowing characteristics and mechanism of the water-entry cavity created by a semi-closed cylinder. For this purpose, an experimental study and a numerical study of the water-entry of a semi-closed cylinder are carried out. According to the results of the experiments and comparison, the cavitating flows between the semi-closed cylinder water entry and the sealing cylinder water entry, and the fluctuation flow pattern form of the semi-closed cylinder cavitation is found around the body. The flow characteristics of the cavity shape are gained by analyzing the image data. A further insight into the mechanisms of perturbation to the flow structure and the cavity fluctuation by the air in the opening cell are studied based on the law of conservation of energy in water entry. According to the results of simulation and comparison with the cavity visualization of experiment, three instability flow phenomena of cavity are formed during the different stages of water-entry, i.e., flow separation destroyed, local flow transformed near cavity, and unique cavity shedding pattern. A further insight into the characteristics of the flow and the distribution of pressure and velocity during the stage of the cavity unstabilized flow is gained. Finally, the formation mechanism of the cavity unstabilized flow is studied based on the boundary layer theory and Helmhotz vortex theory. The obtained results show that the water poured into the cell of cylinder after the opening end has impacted free surface causes the internal air to compress and expand, and as a consequence of these effects, periodic disturbances of flow structure occur around the cavity, then the cavity presents an identical periodic wave flow with air piston motion and the flow stability of cavity is destroyed. At the eve of impacting, the opening end approaches the free surface, which leads to the inflow velocity attenuation rapidly and the pressure increasing in the cell, which creates an initial pressure higher than ambient pressure. Because of the high pressure, air efflux from the cell forms a gas jet injected into the cavity for the first air expansion stage, then the detaching flow is destroyed and the cavity extension diameter is enlarged. The flow in the gas-liquid mixing domain of cavity is seen as an approximate boundary layer flow pattern where favorable pressure gradient on the upwind side and adverse pressure gradient on the lee side appear alternately. As this flow pattern, re-entrant flow acting on the trough of wave cavitation results in the fact that the laminar-turbulent transition is weakened in the trough field and the local gas-liquid mixing domain is thickened to be involved in unstabilized structure as cloud cavitation. The wave cavity presents a partial and multiple shedding pattern occurring at the trough positions in sequence. There is no mutual interference between shedding cavity and the main cavity. Following the cavity shedding, vortex shedding is formed. The vorticity concentrates on the inside of shedding cavity, and the pressure and velocity present a coherent structure.

Water-entry cavity of heated spheres

The present study aims to address the effect of sphere temperature on water-entry cavity. For this purpose, an experiment on vertical water-entry cavity of a heated sphere is conducted by utilizing a high-speed video camera. The temperature of the sphere ranges from 17℃ to 800℃. The complex flow phenomena of water entry, produced by a change in temperature of a sphere, is obtained for the first time. According to the finding, cavity is not formed around the room temperature sphere under the condition of the impact velocity of 1.5 m/s. When the temperature of the sphere is 300℃, the cavity appears, while it disappears when the temperature reaches up to 400℃. Interestingly, cavity appears again as the sphere is heated to a temperature of 700℃. The degrees of drag reduction of the sphere are different in various temperature conditions. Based on the theory of heat transfer and fluid dynamics, we analyze the mechanism for the influences of temperature and velocity on the forming of cavitation. The results show that the heat-transfer efficiency and heat-transfer mode between sphere and water change with the increase of temperature. Meanwhile the turbulent characteristic around the sphere, the surface roughness and hydrophobicity of the sphere are affected by the bubbles and vapor layer. In consequence, these characteristics influence the formation of cavity. The results of the effect of impact velocity on water-entry cavity reveal that the heat transfer performance plays a significant role in the forming of cavity, while the heat transfer efficiency is improved by the increase of impact velocity. The water-entry characteristics are similar to those in flow field under high temperature at low impact velocity as well as under low temperature at high impact velocity. The flow field of water entry looks similar under 330℃ at high impact velocity as well as under 400℃ at low impact velocity. Thus, an abnormal phenomenon appears. That is to say, the cavity size first decreases, and then disappears with the increase of impact velocity for the sphere at 330℃. The heat transfer performance can determine whether a cavity forms under the conditions of the impact velocity ranging from 1.5 m/s to 3.8 m/s. Meanwhile, the impact velocity itself can merely affect the cavity shape. The pitch-off time of the 300℃ sphere is irrelevant to impact velocity, which shows a good consistency with the literature result. Also, this research will be conductive to gaining an insight into the complex flow of water-entry with a heated sphere.

An experimental study of water-entry cavitating flows of an end-closed cylindrical shell based on the high-speed imaging technology

The objective of this present study is to address the cavitating flow patterns and regimes in the water-entry cavity. For this purpose, an experimental study of vertical water-entry cavity of an end-closed cylindrical shell is investigated by using high-speed video cameras and visualization technique. According to the cavitating flows as observed in the experiments, two flow pattern forms of fluctuation cavitation and cloud cavitation are found around the body. A further insight into the characteristics of the cavity shape and the variation in the cavity fluctuations parameters is gained by analyzing the image data. Furthermore, the experiments at different impact velocities are conducted to analyze the effects of impact velocity on the flow patterns and parameters. Finally, the formation mechanisms of cavitation fluctuations and cavitation clouds are studied based on the basic theory of fluid mechanics. The obtained results show that the cavitation flow pattern form of fluctuation cavitation occurs under the impact velocity condition of low speed, and the cloud cavitation occurs under the velocity condition of high speed. As fluctuation cavitation, the maximal extension diameters of cavitation fluctuate periodically along the water depth, and the speeds of extension and shrinkage are both proportional to the extension diameter. The collapses are different for the two flow pattern cavitations, i.e., the fluctuation cavitation, which is of deep closure and closed at the trough of wave cavitation more than once, and the cloud cavitation, which falls off and forms the leading edge of the cylindrical shell. The frequency fluctuation is independent of the impact velocity, the corresponding pinch-off time decreases with increasing the impact velocity, and the pinch-off time decreases in a nearly linear relation with Froude number. The water poured to the cylindrical shell causes the internal air to compress and expand, and as a consequence of these effects, periodic disturbances of pressure distribution and velocity field occur around the leading edge of the cylindrical shell, then the extended intensity of the cross section of the cavity shows variation in this process, which can be defined as fluctuation cavitation pattern. It appears that the re-entrant flow after the pinch-off at the trailing edge of cavity, then the laminar-turbulent transition is waken as a consequence of the re-entrant flow moving upstream, which flow pattern involved in this structure occurs as cloud cavitation.

The performance of the water-entry cavity on a high-pressure gas-driven projectile

We present the experimental results of water-entry cavity on a slender projectile, which moves in the opposite direction of gravity. The regime of the cavity including sheet cavity, supercavity and trailing cavity is exhibited and its relevance to Euler and Weber numbers are illuminated. Meanwhile, various pinch-off performances of the supercavity are analysed and the resulting re-entrance jet or cavity ripples are presented.

Numerical simulation of the water-entry of body based on the Lattice Boltzmann method

In this paper, a lattice Boltzmann single-phase model is implemented to the simulation of the process of body entering water vertically. The initial water-entry process of a two dimensional cylinder and the process of a three dimensional disk entering water vertically at constant speed is simulated. The deformation of free surface and the relationship between the relative closure depth of water-entry cavity of the disk and the Froude number is studied. It is demonstrated that the LBM single-phase method is applicable to the water-entry problems.

The water-entry cavity formed by low Bond number impacts

First Page

On the Water-Entry-Induced Cavity Closure for a Wide Range of Entry Speeds

One of the important research areas in the water-entry problem is the cavity dynamics. A theoretical analysis is presented to predict the dynamics of water-entry cavity up to the first cavity closure, which is generated by a solid body entering a semi-inifinite free surface of water at a wide range of entry speed. Two types of cavity closure, which are surface closure and the deep closure, depending on the magnitude of ambient atmosphere pressure and entry speed are described by the proposed theory. The time of surface closure at the relatively low-speed entry regime is estimated and compared with published experimental data. Currently no experimental data are available for the high-speed entry case.

Water-entry induced cavity pressure

The pressure in a water-entry induced cavity, is analyzed up to the closed cavity (bubble). Water-entry is a highly transient phenomenon, and the evolution of the water-entry cavity must be explained by considering the entry speed, shape of the solid body, atmosphere pressure, and cavity pressure as the primary variables. This work is an extension of the cavity dynamics model recently reported by Lee (1997a). To extend the model for a wide range of entry speeds the cavity pressure is calculated from a one-dimensional quasi-steady flow model. The estimation of the cavity pressure allows us to explain the experimentally observed surface closure phenomena at low entry speeds. Predictions for the time of surface closure are compared with the published experimental data.

A Prediction of Water-Entry Cavity Shape

A method is described for predicting the shape of the cavity formed when a projectile enters the water vertically from air, as a function of time. The method, developed by Birkhoff and based on a hydraulic flow model, has been shown to be applicable for entries of bluff, axisymmetric projectiles. A knowledge of the projectile weight, entry velocity, and cavity-running drag coefficient is required. Predicted and observed cavity shapes are compared for the entry of a sphere at very reduced pressure and the entry of a conical-nosed cylinder from normal air. Excellent agreement is observed over almost the entire cavity length.

Closure to “Discussions of ‘A Prediction of Water-Entry Cavity Shape’” (1971, ASME J. Basic Eng., 93, p. 504)

Closure to “Discussions of ‘A Prediction of Water-Entry Cavity Shape’” (1971, ASME J. Basic Eng., 93, p. 504)

Pressure measurements in the water-entry cavity

Significant experimental results from a study of pressure in the water-entry cavity are presented. Projectiles were fired into water at velocities up to 250 ft./sec and entry angles of 90°, 60°, and 45°. Pressure data obtained using underwater probes were correlated with high-speed motion pictures taken of the entries. Results indicate that the cavity pressure drop prior to surface closure is an order of magnitude greater than previously assumed. As the entry angle is decreased from 90°, the pressure drop decreases. The minimum cavity pressure decreases linearly with increasing entry velocity over the test range. As the entry angle is increased, the minimum entry velocity required to produce a measurable pressure drop becomes greater. An improved pressure-volume correlation is obtained if the volume enclosed by the cavity walls is corrected to account for re-entrant jet volume and air volume enclosed by the splash walls. Cavity pressure during the closed cavity phase behaves approximately according to the isentropic pressure–volume relation. Pressure drop and history are strongly dependent on projectile nose geometry. No appreciable cavity pressure gradient, axial or transverse, was found to exist. Deep closure or cavity collapse is accompanied by relatively high-pressure pulses.

Effect of Surface Condition of a Sphere on Its Water-Entry Cavity

An investigation of factors which influence the formation of a cavity when a sphere enters water vertically is described. It was found that cavities are formed at much lower entry speeds for contaminated spheres than for clean ones, but that there is little dependence on the type of the contaminant. In regard to the scaling of this effect, the tendency to form a cavity varies little with change of size or specific gravity of the sphere. Water-entry cavities are observed to form at velocities much lower than those required for incipient cavitation in the water tunnel; consequently, a relation between the two effects appears improbable. Some dependence of cavity formation on viscosity might be inferred from the observation that cavities were formed at lower entry speeds by spheres coated with liquids of high viscosity than by spheres without this coating.