Water Entry Process Research Articles

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.

Experimental study of the effects of a viscous liquid layer on the cavity dynamics of vertical entry by a sphere into water at low Froude number

The water entry process is relevant to a wide range of engineering applications and has been extensively investigated. Most liquids used in such studies are single-layered, and little attention has been paid to how the structure of a two-layer liquid system affects the splash and cavity formation. In this study, we use high-speed photography to experimentally investigate the water entry of a sphere after it has passed vertically through a layer of highly viscous liquid (dimethicone) at a low Froude number. We investigate the effects of different thicknesses of this dimethicone layer and find that the formation of the splash crown is closely related to both the thickness and the Froude number. In a certain range of dimethicone thickness, the height of the splash interface decreases with the increasing thickness and increases with the decreasing Froude number. The dimensionless interface height at the pinch-off time is found to have a linear relationship with the dimensionless initial velocity of the sphere. Furthermore, the formation of the cavity, including its length and pinch-off depth, depends on the Froude number. However, the pinch-off time is almost independent of the dimethicone thickness and the Froude number, and the cavity length is nearly independent of the dimethicone thickness for all Froude numbers examined.

Different closure patterns of the hollow cylinder cavities with various water-entry velocities

The vertical water-entry processes of a hollow cylinder with three different velocities are investigated both numerically and experimentally. Three different closure patterns and flow characteristics of the air-entraining cavities induced by water-entry processes are discovered and discussed. Our results show that three different closure patterns appear with the increase of entry velocity, the deep-closure, the surface closure on the through-hole jet and on the geometry wall. Three high-speed regions also appear during the water entry process and their characteristics are different with various closure patterns. Besides, with the increase of water entry velocity, the velocity variation will vary from increase to decrease, but their water depths all increase linearly due to the short time and small variations of velocities.

Experimental study on the trajectory of projectile water entry with asymmetric nose shape

In this study, we investigated the water entry trajectory characteristics of a projectile with an asymmetric nose shape at different initial impact velocities and impact angles experimentally. With high speed photography, the water entry cavities and projectile motions were captured to obtain the trajectory curve and the attitude angle of the projectile. Compared to the projectile with a flat nose shape, the experimental results presented that the trajectory of the projectiles with asymmetrical nose shapes shows obvious deflection during the water entry process, and the deflection amplitude of the trajectory increases as the cut angle decreases under the same water entry conditions. It is found that the change trend of the projectile’s attitude angle is the almost same under different impact angle conditions. In addition, for the same type of asymmetric nose shape, the trajectory deflection increases with the increase in impact velocity. Finally, a theoretical model of the water entry trajectory was established to predict the projectile motion and trajectory of the projectile with an asymmetric nose shape before the tail-slap process. We compared the experimental data with the calculated results, and the theoretical calculation gave a good approximation with the experimental results. The maximum error of the displacements between the theoretical results and the experimental results is only 3.25%.

Numerical simulation of the effect of waves on cavity dynamics for oblique water entry of a cylinder

The water entry process associated with complicated unsteady structures, with consideration of the influence of the waves, is not well studied. In the present work, the oblique water entry of a cylinder under different regular waves is numerically investigated. The volume of fluid (VOF) method and the sub-grid scale (SGS) stress model based on the large eddy simulation (LES) method are adopted for the 3-D simulation with six degrees of freedom. The present numerical model is based on a wave model, and as shown by the previous work that the predicted cavity evolution in the calm water agrees well with the experimental results. The present model is validated and it is shown that it could be used to predict the correct wave periods and fluctuations. The cavity evolution mechanism, the dynamic characteristics and the vortex structures are analyzed. The cavity of the water entry with waves closes more quickly than in the calm water case. Finally, several parametric studies of the water entry with different wave heights and water entry locations are carried out. The results provide insights into the effects of the waves on the cavity dynamics for oblique water entry problems.

A dynamic study of the high-speed oblique water entry of a stepped cylindrical-cone projectile

High-speed oblique water entry is an interesting subject, many physical aspects of which remain unknown up to now. Among high-speed air-to-water projectiles, the supercavitating cylindrical-cone (SCC) ones have economic and operational advantages over the other types. However, maintaining stability of the SCC projectiles inside the cavity at shallow entry angles is a challenging issue from both practical and design-related points. The first section of the present study proposes a novel and unique scheme of air-to-water supercavitating projectile design which is called the supercavitating stepped cylindrical-cone (SSCC) projectile. The SSCC scheme is analyzed numerically to investigate the projectile stability improvement at shallow entry angles. The 6DOF dynamics of the SSCC projectile are investigated using the Star-CCM+ commercial code in the presence of three phases of air, water and vapor in a three-dimensional and transient model. Accuracy of numerical results and the model’s ability to simulate the physical phenomena of water entry is validated using experimental results from the literature, and both are in good agreement. In the present study, the high-speed oblique water entry dynamics of the SSCC projectile are investigated for five certain entry angles varying from 10° to 60°. The results show that the SSCC projectile faces intensive unstabilizing forces in the water entry process which leads to a heavy pitching moment and, hence, intensive angular velocity ( $$ \dot{\gamma } $$ ) on the projectile. This study also proves that the presence of step enhances the projectile stability in the entry process. The present study shows that, based on their geometry and mass characteristics, each SSCC projectile is capable of withstanding instability up to a critical value of the angular velocity ( $$ \dot{\gamma }_{\text{Cr}} $$ ). Therefore, projectile stability inside the cavity can be achieved when the value of maximum angular velocity ( $$ \left| {\dot{\gamma }} \right|_{\hbox{max} } $$ ) experienced by the projectile is lower that $$ \dot{\gamma }_{\text{Cr}} $$ (i.e., $$ \left| {\dot{\gamma }} \right|_{\hbox{max} } < \dot{\gamma }_{\text{Cr}} $$ ). The results of this study also show that $$ \left| {\dot{\gamma }} \right|_{\hbox{max} } $$ is inversely correlated with the $$ \gamma $$ , and that it follows a simple equation which is proposed in this study. Therefore, projectile stability inside the cavity can also be practically achieved by adjusting the shooting mechanism at an angle higher than the minimum stable entry angle ( $$ \gamma_{\hbox{min} } $$ ). This study also proposes an effective numerical approach to evaluate $$ \gamma_{\hbox{min} } $$ of a supercavitating projectile. It should be noted that determining the value of $$ \gamma_{\hbox{min} } $$ is an important factor from both a practical and design-related points of view.

Experimental study on the influence of the angle of attack on cavity evolution and surface load in the water entry of a cylinder

The characteristics of cavity evolution and surface load in water entry by a constrained-posture cylinder at different angles of attack are experimentally investigated. High-speed photography is used to capture flow behaviors, and a measurement system is established to measure the pressure on the surface of the cylinder and its acceleration during the process of water entry. The experimental results show that when the cylinder enters the water at a certain angle of attack, the cavity shows an obvious asymmetry. Comparison of angles of attack shows that the cavity evolution and load characteristics during the water entry process are closely related to the angle of attack of the cylinder. Increasing the angle of attack can short the period if cavity pinch-off but prolong the time of surface seal. Meanwhile, the peak value of impact pressure shows a gradual downward trend with the increased angle of attack, and the relationship between the duration of high load and the angle of attack is approximately linear. Moreover, the characteristics of the flow field play an important role in the surface load of the cylinder, an obvious and short-lived negative relative pressure will appear on the surface of the model inside the cavity at the initial stage of water entry, the part of cylinder that is not affected by the cavity and directly interacts with water has a continuous positive pressure trend. In addition, in can be found that there is a significant pressure fluctuation when the cavity separation line passes over the surface.

SPH simulations on water entry characteristics of a re-entry capsule

Smoothed particle hydrodynamics (SPH) is adopted to simulate the peak impact load, the water entry process and the water entry characteristics of a re-entry capsule with the complex capsule motions modelled by a developed six degrees of freedom fluid-solid coupling model. Diffused particle distribution is developed and used in the simulations to decrease memory and computational cost. The results show that the six degrees of freedom model and diffused particle distribution are valid. The results obtained by the improved SPH method match well with experimental results, and the maximal impact load of the capsule may reach more than 10 G, even tens of G. In addition, the peak impact loads are significantly affected by the capsule vertical velocity, the capsule mass, and the pitch angle, while are slightly affected by the horizontal velocity. More concretely, the peak impact load increases with the increase of vertical velocity, and decreases with the increase of mass. However, there is no definite law between the peak load and the pitch angle. These results can provide a foundation for guiding capsule design.

Cavitation bubble dynamics and structural loads of high-speed water entry of a cylinder using fluid-structure interaction method

This paper describes an investigation of the motion, structural response, and cavitation bubble evolution of a cylinder in the high-speed water entry (HSWE) process using a fluid-structure interaction (FSI) method. The effectiveness and accuracy of the FSI method are verified by comparison with experimental results available in the literature. The results show that the cylinder structure is deformed when considering the coupling effect between the fluid and the structure, and the impact load during water entry presents obvious fluctuation characteristics. Meanwhile, the von Mises stress distribution on the two end faces of the cylinder is in a ring shape and propagates as the structure deforms. Moreover, the cavitation bubble dynamics, motion and structural loads of the cylinder under different water entry velocities are investigated. The load at the initial stage is greater with the increase of the water entry velocity, which in turn leads to more significant fluctuation characteristics, thereby increasing the deformation of the structure.

Ship hull slamming analysis with smoothed particle hydrodynamics method

In the marine and ocean engineering area, the water-entry process is a typical problem of fluid-solid interaction, which involves complex phenomenon such as the large deformation of free surface and considerable structure movement. In this process, the predicting impact load and summarizing the evolution law of the free surface deformation have important reference significance for the hull structure design. To address this issue, numerical simulations are carried out using a robust Smoothed Particle Hydrodynamics (SPH) model. The accuracy of the present SPH model is firstly validated by simulating the water entry of bow-flare section in two and three dimensions, respectively. Then, we investigate the variation characteristics of impact load and the evolution of free surface during the entry of the bow-flare ship section with different roll angles (θ=0∘∼20.3∘). Attention is focused on the flow separating phenomenon and the spray jet on the free surface. Finally, the water entry of a three dimensional ship hull is simulated. The velocity and pressure of flow field are analyzed and some conclusions are drawn.

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.

Evolution of slamming load and flow field in water-entry process of trimaran ship section

A slamming motion is a serious issue when a trimaran is sailing on waves. Therefore, it is necessary to study the pressure and vertical acceleration of the measuring point on the ship's surface, and the velocity of the fluid particle of the flow field at different dropping heights, using model tests. First, a vertical water entry model test of a trimaran model was conducted at three different heights. Then, the pressures of five measuring points (at the bottom of the main hull and near the cross deck) and the acceleration of the model were measured. In addition, pressure variations and acceleration peak values are analysed. The time-record curves of the pressure were then fitted using a Gaussian function. Finally, the flow field was obtained using the particle image velocimetry technique. The results show that the peak values of the points in the cross deck and the upside of the main hull were maximum at H = 20 mm; nevertheless, other pressure and peak values of the slamming acceleration measurement points increased as the dropping height increased. Further, the shapes of the pressure curves near the peak value were sharper for the model's bottom than at other positions. Moreover, the flow particle velocity at the bottom of the trimaran model and the free surface between the main and side hulls was higher. There was also a significant amount of pupple generated below the cross deck after the cross deck's slamming. Finally, as the drop height increased, the position of the air-water mixture trended towards the side hull.

Numerical Investigations of Cavitation Nose Structure of a High-Speed Projectile Impact on Water-Entry Characteristics

In this study, a detailed analysis of the influences of cavitation nose structure of a high-speed projectile on the trajectory stability during the water-entry process was investigated numerically. The Zwart-Gerber-Belamri (Z-G-B) cavitation model and the Shear Stress Ttransport (SST)k-ω turbulence model based on the Reynolds Averaged Navier–Stokes (RANS) method were employed. The numerical methodology was validated by comparing the numerical simulation results with the experimental photograph of cavitation shape and the experimental underwater velocity. Based on the numerical methodology, the disk and the conical cavitation noses were selected to investigate the water-entry characteristics. The influences of cavitation nose angle and cavitation nose diameter of the projectile on the trajectory stability and flow characteristics were carried out in detail. The variation features of projectile trajectory, velocity attenuation and drag were conducted, respectively. In addition, the cavitation characteristics of water-entry is presented and analyzed. Results show that the trajectory stability can be improved by increasing the cavitation nose angle, but the drag reduction performance will be reduced simultaneously. Additionally, due to the weakening of drag reduction performance, the lower velocity of the projectile will cause the damage of the cavitation shape and the trajectory instability. Furthermore, the conical cavitation nose has preferable trajectory stability and drag reduction performance than the disk cavitation nose.

Simulation research on water-entry impact force of an autonomous underwater helicopter

Autonomous Underwater Helicopter (AUH) is a novel dish-shaped multi-functional submersible vehicle in the autonomous underwater vehicle (AUV) family. Numerical study of launch and recovery system for AUVs from a research vessel is significant in the overall design. Single-arm crane and air-launch way are the important ways of launching AUVs with the high expertise and security. However, AUVs are still easily subject to a huge impact load which can cause the body damage, malfunction of electronic components, and other serious accidents when AUVs are launching into water. In this paper, unsteady, incompressible, two-phase flow with identified boundary conditions was modeled in the computational domain using Volume of Fluid (VOF) technology, and different overset-grid sizes were set and analyzed to ascertain the accuracy of computational fluid dynamics (CFD) simulation first due to the setting of the grid which will directly affect the accuracy of the calculation results, especially the overset-grid convergence validation. Then, the change of water-entry impact force and velocity of AUH with different water-entry velocities and angles were calculated by CFD analysis software STAR-CCM + solver. The proper immersion angle of the AUH should be 75° under comprehensive analysis and comparison. Besides, the variations of pressure distribution of the AUH in the whole water-entry process were also obtained, which provides reference for the shape optimization in the future work.

Experimental and numerical investigation of the frequency-domain characteristics of impact load for AUV during water entry

Autonomous underwater vehicles (AUVs) are subjected to a very large impact load during the water-entry process, which may damage the structure of the vehicle and affect its motion trajectory. In this paper, five kinds of models with different nose shapes are tested under different water-entry velocities and angles, and the impact acceleration signals are obtained by a sensor. First, the accuracy of the experimental data is verified by comparison with the velocity obtained by the high-speed camera. Then, the ensemble empirical mode decomposition (EEMD) method combined with modal analysis is used to analyse the acceleration signal composition. Subsequently, a numerical simulation model based on the arbitrary Lagrangian Eulerian (ALE) method to describe the water-entering process of the vehicle is established, and the accuracy and capability of the numerical algorithm is verified by comparison with the experimental data. Finally, the frequency-domain characteristics of the impact load are analysed through the shock response spectrum (SRS) method. The result shows that the maximum acceleration shock spectrum of the impact load is related to the peak pulse width of the impact load and independent of the peak value. The smaller the pulse width is, the larger the inflection point frequency and magnification of the shock response spectrum are. The inflection point frequency of the shock response spectrum usually corresponds to the second-order bending natural frequency of the vehicle. The conclusions in this paper will be useful for the design and analysis of the water-entry impact structure of AUVs.

Numerical evaluation of the hydrodynamic impact characteristics of the air launched AUV upon water entry

In this paper, water entry process of air launched AUV is investigated by employing fully coupled finite element method and arbitrary Lagrange–Euler formulation (FEM-ALE) and using penalty coupling technique. Numerical model is established to describe the hydrodynamic characteristics and flow patterns of a high-speed water entry AUV. The effectiveness and accuracy of the numerical simulation are verified quantitatively by the experiments of the earlier study. Selection of suitable advection method and mesh convergence study is carried out during experimental validation process. It is found that appropriate mesh size of impact domain is crucial for numerical simulations and second-order Van Leer advection method is more appropriate for high speed water entry problems. Subsequently, the arbitrary Lagrange–Euler (ALE) algorithm is used to describe the variation laws of the impact load characteristics with water entry velocities, water entry angles and different AUV masses. Dimensionless impact coefficient of AUV at different velocities calculated using ALE method is compared with SPH results. This reveals that ALE method can also simulate the water entry process accurately with less computational cost. This research work can provide beneficial reference information for structure design of AUV and for selection of the water entry parameters.

Numerical simulations for water entry of hydrophobic objects

Based on the boundary data immersion method (BDIM) and the volume of fluid (VOF) method, the water entry process of hydrophobic objects is numerically simulated. The water crown, the cavity and the flow pattern are analyzed. In the present study, the cavity shape caused by the water entry and trajectories of objects are simulated by the numerical method. Simulation results are compared with experimental data, and the comparisons show that the present numerical approach has the ability to predict the complex process of water entry as well as the effects of the density of an object and entry velocity. Numerical results indicate that the depth of pinch-off increases as reducing the characteristic length of the cavity; the pinch-off time increases for the sphere with a larger density; the depth of cylinder, where occurs the cavity shape inversion behavior, is not affected by the entry velocity of the cylinder.

Computational Fluid Dynamics Study of Water Entry Impact Forces of an Airborne-Launched, Axisymmetric, Disk-Type Autonomous Underwater Hovering Vehicle

An autonomous underwater hovering vehicle (AUH) is a novel, dish-shaped, axisymmetric, multi-functional, ultra-mobile submersible in the autonomous underwater vehicle (AUV) family. Numerical studies of nonlinear, asymmetric water entry impact forces on symmetrical, airborne-launched AUVs from conventional single-arm cranes on a research vessel, or helicopters or planes, is significant for the fast and safe launching of low-speed AUVs into the target sea area in the overall design. Moreover, a single-arm crane is one of the important ways to launch AUVs with high expertise and security. However, AUVs are still subject to a huge load upon impact during water entry, causing damage to the body, malfunction of electronic components, and other serious accidents. This paper analyses the water entry impact forces of an airborne-launched AUH as a feasibility study for flight- or helicopter-launched AUHs in the future. The computational fluid dynamics (CFD) analysis software STAR-CCM+ solver was adopted to simulate AUH motions with different water entry speeds and immersion angles using overlapping grid technology and user-defined functions (UDFs). In the computational domain for a steady, incompressible, two-dimensional flow of water with identified boundary conditions, two components (two-phase flow) were modeled in the flow field: Liquid water and free surface air. The variations of stress and velocity versus time of the AUH and fluid structure deformation in the whole water entry process were obtained, which provides a reference for future structural designs of an AUH and appropriate working conditions for an airborne-launched AUH. This research will be conducive to smoothly carrying out the complex tasks of AUHs on the seabed.

Water entry behaviours of hemisphere-head projectiles with high velocity

The water-entry behaviours of projectiles with hemisphere-head were studied experimentally and theoretically, focusing on projectile dynamics and drag coefficient. Based on equivalent cone theory proposed by Baldwin, the equation of drag coefficient was developed to describe the resistance of hemispherical head projectiles from the time when the projectile contacts the water to the time the hemispherical head is submerged. A set of experimental apparatus was set up to record the water-entry process by high-speed photography, the variation of resistance during water-entry was obtained experimentally. Compared the acceleration calculated by conventional method, new method and experimental results, the new method is more consistent with the experimental value.