Numerical study on hydrodynamics of high-speed water entry in random wave environments for full-scale supercavitating vehicles

The high-speed water entry is of great significance in the development of the cross-media equipment. In this paper, the high-speed oblique water entry of a conical projectile is numerically investigated with particular emphasis on the local fluid field and trajectory behaviors. The numerical model is based on the Reynolds average Navier-Stokes (RANS) method with the Volume of Fluid (VOF) approach for capturing complicated multiphase flow characteristics. The present method is validated against the published experimental data by simulating a case of high-speed oblique water entry. The highspeed oblique water entry of the conical projectile under different impact velocities are investigated. The comprehensive process of the water entry, including the initial impact, formation, development, contraction, closure and collapse of the open cavity, have been reproduced. The flow evolution process of the high-speed water entry, which involves the cavity shape and the cavitation evolution, is analyzed comprehensively. Furthermore, the variation trends of the impulsive load, the projectile attitude and the trajectory stability are examined. The study is expected to enhance the understanding of the cavitation evolution, and is helpful for the design of the cross-media equipment.

During high-speed oblique water entry, the continuous impact load experienced by the vehicle can lead to structural damage and influence trajectory stability. This article investigates the load and motion response characteristics of the vehicle with different rudder angles during the entire high-speed water entry process. In the numerical methods, a quaternion-based six degrees of freedom motion system is employed to describe the rigid body motion, while a multiphase Eulerian finite element method serves as the fluid solver. An experiment is conducted to verify the accuracy of the numerical method. Furthermore, the mechanisms underlying the formation of tail slamming normal loads during high-speed oblique water entry of the vehicle at different rudder angles are explored. The loads including axial force coefficient, normal force coefficient, and pitch torque coefficient are extensively discussed. Results indicate that the tail slamming phenomenon and the vehicle's trajectory are significantly influenced by the rudder angle. The design of positive and negative rudder angles causes both the upward and downward tail slamming. The “excellent rudder angle range α̃” for the vehicle during high-speed water entry is defined. Selecting a rudder angle design within this range can effectively reduce the normal load during the tail slamming events, it can result in decreased pitch torque amplitude and form a straighter, more stable trajectory. This work provides new insights into load control during vehicle steering.

The high-speed oblique water entry of a segmented vehicle presents a complex multiphase fluid–structure interaction (FSI) problem, characterized by the evolution of the vapor–liquid cavity and the transient impact loads transmission. This study constructs a high-fidelity numerical model that integrates a multiphase flow solver with a FSI solver to investigate the underlying fluid physics and shock response during initial water entry for a segmented vehicle connected by bolts. The effects of key parameters such as entry velocity and angle on the spatiotemporal evolution of cavity, impact loads transmission, and shock response spectrum (SRS) are systematically investigated. Results show that multiphase FSI during cavity evolution notably amplifies high-frequency fluctuations in acceleration and induces asymmetry stress wave propagation. Segments with longer propagation distances exhibit higher peak axial forces, while connection interfaces experience negative normal contact forces and lateral contact moments. SRS analysis reveals resonant amplification peaks at 600 and 1500 Hz across the segments, with amplitudes reaching 100 g, and higher peaks at the monitoring points. Stress concentration and wave asymmetry generate elevated local stresses at connections and bolts, necessitating protective measures targeting segment-specific load peaks, critical frequency bands, and interface/bolt reinforcement. This study provides an effective multiphase FSI simulation framework and insights into the flow and shock characteristics of a segmented vehicle during high-speed water entry.

Classification of the collapse of a composite fairing during the oblique high-speed water entry

During high-speed oblique water entry, the slender vehicle is subjected to intense impact loads, particularly the normal loads induced by tail slamming. These loads significantly compromise attitude stability and structural integrity. However, the underlying mechanisms of tail slamming dynamics in such configurations have not been fully elucidated. This study conducts a numerical analysis of the oblique water entry of a slender cylinder, focusing on the tail slamming formation mechanisms and the influence of initial motion conditions. A numerical model using on an improved immersed boundary method is established and validated against experimental oblique water-entry data to ensure reliability and accuracy. The results reveal that the pitching moment generated during cylinder crossing the water surface is the primary driver of the pitching motion responsible for the tail slamming. The pressure distribution along the wet area on the cylinder head varies with the water-entry angle, critically influencing the formation characteristics of the pitching moment. As the water-entry angle increases, the evolution curve of pitching moment transitions from a single peak to a positive-negative double peak, and the cavity diameter decreases progressively. The timing and maximum normal impact force of tail slamming exhibit a non-monotonic relationship with the water-entry angle but scale linearly with the water-entry velocity. Furthermore, the dimensionless coefficients of the pitching moment exhibit overlap across different water-entry velocities early in the water-entry process. This work provides novel insight for mitigating tail-slamming loads during high-speed oblique water entry of slender underwater vehicles.

To investigate the fluid-structure interaction (FSI) and structural response characteristics of hollow cylindrical shell during high-speed vertical water entry, this study integrates computational fluid dynamics (CFD) and finite element method (FEM) to develop a numerical simulation framework for fluid-structure coupling in high-speed water entry scenarios. By employing bidirectional coupling between STAR-CCM + and Abaqus, real-time exchange of hydrodynamic loads and structural displacements is achieved, enabling a comprehensive analysis of the effects of varying water entry velocities on the evolution of cavitation patterns and the associated structural responses. The results indicate a strong dependence of cavitation dynamics on entry velocity. As the velocity increases, the initial cavitation structure transitions from a symmetric and closed form to an asymmetric and expanded configuration. The initial water entry velocity not only governs the magnitude of deceleration and penetration depth but also influences the resistance attenuation characteristics. Significant structural deformation occurs during the initial impact phase, with the response exhibiting a nonlinear evolution from elastic deformation to buckling instability. Distinct differences in structural response modes are observed across different water entry velocities.

The hollow cylinder is a special cylindrical body with a through structure in the middle position. A collaborative method based on the finite volume method and the finite element method is used to numerically calculate high-speed vertical water entry of the hollow cylinder. The results show that the hollow cylinder exhibits a unique internal jet phenomenon, and the height of the jet shows an almost linear growth trend. Compared to the completely sealed hollow cylinder, the displacement and velocity of the hollow cylinder after entering into water are greater, but the volume of generated cavities is smaller. The force and stress at the bottom of the hollow cylinder are smaller than those at the bottom of the completely sealed hollow cylinder. The force and stress at the bottom of the hollow cylinder are greater than those at its top position. The greater thickness of the hollow cylinder has greater velocity and displacement, as well as greater peak values of the force and stress at its bottom position. The stress fluctuation at the bottom of the hollow cylinder with a smaller thickness is more pronounced.

Dynamics analysis of high-speed water entry of axisymmetric body using fluid-structure-acoustic coupling method

Analysis of high-speed water entry in semi-sealed cylindrical shells: Cavity formation and self-disturbance characteristics

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.

This paper studied the synchronous parallel high-speed vertical water entry of cylinders through experimental methods. The study found that the double cavity exhibited favorable symmetry characteristics during the synchronous parallel vertical water entry of cylinders at the same speed. The outside of the double cavity develops freely, consistent with the single cavity. The lateral spacing deforms the inside contour of the double cavity. The diameter of the inside cavity increases as the lateral spacing increases and gradually approaches that of a single cavity. The cavity length increases with decreasing lateral spacing. In addition, the maximum diameter and length of the cavity increase with the increase in water entry speed under the same lateral spacing. This paper uses the deformation index β to present the double cavity contour prediction model for the water entry process. The model accurately predicts the cavity contour of a synchronous parallel vertical water entry. Additionally, it is deduced that the critical lateral spacing without mutual influence between cavities in this speed range is approximately 7–8D0. The “grass sprouting” splashing development rules were discovered during the synchronous parallel high-speed vertical water entry.

Investigation of oblique water entry of high-speed supercavitating projectiles using transient fluid-structure interaction simulation

To study the ballistic characteristics of high-speed vertical impact of projectiles on wave liquid surfaces, the method of Detached-Eddy Simulation (DES) with elliptic-blending Reynolds stress model is adopted to numerically simulate the high-speed vertical water entry of projectiles under different fifth-order Stokes wave curvatures. Through experiments, the accuracy and reliability of the numerical method were verified. Based on the numerical simulation method, it is stipulated that the convex curvature of waves is positive and the concave curvature is negative, and the influence of different wave curvatures on water entry trajectories is studied. The research results show that under small curvature wave conditions, the curvature of the entry position has a negligible effect on the axial load during the water entry process; negative curvature positions delay the peak time of the axial load in the entry wave valley compared to positive curvature positions. When the projectile vertically impacts waves at the position with zero curvature at the same actual water entry angle, compared to entering a quiescent free surface, the projectile experiences slower velocity decay, larger axial body loads, earlier peak time of axial load, shorter water entry process, and the trajectory of the projectile is still influenced by the curvature around this position.

Integrated with high-speed oblique water entry tests of a large caliber conical-nosed projectile and numerical simulations based on the arbitrary Lagrange–Euler fluid–structure interaction method, the deflection behavior of projectile during the high-speed oblique water entry in various conditions is investigated systematically in the present paper. First, the rationality and practicality of related finite element method simulation are verified by the ballistic data in the oblique water entry tests. Then, the force mode and load variation characteristics in the projectile as well as the mechanism for the deflection of trajectory are discussed in detail regarding to the oblique water entry at a high-speed of 500 m/s. Furthermore, the influence of various factors, including impact velocity, oblique angle, and attack angle, on the deflection behavior of projectile is analyzed systematically. It is demonstrated that the instability of projectile motion is mainly due to the pitching moment, which is significantly affected by the actual water entry condition. The impact velocity mainly contributes to the projectile deflection rate, and a higher impact velocity generally results in a more rapid trajectory deflection. The water oblique angle affects both the rate and degree of projectile deflection, and the deflection degree displays different trends in different water oblique angle ranges: when the oblique angle is less than 15°, the projectile usually jumps out of the water, i.e., a yaw phenomenon occurs; when the oblique angle locates in the range of 30°–60°, the deflection trend is almost the same, and the projectile gradually deflects from the initial oblique state to a horizontal state, then to a vertical state, and eventually moves downwards in a “launch” posture with its nose opposite to the entry direction; and when the angle increases to 75°, the projectile can no longer rotate to a vertical state after it rotates to a horizontal state, instead it moves downwards in an oblique state with its nose facing upwards. Comparatively, the attack angle affects the deflection direction, and a positive attack angle usually leads to the increase in deflection degree, while a negative attack angle will change the deflection direction. Related research is of significance in predicting the ballistic evolution characteristics of projectile at high-speed oblique water-entry and optimizing the projectile configuration as well as the impact conditions.

Harvesting wideband and random vibration energy in the vehicle environment is a promising route to power mobile electronic devices. Conventional energy harvesters cannot realize steady-state output, making the energy management circuit design difficult. This work presents an electromagnetic harvester with a counterweight unit, a gearbox, and a generator, which can be adapted to wideband automatic energy storage and quantized output release. The counterweight unit with the low-frequency response can effectively sense the weak vibration. The coil spring in the energy storage gear train is in particular used to store low-frequency random vibration energy in the environment and release the energy stored by the coil spring by switching the gear train. Finally, the coil spring drives the generating gear train to realize the steady-state output of mechanical energy to electrical energy. At a frequency of 2.5 Hz and an acceleration of 0.4 g, the average output power of the automatic energy storage and steady-state output release energy harvester (ASSR) by using a coil spring to first store energy and then quantize the output is 114.5 times higher than that of the method of continuous generating without using a coil spring. The ASSR's energy output can charge the lithium battery (3.7 V, 40 mAh) from 2.6 to 3.716 V during a 60 km ride at an average speed of 12.7 km/h while powering the mobile phones and Bluetooth devices continuously through the energy management circuit. The strategy shows the great potential of micro-energy harvester in various wideband random vibration environments for powering electronics.