Study on the Load Characteristics and Ballistic Stability of High-speed Water Entry for Vehicle in Wave Environments

Abstract

The non-constant characteristics of the wave environment substantially impact the flow field structure and motion stability of the trans-medium vehicle. In this paper, a multiphase coupled numerical model of a vehicle with cavitation disk of high-speed water entry under wave interference is established on the basis of the VOF multiphase flow model and overlapping mesh technology. The accuracy of the model is verified through comparisons between experimental data and simulation results. This study systematically investigates the influence mechanisms of parameters such as the water-entry inclination angle, the attack angle, and the wave phase on the impact load and the trajectory stability. The results indicate that the cavity exhibits asymmetric evolution characteristics during the process of wavefront water entry influenced by the relative angle of water entry. The peak axial load at the water entry of the wave crest and trough phases is 1.5 times that of the peak load at the water entry of the wave front. Ballistic destabilization is most pronounced under the wavefront entry condition (70° water entry angle and 3° angle of attack). These findings provide valuable theoretical support for ballistic prediction and attitude control of trans-media vehicles entering water under complex sea states.

Keywords

High-speed / Water entry / Wave / Load characteristics / Ballistic stability

References

[1] Che PQ, Shi Y, Zhao HR, Yu YL, Pan G. Study on the cavity evolution and load characteristics of large projectile during high-speed water entry. Ocean Engineering. 2024, 303: 117673.

[2] Chen C, Wei YJ, Wang C, Bi DF. Numerical analysis of the multiphase flow characteristics in the initial period of water-entry of a projectile at transonic speed. Journal of Vibration and Shock. 2019, 38(6): 46-53

[3] Fan X, Hou Y, Huang ZG, Liu XY, Chen ZH, Xu YM. Effects of apertures on the multiphase flow characteristics of vertical water entry of hollow cylinders. Ocean Engineering. 2025, 340: 122302. Part 2)

[4] Gu JX, Dang JJ, Shi XF, Xu HY, Li DJ, Qin K, Luo K. Water-entry and leveling trajectories of a ventilated supercavitating vehicle at different preset rudder angles. Physics of Fluids. 2025, 376063327.

[5] Guo ZQ, Liu RS, Sun S, Zhang HH. Research on the flow field and trajectory characteristics of high-speed projectile entry water in waves. Physics of Fluids. 2024, 36124124.

[6] He SC, Luo K, Huang C, Gu JX, Ren X. Effect of spinning motion on cavitation and trajectory characteristics of projectile during water entry. Journal of Unmanned Undersea Systems. 2021, 296760-768

[7] Huang QG, Wang C, Shi Y, Pan G, Liu GQ. Study of the cavity and hydrodynamic characteristics of water entry for projectiles with different wave parameters. Ocean Engineering. 2024, 313: 119441. Part 3)

[8] Lee M, Longoria RG, Wilson DE. Cavity dynamics in high-speed water entry. Physics of Fluids. 1997, 93540-550.

[9] Liang JQ, Wang R, Xu BC, Qi XB, Li RJ. Research on influence of angle of attack on process of high-speed water-entry projectile. Journal of Ordnance Equipment Engineering. 2020, 41723-28

[10] Li Q, Lu L, Cai T. Numerical investigations of trajectory characteristics of a high-speed water-entry projectile. AIP Advances. 2020, 10: 095107.

[11] Li Q, Lu L. Numerical investigations of cavitation nose structure of a high-speed projectile impact on water-entry characteristics. Journal of Marine Science and Engineering. 2020, 8(4): 265.

[12] Li Z, Zhang YX, Wang XG, Bai YL, Ren ZY. Research on the trajectory flattening characteristics of supercavitating vehicles during high-speed water entry. Journal of Astronautics. 2025, 465922-934

[13] Li ZY, Hu HB, Wang C, Xie ZL, Chen XP, Yuan ZM, Du P. Hydrodynamics and stability of oblique water entry in waves. Ocean Engineering. 2024, 292: 116506.

[14] Lian YX, Lou HT, Li XC, Wang P, Ma W, Sun TS, Wang LG, Sun C, Xu JW, Yang SQ. Water entry characteristics of an air-droppable underwater glider in waves. Engineering Applications of Computational Fluid Mechanics. 2025, 1912593413.

[15] Liu LX, Chen Y, Li J. Investigation on cylinder water entry in regular wave field using large eddy simulation. International Journal of Multiphase Flow. 2024, 173104759.

[16] Liu ZP, Shi Y, Wu K, Zhao HR, Pan G. Experimental study on load characteristics of vehicle during high-speed water entry. Ocean Engineering. 2023, 288116052. Part 1)

[17] Ma W, Lou HT, Li XC, Wang P, Wang LG, Niu WD, Yang M, Fa S, Song JR, Yang SQ. Study on water entry characteristics of an air-droppable underwater glider in hydrostatic water. Physics of Fluids. 2025, 371017103.

[18] Qian CC, Yu CH, Mu Q, Yi WJ, Guan J. Numerical research of effects of launch speed and launch angle on water entry of high-speed projectile. Journal of Ordnance Equipment Engineering. 2019, 40735-39

[19] Qin Y, Yi WJ, Guan J. Numerical simulation for cavitation flow of high-speed rotating body oblique entering into water. Journal of Ordnance Equipment Engineering. 2019, 40799-104

[20] Shi Y, Pan G, Yan GX, Yim SC, Jiang J. Numerical study on the cavity characteristics and impact loads of AUV water entry. Applied Ocean Research. 2019, 89: 44-58.

[21] Tian Y, Shi FL, Li RB, Zhang JL, Chang X. Effects of wave conditions on the impact loads and stability of a high-speed projectile during oblique water entry. Physics of Fluids. 2025, 37: 093612.

[22] Wang C, Huang QG, Lu L, Pan G, Gao S. Numerical investigation of water entry characteristics of a projectile in the wave environment. Ocean Engineering. 2024, 294116821.

[23] Wang Z, Wu ML, Dai WL. Study on load characteristics of high-speed water-entry of large caliber projectile. Journal of Ballistics. 2020, 32(1): 15-22

[24] Wang YK, Wang L, Liu PA. Numerical simulation of the load for the high speed water-entry of revolving projectile. Journal of Northeast Electric Power University. 2022, 42110-18

[25] Wang S, Jiang YH, Zou ZH, Wang HR. Experimental investigation of a body water entry with a water jet cavitator. Journal of Marine Science and Application. 2025, 24(2): 388-397.

[26] Wang XH, Li P, Sun SM, Yan M. Numerical simulation of projectile’s high-speed water-entry process based on CEL method. Journal of Ship Mechanics. 2022, 26(1): 11-17

[27] Wang JJ, Ming FR, Liu C, Zhang QS, Chen H. Formation mechanism of normal force of a vehicle during the oblique water entry based on multi-phase smoothed particle hydrodynamics. Engineering Analysis with Boundary Elements. 2025, 173: 106156.

[28] Wang LG, Gao HW, Yang SQ, Niu WD, Ma W, Wang C. Design, analysis, and local structural optimization of an air-droppable underwater glider under the impact load during water entry. Ocean Engineering. 2024, 312119013. Part 2)

[29] Wang WH, Wang YY. Numerical study on cylinder entering water in wave. Journal of Shanghai Jiaotong University. 2010, 44101393-1399

[30] Wang S, Guedes Soares C. Stern slamming of a chemical tanker in irregular head waves. Ocean Engineering. 2016, 122: 322-332.

[31] Wu XC, Chang X, Liu SW, Yu PY, Zhou LL, Tian W. Numerical study on the water entry impact forces of an air-launched underwater glider under wave conditions. Shock and Vibration. 2022, 202214330043

[32] Yao XL, Yang Y, Ma GH, Chen YY, Yin Q, Kong DC, Sun LQ, Fan SQ, Fang M. Research on the characteristics and similarity relationships of impact load reduction of a vehicle entering water. Applied Ocean Research. 2024, 142: 103814.

[33] Yu YL, Shi Y, Pan G, Che PQ. Numerical analysis of cavitation and impact load characteristics of supercavitating vehicle entering water at high speed. Journal of Northwestern Polytechnical University. 2022, 403584-591.

[34] Zhang ZF, Shao Y, Zhang Q, Xie YJ, Sui YT, Zhang GY. Mechanism study on the effect of pre-set bubbles near the free surface on the water-entry trajectory stability of vehicles with different length-to-diameter ratios. International Journal of Multiphase Flow. 2026, 194105480.

[35] Zhang LT, Wang ZK, Jia HX. Effect of wave phases and heights on supercavitation flow field and dynamic characteristics of successively fired high-speed projectiles. Journal of Marine Science and Engineering. 2023, 113629.

[36] Zeng QL, Zhao MZ, Fan CY, Wan LR, Wang M, Diao RX. Research on supercavitation phenomenon under the effect of flow field disturbance. Ocean Engineering. 2024, 311118891. Part 1)

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