Supercavitating Projectile Tail-Slaps Based on a Normal Distribution

Abstract

The present study focuses on simulating supercavitating projectile tail-slaps with an analytical method. A model of 3σ-normal distribution tail-slaps for a supercavitating projectile is established. Meanwhile, the σ − κ equation is derived, which is included in this model. Next, the supercavitating projectile tail-slaps are simulated by combining the proposed model and the Logvinovich supercavity section expansion equation. The results show that the number of tail-slaps depends on where the initial several tail-slaps are under the same initial condition. If the distances between the initial several tail-slap positions are large, the number of tail-slaps will considerably decrease, and vice versa. Furthermore, a series of simulations is employed to analyze the influence of the initial angular velocity and the centroid. Analysis of variance is used to evaluate simulation results. The evaluation results suggest that the projectile’s initial angular velocity and centroid have a major impact on the tail-slap number. The larger the value of initial angular velocity, the higher the probability of an increase in tail-slap number. Additionally, the closer the centroid is to the projectile head, the less likely a tail-slap number increase. This study offers important insights into supercavitating projectile tail-slap research.

Keywords

Tail-slaps / Normal distribution / Supercavity / Stability / Supercavitating projectile

References

[1] ChuangHResearch of trajectory characteristics of supersonic-supercavitating projectile, 2017, Xi’an, Northwestern Polytechnical University: 30-35(in Chinese)

[2] FanCY, LiZL, DuMC, YuR. Numerical study on the influence of vehicle diameter reduction and diameter expansion on supercavitation. Applied Ocean Research, 2021, 116: 102870

[3] GuoZT, ZhangW, WangC. Experimental and theoretical study on the high-speed horizontal water entry behaviors of cylindrical projectiles. Journal of Hydrodynamics, 2012, 24(2): 217-225

[4] HeQK, WeiYJ, WangCH, ZhangJZ. Impact dynamics of supercavitating projectile with fluid/structure interaction. Journal of Harbin Institute of Technology, 2013, 20(1): 101-106

[5] HuZM, KhooBC, ZhengJG. The simulation of unsteady cavitating flows with external perturbations. Computers and Fluids, 2013, 77: 112-124

[6] KulkarniSS, PratapR. Studies on the dynamics of a supercavitating projectile. Applied Mathematical Modelling, 2000, 24(2): 113-129

[7] LiDJ, LiFJ, ShiYZ, DangJJ, LuoK. A novel hydrodynamic layout of front vertical rudders for maneuvering underwater supercavitating vehicles. Ocean Engineering, 2020, 215: 107894

[8] LiT, FengJ, XieY, SunYExperimental investigation on projectiles high-speed water entry, 2018

[9] LiuCL, ZhangYW, WangYD, QiXB. Investigation into load characteristics of submarine-launched missile being ejected from launch tube considering the adapter elasticity. Binggong Xuebao/Acta Armamentarii, 2015, 36(2): 379-384(in Chinese)

[10] LvY, XiongT, YiW. Multistability in a simplified underwater supercavity system. International Journal of Bifurcation and Chaos, 2017, 27(8): 1-16

[11] MaoXNonlinear robust control design for a high-speed supercavitating vehicle, 201040-42

[12] MirzaeiM, AlishahiMM, EghtesadM. High-speed underwater projectiles modeling: a new empirical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2015, 37(2): 613-626

[13] MirzaeiM, TaghvaeiH. A novel configuration optimization for high-speed ventilated supercavitating vehicles. Ocean Engineering, 2019, 179: 13-21

[14] Nguyen ThaiD, HorákV, Nguyen VanD, Dao VanD, Nguyen VanH, Do DucL. Ballistics of supercavitating projectiles. Advances in Military Technology, 2018, 13(2): 237-248

[15] NguyenVT, ParkWG. Numerical study of the thermodynamics and supercavitating flow around an underwater high-speed projectile using a fully compressible multiphase flow model. Ocean Engineering, 2022, 257: 111686

[16] RandRH, RudraPImpact dynamics of a supercavitating underwater projectile, 1997

[17] SchaffarM, ReyC, BoeglenGBehavior of supercavitating projectiles fired horizontally in a water tank: Theory and experiments-CFD computations with the OTi-HULL Hydrocode, 2012

[18] SemenenkoVN, NaumovaYI. Study of the supercavitating body dynamics. Supercavitation: Advances and Perspectives A Collection Dedicated to the 70th Jubilee of Yu.N. Savchenko, 20121-230

[19] VlasenkoYDExperimental investigation of supercavitation flow regimes at subsonic and transonic speeds, 20031-8

[20] WangKJ, RongG, MuQ, YiWJ, ChenZH. Double slapping effects on a supercavitation projectile. AIP Advances, 2019, 9(1): 015104

[21] WangKJ, RongG, YinHQ, YiWJ. Dynamic features of kinetic energy supercavitating vehicles. Applied Ocean Research, 2020, 102: 102304

[22] WangKJ, WuYL, HaoSP, RongG. Structural optimization and stability analysis for supercavitating projectiles. Journal of Marine Science and Application, 2023, 22(3): 527-544

[23] WangY, SunXJ, DaiYJ, WuGQ, CaoY, HuangDG. Numerical investigation of drag reduction by heat-enhanced cavitation. Applied Thermal Engineering, 2015, 75: 193-202

[24] XuHY, WangC, WeiYJ, CaoW. On the nonlinear hydrodynamic characteristic of a ventilated supercavitating vehicle with high Froude number. Ocean Engineering, 2023, 268: 113457

[25] YenT, MorabitoMG, ImasL, DzielskiJE, DatlaRInvestigation of cylinder planing on a flat free surface, 2011396-403

[26] YoonK, LiJQ, ShaoSY, KarnA, HongJR. Investigation of ventilation demand variation in unsteady supercavitation. Experimental Thermal and Fluid Science, 2021, 129: 110472

[27] ZhangAM, LiSM, CuiP, LiS, LiuYL. A unified theory for bubble dynamics. Physics of Fluids, 2023, 35(3): 033323

[28] ZhaoX, LyuX, LiD. Modeling of the tail slap for an underwater projectile within supercavitation. Mathematical Problems in Engineering, 2019, 2019(4): 1-10

[29] ZhuX, LiJ. Numerical simulation research on six-degree-of-freedom tail-slap of supercavitating projectile. Chinese Journal of Hydrodynamics, 2022, 37(4): 474-482

[30] ZouW, LiuTX, TangZH, ShiYK. Optimized design of the overall shapes of supercavitating vehicles based on a multi-objective adaptive genetic algorithm. Ocean Engineering, 2023, 286: 115523

[31] ZouW, LiuT, ShiY. Optimization of the maximum range of supercavitating vehicles based on a genetic algorithm. Ocean Engineering, 2021, 239: 109892

RIGHTS & PERMISSIONS

Harbin Engineering University and Springer-Verlag GmbH Germany, part of Springer Nature