王浩宇 , 李木易 , 程少华 , 等 . 航行体高速入水问题研究综述 [J ] . 宇航总体技术 , 2021 , 5 ( 3 ): 65 - 70 .

WANG H Y , LI M Y , CHENG S H , et al . Review of vehicle’s high-speed water entry [J ] . Astronautical Systems Engineering Technology , 2021 , 5 ( 3 ): 65 - 70 . (in Chinese)

CAMERON P J K , ROGERS P H , DOANE J W , et al . An experiment for the study of free-flying supercavitating projectiles [J ] . Journal of Fluids Engineering , 2011 , 133 ( 2 ): 021 303.

RAND R , PRATAPR R , RAMANI D , et al . Impact dynamics of a supercavitating underwater projectile [C ] //Proceedings of the 1997 ASME Design Engineering Technical Conferences . Sacramento, CA, US : ASME , 1997 .

RUZZENE M , SORANNA F . Impact dynamic of elastic stiffened supercavitating underwater vehicles [J ] . Journal of Vibration and Control , 2004 , 10 ( 2 ): 243 - 267 . DOI: 10.1177/1077546304035607 http://doi.org/10.1177/1077546304035607 http://journals.sagepub.com/doi/10.1177/1077546304035607 http://journals.sagepub.com/doi/10.1177/1077546304035607 The dynamic behavior of and the vibration in supercavitating underwater vehicles are here investigated and controlled. Supercavitating vehicles exploit supercavitation as a means to reduce drag and increase their underwater speed. The forces acting on supercavitating vehicles are completely different from those on conventional submerged bodies, since only a tiny percentage of their external surface area is wetted and water-vapor forces are almost negligible. The hydrodynamic stability of supercavitating bodies is achieved through after-body planing, or surfing, along the internal surface of the cavity, or through periodic impacts, or 'tail-slaps', with the interior surface of the cavity. The interactions between the vehicle and the water/cavity interface are sources of structural strains and vibrations, which undermine the structural reliability of the vehicle and affect its guidance. The dynamic behavior of supercavitating vehicles is here analyzed. The vehicles are modeled as slender elastic beams in order to predict their dynamic response under 'tail-slap' conditions both in terms of rigid body motion as well as dynamic strains and vibrations. The developed numerical model predicts the response of the considered class of supercavitating vehicles and it is used to estimate the effect of periodically placed stiffening rings on the amplitude of the vibrations induced by the tail-slap impacts. The analysis is motivated by the need to accurately model the structural characteristics of supercavitating vehicles in order to estimate the vibration transmission paths along the structure and to envision and design systems that improve their guidance and control efficiency. The models here presented will be included in a simulation-based design procedure for supercavitating vehicles, where optimal design configurations will be identified through a multidisciplinary design optimization (MDO) approach. The MDO process will consider structural performance trade-offs in order to determine configurations that simultaneously provide minimum vibrations and maximum structural reliability, with minimum added weight and costs.

RUZZENE M , KAMADA R , BOTTASSO C L , et al . Trajectory optimization strategies of supercavitating underwaters vehicles [J ] . Journal of Vibration and Control , 2008 , 14 ( 5 ): 611 - 644 . DOI: 10.1177/1077546307076899 http://doi.org/10.1177/1077546307076899 http://journals.sagepub.com/doi/10.1177/1077546307076899 http://journals.sagepub.com/doi/10.1177/1077546307076899 Supercavitating vehicles are characterized by substantially reduced hydrodynamic drag, in comparison with fully wetted underwater vehicles. Drag is localized at the nose of the vehicle, where a cavitator generates a cavity that completely envelopes the body, at the fins, and on the vehicle after-body. This unique loading configuration, the complex and non-linear nature of the interaction forces between vehicle and cavity, the unsteady behavior of the cavity itself and memory effects associated with its formation process make the control and maneuvering of supercavitating vehicles particularly challenging. This study presents an initial effort towards the evaluation of optimal trajectories for this class of underwater vehicles. Flight trajectories and maneuvering strategies for supercavitating vehicles are obtained through the solution of an optimal control problem. Given a cost function, and general constraints and bounds on states and controls, the solution of the optimal control problem yields control time histories that maneuver the vehicle according to the desired strategy, together with the associated flight path. The optimal control problem is solved using the direct transcription method, which does not require the derivation of the equations of optimal control and leads to the solution of a discrete parameter optimization problem. Examples of maneuvers and resulting trajectories are given to demonstrate the effectiveness of the proposed methodology and the generality of the formulation.

魏英杰 , 何乾坤 , 王聪 , 等 . 超空泡射弹尾拍问题研究进展 [J ] . 舰船科学与技术 , 2013 , 35 ( 1 ): 7 - 15 .

WEI Y J , HE Q K , WANG C , et al . Review of study on the tail-slap problems of supercavitating projectile [J ] . Ship Science and Technology , 2013 , 35 ( 1 ): 7 - 15 . (in Chinese)

赵成功 , 王聪 , 魏英杰 , 等 . 质心位置对超空泡射弹弹尾拍运动影响分析 [J ] . 北京航空航天大学学报 , 2014 , 40 ( 12 ): 1754 - 1760 .

ZHAO C G , WANG C , WEI Y J , et al . Analysis of the effect of mass center position on tail-slap of supercavitating projectile [J ] . Journal of Beijing University of Aeronautics and Astronautics , 2014 , 40 ( 12 ): 1754 - 1760 . (in Chinese)

赵成功 , 王聪 , 孙铁志 , 等 . 初始扰动对射弹尾拍运动及运动特性影响分析 [J ] . 哈尔滨工业大学学报 , 2016 , 48 ( 10 ): 71 - 76 .

ZHAO C G , WANG C , SUN T Z , et al . Analysis of tail-slapping and ballistics characteristics of supercavitating projectiles under different initial disturbances [J ] . Journal of Harbin Institute of Technology , 2016 , 48 ( 10 ): 71 - 76 . (in Chinese)

古鉴霄 , 党建军 , 黄闯 , 等 . 衡重参数对超空泡射弹有效射程的影响 [J ] . 兵工学报 , 2022 , 43 ( 6 ): 1376 - 1386 . DOI: 10.12382/bgxb.2021.0319 http://doi.org/10.12382/bgxb.2021.0319 为研究衡重参数对超空泡射弹有效射程的影响，基于流体体积多相流模型和刚体空间运动方程组，建立超空化流场和刚体运动相耦合的仿真方法，通过与文献\[23\]试验结果对比验证仿真方法的合理性。通过仿真计算研究超空泡射弹的水下弹道运动特性，获得质心位置、质量等典型衡重参数对射弹有效射程的影响规律。研究结果表明：超空泡射弹的水下弹道具有稳定尾拍现象，尾拍的波长和振幅近似恒定；后移质心可有效增加超空泡射弹的水下增程，质心位置后移9%，水下射程提高14%；增加射弹质量可显著增加水下射程，质量增大150%，水下射程提高70%。

GU J X , DANG J J , HUANG C , et al . Influence of weight parameters on the effective range of supercavitation projectile [J ] . Acta Armamentarii , 2022 , 43 ( 6 ): 1376 - 1386 . (in Chinese) DOI: 10.12382/bgxb.2021.0319 http://doi.org/10.12382/bgxb.2021.0319 To obtain the influence of weight parameters on the effective range of supercavitation projectile，a coupling numerical method of supercavitation flow and rigid body motion is established based on the VOF multiphase flow model and the space motion equations of rigid body. The proposed method is validated by the experimental data in literature Ref\[23\]. The underwater ballistic characteristics of supercavitation projectile were studied，and the influence of typical weight parameters，such as centroid position and mass，on the effective range of the projectile were obtained. The results show that the underwater trajectory of supercavitation projectile has a stable tail-slap phenomenon，and the wavelength and amplitude of tail-slap keep approximately constant. Increasing the distance of centroid position away from the cavitator can effectively increase the underwater range of supercavitation projectile. The range of supercavitation projectile is increased by 14% when the centroid distance is increased by 9%. The mass of supercavitation projectile can be increased to significantly increase the underwater range. The range of supercavitation projectile increases by 70% when its mass is increased by 150%.

梁景奇 , 徐保成 , 王瑞 , 等 . 初速对高速射弹尾拍特性的影响 [J ] . 弹箭与制导学报 , 2020 , 40 ( 2 ): 130 - 134 , 139.

LIANG J Q , XU B C , WANG R , et al . Study on the influence of initial velocity on the characteristics of high speed projectile tail-slapping [J ] . Journal of Projectiles, Rockets, Missiles and Guidance , 2020 , 40 ( 2 ): 130 - 134 , 139. (in Chinese)

梁景奇 , 王瑞 , 徐保成 , 等 . 攻角对高速射弹入水过程影响研究 [J ] . 兵器装备工程学报 , 2022 , 41 ( 7 ): 23 - 28 .

LANG J Q , WANG R , XU B C , et al . Research on influence of angle of attack on process of high-speed water-entry projectile [J ] . Journal of Ordnance Equipment Engineering , 2022 , 41 ( 7 ): 23 - 28 . (in Chinese)

姚忠 , 王瑞 , 祁晓斌 , 等 . 初始扰动对高速射弹尾拍过程流体动力特性与弹道特性的影响 [J ] . 兵工学报 , 2020 , 41 ( 增刊1 ): 46 - 53 .

YAO Z , WANG R , QI X B , et al . The influence of initial disturbance on the hydrodynamic and ballistic characteristics of high-speed projectile during tail slapping [J ] . Acta Armamentarii , 2020 , 41 ( S1 ): 46 - 53 . (in Chinese)

王晓辉 , 李鹏 , 孙士明 , 等 . 射弹高速入水尾拍载荷和弹道特性的数值研究 [J ] . 船舶力学 , 2022 , 26 ( 8 ): 1111 - 1119 .

WANG X H , LI P , SUN S M , et al . Numerical study on hydrodynamic and ballistic characteristics of projectile’s high-speed water-entry process [J ] . Journal of Ship Mechanics , 2022 , 26 ( 8 ): 1111 - 1119 . (in Chinese)

王云 , 袁绪龙 , 吕策 , 等 . 弹体高速入水弯曲弹道实验研究 [J ] . 兵工学报 , 2014 , 35 ( 12 ): 1998 - 2002 . DOI: 10.3969/j.issn.1000-1093.2014.12.010 http://doi.org/10.3969/j.issn.1000-1093.2014.12.010 通过模型高速入水实验，利用高速摄像机拍摄了弹体入水过程和空泡形态演变过程，得到了4种头部外形模型的弹道曲线，并分析了头型、入水角、入水速度对水下弹道的影响。研究结果表明：椭圆斜截头弹体由于其特殊的头部更容易产生偏向水面的弯曲弹道，而其他3种弹体在一定速度内弹道比较稳定，基本趋于直线，虽然在有些工况下弹道发生了偏转，这是由于弹体加工过程中结构误差等造成的弹道不稳定性；入水角对弹道影响比较显著，小的入水角条件下弹体迅速向水面偏转，而入水角增大到一定程度时弹道向缸体底部偏转。所得结论可为高速入水武器的研究提供参考。

WANG Y , YUAN X L , LÜ C , et al . Experimental research on curved trajectory of high-speed water-entry missile [J ] . Acta Armamentarii , 2014 , 35 ( 12 ): 1998 - 2002 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2014.12.010 http://doi.org/10.3969/j.issn.1000-1093.2014.12.010 The experiment about the four geometries are carried out. A digital high-speed camera is used to record the evolution of the water-entry process and cavity shapes. The flat-trajectory curves of the four different geometries are obtained, and the effects of the head shape, entry angle and velocity on the trajectory are analyzed. The results show that the projectile body with oval-beveled warhead is easier to form the curved trajectory because of its special warhead. The other three kinds of trajectories are more stabilized. When it is at certain speed range, the trajectories verge to be linear; when it is at a higher speed, the trajectory may be curved. The effect of entry angle on the trajectory is obvious. When the entry angle is little, its trajectory deflects to the free surface quickly; when it is larger, the trajectory deflects to the bottom of the cylinder. The conclusions provide reference for the research on the water-entry weapons.

邵志宇 , 伍思宇 , 曹苗苗 , 等 . 斜截头弹体入水的弹道特性 [J ] . 兵工学报 , 2022 , 43 ( 6 ): 1255 - 1265 . DOI: 10.12382/bgxb.2021.0301 http://doi.org/10.12382/bgxb.2021.0301 斜截头弹体的入水会发生姿态偏转和弹道弯曲。从理论上分析弹丸在水中的偏转过程，得出斜截头弹体姿态偏转方程。利用AUTODYN软件对斜截头弹体入水过程进行数值模拟，基于模拟结果提出描述弹体质心轨迹的经验公式，并通过试验验证其准确性。设计炮射垂直入水试验，利用高速摄像机记录弹丸的撞击速度和运动过程。试验结果表明：理论分析得出的姿态偏转方程可靠，数值模拟和基于数值模拟得出的质心弹道经验公式的预测精度可信。

SHAO Z Y , WU S Y , CAO M M , et al . Water-entry trajectory of truncated cone-shaped projectile [J ] . Acta Armamentarii , 2022 , 43 ( 6 ): 1255 - 1265 . (in Chinese) DOI: 10.12382/bgxb.2021.0301 http://doi.org/10.12382/bgxb.2021.0301 The attitude deflection and trajectory bending of truncated cone-shaped projectile will occur during water-entry process. The process is analyzed theoretically and the attitude deflection equation is obtained. AUTODYN software is used to simulate the water-entry process of truncated cone-shaped projectile. Based on the simulation results, an empirical formula describing trajectory of centroid is proposed, and its accuracy is verified by experiments.The vertical water entry test of projectile is designed, and the impact velocity and motion process of projectile are recorded by high speed camera. The experimental results show that the attitude deflection equation obtained from theoretical analysis is reliable, and the numerical simulation and empirical formula of centroid trajectory based on numerical simulation is reliable.

华扬 , 施瑶 , 潘光 , 等 . 非对称头型航行器入水空泡形态与弹道特性的实验研究 [J ] . 西北工业大学学报 , 2021 , 39 ( 6 ): 1249 - 1258 .

HUA Y , SHI Y , PAN G , et al . Experimental study on water-entry cavity and trajectory of vehicle with asymmetric nose shape [J ] . Journal of Northwestern Polytechnical University , 2021 , 39 ( 6 ): 1249 - 1258 . (in Chinese) DOI: 10.1051/jnwpu/20213961249 http://doi.org/10.1051/jnwpu/20213961249 https://www.jnwpu.org/10.1051/jnwpu/20213961249 https://www.jnwpu.org/10.1051/jnwpu/20213961249 Different nose shape can cause a significant influence on the water entry trajectory and cavity. In order to study the evolution characteristics of cavity and trajectory of asymmetric nose in the process of water entry, based on the high-speed photography technology, the low-speed water entry comparative experiments were carried out for three different cut-angle nose types of 35°, 40° and 45° under different water entry angles. Through digital image processing technology, the contour of the water entry cavity and motion attitude information of the vehicle at different times are extracted, and the law of influence of the cut angle and entry angle on the cavity and trajectory is obtained. The experimental results show that: the cut angle side of the asymmetric nose can effectively promote the expansion of the cavity, thus forming the asymmetric water entry cavity; the expansion scale of the cavity is positively related to the initial horizontal expansion speed of the cavity and the area of the section of the head; the water entry trajectory of the asymmetric head will deflect to the cut angle side; the smaller the water entry angle is, the shorter the trajectory leveling time is, and the deeper the leveling depth is However, the change of attitude angle is almost independent of the entry angle.

陈诚 , 袁绪龙 , 邢晓琳 , 等 . 预置舵角下超空泡航行体倾斜入水弹道特性研究 [J ] . 兵工学报 , 2018 , 39 ( 9 ): 1780 - 1785 . DOI: 10.3969/j.issn.1000-1093.2018.09.015 http://doi.org/10.3969/j.issn.1000-1093.2018.09.015 为了研究预置舵角下超空泡航行体倾斜入水弹道特性，开展了入水角为20°时的试验研究。超空泡航行体由空气炮加速获得入水初速度，采用高速摄像机记录入水空泡流型，同时由内测系统记录航行体的运动参数和尾部压力变化。对预置舵角为0°和20°时的试验结果进行对比分析，给出了预置舵角下航行体倾斜入水弹道特性，并进一步研究了不同预置舵角对弹道的影响。试验结果表明：预置舵角为0°时航行体以超空泡状态沿直线运动；预置舵角为20°时出现显著的尾拍现象，轴向力和法向力增大，弹道特征体现为偏向水面弯曲，航行体最终以双空泡状态航行，弹道偏转趋势提升；增大预置舵角有助于增强航行体的弹道偏转能力。

CHEN C , YUAN X L , XING X L , et al . Research on the trajectory characteristics of supercavitating vehicle obliquely entering into water at preset rudder angle [J ] . Acta Armamentarii , 2018 , 39 ( 9 ): 1780 - 1785 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2018.09.015 http://doi.org/10.3969/j.issn.1000-1093.2018.09.015 A series of experiments of supercavitating vehicle at the entry angle of 20° are carried out to investigate the trajectory characteristics of supercavitating vehicle at preset rudder angle during oblique water-entry. An air cannon is set up to provide the initial velocity of supercavitating vehicle. The flow pattern in water-entry cavity is captured by using a high-speed video camera, and the variations of the motion parameters and tail pressure are recorded by using a built-in measuring system. The experimental results of supercavitating vehicle navigating at the preset rudder angles of 0° and 20° are analyzed in detail, and the water-entry trajectory characteristics of supercavitating vehicle are given. The influences of different preset rudder angles on the trajectory are further studied. The experimental results show that the vehicle moves along a straight line in a supercavitation state when the preset rudder angle is 0°; a remarkable tail-slapping phenomenon arises, and the axial force and the normal force increase when the preset rudder angle is 20°, thus causing the trajectory to bend to the surface of the water. The vehicle eventually navigates in the state of double-cavity, with enhancing the trajectory deflection. Increasing the preset rudder angle can improve the deflection ability of the vehicle. Key

时素果 , 王亚东 , 刘乐华 , 等 . 预置舵角下超空泡航行体运动过程弹道特性研究 [J ] . 兵工学报 , 2017 , 38 ( 10 ): 1974 - 1979 . DOI: 10.3969/j.issn.1000-1093.2017.10.013 http://doi.org/10.3969/j.issn.1000-1093.2017.10.013 为研究超空泡航行体在水平面机动转弯过程中的弹道特性，采用航行体头部设置预置舵角方法实现，开展了0°、3°和6°预置舵角下航行体自由运动的试验研究。试验在水池中进行，采用高速摄影观察不同预置舵角下的空泡演化过程，采用内测装置测量航行体运动参数，获得了不同预置舵角下超空泡航行体水平运动过程中的弹道特性。试验结果表明：当预置舵角为0°时，航行体侧向力由于非定常因素扰动小幅波动，但均值基本为0；当存在预置舵角时，随着预置舵角的增大，轴向力和侧向力不断增加；预置舵角可以控制超空泡航行体的弹道水平机动转弯，且预置舵角越大、弹道越容易转弯，但舵角过大会导致航行体弹道失稳。

SHI S G , WANG Y D , LIU L H , et al . Research on the trajectory characteristics of supercavitating vehicle at preset rudder angle [J ] . Acta Armamentarii , 2017 , 38 ( 10 ): 1974 - 1979 . (in Chinese)

刘如石 , 郭则庆 , 张辉 . 尾部形状对超空泡射弹尾拍运动影响的数值研究 [J/OL ] . 兵工学报 , 2022 (2022-11-02). https://doi.org/10.12382/bgxb.2022.0689. https://doi.org/10.12382/bgxb.2022.0689 https://doi.org/10.12382/bgxb.2022.0689

LIU R S , GUO Z Q , ZHANG H . Numerical simulation on the influence of tail shapes on the tail-slap of supercavitating projectiles [J/OL ] . Acta Armamentarii , 2022 (2022-11-02). https://doi.org/10.12382/bgxb.2022.0689. https://doi.org/10.12382/bgxb.2022.0689 https://doi.org/10.12382/bgxb.2022.0689 (in Chinese)

袁绪龙 , 栗敏 , 丁旭拓 , 等 . 跨介质航行器高速入水冲击载荷特性 [J ] . 兵工学报 , 2021 , 42 ( 7 ): 1440 - 1449 .

YUAN X L , LI M , DING X T , et al . Impact load characteristics of a trans-media vehicle during high-speed water-entry [J ] . Acta Armamentarii , 2021 , 42 ( 7 ): 1440 - 1449 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2021.07.011 http://doi.org/10.3969/j.issn.1000-1093.2021.07.011 The trans-media vehicle conbines the advantages of missiles and supercavitating weapons, which has higher terminal penetration capability compared to missile and makes up for the shortcoming of short range of supercavitating weapon. The impact load characteristics of a trans-media vehicle during high-speed water-entry and the load-reduction method are the main key technologies for the development of trans-media vehicles. A coupled simulation model for multi-phase flow and trajectory of trans-media vehicle entering into water at high speed was established and verified.The impact load characteristics of trans-media vehicle during high-speed water entry under typical conditions were simulated, and the ballistic parameters of trans-media vehicle in the high-speed water-entry process were compared. The results show that the periodical normal overload is generated during the tail-slapping, which is about 2.7 times as high as the axial overload, and the normal force is mainly composed of the positional force caused by the oscillating angle of attack, and the inertial force is very small and could be ignored. The increase in the water-entry speed speeds up the tail-slapping frequency and decreases the angle of attack oscillation amplitude, and the water-entry speed has little effect on the normal impact force coefficient.

赵成功 , 王聪 , 魏英杰 , 等 . 细长体水下运动空化流场及弹道特性实验 [J ] . 爆炸与冲击 , 2017 , 37 ( 3 ): 439 - 446 .

ZHAO C G , WANG C , WEI Y J , et al . Experiment of cavitation and ballistic characteristics of slender body underwater movement [J ] . Explosion and Shock Waves , 2017 , 37 ( 3 ): 439 - 446 . (in Chinese)

刘喜燕 , 罗凯 , 袁绪龙 , 等 . 扩张尾裙对跨介质航行器高速入水转平弹道特性影响 [J ] . 力学学报 , 2023 , 55 ( 2 ): 343 - 354 .

LIU X Y , LUO K , YUAN X L , et al . Influence of expansion sterns on the flatting trajectory characteristics of a trans-media vehicle during high speed water entry [J ] . Chinese Journal of Theoretical and Applied Mechanics , 2023 , 55 ( 2 ): 343 - 354 . (in Chinese)

王威 , 王聪 , 李聪慧 , 等 . 航行体沾湿区域对空泡尾流结构的影响 [J ] . 兵工学报 , 2019 , 40 ( 10 ): 2111 - 2118 . DOI: 10.3969/j.issn.1000-1093.2019.10.017 http://doi.org/10.3969/j.issn.1000-1093.2019.10.017 为研究航行体沾湿区域对通气超空泡尾流结构的影响，利用计算流体力学方法对超空泡航行体改变攻角过程中沾湿区域和空泡尾部涡量的非定常变化进行数值模拟。通过分析空泡尾部流场压力及涡量的变化，揭示了空泡尾部不同流动结构的转变机理。结果表明：在低弗劳德数条件下，空泡尾部双涡管的上下方存在高压区，受环境压力差的影响，下方压力大于上方，空泡双涡管之间的流动方向向上，形成一对中心上卷的双涡；随着航行体攻角的不断增大，沾湿区域使空泡形成了三涡管尾流结构，涡管下方高压区的压力比上方低，空泡下方双涡管之间的流动方向向下，形成一对中心下卷的双涡；空泡尾部双涡管到三涡管过渡过程中，空泡尾部上下方的压力及流速大小发生交替改变，从而形成了四涡管尾流结构。

WANG W , WANG C , LI C H , et al . The influence of wetted area of vehicle on the wake structure of cavity [J ] . Acta Armamentarii , 2019 , 40 ( 10 ): 2111 - 2118 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2019.10.017 http://doi.org/10.3969/j.issn.1000-1093.2019.10.017 In order to study the influence of wetted area of vehicle on the wake structure of ventilated supercavity, the CFD method was used to simulate the unsteady variations of the wetted area and the vorticity in the wake of a supercavitating vehicle in the process of changing the angle of attack. The transformation mechanisms of different flow structures in the wake of a cavity are revealed by analyzing the changes of pressure and vorticity in the wake flow field. The results show that, under the low Froude number, a high pressure zone exists above and below a twin-vortex tube at the tail of cavity. Due to the influence of environmental pressure difference, the pressure below the tube is higher than that above it. The flow direction between the two vortices is upward to form a pair of twin vortices rolled up in the center. With the increase in the angle of attack of vehicle, the wetted area causes the cavity to form the wake structure of three-vortex tube. The pressure in the high pressure area below the vortex tube is lower than that above it, and the flow direction between the two vortices below the cavity is downward to form a pair of twin vortices rolled down in the center. During the transition from the twin-vortex tube to the three-vortex tube, the pressures and velocities of the upper and lower parts of cavity wake change alternately, thus forming the wake structure of four-vortex tube. Key