黄闯 . 跨声速超空泡射弹的弹道特性研究 [D ] . 西安 : 西北工业大学 , 2017 : 1 - 16 .

HUANG C . Research of trajectory characteristics of supersonic-supercavitating projectiles [D ] . Xi’an : Northwestern Polytechnical University , 2017 : 1 - 16 . (in Chinese)

ZHANG G Y , HOU Z , SUN T Z , et al . Numerical simulation of the effect of waves on cavity dynamics for oblique water entry of a cylinder [J ] . Journal of Hydrodynamics , 2020 , 32 ( 6 ): 1178 - 1190 .

陈诚 , 袁绪龙 , 党建军 , 等 . 超空泡航行器20°角倾斜入水冲击载荷特性试验研究 [J ] . 兵工学报 , 2018 , 39 ( 6 ): 1159 - 1164 . DOI: 10.3969/j.issn.1000-1093.2018.06.016 http://doi.org/10.3969/j.issn.1000-1093.2018.06.016 为探究带圆盘空化器的超空泡航行器倾斜入水过程冲击载荷特性，开展了20°入水角条件下的试验研究。超空泡航行器由空气炮加速获得入水初速度，采用内置惯性测量单元记录载荷变化，试验完成后提取数据进行分析；试验设定了典型入水工况，分析了航行器入水冲击过程轴向载荷的变化特性，进行了入水速度和空化器面积对入水冲击载荷影响的系列试验，分析了各参数下的冲击载荷特性。研究结果表明：航行器入水冲击载荷峰值时刻侵彻距离为空化器直径的1.89倍， 阻力系数为稳定航行阶段的1.33倍；在所研究的范围内入水速度和空化器面积对阻力系数峰值无影响。

CHEN C , YUAN X L , DANG J J , et al . Experimental investigation into impact load during oblique water-entry of a supercavitating vehicle at 20° [J ] . Acta Armamentarii , 2018 , 39 ( 6 ): 1159 - 1164 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2018.06.016 http://doi.org/10.3969/j.issn.1000-1093.2018.06.016 In order to investigate the impact load characteristics of a supercavitating vehicle with a disk cavitator during oblique water-entry, a series of experiments were carried out at the water-entry angle of 20°. An air cannon is set up to provide the initial velocity of supercavitating vehicle. An inertial measurement unit is embedded at the center of gravity of supercavitating vehicle to record the variation of axial impact load, and the data is extracted and analyzed after the experimental test. A typical research case is set up, and the impact load characteristics varying with time are obtained and described in detail. Subsequently, a series of experiments for different entry speeds and cavitator areas are carried out, and the effects of the influence factors on the impact load characteristics are analyzed. The investigation shows that, when the impact load reaches the peak, the penetration distance is 1.89 times of the diameter of cavitator as a reference dimension, and the resistance coefficient is 1.33 times of that in the steady stage. The resistance coefficient is shown to be independent of entry velocity and cavitator area over a wide range of test conditions. Key

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.

陈晨 , 魏英杰 , 王聪 . 小型运动体高速倾斜入水空泡流动数值研究 [J ] . 兵工学报 , 2019 , 40 ( 2 ): 334 - 343 . DOI: 10.3969/j.issn.1000-1093.2019.02.013 http://doi.org/10.3969/j.issn.1000-1093.2019.02.013 为研究小型运动体高速倾斜入水时的空泡流动特性，采用求解雷诺时均Navier-Stokes方程的方法开展数值模拟。应用实验结果验证了数值方法的正确性。基于该方法对入水过程流体动力特性、流场结构特性与空泡发展进行分析，并研究了入水角度对入水流场的影响。研究结果表明：运动体在入水撞击阶段受到较大的阻力、升力和力矩，同时承受着极强的载荷；随着入水的深入，头部半球形高压区逐渐向头部中点移动，且空泡壁面的速度方向由指向水中向指向空泡内过渡；入水角度越小，撞击阶段阻力系数与砰击压力越小，入水后越容易发生弹道偏移，同时拉脱现象发生得越晚，入水空泡的最大尺寸越大。

CHEN C , WEI Y J , WANG C . Computational analysis of cavity flow induced by high-speed oblique water-entry of axisymmetric body [J ] . Acta Armamentarii , 2019 , 40 ( 2 ): 334 - 343 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2019.02.013 http://doi.org/10.3969/j.issn.1000-1093.2019.02.013 The characteristics of cavity flow around a small moving body under the high-speed oblique water-entry are analyzed, and the Reynolds-averaged Navier-Stokes equations are solved for simulation. The computational method is validated by comparing the simulated results with the experimental results. The characteristics of multiphase flow during water-entry and the influence of entry angle on water-entry flow field are investigated based on the computational method. The results show that the moving body is subjected to large drag, lift, moment and impact in the impact phase; the hemisphere-like high pressure area moves from the lower part of nose tip to the center of nose tip as the moving body continues to penetrate; the direction of velocity of cavity wall points to water first and then the cavity; the small entry angle causes small drag coefficient and impact in the impact phase and trajectory deflection; and the cavity is subsequently pulled away and the maximum size of the cavity is large when the moving body enters the water at a small entry angle. Key

LIU H , ZHOU B , HAN X S , et al . Numerical simulation of water entry of an inclined cylinder [J ] . Ocean Engineering , 2020 , 215 : 107908 .

SONG Z J , DUAN W Y , XU G D , et al . Experimental and numerical study of the water entry of projectiles at high oblique entry speed [J ] . Ocean Engineering , 2020 , 211 : 107574 .

方城林 , 魏英杰 , 王聪 , 等 . 不同头型高速射弹垂直入水数值模拟 [J ] . 哈尔滨工业大学学报 , 2016 , 48 ( 10 ): 77 - 82 .

FANG C L , WEI Y J , WANG C , et al . Numerical simulation of vertical high-speed water entry process of projectiles with different heads [J ] . Journal of Harbin Institute of Technology , 2016 , 48 ( 10 ): 77 - 82 . (in Chinese)

SUI Y T , ZHANG A M , MING F R , et al . Experimental investigation of oblique water entry of high-speed truncated cone projectiles: cavity dynamics and impact load [J ] . Journal of Fluids and Structures , 2021 , 104 : 103305 .

刘喜燕 , 袁绪龙 , 罗凯 , 等 . 带尾裙跨介质航行体高速斜入水实验研究 [J ] . 爆炸与冲击 , 2023 , 43 ( 11 ): 108 - 120 .

LIU X Y , YUAN X L , LUO K , et al . Experimental study on high-speed oblique water entry of a trans-media vehicle with tail-skirt [J ] . Explosion and Shock Waves , 2023 , 43 ( 11 ): 108 - 120 . (in Chinese)

YU T S , SHUAI L , FU R M , et al . An experimental study of the water entry trajectories of truncated cone projectiles: The influence of nose parameters [J ] . Physics of Fluids , 2022 , 34 ( 5 ): 052102 .

王云 , 袁绪龙 , 吕策 . 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 . 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.

侯宇 , 黄振贵 , 郭则庆 . 超空泡射弹小入水角高速斜入水试验研究 [J ] . 兵工学报 , 2020 , 41 ( 2 ): 332 - 341 . DOI: 10.3969/j.issn.1000-1093.2020.02.015 http://doi.org/10.3969/j.issn.1000-1093.2020.02.015 为研究超空泡射弹小入水角高速斜入水性能，利用高速摄像技术开展了超空泡射弹入水试验。沿水下弹道轨迹的左侧等距布置压力传感器测试压力变化，分析弹体不同侧滑角入水冲击过程的弹道轨迹、喷溅演变和水下压力波传播特征。结果表明：对于射弹小入水角高速斜入水，弹体小侧滑角入水能形成较光滑透明的入水空泡和稳定的入水弹道，较大的侧滑角易造成空泡内严重雾化、弹道轨迹偏转和弹体损坏等现象，严重程度随侧滑角增大而增大；小侧滑角下弹头空化器及圆锥段斜面与水面的撞击使得入水喷溅在俯视下呈左右近似对称的“蝶”状，侧滑角对前半部分喷溅的左右对称性影响较小，对后半部分喷溅的对称性和范围影响较大，前半部分喷溅的对称轴随着侧滑角增大会出现相应偏转；入水冲击产生的水下压力波变化过程可分成两阶段：由弹体和水域冲击产生的初始压力波动阶段和各压力波叠加的高频脉动阶段，两阶段压力波动因侧滑角增加后入水状态的不同而呈现不同的变化特征。

HOU Y , HUANG Z G , GUO Z Q . Experimental investigation on shallow-angle oblique water-entry of a high-speed supercavitating projectile [J ] . Acta Armamentarii , 2020 , 41 ( 2 ): 332 - 341 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2020.02.015 http://doi.org/10.3969/j.issn.1000-1093.2020.02.015 The shallow-angle oblique water-entry of a high-speed supercavitating projectile is studied by using the high-speed photography technology. The characteristics of the ballistic trajectory, splash formation and underwater pressure wave propagation during the initial water-entry impact at different sideslip angles are observed and analyzed from the underwater pressure signal monitored along the left side of the trajectory. The results show that the small sideslip angle of the projectile has few effect on the smooth cavity formation and the enter trajectory stability during the high-speed oblique water-entry at small entry angle. The larger sideslip angle is able to lead to the severe water atomization in the cavity, the ballistic deflection and the projectile damage. The increase in the sideslip angle can exacerbate this instability. The impacts of the cavitator and the warhead conical section on the free surface at a small entry angle make the splash be an approximate symmetrical “butterfly shape” in birds-eye view. The sideslip angle has inverse influence on the symmetry of the front half of splash comparing with the rear half of splash. Large changes are presented in the splash range with the increase in sideslip angle. The symmetry axis of the front half of splash is deflected with the increase in sideslip angle. The changing process of underwater pressure wave induced by the water-entry impact is divided into two stages: the initial pressure fluctuation stage induced by the initial impact of the projectile on the water and the fluctuation stage of high frequency induced by the superposition of the pressure waves from various directions. The two pressure fluctuation stages show different variation characteristics with the corresponding water entry state due to the increased sideslip angle.Key

孙邃 . 高速射弹倾斜入水过程多相流动特性数值计算 [D ] . 哈尔滨 : 哈尔滨工业大学 , 2018 : 1 - 8 .

SUN S . Numerical calculation of multiphase flow characteristics of high speed projectile in obliqued water entry process [D ] . Harbin : Harbin Institute of Technology , 2018 : 1 - 8 . (in Chinese)

王健 . 回转体入水流固耦合载荷特性研究 [D ] . 哈尔滨 : 哈尔滨工程大学 , 2021 : 1 - 2 .

WANG J . Study on fluid-solid coupling load characteristics of water entry of projectile [D ] . Harbin : Harbin Engineering University , 2021 : 1 - 2 . (in Chinese)

DERAKHSHANIAN M S , HAGHDEL M , ALISHAHI M M , et al . Experimental and numerical investigation for a reliable simulation tool for oblique water entry problems [J ] . Ocean Engineering , 2018 , 160 : 231 - 243 .

张宇 , 王彬文 , 刘小川 . 基于ALE, CEL和SPH方法的球形破片高速冲击充液结构对比研究 [J ] . 计算力学报 , 2022 , 39 ( 6 ): 824 - 831 .

ZHANG Y , WANG B W , LIU X C . Comparative study of fluid-filled structure impacted by high-speed spherical fragments based on ALE, CEL and SPH [J ] . Chinese Journal of Computational Mechanics , 2022 , 39 ( 6 ): 824 - 831 . (in Chinese)

SHI Y , PAN G , YIM S C , et al . Numerical investigation of hydroelastic water-entry impact dynamics of AUVs [J ] . Journal of Fluids and Structures , 2019 , 91 : 102760 .

SHI Y , GAO X F , PAN G , et al . Experimental and numerical investigation of the frequency-domain characteristics of impact load for AUV during water entry [J ] . Ocean Engineering , 2020 , 202 : 107203 .

CHAUDHRY A Z , SHI Y , PAN G , et al . Mechanical characterization of flat faced deformable AUV during water entry impact considering the hydroelastic effects [J ] . Applied Ocean Research , 2021 , 115 : 102849 .

邹田春 , 高飞 , 魏家威 , 等 . 圆柱体垂直入水三维数值模拟及影响因素研究 [J ] . 振动与冲击 , 2022 , 41 ( 10 ): 177 - 185 .

ZOU T C , GAO F , WEI J W , et al . Three-dimensional numerical simulation and influencing factors study on the vertical water entry of a circular cylinder [J ] . Journal of Vibration and Shock , 2022 , 41 ( 10 ): 177 - 185 . (in Chinese)

权晓波 , 包健 , 孙龙泉 , 等 . 基于耦合欧拉-拉格朗日算法的航行体缓冲头帽冲击性能 [J ] . 兵工学报 , 2022 , 43 ( 4 ): 851 - 860 . DOI: 10.12382/bgxb.2021.0168 http://doi.org/10.12382/bgxb.2021.0168 航行体在入水过程中会受到强烈的冲击载荷，过高的冲击载荷极易造成结构破坏和内部设备失灵，研究结构高速入水降载技术具有十分重要的意义。设计一种以预制裂纹碳纤维材料作为外罩、泡沫铝作为内部缓冲材料的缓冲头帽。基于有限元方法，采用耦合欧拉-拉格朗日求解器研究缓冲头帽的降载效果，通过对比数值结果与小球入水实验图像验证数值方法的有效性。分析在不同入水速度和入水角度条件下，缓冲头帽的抗冲击性能、损伤模式以及空泡的发展过程。结果表明：缓冲头帽撞击水面后沿着预制裂纹破碎，泡沫铝压缩吸能；随着自由液面以下的空泡不断向外扩张，破碎的头帽贴着空泡内壁向四周散开；缓冲头帽对于不同入水速度和入水角度的航行体有着良好的降载效果，在最恶劣的垂直入水条件下降载率可达75%以上。

QUAN X B , BAO J , SUN L Q , et al . Impact performance of cushion nose cap of underwater vehicle based on CEL method [J ] . Acta Armamentarii , 2022 , 43 ( 4 ): 851 - 860 . (in Chinese) DOI: 10.12382/bgxb.2021.0168 http://doi.org/10.12382/bgxb.2021.0168 The underwater vehicle will be subjected to strong impact load in the process of water entry，and the excessive impact load can easily cause structural damage and internal equipment failure. The technology of load reduction during high-speed water entry is studied. A cushion nose cap with prefabricated cracked carbon fiber material as outer cover and foamed aluminum as inner cushion material is designed.The numerical simulation is based on the finite element method，and the coupled Euler-Lagrange solver is used to study the load reduction effect of cushion nose cap.The effectiveness of the numerical method is verified by comparing the numerical results with the experimental images of a sphere entering into the water.The impact resistance，damage mode of cushion nose cap and the evolution process of cavitation bubble at different water entry speeds and angles are analyzed. The results show that the cushion nose cap shatters along the prefabricated cracks after hitting the water surface. The foamed aluminum is compressed and absorbs energy.As the cavitation bubble below the free surface expands outward，the broken nose cap spreads around the inner wall of cavitation bubble. The cushion nose cap has a good load-reduction effect on underwater vehicle at different water entry speeds，and water entry angles. Under the worst condition of vertical water entry，the load reduction rate is more than 75%.

魏海鹏 , 史崇镔 , 孙铁志 , 等 . 基于ALE方法的航行体高速入水缓冲降载性能数值研究 [J ] . 爆炸与冲击 , 2021 , 41 ( 10 ): 115 - 126 .

WEI H P , SHI C B , SUN T Z , et al . Numerical simulation of buffer and load reduction of high speed water entry of a vehicle based on ALE method [J ] . Explosion and Shock Waves , 2021 , 41 ( 10 ): 115 - 126 . (in Chinese)

魏英杰 , 杨柳 , 王聪 , 等 . 超弹性球体垂直入水空泡流动研究 [J ] . 空气动力学学报 , 2020 , 38 ( 4 ): 780 - 787 .

WEI Y J , YANG L , WANG C , et al . Vertical water entry of hyperelastic sphere [J ] . Acta Aerodynamica Sinica , 2020 , 38 ( 4 ): 780 - 787 . (in Chinese)

杨柳 . 超弹性球体垂直入水空泡流动及结构响应特性研究 [D ] . 哈尔滨 : 哈尔滨工业大学 , 2021 .

YANG L . Study on cavitating flow and structural response during vertical water entry of hyperelastic spheres [D ] . Harbin : Harbin Institute of Technology , 2021 . (in Chinese)

SUN T Z , ZHOU L , YIN Z H , et al . Cavitation bubble dynamics and structural loads of high-speed water entry of a cylinder using fluid-structure interaction method [J ] . Applied Ocean Research , 2020 , 101 : 102285 .

高英杰 , 孙铁志 , 张桂勇 , 等 . 回转体高速倾斜入水的流场特性及结构响应 [J ] . 爆炸与冲击 , 2020 , 40 ( 12 ): 101 - 113 .

GAO Y J , SUN T Z , ZHANG G Y , et al . Flow characteristics and structure response of high-speed oblique water-entry for a revolution body [J ] . Explosion and Shock Waves , 2020 , 40 ( 12 ): 101 - 113 . (in Chinese)

高英杰 . 基于流固耦合方法的回转体高速入水流场及载荷特性研究 [D ] . 大连 : 大连理工大学 , 2020 .

GAO Y J . Numerical analysis of impact load and flow characteristics of high speed water-entry for a revolution body based on a fluid-structure interaction method [D ] . Dalian : Dalian University of Technology , 2020 . (in Chinese)

HUANG C , LIU Z , LIU Z X , et al . Motion characteristics of high-speed supercavitating projectiles including structural deformation [J ] . Energies , 2022 , 15 : 1933 .

郝常乐 , 党建军 , 陈长盛 , 等 . 基于双向流固耦合的超空泡射弹入水研究 [J ] . 力学学报 . 2022 , 54 ( 3 ): 678 - 687 .

HAO C L , DANG J J , CHEN C S , et al . Numerical study on water entry process of supercavitating projectile by considering bidirectional fluid structure interaction effect [J ] . Chinese Journal of Theoretical and Applied Mechanics , 2022 , 54 ( 3 ): 678 - 687 . (in Chinese)

LEE M , LONGORIA R G , WILSON D E . Cavity dynamics in high-speed water entry [J ] . Physics of Fluids , 1997 , 9 ( 3 ): 540 - 550 .

WALHORN E , HÜBNER B , DINKLER D . Space-time finite elements for fluid-structure interaction [J ] . PAMM , 2002 , 1 ( 1 ): 81 - 82 .

CHEN T , HUANG W , ZHANG W , et al . Experimental investigation on trajectory stability of high-speed water entry projectiles [J ] . Ocean Engineering , 2019 , 175 : 16 - 24 .