黄闯 , 党建军 , 李代金 , 等 . 跨声速运动对射弹阻力及空化特性的影响 [J ] . 兵工学报 , 2016 , 37 ( 8 ): 1482 - 1488 . DOI: 10.3969/j.issn.1000-1093.2016.08.021 http://doi.org/10.3969/j.issn.1000-1093.2016.08.021 为研究在跨声速运动过程中超空泡射弹的流体动力特性和流场的空化情况，基于流体体积分数多相流模型、Schnerr-Sauer 空化模型、Realizable k-ε湍流模型、Tait液体状态方程和运动框架模型构建了可压缩超空化流场的数值模型，通过与文献\[11\]试验结果进行对比，完成模型验证，采用数值方法模拟在马赫数为0.202~1.281速度范围内射弹的外流场。研究结果显示：跨声速运动过程中超空泡射弹的阻力系数与流场驻点的密度峰值有关，随速度的升高而显著增大；激波对弹体附近超空泡的形态和尺度有显著的影响，亚声速工况下超空泡尺寸与理论值接近并且受速度的影响很小，超声速工况下超空泡的尺寸随速度的增加而大幅度减小。研究结果对超空泡射弹的外形设计和弹道预报有参考价值。

HUANG C , DANG J J , LI D J , et al . Influence of transonic motion on resistance and cavitation characteristics of projectiles [J ] . Acta Armamentarii , 2016 , 37 ( 8 ): 1482 - 1488 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2016.08.021 http://doi.org/10.3969/j.issn.1000-1093.2016.08.021 In order to research the resistance characteristics and flow cavitation of supercavitation projectiles during transonic motion, a numerical model of a compressible and supercaitation flow field is established based on VOF multiphase model, Schnerr-Sauer cavitation model, realizable k-ε turbulence model, Tait liquid state equation and moving frame model.The proposed model is validated by comparing the numerical results with those in Ref.\[11\], and the external flow field of supercavitation projectile flying at Mach number between 0.202 and 1.281 is simulated. The simulated results show that, during transonic motion, the resistance coefficient of projectile is related to the peak value of density at the stationary point of flow field and increases with the increase in flying speed; and the shockwaves have significant influence on the shapes and dimensions of supercavities near projectile. Under subsonic condition, the flying speed of projectile has no significant influence on the dimensions of supercavities, and the shapes of supercavities coincide with theoretical results; under supersonic condition, the dimensions of supercavities decrease sharply with the increase in flying speed.

SARANJAM B . Experimental and numerical investigation of an unsteady supercavitating moving body [J ] . Ocean Engineering , 2013 , 59 ( 2 ): 9 - 14 . DOI: 10.1016/j.oceaneng.2012.12.021 http://doi.org/10.1016/j.oceaneng.2012.12.021 https://linkinghub.elsevier.com/retrieve/pii/S0029801812004301 https://linkinghub.elsevier.com/retrieve/pii/S0029801812004301

孟庆昌 , 张志宏 , 顾建农 , 等 . 超空泡射弹尾拍分析与计算 [J ] . 爆炸与冲击 , 2009 , 29 ( 1 ): 56 - 60 .

MENG Q C , ZHANG Z H , GU J N , et al . Analysis and calculation for tail-slaps of supercavitating projectiles [J ] . Explosion and Shock Waves , 2009 , 29 ( 1 ): 56 - 60 . (in Chinese)

RAND R , PRATAP 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 .

LOGVINOVICH G V . Some problems of supercavitating flows [C ] // Proceedings of NATO-AGARD. Kiev, Ukraine:AGARD , 1998 : 18 .

RUZZENE M , SORANNA F . Impact dynamics 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 for 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.

PUTILIN S I . Some features of a supercavitating model dynamic [J ] . International Journal of Fluid Mechanics Research , 2001 , 28 ( 5 ): 631 - 643 .

PUTILIN S I . Stability of supercavitating slender body during water entry and underwater motion [C ] // Proceedings of NATO-AGARD. Kiev, Ukraine:AGARD , 1998 : 27 .

MANSOUR M Y , MANSOUR M H , MOSTAFA N H , et al . Numerical and experimental investigation of supercavitating flow development over different nose shape projectiles [J ] . IEEE Journal of Oceanic Engineering , 2020 , 45 ( 4 ): 1370 - 1385 . DOI: 10.1109/JOE.48 http://doi.org/10.1109/JOE.48 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=48 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=48

WANG K J , RONG G , YIN H Q , et al . Dynamic features of kinetic energy supercavitating vehicles [J ] . Applied Ocean Research , 2020 , 102 : 102304 . DOI: 10.1016/j.apor.2020.102304 http://doi.org/10.1016/j.apor.2020.102304 https://linkinghub.elsevier.com/retrieve/pii/S0141118720305149 https://linkinghub.elsevier.com/retrieve/pii/S0141118720305149

JIANG Y H , JEONG S W , AHN B K , et al . Experimental investigation of drag characteristics of ventilated supercavitating vehicles with different body shapes [J ] . Physics of Fluids , 2019 , 31 ( 5 ): 052106 . DOI: 10.1063/1.5092542 http://doi.org/10.1063/1.5092542 https://pubs.aip.org/pof/article/31/5/052106/991846/Experimental-investigation-of-drag-characteristics https://pubs.aip.org/pof/article/31/5/052106/991846/Experimental-investigation-of-drag-characteristics This paper presents an experimental investigation on drag characteristics and flow physics of ventilated supercavitating objects with different body shapes. The test model consists of a disk-type cavitator with two different forebodies (slender and blunt shape) and three different rear bodies (flat, shrinkage, and expanded shape). Experiments are conducted in a cavitation tunnel of the Chungnam National University. First, the drag forces acting on different body-combinations in fully wetted conditions are measured. The results show that the drag coefficients strongly depend on the body shapes. It explains in detail through particle image velocimetry measurements. Second, the drag characteristics are systematically examined over a broad range of ventilation rates. The formation and the drag characteristics of the foamy and clear supercavity flow are investigated for different Froude number conditions. The results reveal that the drag of the blunt forebody is smaller than that of the slender fore body in foamy cavity conditions. In ventilated supercavity conditions, supercavity shapes according to Froude numbers are examined and corresponding effects on drag characteristics are analyzed. The results show that the drag coefficients of the models with the expanded rear body are larger than that of models with the flat and shrinkage rear bodies until the cavity covers the body.

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 disturbanceon the hydrodynamic and ballistic characteristics of high-speed projectile during tail slapping [J ] . Acta Armamentarii , 2020 , 41 ( S1 ): 46 - 53 . (in Chinese)

梁景奇 , 徐保成 , 王瑞 , 等 . 初速对高速射弹尾拍特性影响研究 [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 tailslapping [J ] . Journal of Projectiles,Rockets,Missiles and Guidance , 2020 , 40 ( 2 ): 130 - 134 ,139. (in Chinese)

赵成功 , 王聪 , 魏英杰 , 等 . 质心位置对超空泡射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 , WAN C , WEI Y J , et al . Analysis of 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)

陈伟善 , 郭则庆 , 刘如石 , 等 . 空化器形状对超空泡射弹尾拍运动影响的数值研究 [J ] . 工程力学 , 2020 , 37 ( 4 ): 248 - 256 .

CHEN W S , GUO Z Q , LIU R S , et al . Numerical simulation on the influence of cavitator shapes on the tail-slap of supercavitating projectiles [J ] . Engineering Mechanics , 2020 , 37 ( 4 ): 248 - 256 . (in Chinese)

祝许皓 , 李杰 . 超空泡射弹六自由度尾拍运动数值模拟研究 [J ] . 水动力学研究与进展A辑 , 2022 , 37 ( 4 ): 474 - 482 .

ZHU X H , LI J . Numerical simulation research on six-degree-of-freedom tail-slap of supercavitating projectile [J ] . Chinese Journal of Hydrodynamics , 2022 , 37 ( 4 ): 474 - 482 . (in Chinese)

侯东伯 , 王聪 , 夏维学 , 等 . 弹性尾缘对超空泡航行体空泡形态与压力脉动特性影响的水洞试验研究 [J ] . 兵工学报 , 2020 , 41 ( 3 ): 534 - 541 . DOI: 10.3969/j.issn.1000-1093.2020.03.014 http://doi.org/10.3969/j.issn.1000-1093.2020.03.014 为分析弹性尾缘对超空泡航行体水动力特性的影响，设计一种带有可变刚度弹性尾缘的航行体模型。通过水洞试验研究了弹性尾缘航行体模型在不同压差系数、不同通气率下的空泡形态与压力脉动。试验中采用工业摄像机采集尾缘形态与流场结构，同时利用动态测试系统采集弹性尾缘区域特征点的压力脉动信息。通过空泡形态变化与特征点压力脉动变化对比分析，得到如下结论：弹性尾缘的变形随压差系数的增加而增大，当变形后的弹性尾缘直径达到航行体主体直径的1.35倍时，弹性尾缘对空泡形态有明显的影响，空泡闭合点前移至尾缘前方，尾缘后方的模型表面进入沾湿状态且压力增大；变形继续增加后，弹性尾缘后方形成了剧烈波动的尾空泡并导致沾湿面积减少，模型表面压力减小。

HOU D B , WANG C , XIA W X , et al . Experimental investigation into the cavity shape and pressure characteristics of supercavitating vehicle with elastic trailing edge [J ] . Acta Armamentarii , 2020 , 41 ( 3 ): 534 - 541 . (in Chinese)

马文轩 , 于勇 , 胡俊 . 小口径超空泡子弹头部外形的优化设计 [J ] . 爆炸与冲击 , 2022 , 42 ( 3 ): 101 - 113 .

MA W X , YU Y , HU J . Optimal design of the head shape of a small-caliber supercavitating projectile [J ] . Explosion and Shock Waves , 2022 , 42 ( 3 ): 101 - 113 . (in Chinese)

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