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HUANG B , WANG G Y , QUAN X B , et al . Experimental study on fluctuating hydrodynamics around axisymmetric bodies [J ] . Engineering Mechanics , 2012 , 29 ( 2 ): 239 - 244 . (in Chinese)

尤天庆 , 张嘉钟 , 王聪 , 等 . 航行体出水过程头部流场载荷特性分析 [J ] . 北京航空航天大学学报 , 2011 , 37 ( 5 ): 610 - 614 .

YOU T Q , ZHANG J Z , WANG C , et al . Characteristic analysis of flow load around head during vehicles exit of water [J ] . Journal of Beijing University of Aeronautics and Astronautics , 2011 , 37 ( 5 ): 610 - 614 . (in Chinese)

陈玮琪 , 王宝寿 , 颜开 , 等 . 物体垂直出入水的非定常空泡数学模型 [J ] . 应用数学与力学 , 2013 , 34 ( 11 ): 1130 - 1140 .

CHEN W Q , WANG B S , YAN K , et al . Model of the unsteady vertical water-entry and water-exit cavities [J ] . Applied Mathematics and Mechanics , 2013 , 34 ( 11 ): 1130 - 1140 . (in Chinese)

陈玮琪 , 王宝寿 , 颜开 , 等 . 空化器出水非定常垂直空泡的研究 [J ] . 力学学报 , 2013 , 45 ( 1 ): 76 - 82 . DOI: 10.6052/0459-1879-12-164 http://doi.org/10.6052/0459-1879-12-164 对空化器朝水面高速运动产生的非定常垂直空泡进行了理论研究. 建立了受水面和重力影响下的水下垂直空泡长度变化数学方程, 从方程中导出了非定常垂直空泡长度计算公式, 利用公式计算了空化器出水后空泡从脱落、收缩到溃灭的时间. 对带空化器的航行体, 公式还可以计算脱落空泡溃灭高压作用在航行体上的位置, 最后给出了避免溃灭高压作用在航行体上的条件和判据.

CHEN W Q , WANG B S , YAN K , et al . Study on the unsteady vertical cavity of the exit-water cavitor [J ] . Chinese Journal of Theoretical and Applied Mechanics , 2013 , 45 ( 1 ): 76 - 82 . (in Chinese) DOI: 10.6052/0459-1879-12-164 http://doi.org/10.6052/0459-1879-12-164 The unsteady vertical cavity produced by the underwater cavitator moving rapidly towards the water surface is investigated theoretically. The mathematical model of the unsteady vertical cavity under water is presented; the formula of the vertical cavity length influenced by the gravity and water surface is derived, and the life span of cavity shedding from exit-water cavitator is also obtained from the formula. For the underwater body with cavitator, the acting position in the body of the high-pressure produced by the collapsed cavity is also calculated by the formula; moreover, the condition and criterion of keeping the underwater body from collapse high-pressure is presented.

张忠宇 , 姚熊亮 , 张阿漫 . 小攻角下三维细长体定常空化形态研究 [J ] . 物理学报 , 2013 , 62 ( 20 ): 204701 .

ZHANG Z Y , YAO X L , ZHANG A M . Cavitation shape of the three-dimensional slender at a small attack angle in a steady flow [J ] . Acta Physica Sinica , 2013 , 62 ( 20 ): 204701 . (in Chinese) DOI: 10.7498/aps.62.204701 http://doi.org/10.7498/aps.62.204701 http://wulixb.iphy.ac.cn/article/doi/10.7498/aps.62.204701 http://wulixb.iphy.ac.cn/article/doi/10.7498/aps.62.204701

张阿漫 , 王诗平 , 白兆宏 , 等 . 不同环境下气泡脉动特性实验研究 [J ] . 力学学报 , 2011 , 43 ( 1 ): 71 - 83 . DOI: 10.6052/0459-1879-2011-1-lxxb2010-278 http://doi.org/10.6052/0459-1879-2011-1-lxxb2010-278 水下爆炸气泡对舰船结构造成严重的毁伤, 海上实船爆炸实验是考核水下爆炸气泡对舰船毁伤威力最直接、最有效的方法, 然而真实情况的舰船水下爆炸实验难以进行.为此, 在已有研究成果的基础上, 设计实验电路, 利用电容在相对较低的电压下放电打火产生的电火花气泡来模拟水下爆炸气泡, 设计多组实验工况来模拟气泡在不同环境下的运动特性. 研究气泡在不同环境下的脉动特性、射流特征, 揭示一些特殊的实验现象, 总结环境对气泡运动的影响规律.

ZHANG A M , WANG S P , BAI Z H , et al . Experimental study on bubble pulse features under different circumstances [J ] . Chinese Journal of Theoretical and Applied Mechanics , 2011 , 43 ( 1 ): 71 - 83 . (in Chinese) DOI: 10.6052/0459-1879-2011-1-lxxb2010-278 http://doi.org/10.6052/0459-1879-2011-1-lxxb2010-278 Underwater explosion bubbles do severe damage to warshipstructures, and the particularity of underwater explosion and the quality ofwater bring great difficulties to get a clear picture. So lots oflaboratories all around the world make use of discharge or laser to generatebubbles to replace real underwater explosion experiments.Based on the designation from Turangan et al and Abdolranman Dadvand, anelectric circuit with a relatively low voltage 200V and three shunt-wound2200\muF capacitances is used to generate bubbles by discharge ina 500mm\times500mm\times500mm water tank to study underwater bubbledynamics. The experiment setup is safe, stable, low in costs and simple tofix. It can generate bubbles with radius up to 12~15mm.A device generating bubble by a relatively low voltage is designed to studybubble dynamics in detail under various boundary conditions in this paper.Main conclusions are obtained below by comparison and analysis:(1) A voltage of 200 V is adopted to generate bubble by discharge in water inthis paper. The voltage is fairly low yet the bubble generated is relativelylarge in size. The pictures shot are pretty clear as well.(2) There are copper wires burning inside the bubble throughout theexpansion process, causing the temperature inside bubble to rise apparentlyhigher and result in the small calculated value of bubble pulsing period. Sop_v within the bubble is actually very large and the calculated p_v ofa single bubble pulsing in free field is 5.8\times 10^4 Pa.(3) Bubble's second pulsing energy is merely 5{\%}\sim 15{\%} of the firstpulsing energy and the pulsing energy after the second pulse can be ignored.(4) \gamma, the dimensionless standoff is defined betweenbubble and boundary. When \gamma \ge 2.8, the influence of the wall tobubble can be neglected. When 1.95 \le \gamma \le 2.8, no jet is formedduring the first cycle of bubble pulse. When \gamma \le 1.53, jet is formedduring the first cycle of bubble pulse, and the smaller \gamma is, thelarger bubble migration distance and the more fiercely the jet would be.(5) The bubble jetting velocity is minimum when the dimensionless standoff\gamma is around 0.8.(6) Bubble will interact strongly with boundaries when it moves near theshipboard and the free surface. It can be seen from the experiments that thebubble may produce jets that are towards two different directions whencollapsing near the free surface and the shipboard, and this will certainlylead to the weakening effect of bubble attack to the shipboard.

王诗平 , 张阿漫 , 刘云龙 , 等 . 圆形破口附近气泡动态特性实验研究 [J ] . 物理学报 , 2013 , 62 ( 6 ): 064703 .

WANG S P , ZHANG A M , LIU Y L , et al . Experimental research on bubble dynamics near circular hole of plate [J ] . Acta Physica Sinica , 2013 , 62 ( 6 ): 064703 . (in Chinese) DOI: 10.7498/aps http://doi.org/10.7498/aps https://wulixb.iphy.ac.cn/ https://wulixb.iphy.ac.cn/

王一伟 , 黄晨光 , 杜特专 , 等 . 航行体垂直出水载荷与空泡溃灭机理分析 [J ] . 力学学报 , 2012 , 44 ( 1 ): 39 - 48 . DOI: 10.6052/0459-1879-2012-1-lxxb2011-139 http://doi.org/10.6052/0459-1879-2012-1-lxxb2011-139 针对航行体水下垂直发射出水载荷机理问题, 首先开展了典型工况全过程的数值模拟, 得到了航行体肩、尾空泡及表面压力的演化过程, 并与试验结果进行了对比验证. 在此基础上揭示了航行体肩部空泡溃灭的过程和机制, 进而提出了出水溃灭压力的物理模型, 探索了空泡厚度、水层厚度、声速等重要参数的影响, 讨论了试验溃灭压力相似律等相关问题.

WANG Y W , HUANG C G , DU T Z , et al . Mechanism analysis about cavitation collapse load of underwater vehicles in a vertical launching process [J ] . Chinese Journal of Theoretical and Applied Mechanics , 2012 , 44 ( 1 ): 39 - 48 . (in Chinese)

王一伟 , 黄晨光 , 吴小翠 , 等 . 航行体水下垂直发射空泡脱落条件研究 [J ] . 工程力学 , 2015 , 32 ( 4 ): 544 - 550 .

WANG Y W , HUANG C G , WU X C , et al . Investigation of cavities shedding condition on underwater vehicles in the vertical launch process [J ] . Engineering Mechanics , 2015 , 32 ( 4 ): 544 - 550 . (in Chinese)

胡影影 , 朱克勤 , 席葆树 , 等 . 半无限长柱体出水数值模拟 [J ] . 清华大学学报(自然科学版) , 2002 , 42 ( 2 ): 235 - 238 .

HU Y Y , ZHU K Q , XI B S , et al . Numerical simulation of a semi-infinite cylinder exited from water [J ] . Journal of Tsinghua University(Science and Technology) , 2002 , 42 ( 2 ): 235 - 238 . (in Chinese)

王红萍 , 李智生 , 阎肖鹏 . 艇速对水下航行体出水姿态影响研究 [J ] . 舰船电子工程 , 2019 , 39 ( 1 ): 135 - 138 .

WANG H P , LI Z S , YAN X P . Analysis of submarine velocity and its effects on exceeding water gesture of an underwater vehicle [J ] . Ship Electronic Engineering , 2019 , 39 ( 1 ): 135 - 138 . (in Chinese)

权晓波 , 李岩 , 魏海鹏 , 等 . 航行体出水过程空泡溃灭特性研究 [J ] . 船舶力学 , 2014 , 32 ( 4 ): 545 - 549 .

QUAN X B , LI Y , WEI H P , et al . Cavitation collapse characteristic research in the out-of-water progress of underwater vehicles [J ] . Journal of Ship Mechanics , 2014 , 32 ( 4 ): 545 - 549 . (in Chinese)

赵蛟龙 , 郭百森 , 孙龙泉 , 等 . 细长体倾斜出水的实验研究 [J ] . 爆炸与冲击 , 2016 , 36 ( 1 ): 113 - 120 .

ZHAO J L , GUO B S , SUN L Q , et al . Experimental study on oblique water-exit of slender bodies [J ] . Explosion and Shock Waves , 2016 , 36 ( 1 ): 113 - 120 . (in Chinese)

张军 , 李英浩 , 金朋寿 . 垂直及斜出水流场的二维及三维TR-PIV试验 [J ] . 船舶力学 , 2005 ( 2 ): 9 - 17 .

ZHANG J , LI Y H , JIN P S . 2D and 3D time-resolved PIV experiments on flow field around vertical and inclined water-exit body [J ] . Journal of Ship Mechanics , 2005 ( 2 ): 9 - 17 . (in Chinese)

KUMAR P , MAHESH K . Large-eddy simulation of flow over an axisymmetric body of revolution [J ] . Journal of Fluid Mechanics , 2018 , 853 : 537 - 563 . DOI: 10.1017/jfm.2018.585 http://doi.org/10.1017/jfm.2018.585 https://www.cambridge.org/core/product/identifier/S0022112018005852/type/journal_article https://www.cambridge.org/core/product/identifier/S0022112018005852/type/journal_article Wall-resolved large-eddy simulation (LES) is used to simulate flow over an axisymmetric body of revolution at a Reynolds number,$Re=1.1\\times 10^{6}$, based on the free-stream velocity and the length of the body. The geometry used in the present work is an idealized submarine hull (DARPA SUBOFF without appendages) at zero angle of pitch and yaw. The computational domain is chosen to avoid confinement effects and capture the wake up to fifteen diameters downstream of the body. The unstructured computational grid is designed to capture the fine near-wall flow structures as well as the wake evolution. LES results show good agreement with the available experimental data. The axisymmetric turbulent boundary layer has higher skin friction and higher radial decay of turbulence away from the wall, compared to a planar turbulent boundary layer under similar conditions. The mean streamwise velocity exhibits self-similarity, but the turbulent intensities are not self-similar over the length of the simulated wake, consistent with previous studies reported in the literature. The axisymmetric wake shifts from high-$Re$to low-$Re$equilibrium self-similar solutions, which were only observed for axisymmetric wakes of bluff bodies in the past.

金大桥 , 王聪 , 魏英杰 , 等 . 水下轴向串列双圆柱体带空泡绕流研究 [J ] . 哈尔滨工程大学学报 , 2010 , 31 ( 10 ): 1329 - 1334 .

JIN D Q , WANG C , WEI Y J , et al . Cavitating flow study of an under water two axial-circular cylinder in tandem arrangement [J ] . Journal of Harbin Engineering University , 2010 , 31 ( 10 ): 1329 - 1334 . (in Chinese)

程丽 , 张亮 , 吴德铭 , 等 . 无升力双体水动力干扰计算 [J ] . 哈尔滨工程大学学报 , 2005 , 26 ( 1 ): 1 - 6 .

CHENG L , ZHANG L , WU D M , et al . Hydrodynamic interactions between two under water non-lifting bodies [J ] . Journal of Harbin Engineering University , 2005 , 26 ( 1 ): 1 - 6 . (in Chinese)

宋武超 , 魏英杰 , 路丽睿 , 等 . 基于势流理论的回转体并联入水双空泡演化动力学研究 [J ] . 物理学报 , 2018 , 67 ( 22 ): 224702 .

SONG W C , WEI Y J , LU L R , et al . Dynamic characteristics of parallel water-entry cavity based on potential flow theory [J ] . Acta Physica Sinica , 2018 , 67 ( 22 ): 224702 . (in Chinese) DOI: 10.7498/aps http://doi.org/10.7498/aps https://wulixb.iphy.ac.cn/ https://wulixb.iphy.ac.cn/

CHEN Y , LI J , GONG Z X , et al . LES investigation on cavitating flow structures and loads of water-exiting submerged vehicles using a uniform filter of octree-based grids [J ] . Ocean Engineering , 2021 , 225 ( 1 ): 108811 . DOI: 10.1016/j.oceaneng.2021.108811 http://doi.org/10.1016/j.oceaneng.2021.108811 https://linkinghub.elsevier.com/retrieve/pii/S0029801821002468 https://linkinghub.elsevier.com/retrieve/pii/S0029801821002468

夏雪湔 , 黄政 . 轴对称钝物体的尾涡结构 [J ] . 力学学报 , 1990 ( 3 ): 347 - 350 , 385 - 386 .

XIA X J , HUANG Z . Vortex structure in the wake of the axisymmetric bluff bodies [J ] . Chinese Journal of Theoretical and Applied Mechanics , 1990 ( 3 ): 347 - 350 , 385 - 386 . (in Chinese)

GAO S , SHI Y , PAN G , et al . The transient vortex structure in the wake of an axial-symmetric projectile launched underwater [J ] . Physics of Fluids , 2022 , 34 : 065109 . DOI: 10.1063/5.0095817 http://doi.org/10.1063/5.0095817 https://pubs.aip.org/pof/article/34/6/065109/2847153/The-transient-vortex-structure-in-the-wake-of-an https://pubs.aip.org/pof/article/34/6/065109/2847153/The-transient-vortex-structure-in-the-wake-of-an This paper provides refined wake simulations for an underwater projectile launch using an improved delayed detached eddy simulation with the energy equation, volume of fluid, and the overlapping grid technique. Additionally, the projectile wake vortex was analyzed for different Froude numbers and dimensionless transverse flow speeds. Verifications of the numerical method, grid independence, vortex identification method, and time step size are presented. Through a systematic comparison of the wake morphologies, the flow fields and vortex structures in the wakes were analyzed in detail, and the wake vortex evolution mechanisms were explored. The results show that the Kelvin–Helmholtz instability was observed, and the wake flow of the projectile launched underwater contains a complex vortical system that directly determines the wake instabilities. The resulting multiple sub-vortex structures are compact and closely arranged near the central axis without the transverse flow effect. However, compared with cases having no transverse flow, the large-scale double spiral vortex structure in the wake with a transverse flow is more difficult to fracture. In addition, the U-shaped vortex in the secondary vortex is also obviously generated in the wake during the double spiral vortex structure evolution. With an increase in the Froude number, the vortex legs are gradually apparent and, together with the shedding vortex rings in the wake, form a hairpin vortex structure. With an increase in the dimensionless transverse flow speed, the number of sub-vortex rings derived from the shedding vortex in the wake increases significantly, resulting in a more complex interaction mechanism.

GAO S , SHI Y , PAN G , et al . A study on the flow interference characteristics of projectiles successively launched underwater [J ] . International Journal of Multiphase Flow , 2022 , 151 : 104066 . DOI: 10.1016/j.ijmultiphaseflow.2022.104066 http://doi.org/10.1016/j.ijmultiphaseflow.2022.104066 https://linkinghub.elsevier.com/retrieve/pii/S0301932222000763 https://linkinghub.elsevier.com/retrieve/pii/S0301932222000763