LOTH E , FAETH G M . Structure of underexpanded round air jets submerged in water [J ] . International Journal of Multiphase Flow , 1989 , 15 ( 4 ): 589 - 603 . DOI: 10.1016/0301-9322(89)90055-4 http://doi.org/10.1016/0301-9322(89)90055-4 https://linkinghub.elsevier.com/retrieve/pii/0301932289900554 https://linkinghub.elsevier.com/retrieve/pii/0301932289900554

LOTH E , FAETH G M . Study of plane under-expanded air jets in water [C ] //Proceedings of the AIAA 20th Fluid Dynamics, Plasma Dynamics and Lasers Conference. Buffalo, NY,US:AIAA , 1989 .

TANG J N , WANG N F , SHYY W . Flow structures of gaseous jets injected into water for underwater propulsion [J ] . Acta Mechanica Sinica , 2011 , 27 ( 4 ): 461 - 472 . DOI: 10.1007/s10409-011-0474-4 http://doi.org/10.1007/s10409-011-0474-4 http://link.springer.com/10.1007/s10409-011-0474-4 http://link.springer.com/10.1007/s10409-011-0474-4

施红辉 , 王柏懿 , 戴振卿 . 水下超声速气体射流的力学机制研究 [J ] . 中国科学: 物理学力学天文学 , 2010 , 40 ( 1 ): 92 - 100 .

SHI H H , WANG B Y , DAI Z Q . Research on the mechanics of underwater supersonic gas jets [J ] . Science China: Physics, Mechanics & Astronomy , 2010 , 40 ( 1 ): 92 - 100 . (in Chinese)

施红辉 , 汪剑锋 , 陈帅 , 等 . 水下超声速气体射流初期流场特性的实验研究 [J ] . 中国科学技术大学学报 , 2014 , 44 ( 3 ): 233 - 237 .

SHI H H , WANG J F , CHEN S , et al . Experimental study on flow characteristics at the initial injection stage of underwater supersonic gas jets [J ] . Journal of University of Science and Technology of China , 2014 , 44 ( 3 ): 233 - 237 . (in Chinese)

黄楠 , 陈志华 , 王争论 . 水下超声速气体射流线性稳定性研究 [J ] . 推进技术 , 2021 , 42 ( 3 ): 550 - 559 .

HUANG N , CHEN Z H , WANG Z L . Linear stability of underwater supersonic gas jet [J ] . Journal of Propulsion Technology , 2021 , 42 ( 3 ): 550 - 559 . (in Chinese)

ZHANG X Y , LI S P , YANG B Y , et al . Flow structures of over-expanded supersonic gaseous jets for deep-water propulsion [J ] . Ocean Engineering , 2020 , 213 : 107611 . DOI: 10.1016/j.oceaneng.2020.107611 http://doi.org/10.1016/j.oceaneng.2020.107611 https://linkinghub.elsevier.com/retrieve/pii/S0029801820306156 https://linkinghub.elsevier.com/retrieve/pii/S0029801820306156

张小圆 , 李世鹏 , 杨保雨 , 等 . 潜航飞行体深水超音速气体射流的流动稳定性研究 [J ] . 兵工学报 , 2019 , 40 ( 12 ): 2385 - 2398 . DOI: 10.3969/j.issn.1000-1093.2019.12.001 http://doi.org/10.3969/j.issn.1000-1093.2019.12.001 深水固体火箭推进系统的可靠性和稳定性决定了整个潜航飞行体的弹道精度和飞行稳定性，其工作过程为典型的水下超音速气体射流流动过程。通过建立二维平面垂直射流几何模型，采用分离涡湍流模型仿真分析了深水条件下超音速气体射流的形貌拟序特征以及流场参数的不稳定振荡特性，对水下推进系统推力振荡现象产生的基本流动机理进行了分析。结果表明：水下超音速气体射流尾流存在高频小幅振荡，同时伴随间歇大幅振荡，这种现象与气体和水湍流混合以及中心气路激波系的不稳定运动有关；中心气路激波系的不稳定运动以及失稳重建过程会导致尾部空间压强的剧烈振荡，最终造成推力的不稳定振荡。通过对推力振荡特性的分析发现：水深越深，推力振荡幅值越大、振荡频率越高；喷管出口壁面直径越大，推力振荡幅值越大、振荡频率越高。

ZHANG X Y , LI S P , YANG B Y , et al . Analysis of the flow instability of supersonic gaseous jets for submarine vehicles working in deep water [J ] . Acta Armamentarii , 2019 , 40 ( 12 ): 2385 - 2398 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2019.12.001 http://doi.org/10.3969/j.issn.1000-1093.2019.12.001 The reliability and stability of underwater solid rocket motor propulsion system are crucial to the ballistic accuracy and flight stability of submarine vehicles. The working process of the motor is the flow process of typical supersonic gaseous jets underwater. A planar vertical two-dimensional jet geometric model is established, and the detached-eddy simulation turbulence model is used to simulate and analyze the flow field of supersonic gaseous jets in deep-water, and the oscillation characteristics of parameters in the flow field are monitored and analyzed. The underlying flow mechanism due to thrust oscillation of underwater solid rocket motor is addressed. The results show that a high-frequency oscillation occurs in the gas wake of the underwater solid rocket motor, and is accompanied by a high-amplitude intermittent oscillation. The oscillation is related to the unstable motion of shock waves along the central gas path, which leads to a sharp oscillation of pressure in the tail space, ultimately causing thrust instability. The analysis of thrust oscillation characteristics indicates that the deeper the water depth is, the larger the thrust oscillation amplitude is, and the higher the frequency is; and the larger the diameter of wall at nozzle exit is, the larger the thrust oscillation amplitude is, and the higher the frequency is. Key

张小圆 , 李世鹏 , 杨保雨 , 等 . 水下固体火箭发动机垂直气体射流结构和推力影响研究 [J ] . 推进技术 , 2021 , 42 ( 5 ): 961 - 969 .

ZHANG X Y , LI S P , YANG B Y , et al . Flow structures of vertical gaseous jets and effects of thrust of underwater solid rocket motor [J ] . Journal of Propulsion Technology , 2021 , 42 ( 5 ): 961 - 969 . (in Chinese)

王利利 , 刘影 , 李达钦 , 等 . 固体火箭发动机水下超音速射流数值研究 [J ] . 兵工学报 , 2019 , 40 ( 6 ): 1161 - 1170 . DOI: 10.3969/j.issn.1000-1093.2019.06.006 http://doi.org/10.3969/j.issn.1000-1093.2019.06.006 固体火箭发动机水下点火射流是高温高压条件下复杂的多相流过程，为研究其流场特性与推力特性，选取扩张比分别为3.4和14.0的拉瓦尔喷管模型进行数值模拟。采用计算流体力学方法分析高速燃气超音速射流过程的流场与推力演化过程，揭示高温高压气体与水环境之间的相互作用规律。结果表明：固体火箭发动机水下射流流场结构与推力特性呈周期性变化，根据流场特征可分为颈缩、胀鼓、回击3个阶段；水环境与射流气体之间的相互作用是导致背压振荡的直接原因，同时导致激波运动、动量推力与压差推力的振荡。对比两种扩张比喷管的射流可知，扩张比为14.0的喷管射流形貌与流场结构的周期性变化更明显，扩张比为3.4的喷管背压振荡频率高、周期性特征弱、推力更稳定。

WANG L L , LIU Y , LI D Q , et al . Numerical study of underwater supersonic gas jets for solid rocket engine [J ] . Acta Armamentarii , 2019 , 40 ( 6 ): 1161 - 1170 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2019.06.006 http://doi.org/10.3969/j.issn.1000-1093.2019.06.006 The ignition process of gas jets under water is essentially complex, including multiphase flow and complicated flow structures. The Laval nozzle models with expansion ratios of 3.4 and 14.0 are numerically simulated. The CFD method is applied to study the flow structures and corresponding thrust characteristics of rocket engine and analyze the interaction between the high-speed gas jets and water environment. The results show that the flow structures and thrust characteristics of engine change periodically, and the process can be divided into three stages: necking, bulge and return stroke. The interaction between the water environment and the gas jet is the immediate cause leading to the back pressure oscillation, which also induces the fluctuation of shock waves, momentum thrust and pressure differential thrust. For the nozzles with different expansion ratios, the periodic variation of jets pattern and flow structures for the nozzle with expansion ratio of 14 can be more obviously observed, and the oscillation frequency of back pressure for the nozzle with expansion ratio of 3.4 is higher, accompanied with weak periodic characteristics and more stable thrust characteristics. Key

权晓波 , 王占莹 , 刘元清 , 等 . 水环境下喷管流动分离数值研究 [J ] . 固体火箭技术 , 2020 , 43 ( 1 ): 8 - 15 .

QUAN X B , WANG Z Y , LIU Y Q , et al . Numerical simulation research on the flow separation of solid rocket motor in water environment [J ] . Journal of Solid Rocket Technology , 2020 , 43 ( 1 ): 8 - 15 . (in Chinese)

许海雨 , 罗凯 , 黄闯 , 等 . 通气超空化对水下火箭发动机性能影响 [J ] . 哈尔滨工业大学学报 , 2021 , 53 ( 6 ): 41 - 47 .

XU H Y , LUO K , HUANG C , et al . Influence of ventilated supercavitation on underwater rocket engine [J ] . Journal of Harbin Institute of Technology , 2021 , 53 ( 6 ): 41 - 47 . (in Chinese)

乌岳 , 李卓 , 江晓瑞 . 水下点火固体火箭发动机两相流流场数值分析 [J ] . 航空动力学报 , 2018 , 33 ( 10 ): 2508 - 2514 .

WU Y , LI Z , JIANG X R . Numerical analysis for underwater ignition two-phase flow field of solid rocket motor [J ] . Journal of Aerospace Power , 2018 , 33 ( 10 ): 2508 - 2514 . (in Chinese)

邹延兵 , 卓长飞 , 封锋 . 火箭发动机水下启动过程流场数值模拟研究 [J ] . 弹道学报 , 2016 , 28 ( 4 ): 30 - 35 , 41. 利用流体分析软件Fluent对水下火箭发动机启动过程流场进行了仿真。基于压力的求解器,采用了二维双精度解算器和轴对称理想水流场模型; 时间采用一阶隐式离散; 压力速度修正选用SIMPLE方法; 多相流采用VOF模型; 湍流模型采用K-epsilon模型,对处于50 m深水中的火箭发动机启动过程中喷管流场、尾流场进行了详细研究,分析了各参数的变化过程对喷管性能的影响。结果表明,对于给定的喷管,当喷管达到了超音速流动之后,马赫数都是确定的,当地的静压和总压成正比; 水下火箭发动机轴向压力总体的变化趋势是在振荡中逐渐减少的,最后降低到环境压力; 不同时刻轴线上温度的分布规律和速度基本相似。

ZOU Y B , ZHUO C F , FENG F . Numerical simulation of flow field for underwater starting process of rocket engine [J ] . Journal of Ballistics , 2016 , 28 ( 4 ): 30 - 35 , 41. (in Chinese)

王晓辉 , 张珂 , 褚学森 , 等 . 水下点火推进尾空泡振荡的研究 [J ] . 船舶力学 , 2020 , 24 ( 2 ): 136 - 144 .

WANG X H , ZHANG K , CHU X S , et al . Research on the pressure oscillation process of tail bubble of underwater igniting propulsion [J ] . Journal of Ship Mechanics , 2020 , 24 ( 2 ): 136 - 144 . (in Chinese)

汤龙生 , 刘宇 , 吴智锋 , 等 . 水下超声速燃气射流气泡的生长及压力波传播特性实验研究 [J ] . 推进技术 , 2011 , 32 ( 3 ): 417 - 420 .

TANG L S , LIU Y , WU Z F , et al . Experimental study on characteristics of bubble growth and pressure wave propagation by supersonic gas jets under water [J ] . Journal of Propulsion Technology , 2011 , 32 ( 3 ): 417 - 420 . (in Chinese)

贾有军 , 张胜敏 , 尤俊峰 , 等 . 固体发动机水下点火尾流变化过程试验研究 [J ] . 固体火箭技术 , 2015 , 38 ( 5 ): 660 - 663 , 678.

JIA Y J , ZHANG S M , YOU J F , et al . Experimental research on the changing process of underwater ignition wake of solid rocket motor [J ] . Journal of Solid Rocket Technology , 2015 , 38 ( 5 ): 660 - 663 , 678. (in Chinese)

张春 , 郁伟 , 王宝寿 . 水下超声速燃气射流的初期流场特性研究 [J ] . 兵工学报 , 2018 , 39 ( 5 ): 961 - 968 . DOI: 10.3969/j.issn.1000-1093.2018.05.016 http://doi.org/10.3969/j.issn.1000-1093.2018.05.016 针对超声速燃气射流在静水介质中扩展的复杂多相流动问题，在压力水筒中开展了固体火箭发动机水下点火实验；基于雷诺时均Navier-Stokes方法和流体体积模型，对相同工况进行了燃气与水耦合数值求解。研究结果表明：水下燃气射流迅速建立超声速流动后，高速射流的冲击作用导致燃气泡呈现出帽状特征，并逐渐演变为类椭球体的气囊，平均轴向扩展速度约为40 m/s；燃气泡内部流动结构复杂，存在两个剪切涡环与重复出现的激波胞格，射流边界与燃气泡边界的相互作用会导致射流后续演化的不稳定；燃气扩展时通过压力波在水流场中产生高压区，其压力峰值在振荡中逐渐与环境压力匹配，喷管堵盖打开压力、出口截面积是影响推力峰值的重要因素。

ZHANG C , YU W , WANG B S . Research on the initial flow field characteristics of underwater supersonic gas jets [J ] . Acta Armamentarii , 2018 , 39 ( 5 ): 961 - 968 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2018.05.016 http://doi.org/10.3969/j.issn.1000-1093.2018.05.016 To investigate the complex multiphase flow of supersonic gas jets in still water, an underwater ignition experiment of solid rocket motor is conducted in the pressure tank, and the numerically simulated results of gas-water coupling for the same case are obtained by using Reynolds-averaged Navier-Stokes(RANS) method and volume of fluid(VOF) model. The results show that, after underwater gas jets achieve supersonic flow, the gas bubble appears to be cap-like due to the jet impact effect. Then the gas bubble gradually evolves into an ellipsoid-shaped gasbag with average axial expansion velocity of about 40 m/s. The flow structures inside the gas bubble are very complex, where two shear vortex rings and repeated shock cells exist. The interaction between the boundaries of gas jet and gas bubble may induce the instability of gas jet in the subsequent evolution stage. It is also demonstrated that there exists a part of high pressure in the flow field, and the pressure peaks gradually match with the environmental pressure in the oscillation process. The pressure of opening nozzle closure and the area of nozzle outlet are the two important factors that affects thrust peak value.Key

唐金兰 , 刘佩进 . 固体火箭发动机原理 [M ] . 北京 : 国防工业出版社 , 2013 : 16 - 20 .

TANG J L , LIU P J . Principle of solid rocket motor [M ] . Beijing : National Defense Industry Press , 2013 : 16 - 20 . (in Chinese)

于邵祯 , 姜毅 , 周笑飞 , 等 . 耦合尾喷管堵盖运动的发射箱内流场研究 [J ] . 兵工学报 , 2014 , 35 ( 11 ): 1805 - 1812 . DOI: 10.3969/j.issn.1000-1093.2014.11.011 http://doi.org/10.3969/j.issn.1000-1093.2014.11.011 利用初始冲击波超压完成前后盖开启过程的贮运发射箱已得到广泛应用。为研究含尾喷管堵盖的冲击波超压形成过程及对后易碎盖的作用效果，应用有限元方法并结合动网格技术建立了导弹点火后堵盖的运动模型，并通过实验方法对仿真结果进行了验证。结合计算结果可清晰地看到尾焰流场的形成过程，并得到了冲击波超压在后易碎盖表面的随时间变化曲线。研究表明：受堵盖的影响，冲击波超压首先形成并冲击后易碎盖，燃气由堵盖的边缘向中心汇聚形成主流，在对后易碎盖的冲击时间和作用位置上与冲击波作用有明显的不同；后易碎盖主要受到冲击波超压作用实现碎裂变形，在堵盖运动的投影区域首先达到最大受力，瞬时峰值达5×10⁵ Pa.

YU S Z , JIANG Y , ZHOU X F , et al . Research on distribution of flow field in launching canister with the effect of nozzle closure [J ] . Acta Armamentarii , 2014 , 35 ( 11 ): 1805 - 1812 . (in Chinese)

杨保雨 . 水下大深度火箭发动机垂直射流仿真与实验研究 [D ] . 北京 : 北京理工大学 , 2019 .

YANG B Y . The numerical simulation and experimental study on vertical gas jet of solid rocket motor in deep water [D ] . Beijing : Beijing Institute of Technology , 2019 . (in Chinese)

唐嘉宁 , 李世鹏 , 王宁飞 . 水下固体火箭发动机的负推力现象研究 [J ] . 固体火箭技术 , 2012 , 35 ( 3 ): 325 - 329 , 343.

TANG J N , LI S P , WANG N F . Study on the negative thrust of the underwater solid rocket engines [J ] . Journal of Solid Rocket Technology , 2012 , 35 ( 3 ): 325 - 329 , 343. (in Chinese)