夏维学 . 圆柱体入水复合运动多相流动特性研究 [D ] . 哈尔滨 : 哈尔滨工业大学 , 2020 .

XIA W X . Study on multiphase flow characteristics in water-entry compound movement of cylinders [D ] . Harb in:Harbin Institute of Technology, 2020 . (in Chinese)

ZHOU X , ZHOU S M , LI D K , et al . Research on design and cushioning performance of combined lunar landing airbag [J ] . Acta Astronautica , 2022 , 191 : 55 - 78 . DOI: 10.1016/j.actaastro.2021.10.033 http://doi.org/10.1016/j.actaastro.2021.10.033 https://linkinghub.elsevier.com/retrieve/pii/S0094576521005749 https://linkinghub.elsevier.com/retrieve/pii/S0094576521005749

MEDURI S , CREMONESI M , FRANGI A , et al . A Lagrangian fluid-structure interaction approach for the simulation of airbag deployment [J ] . Finite Elements in Analysis and Design , 2022 , 198 : 103659 . DOI: 10.1016/j.finel.2021.103659 http://doi.org/10.1016/j.finel.2021.103659 https://linkinghub.elsevier.com/retrieve/pii/S0168874X21001384 https://linkinghub.elsevier.com/retrieve/pii/S0168874X21001384

尹礼航 , 徐伟 , 施亮 , 等 . 复合结构气囊隔振器动静态特性试验研究 [J ] . 振动与冲击 , 2021 , 40 ( 19 ): 187 - 192 .

YIN L H , XU W , SHI L , et al . Tests for dynamic and static characteristics of compound structure air spring [J ] . Journal of Vibration and Shock , 2021 , 40 ( 19 ): 187 - 192 . (in Chinese)

CADOGAN D , SANDY C , GRAHNE M . Development and evaluation of the MARS pathfinder inflatable airbag landing system [J ] . Acta Astronautica , 2002 , 50 ( 10 ): 633 - 640 . DOI: 10.1016/S0094-5765(01)00215-6 http://doi.org/10.1016/S0094-5765(01)00215-6 https://linkinghub.elsevier.com/retrieve/pii/S0094576501002156 https://linkinghub.elsevier.com/retrieve/pii/S0094576501002156

BOWN N W , DARLEY M G . Advanced airbag landing systems for planetary landers [C ] // Proceedings of the 18th AIAA Aerodynamic Decelerator Systems Technology Conference and Seminar.Munich,Germany:AIAA , 2005 -1615: 1 - 16 .

陈洋 , 吴亮 , 曾国伟 , 等 . 带环形密闭气囊弹体入水冲击过程的数值分析 [J ] . 爆炸与冲击 , 2018 , 38 ( 5 ): 1155 - 1164 .

CHEN Y , WU L , ZENG G W , et al . Numerical analysis of the water entry process of a projectile with a circular airbag [J ] . Explosion and Shock Waves , 2018 , 38 ( 5 ): 1155 - 1164 . (in Chinese)

孙潘 , 李斌 , 温金鹏 , 等 . 水下无人航行器折叠气囊充气展开特性模拟 [J ] . 兵工学报 , 2020 , 41 ( 12 ): 2540 - 2549 . DOI: 10.3969/j.issn.1000-1093.2020.12.020 http://doi.org/10.3969/j.issn.1000-1093.2020.12.020 为深入了解水下航行器助浮折叠气囊的充气展开行为，对水下环形折叠气囊的充气展开特性进行相关研究。基于初始矩阵法，建立环形助浮折叠气囊的有限元模型。基于控制体积方法，采用有限元分析软件LS-DYNA进行折叠气囊的展开仿真计算。通过与地面展开试验的初步对比，验证气囊环向折叠建模方法的有效性。考虑不同水深带来的外部压力效应不同，进一步分析充气压力、充气管径、水深、环境热交换等设计参数对水下折叠气囊展开过程的影响。结果表明：气囊极限工作深度随充气压力的升高而线性增加；充气时间随充气管径的增加而减小；环境与展开系统的传热作用主要发生在气囊与环境之间，在气囊与气瓶充气平衡后进行，气囊完全展开的时间随着传热系数增加而减小。

SUN P , LI B , WEN J P , et al . Simulation of inflatable deployment characteristics of folding airbags for underwater unmanned vehicle [J ] . Acta Armamentarii , 2020 , 41 ( 12 ): 2540 - 2549 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2020.12.020 http://doi.org/10.3969/j.issn.1000-1093.2020.12.020 In order to further understand the inflation and deployment behavior of buoyancy assisted foldable airbag for underwater unmanned vehicle (UUV)，the inflation and deployment characteristics of UUV annular foldable airbag are studied. The finite element model of annular folding airbag is established based on the initial matrix method. Based on the control volume method，finite element analysis software LS-DYNA is used to simulate the deployment of folding airbag. The validity of the method is verified by comparing with the ground experiment.Considering the different external pressure effects caused by different water depths，the influences of design parameters, such as inflation pressure， inflation pipe diameter，water depth and environmental heat exchange, on the deployment process of underwater foldable airbag are calculated and analyzed.The results show that the limit working depth increases linearly with the increase in inflation pressure，and the inflation time decreases with the increase in inflation diameter. The heat transfer between the environment and the deployment system mainly occurs between the airbag and the environment.After the airbag and the gas cylinder are inflated and balanced，the time of complete deployment of airbag decreases with the increase in the heat transfer coefficient.

张晓光 , 李斌 , 党会学 , 等 . 水下航行体充气上浮仿真方法研究 [J ] . 兵工学报 , 2020 , 41 ( 7 ): 1249 - 1261 . DOI: 10.3969/j.issn.1000-1093.2020.07.001 http://doi.org/10.3969/j.issn.1000-1093.2020.07.001 为研究气囊展开对水下航行体充气上浮过程中的姿态变化以及运动轨迹的影响，提出一种多学科协同仿真方法。建立水下气囊的展开动力学模型，基于控制体积算法获得气囊充气展开过程的体积膨胀率曲线；在保持气囊体积膨胀率等效的条件下，建立可以同时耦合航行体6自由度刚体运动和气囊局部变形的水动力模型，并基于Navier-Stokes方程进行计算。通过仿真计算，得到水下航行体充气上浮的精细化过程，并获得水下航行体上浮时合力分量的时间历程曲线和姿态变化数据。结果表明：气囊的增浮作用能有效实现航行体的上浮回收；在上浮过程中，由于漩涡结构的不对称性使得航行体受到一定侧向力的作用，上浮时处于螺旋上升过程；上浮时，航行体会受到水流提供的竖向力作用，因此为加快上浮，上浮前应尽量调整航行体的攻角为正。

ZHANG X G , LI B , DANG H X , et al . A simulation method for inflatable floating of underwater vehicle [J ] . Acta Armamentarii , 2020 , 41 ( 7 ): 1249 - 1261 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2020.07.001 http://doi.org/10.3969/j.issn.1000-1093.2020.07.001 A multidisciplinary co-simulation method is proposed to study the influence of airbag deployment on the attitude and trajectory of underwater vehicle during the inflatable floating. A dynamic model of underwater airbag deployment is established, and the volume expansion curve is obtained based on the control volume algorithm. A hydrodynamic model that can simultaneously couple the six-degrees-of-freedom rigid body motion of vehicle and the local deformation of airbag is established under the condition that the volume expansion rate of airbag is equivalent. The calculation is carried out based on the Navier-Stokes equation. Through the simulation calculation, the refinement process of underwater vehicle's floating is obtained, and the resultant force component-time history curves and the attitude data of underwater vehicle during floating are obtained. The results show that the buoyancy of airbag can effectively make the vehicle float; during floating, the vehicle is subjected to a certain lateral force because of the asymmetry of the vortex structure, and it is in a ‘spiral' upward process when it floats; and the vehicle is subjected to the vertical force provided by the current. In order to speed up, the angle of attack of vehicle should be adjusted to be positive before it goes up. Key

孙龙泉 , 王都亮 , 李志鹏 , 等 . 基于CEL方法的航行体高速入水泡沫铝缓冲装置降载性能分析 [J ] . 振动与冲击 , 2021 , 40 ( 20 ): 80 - 88 .

SUN L Q , WANG D L , LI Z P , et al . Analysis on load reduction performance of foamed aluminum buffer device for high speed water entry of vehicle based on a CEL method [J ] . Journal of Vibration and Shock , 2021 , 40 ( 20 ): 80 - 88 . (in Chinese)

VON KARMAN T . The impact on seaplane floats during landing:NACA-TN-321 [R ] . Washington,D.C. , US : National Advisory Committee , 1929 : 19930081174 .

ROSS S , HICKS P D . A comparison of pre-impact gas cushioning and Wagner theory for liquid-solid impacts [J ] . Physics of Fluids , 2019 , 31 ( 4 ): 042101 . DOI: 10.1063/1.5086510 http://doi.org/10.1063/1.5086510 https://pubs.aip.org/pof/article/31/4/042101/991289/A-comparison-of-pre-impact-gas-cushioning-and https://pubs.aip.org/pof/article/31/4/042101/991289/A-comparison-of-pre-impact-gas-cushioning-and The normal impact of a symmetric rigid body with an initially quiescent liquid half-space is considered using both Wagner theory and a model of viscous gas pre-impact cushioning. The predictions of these two theories are compared for a range of different body shapes. Both theories assume that the impactor has small deadrise angle. Novel solutions of the Wagner normal impact problem for a symmetric body with a power-law shape are presented, which generalize the well-known results for a parabola and a wedge. For gas cushioned pre-impacts, it is shown that a pocket of gas is entrained even for body shapes with a cusp at the body minimum. A scaling law is developed that relates the dimensions of the trapped gas pocket to the slope of the body. For pre-impact gas cushioning, surface tension is shown to smooth the liquid free-surface and delay the instant of touchdown for a smooth parabolic body, while for a wedge, increasing surface tension initially delays touchdown, before hastening touchdown as the importance of surface tension is increased further. For a flat-bottomed wedge, gas entrainment is again predicted in the gas-cushioning model although the location of initial touchdown, either on the transition between the wedge and the flat bottom or along the side of the wedge, now depends upon the parameters of the body shape.

ARISTOFF J M , BUSH J W M . Water entry of small hydrophobic spheres [J ] . Journal of Fluid Mechanics , 2009 , 619 : 45 - 78 . DOI: 10.1017/S0022112008004382 http://doi.org/10.1017/S0022112008004382 https://www.cambridge.org/core/product/identifier/S0022112008004382/type/journal_article https://www.cambridge.org/core/product/identifier/S0022112008004382/type/journal_article We present the results of a combined experimental and theoretical investigation of the normal impact of hydrophobic spheres on a water surface. Particular attention is given to characterizing the shape of the resulting air cavity in the low Bond number limit, where cavity collapse is driven principally by surface tension rather than gravity. A parameter study reveals the dependence of the cavity structure on the governing dimensionless groups. A theoretical description based on the solution to the Rayleigh–Besant problem is developed to describe the evolution of the cavity shape and yields an analytical solution for the pinch-off time in the zero Bond number limit. The sphere's depth at cavity pinch-off is also computed in the low Weber number, quasi-static limit. Theoretical predictions compare favourably with our experimental observations in the low Bond number regime, and also yield new insight into the high Bond number regime considered by previous investigators. Discrepancies are rationalized in terms of the assumed form of the velocity field and neglect of the longitudinal component of curvature, which together preclude an accurate description of the cavity for depths less than the capillary length. Finally, we present a theoretical model for the evolution of the splash curtain formed at high Weber number and couple it with the underlying cavity dynamics.

SUI Y T , LI S , MING F R , 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 . DOI: 10.1063/5.0089366 http://doi.org/10.1063/5.0089366 https://pubs.aip.org/pof/article/34/5/052102/2846679/An-experimental-study-of-the-water-entry https://pubs.aip.org/pof/article/34/5/052102/2846679/An-experimental-study-of-the-water-entry We report on an experimental study of the trajectories of truncated cone projectiles on water entry. The water entry trajectory stability is of great significance to the motion control of projectile. In this paper, the truncated cone nose shape can be described by the area of the leading plane and the cone angle α. Two high-speed cameras are used to capture the trajectories of the projectiles and the initial stage of cavity dynamics. We reveal that the trajectory stability of a projectile is highly dependent on the wetted surface of the nose, which is determined by the location of the separation line between the surfaces of the cavity and body. The increase in the leading plane area is beneficial to the formation of a stable trajectory, in which only the leading plane is wetted. In an unstable trajectory case, the large hydrodynamic moment from the wetted surface on the side of the nose causes a significant rotation of the projectile. However, for the projectile with the cone angle α≳60°, though the side of the nose is fully wetted, the trajectory of the projectile turns into stable again. Results show that the attitude deflection of the projectile is determined by the cone angle of the nose. It is also found that the attitude deflection results in an irregular cavity, which further aggravates the rotation of the projectile. We quantify the relationship between the trajectory stability and two nose parameters systematically, and a phase diagram is obtained for a large parameter space. The findings in this work can be used as a reference for future designs to ensure stable trajectories on water entry.

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)

SUN L Q , WANG D L , CHEN Y Y , et al . Numerical and experimental investigation on the oblique water entry of cylinder [J ] . Science Progress , 2020 , 103 ( 3 ):0036850420940889.

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%.

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林赓 . 气囊结构落水砰击瞬态流固耦合特性研究 [D ] . 哈尔滨 : 哈尔滨工程大学 , 2016 .

LIN G . Study of characteristic of transient fluid-structure interaction of structures with airbags slamming [D ] . Harbin : Harbin Engineering University , 2016 . (in Chinese)

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 . DOI: 10.1016/j.apor.2021.102849 http://doi.org/10.1016/j.apor.2021.102849 https://linkinghub.elsevier.com/retrieve/pii/S0141118721003217 https://linkinghub.elsevier.com/retrieve/pii/S0141118721003217