基于边界元法的三维结构体滑跳运动数值仿真

杨超; 姜宇; 吴志刚

doi:10.13700/j.bh.1001-5965.2022.0141

基于边界元法的三维结构体滑跳运动数值仿真

doi: 10.13700/j.bh.1001-5965.2022.0141

北京航空航天大学航空科学与工程学院, 北京 100083

详细信息

通讯作者:
吴志刚, E-mail: wuzhigang@buaa.edu.cn

中图分类号: O353.4
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出版历程
- 收稿日期: 2022-03-11
- 录用日期: 2022-05-27
- 网络出版日期: 2022-06-02

Numerical simulation of skipping motion of three-dimensional structure based on boundary element method

School of Aeronautic Science and Engineering, Beihang University, Beijing 100083, China

More Information

Corresponding author: WU Zhigang, E-mail: wuzhigang@buaa.edu.cn

摘要

摘要:
利用滑跳运动实现近水面高速机动飞行的击水式飞行器是近年来的热点问题，三维结构体高速斜入水冲击载荷求解是滑跳运动数值仿真的关键步骤。针对滑跳运动开展研究，建立了一种基于边界元法的可以考虑结构弹性效应的三维结构体近水面滑跳运动时域数值仿真方法。高速斜入水冲击载荷由边界元法求得，利用状态方程直接积分法求解得到结构节点位移动力响应，并通过滑跳运动动力学模型更新结构体的质心位置及运动速度。针对钢球高速斜入水冲击现象进行数值仿真并与试验结果对比，验证了所提方法的准确性。开展三维刚性球冠体的近水面滑跳运动时域数值仿真和变参分析，得到了结构质量、初始高度、水平抛出速度和半径大小4种参数对球冠体滑跳运动的影响规律。考虑结构弹性效应后，高速斜入水冲击载荷减小，对球冠体滑跳运动也有一定影响。
- 滑跳运动 /
- 边界元法 /
- 入水冲击 /
- 流固耦合 /
- 球冠体
Abstract:
In recent years, the water striking aircraft which realizes high-speed maneuvering flight near the water surface by using skipping motion has become one of the hot issues in research, and the solution of high-speed oblique water impact load of three-dimensional structure is the key step of skipping motion numerical simulation. Based on the boundary element method, a time-domain numerical simulation method of water surface skipping of three-dimensional structure considering structural elastic effect is established. The high-speed oblique water impact load is obtained by the boundary element method, and the displacement dynamic response of the structural node is obtained by the direct integration method of the state equation. Moreover, the centroid position and motion speed of the structure are updated by the skipping motion dynamic model. To verify the accuracy of the fluid load solution algorithm of this method, the numerical simulation of high-speed oblique water impact of steel sphere is carried out and compared with the experimental value. The time-domain numerical simulation and variable parameter analysis of skipping motion of three-dimensional rigid spherical crown are carried out. Then, the effects of structural mass, initial height, horizontal throw speed and radius on the skipping motion of the spherical crown are obtained. After considering the elastic effect, the impact load of high-speed oblique water entry decreases, which also has a certain influence on the sliding and jumping motion of the spherical crown.
- skipping motion /
- boundary element method /
- water inflow impact /
- fluid solid coupling /
- spherical crown

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图 1 球冠体近水面滑跳运动问题示意图

Figure 1. Schematic diagram of near-water-surface skipping motion of hemispherical structure

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图 2 时域迭代求解方法基本原理

Figure 2. Basic principle of time domain iterative solution method

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图 3 常值三角形单元

Figure 3. Constant triangular element

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图 4 速度分量求解示意图

Figure 4. Schematic diagram of velocity component solution

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图 5 浸湿表面示意图

Figure 5. Schematic diagram of water soaked surface

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图 6 斜入水冲击载荷模型单元边界条件

Figure 6. Element boundary conditions of oblique water impact load model

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图 7 时域迭代求解方法流程

Figure 7. Flow chart of time domain iterative solution method

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图 8 钢球高速斜入水试验示意图

Figure 8. Schematic diagram of high speed oblique water entry test of steel sphere

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图 9 离开水面速度数值计算结果与试验值对比

Figure 9. Comparison between calculated and experimental values of velocity leaving water surface

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图 10 离开水面倾角数值计算结果与试验值对比

Figure 10. Comparison between calculated and experimental values of dip angle leaving water surface

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图 11 球冠体有限元模型

Figure 11. Finite element model of spherical crown

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图 12 初始未受扰动的流场

Figure 12. Initial undisturbed flow field

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图 13 滑跳运动轨迹仿真结果

Figure 13. Simulation results of skipping motion trajectory

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图 14 滑跳运动垂向速度时历曲线

Figure 14. Vertical velocity time history curve of skipping motion

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图 15 第1次触水垂向速度时历曲线

Figure 15. Vertical velocity time history curve in the first contact with water

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图 16 滑跳运动水平速度时历曲线

Figure 16. Horizontal velocity time history curve of skipping motion

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图 17 第1次触水水平速度时历曲线

Figure 17. Horizontal velocity time history curve in the first contact with water

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图 18 第1次触水垂向受力时历曲线

Figure 18. Vertical stress time history curve in the first contact with water

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图 19 第1次触水水平受力时历曲线

Figure 19. Horizontal stress time history curve in the first contact with water

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图 20 不同结构质量的滑跳轨迹对比

Figure 20. Comparison of skipping motion trajectory with different structural quality

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图 21 不同结构质量的滑跳垂向速度时历对比

Figure 21. Time history comparison of skipping motion vertical velocity with different structural quality

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图 22 不同结构质量的滑跳水平速度时历对比

Figure 22. Time history comparison of skipping motion horizontal velocity with different structural quality

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图 23 不同初始高度的滑跳轨迹对比

Figure 23. Comparison of skipping motion trajectories with different initial heights

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图 24 不同初始高度的滑跳垂向速度时历对比

Figure 24. Time history comparison of skipping motion vertical velocity with different initial heights

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图 25 不同初始高度的滑跳水平速度时历对比

Figure 25. Time history comparison of skipping motion horizontal velocity with different initial heights

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图 26 不同水平抛出速度的滑跳轨迹对比

Figure 26. Comparison of skipping motion trajectories with different horizontal throw speeds

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图 27 不同水平抛出速度的滑跳垂向速度时历对比

Figure 27. Time history comparison of skipping motion vertical velocity with different horizontal throw speeds

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图 28 不同半径大小的滑跳轨迹对比

Figure 28. Comparison of skipping motion trajectories with different radius sizes

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图 29 不同半径大小的滑跳垂向速度时历对比

Figure 29. Time history comparison of skipping motion vertical velocity with different radius sizes

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图 30 不同半径大小的滑跳水平速度时历对比

Figure 30. Time history comparison of skipping motion horizontal velocity with different radius sizes

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图 31 有无弹性效应的第1次触水垂向受力时历对比

Figure 31. Time history comparison of vertical stress in the first contact with water with or without elastic effect

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图 32 有无弹性效应的第1次触水水平受力时历对比

Figure 32. Time history comparison of horizontal stress in the first contact with water with or without elastic effect

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图 33 有无弹性效应的滑跳轨迹对比

Figure 33. Comparison of skipping motion trajectories with or without elastic effect

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图 34 有无弹性效应的滑跳垂向速度时历对比

Figure 34. Time history comparison of skipping motion vertical velocity with or without elastic effect

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图 35 有无弹性效应的滑跳水平速度时历对比

Figure 35. Time history comparison of skipping motion horizontal velocity with or without elastic effect

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图 36 球冠体最低点的弹性变形时历曲线

Figure 36. Time history curves of elastic deformation at the lowest point of spherical crown

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参考文献(39)

[1]	孙士明, 陈玮琪, 王宝寿, 等. 航行体近水面滑跳运动试验研究[J]. 数字海洋与水下攻防, 2019, 2(2): 79-87. https://www.cnki.com.cn/Article/CJFDTOTAL-DOUW201902014.htm SUN S M, CHEN W Q, WANG B S, et al. Experimental research on near-water-surface skipping motion of vehicle[J]. Digital Ocean & Underwater Warfare, 2019, 2(2): 79-87(in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-DOUW201902014.htm
[2]	孙士明, 陈玮琪, 王宝寿. 跨介质航行体研究现状及关键技术[J]. 水中兵器, 2016 (4): 1-7. SUN S M, CHEN W Q, WANG B S. Research status and key technologies of cross-media navigation vehicles[J]. Underwater Weapon, 2016(4): 1-7(in Chinese).
[3]	裴譞, 张宇文, 李闻白, 等. 跨介质飞行器气/水两相弹道仿真研究[J]. 工程力学, 2010, 27(8): 223-228. https://www.cnki.com.cn/Article/CJFDTOTAL-GCLX201008039.htm PEI X, ZHANG Y W, LI W B, et al. Simulation and analysis on the gas/water two-phase ballistics of trans-media aircraft[J]. Engineering Mechanics, 2010, 27(8): 223-228(in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-GCLX201008039.htm
[4]	王伟, 张宇文, 朱灼. 跨介质飞行器弹道仿真分析[J]. 计算机仿真, 2011, 28(12): 1-4. doi: 10.3969/j.issn.1006-9348.2011.12.001 WANG W, ZHANG Y W, ZHU Z. Simulation and analysis on ballistic trajectory of trans-media aircraft[J]. Computer Simulation, 2011, 28(12): 1-4(in Chinese). doi: 10.3969/j.issn.1006-9348.2011.12.001
[5]	李金洪, 杨安强, 粟凌云. 跨介质UAV水面滑跳转向特性建模与仿真[J]. 鱼雷技术, 2012, 20(6): 401-406. https://www.cnki.com.cn/Article/CJFDTOTAL-YLJS201206001.htm LI J H, YANG A Q, SU L Y. Modeling and simulation of dynamic characteristics of slide jump steering trajectory for trans-media UAV[J]. Torpedo Technology, 2012, 20(6): 401-406(in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-YLJS201206001.htm
[6]	ZHAO R, FALTINSEN O. Water entry of two-dimensional bodies[J]. Journal of Fluid Mechanics, 1993, 246(1): 593-612.
[7]	樊征, 刘莹莹. 掠海飞行器主动触水撞水力分析[J]. 固体火箭技术, 2012, 35(6): 722-725. https://www.cnki.com.cn/Article/CJFDTOTAL-GTHJ201206004.htm FAN Z, LIU Y Y. Analysis on slamming force of active water impact for sea skimming vehicle[J]. Journal of Solid Rocket Technology, 2012, 35(6): 722-725(in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-GTHJ201206004.htm
[8]	XU G D, DUAN W Y, WU G X. Numerical simulation of oblique water entry of an asymmetrical wedge[J]. Ocean Engineering, 2008, 35(16): 1597-1603. doi: 10.1016/j.oceaneng.2008.08.002
[9]	FALTINSEN O M, CHEZHIAN M. A generalized Wagner method for three-dimensional slamming[J]. Journal of Ship Research, 2005, 49(4): 279-287. doi: 10.5957/jsr.2005.49.4.279
[10]	顾懋祥, 程贯一, 张效慈. 平头旋转壳撞水水弹性效应的研究[J]. 水动力学研究与进展: A辑, 1991, 6(1): 42-51. GU M X, CHENG G Y, ZHANG X C. Study on hydroelastic effect of a blunt rotatory shell impacting with water[J]. Journal of Hydrodynamics: Ser. A, 1991, 6(1): 42-51(in Chinese).
[11]	TAKAGI K. Influence of elasticity on hydrodynamic impact problem[J]. Journal of the Kansai Society of Naval Architects, Japan, 1994, 222: 97-106.
[12]	张岳青, 徐绯, 李建辰, 等. 结构物入水冲击表面压力的模型研究及应用[J]. 机械强度, 2017, 39(1): 33-39. https://www.cnki.com.cn/Article/CJFDTOTAL-JXQD201701006.htm ZHANG Y Q, XU F, LI J C, et al. Model study and application on surface pressure measurement of structure water entry[J]. Journal of Mechanical Strength, 2017, 39(1): 33-39(in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-JXQD201701006.htm
[13]	张岳青, 白治宁, 曾小凡, 等. 楔形和弧形结构入水冲击响应研究[J]. 船舶力学, 2020, 24(3): 400-408. https://www.cnki.com.cn/Article/CJFDTOTAL-CBLX202003014.htm ZHANG Y Q, BAI Z N, ZENG X F, et al. Study of water impact response of wedge-and-arc-shaped structures[J]. Journal of Ship Mechanics, 2020, 24(3): 400-408(in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-CBLX202003014.htm
[14]	MOHAMMAD J, MAURIZIO P. Water entry of compliant slender bodies: Theory and experiments[J]. International Journal of Mechanical Sciences, 2018, 149: 514-529.
[15]	WU G X, SUN H, HE Y S. Numerical simulation and experimental study of water entry of a wedge in free fall motion[J]. Journal of Fluids and Structures, 2004, 19(3): 277-289.
[16]	WU G X. Numerical simulation of water entry of twin wedges[J]. Journal of Fluids and Structures, 2006, 22(1): 99-108.
[17]	BATHE K J. 有限元法[M]. 2版. 轩建平, 译. 北京: 高等教育出版社, 2016. BATHE K J. Finite element procedures[M]. 2nd ed. XUAN J P, translated. Beijing: Higher Education Press, 2016(in Chinese).
[18]	姚振汉, 王海涛. 边界元法[M]. 北京: 高等教育出版社, 2010. YAO Z H, WANG H T. Boundary element methods[M]. Beijing: Higher Education Press, 2010(in Chinese).
[19]	王永虎, 石秀华, 李文哲, 等. 斜入水高速冲击的理论建模及缓冲分析[J]. 机械科学与技术, 2008, 27(6): 766-769. https://www.cnki.com.cn/Article/CJFDTOTAL-JXKX200806017.htm WANG Y H, SHI X H, LI W Z, et al. Modeling and cushioning analysis of oblique water entry with high velocity[J]. Mechanical Science and Technology for Aerospace Engineering, 2008, 27(6): 766-769(in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-JXKX200806017.htm
[20]	陈占晖, 卢永锦. 高速运动物体砰击水面后的动力学特性研究[J]. 船舶工程, 2009, 31(3): 62-65. https://www.cnki.com.cn/Article/CJFDTOTAL-CANB200903020.htm CHEN Z H, LU Y J. Study on the dynamic characteristics of high-speed object slamming water[J]. Ship Engineering, 2009, 31(3): 62-65(in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-CANB200903020.htm
[21]	郑金伟, 宗智. 三维刚体椭圆头结构高速倾斜入水冲击模拟[J]. 船海工程, 2012, 41(3): 7-9. https://www.cnki.com.cn/Article/CJFDTOTAL-WHZC201203004.htm ZHENG J W, ZONG Z. 3-dimensional numerical simulation of rigid elliptic structure inclined water-entry at high speed[J]. Ship & Ocean Engineering, 2012, 41(3): 7-9(in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-WHZC201203004.htm
[22]	SCOLAN Y. Oblique water entry of a three dimensional body[J]. International Journal of Naval Architecture and Ocean Engineering, 2014, 6(4): 1197-1208.
[23]	TSAI H W, WU W F, LAI C L. An experimental study of non-spinning stone-skipping process[J]. Experimental Thermal and Fluid Science, 2021, 123: 1-10.
[24]	LI C H, WANG C, WEI Y J, et al. Numerical investigation on the cavity dynamics and deviation characteristics of skipping stones[J]. Journal of Fluids and Structures, 2021, 104: 1-16.
[25]	卢炽华, 何友声. 二维弹性结构入水冲击过程中的流固耦合效应[J]. 力学学报, 2000, 32(2): 129-140. https://www.cnki.com.cn/Article/CJFDTOTAL-LXXB200002000.htm LU C H, HE Y S. Coupled analysis of nonlinear interaction between fluid and structure during impact[J]. Acta Mechanica Sinica, 2000, 32(2): 129-140(in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-LXXB200002000.htm
[26]	李井煜, 卢晓平, 赵鹏伟. 直接边界元法解势流速度场问题[J]. 中国舰船研究, 2015, 10(1): 68-75. https://www.cnki.com.cn/Article/CJFDTOTAL-JCZG201501010.htm LI J Y, LU X P, ZHAO P W. Direct boundary element method for the problem of potential flow velocity field[J]. Chinese Journal of Ship Research, 2015, 10(1): 68-75(in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-JCZG201501010.htm
[27]	王献孚. 计算船舶流体力学[M]. 上海: 上海交通大学出版社, 1992. WANG X F. Computational ship hydrodynamics[M]. Shanghai: Shanghai Jiaotong University Press, 1992(in Chinese).
[28]	闫发锁, 于龙超, 赵九龙, 等. 轴对称体砰击载荷的三维动网格数值计算[J]. 中国海洋大学学报, 2017, 47(5): 113-120. https://www.cnki.com.cn/Article/CJFDTOTAL-QDHY201705016.htm YAN F S, YU L C, ZHAO J L, et al. Numerical calculation of the slamming load for axisymmetric geometries using 3D dynamic mesh[J]. Periodical of Ocean University of China, 2017, 47(5): 113-120(in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-QDHY201705016.htm
[29]	WAGNER V H. Phenomena associated with impacts and sliding on liquid surfaces[J]. Journal of Applied Mathematics and Mechanics, 1932, 12: 193-215.
[30]	WARDLAW A B, MORRISON A M, BALDWIN J L. Prediction of impact pressures, forces, and moments during vertical and oblique water entry[R]. [S. l. ]: Naval Surface Weapons Center White Oak Lab Silver Spring Md, 1977.
[31]	JOHNSON W, REID S R. Ricochet of spheres off water[J]. Journal of Mechanical Engineering Science, 1975, 17(2): 71-81.
[32]	HUTCHINGS I M. The ricochet of spheres and cylinders from the surface of water[J]. International Journal of Mechanical Sciences, 1976, 18(5): 243-247.
[33]	是长春. 平板湍流摩阻系数的显式表达式[J]. 航空学报, 1986, 9(6): B299-B302. https://www.cnki.com.cn/Article/CJFDTOTAL-HKXB198806019.htm SHI C C. An explicit expression of the turbulent frictional drag coefficient for a flat plate[J]. Acta Aeronautica et Astronautica Sinica, 1986, 9(6): B299-B302(in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-HKXB198806019.htm
[34]	张森文, 曹开彬. 计算结构动力响应的状态方程直接积分法[J]. 计算力学学报, 2000, 17(1): 94-118. https://www.cnki.com.cn/Article/CJFDTOTAL-JSJG200001014.htm ZHANG S W, CAO K B. Direct integration of state equation method for dynamic response of structure[J]. Chinese Journal of Computational Mechanics, 2000, 17(1): 94-118(in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-JSJG200001014.htm
[35]	方同, 薛璞. 振动理论及应用[M]. 西安: 西北工业大学出版社, 1998. FANG T, XUE P. Vibration theory and application[M]. Xi'an: Northwest University of Technology Press, 1998(in Chinese).
[36]	诸德超, 邢誉峰, 程伟, 等. 工程振动基础[M]. 北京: 北京航空航天大学出版社, 2004. ZHU D C, XING Y F, CHENG W, et al. Engineering vibration foundation[M]. Beijing: Beihang University Press, 2004(in Chinese).
[37]	杨超, 吴志刚, 万志强, 等. 飞行器气动弹性原理[M]. 北京: 北京航空航天大学出版社, 2011. YANG C, WU Z G, WAN Z Q, et al. Principle of aircraft aeroelasticity[M]. Beijing: Beihang University Press, 2011(in Chinese).
[38]	钱杏芳, 林瑞雄, 赵亚男. 导弹飞行力学[M]. 北京: 北京理工大学出版社, 1987. QIAN X F, LIN R X, ZHAO Y N. Missile flight mechanics[M]. Beijing: Beijing Institute of Technology Press, 1987(in Chinese).
[39]	SOLIMAN A S, REID S R, JOHNSON W. The effect of spherical projectile speed in ricochet off water and sand[J]. International Journal of Mechanical Sciences, 1976, 18(6): 279-284.