Characteristics of Fluid-structure Interaction of High-speed Projectile at Different Angles of Attack during Water Entry

doi:10.12382/bgxb.2024.0007

Abstract

Abstract:

The magnitude of structural response (deformation) of a projectile during high-speed water entry plays a crucial role in determining the projectile’s safe entry into the water. At present, the numerical computational methods based on rigid-body models fail to fully elucidate the intricate coupled interactions among multiphase flow, hydrodynamics and projectile structural responses during the water entry process under the influence of the initial disturbances. To address this challenge, a fluid-structure interaction numerical computational method for high-speed water entry is developed based on the principles of fluid mechanics and structural dynamics. This method is specifically tailored to investigate the influence of the angle of attack on the high-speed water entry process of a specific projectile, focusing on analyzing the interaction among supercavity evolution, impact loads, projectile motion and structural deformations under varying angles of attack. The research findings revealed the following key insights: As the angle of attack increases, a pronounced impact occurs between the lower surface of projectile and the supercavity wall, resulting in the curvature of supercavity wall; For the specific projectile considered in the study, a secondary peak load occurs as the projectile tail strikes the liquid surface at an angle of attack of more than 3°, inducing the bending moments from wetting and the plastic deformation of projectile, ultimately leading to significant bending of the tail, with maximum wetting-induced surface pressure exceeding 10MPa; The stress of the projectile remains below the yield strength of its material although the projectile undergoes the bending moments as a result of the concurrent loading on both the projectile head and tail at an angle of attack of 2°, thereby precluding plastic deformation. Consequently, for the specific projectile, an angle of attack of 2° or less is recommended for safe water entry.

Key words: fluid-structure interaction, high-speed oblique water entry, angle of attack, supercavity, structural deformation, impact load

CLC Number:

LIU Xiangyan, YU Nan, HUANG Zhengui, CHEN Zhihua, MA Changsheng, QIU Rongxian. Characteristics of Fluid-structure Interaction of High-speed Projectile at Different Angles of Attack during Water Entry[J]. Acta Armamentarii, 2024, 45(10): 3415-3429.

Figures/Tables 29

Fig.1 Flowchart of fluid-structure interaction calculation

Fig.2 Comparison of oscillation and deformation of flexible plate

Fig.3 Comparison of experimental supercavities in Ref.[33] and numerically calculated supercavities

Fig.4 Comparison of experimental water entry trajectory in Ref.[33] and numerically calculated water entry trajectory

Fig.5 Size of projectile model

Table 1 Material properties of 45 steel[27]

密度/(kg·m^-3)	杨氏模量/GPa	泊松比
7850	210	0.29

Table 2 Johnson-Cook parameters of 45 steel[27]

A/MPa	B/MPa	C	n	m	T_m/K	T_t/K
595	580	0.023	0.133	2.03	1765.15	298.15

Fig.6 Computational domain

Fig.7 Max value of y m a x + on the surface of projectile

Fig.8 The value of y+ on the surface of projectile for t=0.3ms

Fig.9 Mesh division of fluid solver

Fig.10 Projectile mesh division

Table 3 Mesh irrelevance comparison table

网格	流场网格数/10⁴	弹体网格数/10⁴
1	499.01	4.41
2	698.57	8.28
3	900.04	11.35

Fig.11 Comparison of calculated results from different meshes

Fig.12 Morphological evolution of supercavity

Fig.13 Wetting of the lower surface of projectile

Fig.14 Pressure of the lower surface of projectile

Fig.15 Velocity change of central point of caviter

Fig.16 Change of projectile attitude

Fig.17 Change of total load during water entry

Fig.18 Wetting and pressure distribution on the lower surface of projectile before and after water entry

Fig.19 Wetting and pressure distribution before and after the second peak of load for α=3°, 4°, 5°

Fig.20 Stress distribution on the surface and longitudinal section of projectile at 1.2ms for α=0°, 1°, 2°

Fig.21 Schematic diagram of force on the projectile and the stress distribution of projectile at 1.2ms for α=2°

Fig.22 Stress distribution on the surface and longitudinal section of projectile at 1.2ms for α=3°, 4°, 5°

Fig.23 Equivalent plastic strain of the surface and longitudinal section of the projectile at 1.2ms under α=3°, 4°, 5°

Fig.24 Location of data monitoring point of projectile

Fig.25 Correspondence between the total load and the equivalent plastic strain at the monitoring point for α=3°, 4°,5°

Table 4 Comparison of the onset time of each stage of plastic strain at the monitoring point and the time of the characteristic point of projectile movement for α=4°, 5° ms

典型阶段	α/(°)
典型阶段	4	5
增长段1起始时刻	0.80	0.70
转速激增时刻(ω_r=311.05rad/s)	0.80	0.72
渐缓段起始时刻(增长段1结束时刻)	0.96	0.84
射弹转平时刻	1.06	0.96
增长段2起始时刻(渐缓段结束时刻)	1.14	1.00

References 33

[1]	黄闯. 跨声速超空泡射弹的弹道特性研究[D]. 西安: 西北工业大学, 2017: 1-16.
	HUANG C. Research of trajectory characteristics of supersonic-supercavitating projectiles[D]. Xi’an: Northwestern Polytechnical University, 2017: 1-16. (in Chinese)
[2]	ZHANG G Y, HOU Z, SUN T Z, et al. Numerical simulation of the effect of waves on cavity dynamics for oblique water entry of a cylinder[J]. Journal of Hydrodynamics, 2020, 32(6): 1178-1190.
[3]	陈诚, 袁绪龙, 党建军, 等. 超空泡航行器20°角倾斜入水冲击载荷特性试验研究[J]. 兵工学报, 2018, 39(6): 1159-1164. doi: 10.3969/j.issn.1000-1093.2018.06.016
	CHEN C, YUAN X L, DANG J J, et al. Experimental investigation into impact load during oblique water-entry of a supercavitating vehicle at 20°[J]. Acta Armamentarii, 2018, 39(6): 1159-1164. (in Chinese) doi: 10.3969/j.issn.1000-1093.2018.06.016
[4]	袁绪龙, 栗敏, 丁旭拓, 等. 跨介质航行器高速入水冲击载荷特性[J]. 兵工学报, 2021, 42(7): 1440-1449.
	YUAN X L, LI M, DING X T, et al. Impact load characteristics of a trans-media vehicle during high-speed water-entry[J]. Acta Armamentarii, 2021, 42(7): 1440-1449. (in Chinese) doi: 10.3969/j.issn.1000-1093.2021.07.011
[5]	陈晨, 魏英杰, 王聪. 小型运动体高速倾斜入水空泡流动数值研究[J]. 兵工学报, 2019, 40(2): 334-343. doi: 10.3969/j.issn.1000-1093.2019.02.013
	CHEN C, WEI Y J, WANG C. Computational analysis of cavity flow induced by high-speed oblique water-entry of axisymmetric body[J]. Acta Armamentarii, 2019, 40(2): 334-343. (in Chinese) doi: 10.3969/j.issn.1000-1093.2019.02.013
[6]	LIU H, ZHOU B, HAN X S, et al. Numerical simulation of water entry of an inclined cylinder[J]. Ocean Engineering, 2020, 215: 107908.
[7]	SONG Z J, DUAN W Y, XU G D, et al. Experimental and numerical study of the water entry of projectiles at high oblique entry speed[J]. Ocean Engineering, 2020, 211: 107574.
[8]	方城林, 魏英杰, 王聪, 等. 不同头型高速射弹垂直入水数值模拟[J]. 哈尔滨工业大学学报, 2016, 48(10): 77-82.
	FANG C L, WEI Y J, WANG C, et al. Numerical simulation of vertical high-speed water entry process of projectiles with different heads[J]. Journal of Harbin Institute of Technology, 2016, 48(10): 77-82. (in Chinese)
[9]	SUI Y T, ZHANG A M, MING F R, et al. Experimental investigation of oblique water entry of high-speed truncated cone projectiles: cavity dynamics and impact load[J]. Journal of Fluids and Structures, 2021, 104: 103305.
[10]	刘喜燕, 袁绪龙, 罗凯, 等. 带尾裙跨介质航行体高速斜入水实验研究[J]. 爆炸与冲击, 2023, 43(11): 108-120.
	LIU X Y, YUAN X L, LUO K, et al. Experimental study on high-speed oblique water entry of a trans-media vehicle with tail-skirt[J]. Explosion and Shock Waves, 2023, 43(11): 108-120. (in Chinese)
[11]	YU T S, SHUAI L, FU R M, 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.
[12]	王云, 袁绪龙, 吕策. 弹体高速入水弯曲弹道实验研究[J]. 兵工学报, 2014, 35(12): 1998-2002. doi: 10.3969/j.issn.1000-1093.2014.12.010
	WANG Y, YUAN X L, LÜ C. Experimental research on curved trajectory of high-speed water-entry missile[J]. Acta Armamentarii, 2014, 35(12): 1998-2002. (in Chinese) doi: 10.3969/j.issn.1000-1093.2014.12.010
[13]	侯宇, 黄振贵, 郭则庆. 超空泡射弹小入水角高速斜入水试验研究[J]. 兵工学报, 2020, 41(2): 332-341. doi: 10.3969/j.issn.1000-1093.2020.02.015
	HOU Y, HUANG Z G, GUO Z Q. Experimental investigation on shallow-angle oblique water-entry of a high-speed supercavitating projectile[J]. Acta Armamentarii, 2020, 41(2): 332-341. (in Chinese) doi: 10.3969/j.issn.1000-1093.2020.02.015
[14]	孙邃. 高速射弹倾斜入水过程多相流动特性数值计算[D]. 哈尔滨: 哈尔滨工业大学, 2018: 1-8.
	SUN S. Numerical calculation of multiphase flow characteristics of high speed projectile in obliqued water entry process[D]. Harbin: Harbin Institute of Technology, 2018: 1-8. (in Chinese)
[15]	王健. 回转体入水流固耦合载荷特性研究[D]. 哈尔滨: 哈尔滨工程大学, 2021: 1-2.
	WANG J. Study on fluid-solid coupling load characteristics of water entry of projectile[D]. Harbin: Harbin Engineering University, 2021: 1-2. (in Chinese)
[16]	DERAKHSHANIAN M S, HAGHDEL M, ALISHAHI M M, et al. Experimental and numerical investigation for a reliable simulation tool for oblique water entry problems[J]. Ocean Engineering, 2018, 160: 231-243.
[17]	张宇, 王彬文, 刘小川. 基于ALE, CEL和SPH方法的球形破片高速冲击充液结构对比研究[J]. 计算力学报, 2022, 39(6): 824-831.
	ZHANG Y, WANG B W, LIU X C. Comparative study of fluid-filled structure impacted by high-speed spherical fragments based on ALE, CEL and SPH[J]. Chinese Journal of Computational Mechanics, 2022, 39(6): 824-831. (in Chinese)
[18]	SHI Y, PAN G, YIM S C, et al. Numerical investigation of hydroelastic water-entry impact dynamics of AUVs[J]. Journal of Fluids and Structures, 2019, 91: 102760.
[19]	SHI Y, GAO X F, PAN G, et al. Experimental and numerical investigation of the frequency-domain characteristics of impact load for AUV during water entry[J]. Ocean Engineering, 2020, 202: 107203.
[20]	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.
[21]	邹田春, 高飞, 魏家威, 等. 圆柱体垂直入水三维数值模拟及影响因素研究[J]. 振动与冲击, 2022, 41(10): 177-185.
	ZOU T C, GAO F, WEI J W, et al. Three-dimensional numerical simulation and influencing factors study on the vertical water entry of a circular cylinder[J]. Journal of Vibration and Shock, 2022, 41(10): 177-185. (in Chinese)
[22]	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
	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
[23]	魏海鹏, 史崇镔, 孙铁志, 等. 基于ALE方法的航行体高速入水缓冲降载性能数值研究[J]. 爆炸与冲击, 2021, 41(10): 115-126.
	WEI H P, SHI C B, SUN T Z, et al. Numerical simulation of buffer and load reduction of high speed water entry of a vehicle based on ALE method[J]. Explosion and Shock Waves, 2021, 41(10): 115-126. (in Chinese)
[24]	魏英杰, 杨柳, 王聪, 等. 超弹性球体垂直入水空泡流动研究[J]. 空气动力学学报, 2020, 38(4): 780-787.
	WEI Y J, YANG L, WANG C, et al. Vertical water entry of hyperelastic sphere[J]. Acta Aerodynamica Sinica, 2020, 38(4): 780-787. (in Chinese)
[25]	杨柳. 超弹性球体垂直入水空泡流动及结构响应特性研究[D]. 哈尔滨: 哈尔滨工业大学, 2021.
	YANG L. Study on cavitating flow and structural response during vertical water entry of hyperelastic spheres[D]. Harbin: Harbin Institute of Technology, 2021. (in Chinese)
[26]	SUN T Z, ZHOU L, YIN Z H, et al. Cavitation bubble dynamics and structural loads of high-speed water entry of a cylinder using fluid-structure interaction method[J]. Applied Ocean Research, 2020, 101: 102285.
[27]	高英杰, 孙铁志, 张桂勇, 等. 回转体高速倾斜入水的流场特性及结构响应[J]. 爆炸与冲击, 2020, 40(12): 101-113.
	GAO Y J, SUN T Z, ZHANG G Y, et al. Flow characteristics and structure response of high-speed oblique water-entry for a revolution body[J]. Explosion and Shock Waves, 2020, 40(12): 101-113. (in Chinese)
[28]	高英杰. 基于流固耦合方法的回转体高速入水流场及载荷特性研究[D]. 大连: 大连理工大学, 2020.
	GAO Y J. Numerical analysis of impact load and flow characteristics of high speed water-entry for a revolution body based on a fluid-structure interaction method[D]. Dalian: Dalian University of Technology, 2020. (in Chinese)
[29]	HUANG C, LIU Z, LIU Z X, et al. Motion characteristics of high-speed supercavitating projectiles including structural deformation[J]. Energies, 2022, 15: 1933.
[30]	郝常乐, 党建军, 陈长盛, 等. 基于双向流固耦合的超空泡射弹入水研究[J]. 力学学报. 2022, 54(3): 678-687.
	HAO C L, DANG J J, CHEN C S, et al. Numerical study on water entry process of supercavitating projectile by considering bidirectional fluid structure interaction effect[J]. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(3): 678-687. (in Chinese)
[31]	LEE M, LONGORIA R G, WILSON D E. Cavity dynamics in high-speed water entry[J]. Physics of Fluids, 1997, 9(3): 540-550.
[32]	WALHORN E, HÜBNER B, DINKLER D. Space-time finite elements for fluid-structure interaction[J]. PAMM, 2002, 1(1): 81-82.
[33]	CHEN T, HUANG W, ZHANG W, et al. Experimental investigation on trajectory stability of high-speed water entry projectiles[J]. Ocean Engineering, 2019, 175: 16-24.