Trajectories and Attitudes of a Slender Submarine with Large Amplitude Motions under the Action of Internal Solitary Waves

doi:10.12382/bgxb.2023.0313

Abstract

Abstract:

The large internal solitary waves inside the ocean may pose a threat to the navigation stability and safety of a submarine. A time-domain solution model for the large motion of the slender submarine structure under the internal solitary waves in two-layer flow is established to explore the motion response characteristics of submarine when encountering the internal solitary waves head-on. The nonlinear forces caused by the coupling of various degrees of freedom motions are considered in the model, the internal solitary wave forces are calculated by Morison equation and Froude-Krylov force, and the static changes caused by the propagation of internal solitary wave are calculated by integrating the static pressure on the surface of submarine. The accuracy of the proposed model is verified by comparing with experimental results of physical models and computational fluid dynamics numerical results, and the motion trajectories and attitudes of SUBOFF submarine at different depths and speeds in two layers of flow are calculated by this model. The numerical results show that, under the action of internal solitary waves, the submarines above and at the density layered interface move along the propagation direction of internal solitary waves, the submarine below the density layered interface moves against the propagation direction of internal isolated waves; Vertically, the submarine will experience a significant drop in depth, and it sinks first and then floats. The submarine shows different trajectories and attitudes at different depths and speeds.

Key words: submarine, internal solitary wave, nonlinear force, motion trajectory, Morison equation

CLC Number:

O352
TV139.2

LIU Xindan, GOU Ying, TENG Bin. Trajectories and Attitudes of a Slender Submarine with Large Amplitude Motions under the Action of Internal Solitary Waves[J]. Acta Armamentarii, 2024, 45(6): 1854-1865.

Figures/Tables 15

Fig.1 Coordinate system and parameter definition

Fig.2 Coordinate system of submarine motion

Table 1 Recommended values of CD and CM

各国规范	中国海港水文规范(2013)	美国API规范 (1981)	挪威DNV规范 (1974)
C_D	1.2	0.6~1.0	0.5~1.2
C_M	2.0	1.5~2.0	2.0

Fig.3 Comparison between theoretical and experimental values of horizontal velocity of water particle

Fig.4 Comparison of experimental and numerical results on the motion response of submarine

Fig.5 Wavefront comparison of internal solitary wave

Fig.6 Vertical force comparison of submarine

Table 2 Characteristic parameters of internal solitary waves

参数	数值
h₁/m	180
h₂/m	2820
ρ₁/(kg·m^-3)	1025
ρ₂/(kg·m^-3)	1028
η₀/m	-120

Fig.7 Velocity vector graph of internal solitary wave flow field

Fig.8 Comparison of numerical results considering and not considering the coupling term in internal solitary wave forces in Case 1

Fig.9 Comparison of numerical results considering and not considering the coupling term in internal solitary wave forces in Case 2

Fig.10 Motion trajectories and pitch angles of submarine at different depths

Fig.11 Movement process of the submarine at different depths in internal solitary wave flow field

Fig.12 Vertical forces and torques on the submarine at different speeds

Fig.13 Motion trajectories and pitch angles of submarine at different speeds

References 26

[1]	CAI S Q, XIE J S, HE J L. An overview of internal solitary waves in the South China Sea[J]. Surveys in Geophysics, 2012, 33(5):927-943.
[2]	DU T, TSENG Y H, YAN X H. Impacts of tidal currents and kuroshio intrusion on the generation of nonlinear internal waves in Luzon strait[J]. Journal of Geophysical Research, 2008, 113(C8):1-15.
[3]	徐肇延. 海洋内波动力学[M]. 北京: 科学出版社, 1999.
	XU Z Y. Ocean internal wave dynamics[M]. Beijing: Science Press, 1999. (in Chinese)
[4]	ZHI C H, WANG H W, CHEN K, et al. Theoretical and experimental investigation on strongly nonlinear internal solitary waves moving over slope-shelf topography[J]. Ocean Engineering, 2021: 223, 108645.
[5]	ZOU P X, BRICKER J D, UIJTTEWAAL W S J. The impacts of internal solitary waves on a submerged floating tunnel[J]. Ocean Engineering, 2021, 238: 109762.
[6]	WANG T X, HUANG X D, ZHAO W, et al. Internal solitary wave activities near the indonesian submarine wreck site inferred from satellite images[J]. Journal of Marine Science and Engineering, 2022, 10(2):197-208.
[7]	GONG Y K, XIE J S, XU J X, et al. Oceanic internal solitary waves at the indonesian submarine wreckage site[J]. Acta Oceanologica Sinica, 2022, 41(3):109-113.
[8]	WEI G, DU H, XU X H, et al. Experimental investigation of the generation of large-amplitude internal solitary wave and its interaction with a submerged slender body[J]. Science China Physics Mechanics & Astronomy, 2014, 57(2): 301-310
[9]	付东明, 尤云祥, 李巍. 两层流体中内孤立波与潜体相互作用数值模拟[J]. 海洋工程, 2009, 27(3):38-44.
	FU D M, YOU Y X, LI W. Numerical simulation of the interaction between internal solitary waves and submerged bodies in a two-layer fluid[J]. The Ocean Engineering, 2009, 27(3):38-44. (in Chinese)
[10]	HE G H, XIE H F, ZHANG Z, et al. Numerical Investigation of internal solitary wave forces on a moving submarine[J]. Journal of Marine Science and Engineering, 2022, 10(8): 1020.
[11]	CAI S Q, LONG X M, GAN Z J. A method to estimate the forces exerted by internal solitons on cylindrical piles[J]. Ocean Engineering, 2003, 30(5):673-689.
[12]	WANG S D, WEI G, DU H, et al. Experimental investigation of the wave-flow structure of an oblique internal solitary wave and its force exerted on a slender body[J]. Ocean Engineering, 2020, 201: 107057.
[13]	PU X, DU H, WANG S D, et al. Experimental and theoretical study of internal solitary wave loads on a submerged slender body[J]. Ocean Engineering, 2023, 272:113936.
[14]	殷文明, 郭海燕, 吴凯锋, 等. 内孤立波对水平圆柱潜体作用力的计算[J]. 浙江大学学报(工学版), 2016, 50(7):1252-1275.
	YIN W M, GUO H Y, WU K F, et al. Calculation of internal solitary wave force on horizontal submerged circular[J]. Journal of Zhejiang University(Engineering Science), 2016, 50(7):1252-1275. (in Chinese)
[15]	CUI J N, DONG S, WANG Z F, et al. Kinematic response of submerged structures under the action of internal solitary waves[J]. Ocean Engineering, 2020, 196:106814.
[16]	陈杰, 尤云祥, 刘晓东, 等. 内孤立波与有航速潜体相互作用数值模拟[J]. 水动力学进展A辑, 2010, 25(3):345-351.
	CHEN J, YOU Y X, LIU X D, et al. Numerical simulation of interaction of internal solitary waves with a moving submarine[J]. Chinese Journal of Hydrodynamics, 2010, 25(3): 345-351. (in Chinese)
[17]	杨帆. 海洋内孤立波与水下潜器相互作用研究[D]. 镇江: 江苏科技大学, 2016.
	YANG F. Study on the interaction between internal solitary waves and the submerged body[J]. Zhenjiang: Jiangsu University of Science and Technology, 2016. (in Chinese)
[18]	刘孟奇. 潜体在内孤立波作用下多自由度运动的数值研究[D]. 大连: 大连理工大学, 2021.
	LIU M Q. Numerical study of multi-degree-of-freedom motion of a submerged body subjected to internal solitary waves[D]. Dalian: Dalian University of Technology, 2021. (in Chinese)
[19]	冯康佳, 姚志崇, 胡芳琳, 等. 潜水器穿越内孤立波运动特性仿真分析[J]. 水动力学研究与进展A辑, 2022, 37(4): 468-473.
	FENG K J, YAO Z C, HU F L, et al. Motion simulation of submarine passing through internal solitary wave[J]. Chinese Journal of Hydrodynamics, 2022, 37(4): 468-473. (in Chinese)
[20]	李玉成, 滕斌. 波浪对海上建筑物的作用[M]. 北京: 海洋出版社, 2015.
	LI Y C, TENG B. Wave action on maritime structures[M]. Beijing: China Ocean Press, 2015. (in Chinese)
[21]	唐俊, 刘岩岩, 闫一天. 水下航行器仿生非光滑表面减阻特性[J]. 兵工学报, 2022, 43(5):1135-1143. doi: 10.12382/bgxb.2021.0204
	TANG J, LIU Y Y, YAN Y T. Drag reduction characteristics of bionic non-smooth surface for underwater vehicle[J]. Acta Armamentarii, 2022, 43(5): 1135-1143. (in Chinese) doi: 10.12382/bgxb.2021.0204
[22]	RODDY R F. Investigation of the stability and control characteristics of several configurations of the DARPA SUBOFF model (DTRC model 5470) from captive-model experiments:DTRC/SHD-1298-08[R]. Bethesda, MD, US: David Taylor Research Center, 1990.
[23]	黄文昊, 尤云祥, 王旭. 有限深两层流体中内孤立波造波实验及其理论模型[J]. 物理学报, 2013, 62 (8):084705.
	HUANG W H, YOU Y X, WANG X, et al. Wave-making experiments and theoretical models for internal solitary waves in a two-layer fluid of finite depth[J]. Acta Physica Sinica, 2013, 62 (8):084705. (in Chinese)
[24]	ZHAO Z X, KLEMAS V, ZHENG Q N, et al. Remote sensing evidence for baroclinic tide origin of internal solitary waves in the northeastern South China Sea[J]. Geophysical Research Letters, 2004, 31(6): L06302.
[25]	ZHENG Q N, SUSANTO R D, HO C R, et al. Statistical and dynamical analyses of generation mechanisms of solitary internal waves in the northern South China Sea[J]. Journal of Geophysical Research: Oceans, 2007, 112(C3):C03021.
[26]	OSTROVSKY L A, STEPANYANTS Y A. Do internal solitons exist in the ocean[J]. Reviews of Geophysics, 1989, 27: 293-310.