Analysis of Acoustic Scattering Characteristics of Underwater Targets Based on Kirchhoff Approximation and Curved Triangular Mesh

doi:10.12382/bgxb.2022.0374

Abstract

Abstract:

For the fast prediction of echo characteristics of unerwater complex targets, the Kirchhoff approximation and curved triangular mesh are employed to build the acoustic scattering model of underwater targets. The target surface is discretized into the curved triangular mesh, and the Gauss-Legendre quadrature method is used to directly calculate the scattering acoustic fields over curved elements in the bright areas. The sum of these scattering fields is the total scattering acoustic field of the target. Four typical targets, namely, rigid sphere, finite elliptical cylinder, cylinder with a hemispherical cap and scaled Benchmark model are considered, and the reliability of the curved element method for calculating target strength is verified by comparing with the planar element method using flat triangular element and experimental measurement. The numerical examples indicate that this method has good accuracy and high computational efficiency.

Key words: Kirchhoff approximation, curved element method, numerical integration, acoustic scattering, target strength

CLC Number:

TB56

XUE Yaqiang, PENG Zilong, YU Qiang, ZHANG Chunyu, ZHOU Fulin, LIU Jinwei. Analysis of Acoustic Scattering Characteristics of Underwater Targets Based on Kirchhoff Approximation and Curved Triangular Mesh[J]. Acta Armamentarii, 2023, 44(8): 2424-2431.

Figures/Tables 15

Fig.1 Coordinate diagram for Kirchhoff approximation integration method

Fig.2 Mapping between a reference triangle and curved triangle with six nodes

Fig.3 Target strength of the sphere

Table 1 Mesh and time for computing TS of the sphere

网格尺寸/mm	网格数	曲面三角形数值积分		平面三角形板块元
网格尺寸/mm	网格数	节点数	时长/ms	节点数	时长/ms
30	29998	59998	1051	15001	1743
25	42464	84930	1472	21234	2168
20	66872	133746	2243	33438	4583

Fig.4 L2-norm for TS of the sphere with different mesh sizes

Fig.5 Sound scattering from a finite elliptical cylinder

Fig.6 TS of the elliptical cylinder with different frequencies

Fig.7 TS of the elliptical cylinder with different incidence angles

Table 2 Mesh and time for computing TS of the elliptical cylinder

网格尺寸/mm	网格数	曲面三角形数值积分		平面三角形板块元
网格尺寸/mm	网格数	节点数	时长/ms	节点数	时长/ms
25	132302	265528	924	66613	1308
20	206498	414148	1469	103825	2198

Fig.8 Acoustic scattering from a cylinder with a hemispherical cap

Fig.9 TS of the cylinder with a hemispherical cap at the incident angle around the abeam direction

Fig.10 TS of the cylinder with a hemispherical cap under different incidence angles

Fig.11 Scaled model of Benchmark submarine

Fig.12 Arrangement of experiment equipment

Fig.13 Echo strength of scaled Benchmark model

References 22

[1]	汤渭霖, 范军, 马忠成. 水下目标声散射[M]. 北京: 科学出版社, 2018.
	TANG W L, FAN J, MA Z C. Acoustic scattering of underwater targets[M]. Beijing: Science Press, 2018. (in Chinese)
[2]	ZAMPOLLI M, TESEI A, JENSEN F B, et al. A computationally efficient finite element model with perfectly matched layers applied to scattering from axially symmetric objects[J]. Journal of the Acoustical Society of America, 2007, 122(3): 1472-1485. pmid: 17927408
[3]	GONZALEZ J D, LAVIA E F, BLANC S, et al. Boundary element method to analyze acoustic scattering from a coupled swimbladder-fish body configuration[J]. Journal of Sound and Vibration, 2020, 486: 115609. doi: 10.1016/j.jsv.2020.115609 URL
[4]	龚家元, 安俊英, 马力, 等. 边界元奇异与近奇异数值积分方法及其应用于大规模声学问题[J]. 声学学报, 2016, 41: 768-775.
	GONG J Y, AN J Y, MA L, et al. Numerical quadrature for singular and near-singular integrals of boundary element method and its applications in large-scale acoustic problems[J]. Acta Acustica, 2016, 41: 768-775. (in Chinese)
[5]	陈鑫, 罗祎, 李爱华. 水下弹性角反射器声散射特性[J]. 兵工学报, 2018, 39: 2236-2242. doi: 10.3969/j.issn.1000-1093.2018.11.018
	CHEN X, LUO Y, LI A H. Acoustic scattering characteristics of underwater elastic corner reflectors[J]. Acta Armamentarii, 2018, 39: 2236-2242. (in Chinese) doi: 10.3969/j.issn.1000-1093.2018.11.018
[6]	GANESH M, HAWKINS S C. A numerically stable T-matrix method for acoustic scattering by nonspherical particles with large aspect ratios and size parameters[J]. Journal of the Acoustical Society of America, 2022, 151(3): 1978-1988. doi: 10.1121/10.0009679 pmid: 35364906
[7]	ZHAO C, ZHANG T, HOU G X. Finite-difference time-domain modeling for underwater acoustic scattering applications based on immersed boundary method[J]. Applied Acoustics, 2022, 193: 108764. doi: 10.1016/j.apacoust.2022.108764 URL
[8]	范军, 汤渭霖, 卓琳凯. 声呐目标回声特性预报的板块元方法[J]. 船舶力学, 2012, 16(1/2): 171-180.
	FAN J, TANG W L, ZHUO L K. Planar elements method for forecasting the echo characteristics from sonar targetsAcoustic scattering of underwater targets[J]. Journal of Ship Mechanics, 2012, 16(1/2): 171-180. (in Chinese)
[9]	陈文剑, 孙辉. 计算水下凹面目标散射声场的声束弹跳法[J]. 声学学报, 2013, 38: 147-152.
	CHEN W J, SUN H. A shooting and bouncing beams method for calculating the acoustic scattering field of concave targets[J]. Acta Acustica, 2013, 38: 147-152. (in Chinese)
[10]	PENG Z L, WANG B, FAN J. Simulation and experimental studies on acoustic scattering characteristics of surface targets[J]. Applied Acoustics, 2018, 137: 140-147. doi: 10.1016/j.apacoust.2018.02.014 URL
[11]	刘成元, 张明敏, 程广利, 等. 一种改进的板块元目标回声计算方法[J]. 海军工程大学学报, 2008: 25-27, 31.
	LIU C Y, ZHANG M M, CHENG G L, et al. Improved planar element method for computing target echo[J]. Journal of naval university of engineering, 2008: 25-27, 31. (in Chinese)
[12]	PIGNIER N J, O’REILLY C J, BOIJ S. A Kirchhoff approximation-based numerical method to compute multiple acoustic scattering of a moving source[J]. Applied Acoustics, 2015, 96: 108-117. doi: 10.1016/j.apacoust.2015.03.016 URL
[13]	HIPTMAIR R, MOIOLA A, PERUGIA I. Trefftz discontinuous Galerkin methods for acoustic scattering on locally refined meshes[J]. Applied Numerical Mathematics, 2014, 79: 79-91. doi: 10.1016/j.apnum.2012.12.004 URL
[14]	CHAILLAT S, GROTH S P, LOSEILLE A. Metric-based anisotropic mesh adaptation for 3D acoustic boundary element methods[J]. Journal of Computational Physics, 2018, 372: 473-499. doi: 10.1016/j.jcp.2018.06.048 URL
[15]	ABAWI A T. Kirchhoff scattering from non-penetrable targets modeled as an assembly of triangular facets[J]. Journal of the Acoustical Society of America, 2016, 140(3): 1878-1886. pmid: 27914371
[16]	WANG B, WANG W H, FAN J, et al. Modeling of bistatic scattering from an underwater non-penetrable target using a Kirchhoff approximation method[J]. Defence Technology, 2022, 18(7): 1097-1106. doi: 10.1016/j.dt.2022.04.008
[17]	WU T W, WAN G C. Numerical modeling of acoustic radiation and scattering from thin bodies using a Cauchy principal integral equation[J]. The Journal of the Acoustical Society of America, 1992, 92(5): 2900-2906. doi: 10.1121/1.404375 URL
[18]	FOOTE K G, FRANCIS D T. Comparing Kirchhoff-approximation and boundary-element models for computing gadoid target strengths[J]. Journal of the Acoustical Society of America, 2002, 111(4): 1644-1654. pmid: 12002847
[19]	VENÅS J V, KVAMSDAL T. Isogeometric boundary element method for acoustic scattering by a submarine[J]. Computer Methods in Applied Mechanics and Engineering, 2020, 359: 112670. doi: 10.1016/j.cma.2019.112670 URL
[20]	RATHOD H T, SHAJEDUL KARIM M. An explicit integration scheme based on recursion for the curved triangular finite elements[J]. Computers & Structures, 2002, 80(1): 43-76. doi: 10.1016/S0045-7949(01)00156-0 URL
[21]	陈云飞, 李桂娟, 王振山, 等. 水中目标回波亮点统计特征研究[J]. 物理学报, 2013, 62(8): 284-294.
	CHEN Y F, LI G J, WANG Z S, et al. Statistical feature of underwater target echo highlight[J]. Acta Physica Sinica, 2013, 62(8): 284-294. (in Chinese)
[22]	NELL C W, GILROY L E. An improved BASIS model for the BeTSSi submarine: TR 2003-199[R]. Cumberland St, Ottawa, Canada: Defence Research and Development Canada, 2003.