基于Kirchhoff近似与曲面三角形网格的水下目标声散射特性分析

doi:10.12382/bgxb.2022.0374

摘要/Abstract

摘要：

针对水下复杂目标回波特性快速预报问题,采用Kirchhoff近似和曲面三角形网格建立目标声散射特性分析模型。将目标表面离散为曲面三角形网格,采用高斯-勒让德求积方法直接计算亮区内曲面元上的散射声场并求和,得到目标的总散射声场。计算刚性球、椭圆柱、球冠柱和Benchmark缩比模型4种典型目标的目标强度,与采用平面三角形单元的板块元方法及实验测试等结果对比,验证曲面元方法的可靠性。数值算例结果表明,该方法具有良好的精度与计算效率。

关键词: Kirchhoff近似, 曲面元方法, 数值积分, 声散射, 目标强度

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

中图分类号:

TB56

薛亚强, 彭子龙, 俞强, 张春雨, 周富霖, 刘进伟. 基于Kirchhoff近似与曲面三角形网格的水下目标声散射特性分析[J]. 兵工学报, 2023, 44(8): 2424-2431.

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.

图/表 15

图1 Kirchhoff近似积分方法的坐标示意图

Fig.1 Coordinate diagram for Kirchhoff approximation integration method

图2 参数三角形与六节点曲面三角形之间的映射

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

图3 球的目标强度

Fig.3 Target strength of the sphere

表1 计算球目标强度所需的网格及时长

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

图4 不同网格尺寸下球目标强度的L2范数

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

图5 有限长椭圆柱声散射

Fig.5 Sound scattering from a finite elliptical cylinder

图6 不同频率下椭圆柱的目标强度

Fig.6 TS of the elliptical cylinder with different frequencies

图7 不同入射角下椭圆柱的目标强度

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

表2 计算椭圆柱目标强度所需的节点数量及时长

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

图8 球冠圆柱声散射

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

图9 正横方向入射时球冠圆柱的目标强度

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

图10 不同入射角下球冠圆柱的目标强度

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

图11 按比例缩小的Benchmark潜艇模型

Fig.11 Scaled model of Benchmark submarine

图12 试验设备布置图

Fig.12 Arrangement of experiment equipment

图13 Benchmark缩比模型的回声强度

Fig.13 Echo strength of scaled Benchmark model

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