﻿ 声波在海底界面反射系数仿真计算分析
 舰船科学技术  2022, Vol. 44 Issue (16): 126-129    DOI: 10.3404/j.issn.1672-7649.2022.16.026 PDF

Simulation and analysis of reflection coefficient of acoustic waves at seabed interface
GONG Chang-xin, Li Wei, JIANG Hao-yang
School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
Abstract: In order to study the influence of parameters fluctuation of underwater sediment medium on reflection coefficient of seafloor interface, this paper adopts acoustic finite element model and Biot porous elastic wave theory model combined with PML technology. Firstly, using COMSOL Multiphysics simulation and analysis software, the acoustic field calculation model of layered medium with two layers of ideal fluid is established. The correctness of the proposed solution is verified by comparing with the analytic solution. Then, the water-porous media model was established by using porous elastic media to simulate the seafloor sediments, and the calculated results were in good agreement with the references. Finally, a parametric simulation analysis was carried out on the porous media to calculate the acoustic reflection coefficient at different frequencies and incident angles, and the influence law of the fluctuation of parameters such as porosity of porous media, fluid density and solid density on the acoustic reflection coefficient was obtained.
Key words: submarine interface     underwater sediment     porous elastic wave     sound reflection
0 引　言

1 计算模型 1.1 分层介质模型

 ${p}_{1}={P}_{i}{e}^{i\left(\omega t-{k}_{1}x\right)}+{P}_{r}{e}^{i\left(\omega t+{k}_{1}x\right)} ,$ (1)

 ${p}_{2}={P}_{t}{e}^{i\left(\omega t-{k}_{2}x\right)} ,$ (2)

2种介质中质点速度分别为：

 ${v}_{1}=\frac{{P}_{i}}{{\rho }_{1}{c}_{1}}{e}^{i\left(\omega t-{k}_{1}x\right)}-\frac{{P}_{r}}{{\rho }_{1}{c}_{1}}{e}^{i\left(\omega t+{k}_{1}x\right)},$ (3)
 ${v}_{2}=\frac{{P}_{t}}{{\rho }_{2}{c}_{2}}{e}^{i\left(\omega t-{k}_{2}x\right)}{\text{。}}$ (4)

 ${\left({p}_{1}\right)}_{x=0}={\left({p}_{2}\right)}_{x=0} , {\left({v}_{1}\right)}_{x=0}={\left({v}_{2}\right)}_{x=0},$

 ${r}_{p}=\frac{{\rho }_{2}{c}_{2}-{\rho }_{1}{c}_{1}}{{\rho }_{2}{c}_{2}+{\rho }_{1}{c}_{1}} 。$ (5)

 ${r}_{P}=\frac{m\mathit{{\rm{cos}}}{\theta }_{i}-\sqrt{{n}^{2}-{\mathit{{\rm{sin}}}}^{2}{\theta }_{i}}}{m\mathit{{\rm{cos}}}{\theta }_{i}+\sqrt{{n}^{2}-{\mathit{{\rm{sin}}}}^{2}{\theta }_{i}}} ,$ (6)

 图 1 模型示意图 Fig. 1 The diagram of the model

 图 2 反射系数随特性阻抗比变化曲线 Fig. 2 Curve of reflection coefficient with characteristic impedance ratio

 图 3 总声压场 Fig. 3 The acoustic pressure field

 图 4 反射系数随入射角变化曲线 Fig. 4 Curve of reflection coefficient with incident angle
1.2 水-多孔介质模型

 图 5 水-多孔介质计算模型 Fig. 5 Computational model for water-porous media

 图 6 不同入射角下反射系数随频率变化曲线 Fig. 6 Curve of reflection coefficient with frequency for different incident angles

 图 7 不同频率下反射系数随入射角变化曲线 Fig. 7 Curve of reflection coefficient with incident angle for four different frequencies
2 多孔介质参数分析

1）对于多孔介质孔隙率 $\beta$ ，在初始值0.47基础上取附近5个值0.446 5，0.458 3，0.470 0，0.4818，0.4935，计算水-沉积物界面的反射系数。由图8可知，在1000 Hz时，任意入射角下，随着孔隙率的增加，反射系数逐渐减小。由图9可知，在平面波垂直入射时，10～105 Hz频率范围内，随着孔隙率增加，反射系数逐渐减小。

 图 8 不同孔隙率下反射系数随入射角变化曲线 Fig. 8 Curve of reflection coefficient with incident angle for different porosity

 图 9 不同孔隙率下反射系数随频率变化曲线 Fig. 9 Curve of reflection coefficient with frequency for different porosity

2）对于流体密度 ${\ \rho }_{f}$ ，在初始值1000基础上取附近5个值950，975，1 000，1 025，1 050，计算介质界面的反射系数。由图10可知在1 000 Hz时，随着入射角的增加，反射系数随 ${\ \rho }_{f}$ 的变化情况在45°入射角出现反转，在小入射角时，随着 ${\ \rho }_{f}$ 增大，反射系数逐渐减小，在大入射角时，随着 ${\ \rho }_{f}$ 增大，反射系数逐渐增大。由图11可知在平面波垂直入射时，10～105 Hz频率范围内，随着 ${\ \rho }_{f}$ 增大，反射系数逐渐减小。

 图 10 不同流体密度下反射系数随入射角变化曲线 Fig. 10 Curve of reflection coefficient with incident angle for different fluid density

 图 11 不同流体密度下反射系数随频率变化曲线 Fig. 11 Curve of reflection coefficient with frequency for different fluid density

3）对于固体颗粒密度 ${\ \rho }_{s}$ ，在初始值2 650基础上取附近5个值2 518，2 584，2 650，2 716，2 783，计算介质界面的反射系数。由图12可知在1 000 Hz下，随着入射角的增加，反射系数随 ${\ \rho }_{s}$ 的变化情况在40°入射角出现反转，在小入射角时，随着 ${\ \rho }_{s}$ 增大，反射系数逐渐增大，在大入射角时，随着 ${\ \rho }_{s}$ 增大，反射系数逐渐减小。由图13可知在平面波垂直入射时，10～105 Hz频率范围内，随着 ${\ \rho }_{s}$ 增大，反射系数逐渐增大。

 图 12 不同固体密度下反射系数随入射角变化曲线 Fig. 12 Curve of reflection coefficient with incident angle for different solid density

 图 13 不同固体密度下反射系数随频率变化曲线 Fig. 13 Curve of reflection coefficient with frequency for different solid density
3 结　语

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