Sound propagation characteristics of underwater steady-state vortex field
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摘要:
基于射线声学理论研究了水下稳态涡流场的声传播特性。首先, 根据移动介质中的程函方程, 推导了二维稳态涡流场的射线微分方程组, 实现了声波通过涡流场的声线轨迹模拟, 获取了通过不同涡流场的声信号; 然后, 基于稳态涡流场的声传播特性, 构建了接收声信号相位与涡流场特征参数之间的映射关系, 通过数值仿真反演稳态涡流场特征参数, 仿真结果与理论值的相对误差在15%以内。仿真结果表明: 基于射线理论可以有效模拟声信号通过涡流场的声线轨迹及信号变化, 具有直观、计算效率高的优势; 随着涡环量增大, 涡流对声传播的影响更为明显; 利用声信号相位可实现对速度分布、涡核位置、涡环量等涡流场特征参数的估计。
Abstract:The sound propagation characteristics of underwater steady-state vortex field are analyzed based on the ray acoustics theory. The ray differential equations in the two-dimensional steady-state vortex field are derived using the Eikonal equation in a moving medium. The receiving acoustic signal is obtained by the simulated ray trajectory of the sound wave passing through the vortex field. The mapping relationship between the phase of the received acoustic signal and the characteristic parameters of the vortex field is established rooted in the sound propagation characteristics of the vortex field. The characteristic parameters of the vortex field are inverted by numerical simulation with a relative error of less than 15% when compared to the theoretical value. The simulation results demonstrate the effective simulation of the phase change and sound ray trajectory, harnessing the advantages of intuitive visualization and efficient computation by ray acoustic theory. The numerical simulation also verifies that as the circulation of vortex increases, the impact of vortex on sound propagation becomes more pronounced. The characteristic parameters of the vortex field such as velocity distribution, vortex core position, and vortex circulation, can be estimated based on the phase change.
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图 5 不同马赫数情况下声线传播轨迹 (a)
$ Ma = 4.6 \times {10^{ - 4}} $ ; (b) Ma$ = 4.6 \times {10^{ - 2}} $ 
图 6 接收声信号振幅比、相位差变化分析 (a) 振幅比
$A^R$ 随阵元位置变化(y方向)曲线; (b) 相位差$ \Delta \varphi $ 随阵元位置变化(y方向)曲线表 1 涡流场特征参数反演
仿真
条件涡流特征参数 理论值 估计值 相对
误差条件II 涡核位置 y = 0 cm y = 0 cm 0.0% 涡环量 0.0146 rad 0.0142 rad 2.7% 涡核半径 0.24 cm 0.25 cm 4.2% 最大切向速度 0.69 m/s 0.6654 m/s 3.6% 条件III 涡核位置 y = 1.5 cm y = 1.5 cm 0.0% 涡环量 0.0146 rad 0.0141 rad 3.4% 涡核半径 0.24 cm 0.25 cm 4.2% 最大切向速度 0.69 m/s 0.6427 m/s 6.9% 条件IV 涡核位置 y = 0 cm y = 0 cm 0.0% 涡环量 0.0104 rad 0.0101 rad 2.9% 涡核半径 0.24 cm 0.25 cm 4.2% 最大切向速度 0.69 m/s 0.5944 m/s 13.8% 
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