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 应用科技  2018, Vol. 45 Issue (6): 22-26  DOI: 10.11991/yykj.201805003 0

### 引用本文

WANG Shiyang, HAN Kang, TANG Shouqi, et al. Study of the ship acoustic field based on the coupling of LES and FW-H equation[J]. Applied Science and Technology, 2018, 45(6), 22-26. DOI: 10.11991/yykj.201805003.

### 文章历史

1. 中国船舶工业公司 第七〇八研究所，上海 200011;
2. 哈尔滨工程大学 船舶工程学院，黑龙江 哈尔滨 150001

Study of the ship acoustic field based on the coupling of LES and FW-H equation
WANG Shiyang1, HAN Kang2, TANG Shouqi2, WANG Wenquan1
1. Marine Design and Research Institute of China, Shanghai 200011, China;
2. College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, China
Abstract: In order to optimize noise performance of the ship and improve concealability of the ship, this paper studies the sound field of the ship on the surface of ocean. As for a certain type of ships, this study combined the computational fluid dynamics (CFD) theory with the Reynolds mean N-S equation and used the large eddy simulation (LES) method to make equations closed. The simulation calculation for flow field around the hull was carried out, and the results were compared with the test results. Then the FW-H acoustic model was loaded to simulate flow noise acoustic field of the hull under various speed. As is known from flow field calculation results: the calculated value of hull resistance under different speed agrees well with the test data; get the noise class of monitored spots from acoustic field calculation under different frequencies, and analyze the sound directivity and attenuation of different section location under different frequencies. According to analysis of the sound pressure level (SPL) of characteristic point, it can be derived that the flow noise of hull mainly concentrates in the low-frequency stage, and noise attenuation rate decreases with increase of frequency. Simulation results show that the calculation method adopted in this paper can simulate the flow field and acoustic field accurately, providing a feasible way for studying flow noise of the ship.
Keywords: noise    surface ship    LES    FW-H acoustic model    flow noise    flow field    sound field    acoustic directivity map

1 数学模型

 $\frac{{\partial \rho }}{{\partial t}} + \frac{{\partial (\rho {{\bar u}_i})}}{{\partial {x_i}}} = 0$
 $\frac{\partial }{{\partial t}}\left( {\rho {{\bar u}_i}} \right) + \frac{\partial }{{\partial {x_j}}}\left( {\rho {{\bar u}_i}{{\bar u}_j}} \right) = - \frac{{\partial \bar P}}{{\partial {x_i}}} + \frac{\partial }{{\partial {x_j}}}\left( {\mu \frac{{\partial {\sigma _{ij}}}}{{\partial {x_j}}}} \right) - \frac{{\partial {\tau _{ij}}}}{{\partial {x_j}}}$
 $\left\{ \begin{gathered} {\sigma _{ij}} = \left[ {\mu \left( {\frac{{\partial {{\bar u}_i}}}{{\partial {x_j}}} + \frac{{\partial {{\bar u}_j}}}{{\partial {x_i}}}} \right)} \right] - \frac{2}{3}\mu \frac{{\partial {u_i}}}{{\partial {x_j}}}{\delta _{ij}} \\ {\tau _{ij}} = \rho \overline {{u_i}{u_j}} - \rho {{\bar u}_i}{{\bar u}_j} \quad\quad\quad\quad\quad\quad\\ \end{gathered} \right.$

Willimas与Hawkings在Curle方程的基础上进行扩展，加入广义函数并且考虑物面的作用，便得出FW-K方程：

 \begin{aligned} \frac{1}{{{C_0}^2}}\frac{{{\partial ^2}p'}}{{\partial {t^2}}} - {\nabla ^2}p' =& \frac{{{\partial ^2}}}{{\partial {x_i}\partial {x_j}}}\left[ {{T_{ij}}H\left( f \right)} \right] - \\ &\frac{\partial }{{\partial {x_i}}}\left\{ {\left[ {{p_{ij}}{n_j} + \rho {u_i}({u_n} - {v_n})} \right]\delta (f)} \right\} +\quad\quad\\& \frac{\partial }{{\partial t}}\left\{ {\left[ {{\rho _0}{v_n} + \rho ({u_n} - {v_n})} \right]\delta (f)} \right\}\quad \quad\quad\quad\\ \end{aligned}

2 计算模型及网格划分 2.1 计算模型的建立及网格划分

2.2 理想化边界条件

3 计算结果分析 3.1 流场计算结果及验证

3.2 声场计算结果及分析