﻿ 双体船湍流脉动压力激励水下辐射噪声预报研究
 舰船科学技术  2020, Vol. 42 Issue (8): 38-42    DOI: 10.3404/j.issn.1672-7649.2020.08.007 PDF

Research on prediction of noise radiation from turbulent pressure fluctuations on catamarans
GONG Cheng, LI Cong, ZHAO Chao, WANG Wei
Marine Design and Research Institute of China, Shanghai 200011, China
Abstract: By using large eddy simulation (LES), numerical computations of turbulent pressure fluctuations on a catamaran have been carried out both on scale model and full scale ship. Based on the result, a prediction of hydrodynamic noise radiating from catamarans has been executed by using acoustic FEM method. The simulation result matched well with the experiment, thus showed the effectiveness of LES method in simulating the distribution of turbulent pressure. Besides, based on the input of the turbulent pressure fluctuations, the radiation noise acquired by acoustic FEM method corresponded with the result of traditional SEA method in high-frequency stage, while in low-frequency stage, the result is higher than that of SEA method, which can be more reasonable to predict hydrodynamic noise of catamarans.
Key words: catamaran     turbulent pressure fluctuations     acoustic FEM     hydrodynamic noise
0 引　言

1 数值计算方法 1.1 大涡模拟控制方程

 $\phi = \overline \phi + \phi '{\text{，}}$ (1)

 $\frac{{\partial \rho }}{{\partial t}} + \frac{\partial }{{\partial {x_i}}}(\rho {\bar u_i}) = 0{\text{，}}$ (2)
 $\frac{\partial }{{\partial t}}(\rho {\bar u_i}) + \frac{\partial }{{\partial {x_j}}}(\rho {\bar u_i}{\bar u_j}) = \frac{\partial }{{\partial {x_j}}}(\mu \frac{{\partial {\sigma _{ij}}}}{{\partial {x_j}}}) - \frac{{\partial \bar p}}{{\partial {x_i}}} - \frac{{\partial {\tau _{ij}}}}{{\partial {x_j}}}{\text{，}}$ (3)

 $\frac{{\partial {{\bar u}_i}}}{{\partial {x_i}}} = 0{\text{，}}$ (4)
 $\frac{{\partial {{{\tilde {\bar u}}}_i}}}{{\partial t}} + \frac{\partial }{{\partial {x_j}}}({{\tilde {\bar u}}_i}{{\tilde {\bar u}}_j}) = - \frac{{\partial {\tilde {\bar p}}}}{{\partial {x_i}}} - \frac{{\partial {T_{ij}}}}{{\partial {x_j}}} + \frac{1}{{\rm{Re} }}\frac{{{\partial ^2}{\tilde {\bar u}}{}_i}}{{\partial {x_j}\partial {x_j}}}{\text{，}}$ (5)

 ${T_{ij}} = \widetilde {\overline {{u_i}{u_j}} } - {{\tilde {\bar u}}_i}{{\tilde {\bar u}}_j}{\text{。}}$ (6)
1.2 声学有限元法

 $p\left( {\vec r} \right) \approx \sum\limits_{i = 1}^n {{N_i}\left( {\vec r} \right){p_i}} = \left[ {{N_i}} \right]\left\{ {{p_i}} \right\}{\text{。}}$ (7)

 $\left\{ {\left[ {{K_a}} \right] + j\omega \left[ {{C_a}} \right] - {\omega ^2}\left[ {{M_a}} \right]} \right\}\left\{ {{p_i}} \right\} = \left\{ {{P_a}} \right\}{\text{，}}$ (8)

 $\left\{ {\left[ {{K_s}} \right] + j\omega \left[ {{C_s}} \right] - {\omega ^2}\left[ {{M_s}} \right]} \right\}\left\{ {{\delta _i}} \right\} = \left\{ {{F_s}} \right\}{\text{，}}$ (9)

 $\begin{split} & \left\{ {\left[ {\begin{array}{*{20}{c}} {{K_s}}&{{K_c}} \\ 0&{{K_a}} \end{array}} \right] + j\omega \left[ {\begin{array}{*{20}{c}} {{C_s}}&0 \\ 0&{{C_a}} \end{array}} \right] - {\omega ^2}\left[ {\begin{array}{*{20}{c}} {{M_s}}&0 \\ { - {\rho _0}K_c^{\rm{T}}}&{{M_a}} \end{array}} \right]} \right\}\\ &\left\{ {\begin{array}{*{20}{c}} {{\delta _i}} \\ {{p_i}} \end{array}} \right\} = \left\{ {\begin{array}{*{20}{c}} {{F_s}} \\ {{P_a}} \end{array}} \right\}{\text{。}}\end{split}$ (10)

2 湍流脉动压力的数值模拟 2.1 试验与数值模型

 图 1 测点布置 Fig. 1 Measuring-point arrangement

 图 2 双体船计算与网格划分 Fig. 2 Computational domain and meshing of the catamaran

2.2 数值计算结果 2.2.1 模型脉动压力计算与验证

 图 3 P1点脉动压力计算与试验对比 Fig. 3 Comparison between simulation and experiment of turbulent pressure fluctuations at point P1

 图 4 P5点脉动压力计算与试验对比 Fig. 4 Comparison between simulation and experiment of turbulent pressure fluctuations at point P5

 图 5 P10点脉动压力计算与试验对比 Fig. 5 Comparison between simulation and experiment of turbulent pressure fluctuations at point P10

 图 6 P19点脉动压力计算与试验对比 Fig. 6 Comparison between simulation and experiment of turbulent pressure fluctuations at point P19

 图 7 实船表面流线分布 Fig. 7 Streamline distribution of full scale ship

2.2.2 实船脉动压力计算

 图 8 实船水下部分压力分布 Fig. 8 Pressure distribution of underwater part of full scale ship

 图 9 实船各测点脉动压力（1/3 oct） Fig. 9 Turbulent pressure fluctuations of full scale ship at different points（1/3 oct）
3 船体水下辐射噪声预报

 图 10 试验及仿真计算结果 Fig. 10 Comparison between simulation and experiment result

 图 11 双体船水下结构有限元模型 Fig. 11 FEM model of the catamaran’s underwater structure

 图 12 外场流体区域有限元模型 Fig. 12 FEM model of fluid region

 图 13 振动测点位置 Fig. 13 Positions of vibration measuring-points

 图 14 支柱测点法向振速谱级（1/3 oct） Fig. 14 Normal vibration velocity spectrum level of measuring-points on pillar area

 图 15 潜体测点法向振速谱级（1/3 oct） Fig. 15 Normal vibration velocity spectrum level of measuring-points on submersible area

 图 16 有限元法与统计能量法计算结果对比 Fig. 16 Comparison between results from FEM and SEA method
4 结　语

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