﻿ 局部开孔深腔流噪声发声机理研究
 舰船科学技术  2019, Vol. 41 Issue (1): 26-32 PDF

1. 海军工程大学 动力工程学院，湖北 武汉 430033;
2. 海军工程大学 船舶振动噪声重点实验室，湖北 武汉 430033

Research on flow noise mechanism of the deep cavity with local hole
LI Rong-hua1, LOU Jing-jun2, ZHU Shi-jian2
1. College of Power Engineering, Naval University of Engineering, Wuhan 430033, China;
2. National Key Laboratory on Ship Vibration and Noise, Naval University of Engineering, Wuhan 430033, China
Abstract: Comparing to the former researches which focused on the model of cavity with a single full hole, this paper is based on the large eddy simulation and acoustic analogy theory to study on the flow noise mechanism produced by the deep cavity with a local hole. Firstly, according to the vorticity and pressure magnitude contours of the flow field, the vortex-acoustic feedback model is established to explain the situation that the exciting force of different measurement points have the same period but different phases. Secondly, by analyzing the power spectral of different measurement points' pressure and the Cavity Acoustic mode frequency, the pressure pulsation of the upper edge of the hole's back wall is confirmed as the main source of the flow noise produced by the local hole. Finally, the accuracy of the simulation results is verified by comparing the measured spectral characteristics of the sound field with the prediction results of the empirical formula.
Key words: local hole     deep cavity     flow noise mechanism     vortex-acoustic feedback     force pulsation
0 引　言

 图 1 孔腔模型 Fig. 1 The model of open cavity
1 数值求解方法 1.1 大涡模拟

 $\overline {{u_i}} (x,t) = \frac{1}{{{\Delta ^3}}}\int_{ - \frac{\Delta }{2}}^{\frac{\Delta }{2}} {\int_{ - \frac{\Delta }{2}}^{\frac{\Delta }{2}} {\int_{ - \frac{\Delta }{2}}^{\frac{\Delta }{2}} {{u_i}\left( {\xi ,t} \right)G\left( {x - \xi } \right)} } } {\rm d}{\xi _1}{\rm d}{\xi _2}{\rm d}{\xi _3}\text{。}\!\!\!\!$ (1)

 $G\left( {x - \xi } \right) = \left\{ \begin{array}{l} 1,\left| \eta \right| \leqslant \Delta /2\text{，}\\ 0,\left| \eta \right| > \Delta /2\text{。} \end{array} \right.$ (2)

 $\frac{{\partial \rho }}{{\partial t}} + \frac{\partial }{{\partial {x_i}}}\left( {\rho \overline {{u_i}} } \right) = 0\text{，}$ (3)
 $\frac{\partial }{{\partial t}}\left( {\rho \overline {{u_i}} } \right) + \frac{\partial }{{\partial {x_j}}}\left( {\rho \overline {{u_i}} \overline {{u_j}} } \right) = \frac{\partial }{{\partial {x_j}}}\left( {\nu \frac{{\partial {\sigma _{ij}}}}{{\partial {x_j}}}} \right) - \frac{{\partial \overline p }}{{\partial {x_i}}} - \frac{{\partial {\tau _{ij}}}}{{\partial {x_j}}}\text{。}$ (4)

1.2 FW-H声类比

FW-H方程本质上是非齐次方程，其可以从连续方程以及N-S方程中演化得来，FW-H方程如下：

 $\begin{split} & \frac{1}{{a_0^2}}\frac{{{\partial ^2}p'}}{{\partial {t^2}}} - {\nabla ^2}p' = \frac{{{\partial ^2}}}{{\partial {x_i}\partial {x_j}}}\left\{ {{T_{ij}}H\left( f \right)} \right\} - \\ & \frac{\partial }{{\partial {x_i}}}\left\{ {\left[ {{P_{ij}}{n_j} + \rho {u_i}\left( {{u_n} - {v_n}} \right)} \right]\delta \left( f \right)} \right\} + \\ & \frac{\partial }{{\partial t}}\left\{ {\left[ {{\rho _0}{v_n} + \rho \left( {{u_n} - {v_n}} \right)} \right]\delta \left( f \right)} \right\}\text{。} \end{split}$ (5)

 ${T_{ij}} = \rho {u_i}{u_j} + {P_{ij}} - a_0^2\left( {\rho - {\rho _0}} \right){\delta _{ij}}\text{，}$

 $p' = {p'_T}\left( {\vec x,t} \right) + {p'_L}\left( {\vec x,t} \right)\text{。}$ (6)

 ${p'_L} = \frac{1}{{4{\text{π}} }}\left\{ {\frac{1}{{{a_0}}}\int\limits_{f = 0} {\left[ {\frac{{{{\dot L}_r}}}{r}} \right]} {\rm d}S + \int\limits_{f = 0} {\left[ {\frac{{{L_r} - {L_M}}}{{{r^2}}}} \right]} {\rm d}S} \right\}\text{，}$
 ${p'_T} = \frac{1}{{4{\text{π}}}}\left\{ {\int\limits_{f = 0} {\frac{{{\rho _0}\left( {{{\dot U}_n} + {U_n}} \right)}}{r}} {\rm d}S} \right\}\text{，}$
 ${U_i} = {v_i} + \frac{\rho }{{{\rho _0}}}\left( {{u_i} - {v_i}} \right)\text{，}$
 ${L_i} = {P_{ij}}{\hat n_j} + \rho {u_i}\left( {{u_n} - {v_n}} \right)\text{。}$

1.3 计算模型与CFD计算参数设置

 图 3 计算域示意图 Fig. 3 Figure of calculation zone

 图 4 网格及边界条件示意图 Fig. 4 The flow field meshes and boundary conditions

2 计算分析

2.1 流场分析

t=0时刻xOy切面上流场涡量-压强分布云图如图6所示。在t=0时刻，此时孔壁上缘3点附近涡量分布集中，下缘1点处涡量分布较少。由涡运动相关知识可知，在漩涡中，由于离心力被压力所平衡，涡核处离心力最低，压力也最小，所以此时在开口上缘区域压强分布较小，下缘区域压强分布较大。但是由于涡运动对开口上缘附近壁面产生较大冲击，有较大脉动压力，等效为偶极子声源，此时在孔后壁上缘处所产生的声压也较大，随着声波向孔前壁方向传播，对涡结构运动产生排挤，促使后续向孔后壁迁移的涡结构同时向开口下缘移动。

 图 6 t=0时刻涡量-压强云图 Fig. 6 Vorticity-pressure contours of t=0

t=0.25 T时刻xOy切面上流场涡量-压强分布云图如图7所示。在上一时刻腔体后壁上缘声源所产生声压的作用下，涡结构向孔后壁移动的同时，逐渐向下缘移动，且随着涡的不断耗散和向后移动，在孔后壁上缘的涡量得不到补充，因此上缘涡量分布减少，而下缘的涡量分布增多。在涡的作用下，下缘1点处附近的压强减小，上缘3点处附近的压强增大，虽然此时3点附近下缘区域的涡量分布增大，对下缘作用产生的脉动压力也增大，但是由此声源产生的声压仍小于由上缘壁面产生的声压，因此在壁面上缘声源产生的大声压作用下，向孔后壁迁移的涡结构继续向开口下缘移动。

 图 7 t=0.25 T时刻涡量-压强云图 Fig. 7 Vorticity-pressure contours of t=0.25 T

t=0.4 T时刻xOy切面上涡量-压强分布云图如图8所示。随着孔壁上缘涡的不断耗散，同时由孔前壁向后壁移动的涡向下缘移动，在孔后壁上缘3点处的涡量持续得不到补充，因此上缘3点处的涡量分布达到周期内的最小值，周边压强较大。而下缘1点处由于涡的持续补充，此时涡量达到较大值，周边压强较小。同理，由于此时在孔后壁下缘处的涡量较大，涡结构运动过程中对开口下缘腔壁造成冲击，产生较大脉动压力，从而作为声源产生较大声压，随着声波向开口前缘传播，对向后运动的涡结构产生排挤，导致向孔后壁迁移的涡结构逐渐向开口上缘移动。

 图 8 t=0.4 T时刻涡量-压强云图 Fig. 8 Vorticity-pressure contours of t=0.5 T

t=0.75 T时刻xOy切面上涡量-压强分布云图如图9所示。由于孔后壁腔体下缘发声产生的声压随着声波向孔前壁方向传播对涡结构产生排挤，因此从孔前壁向后壁迁移的涡逐渐向开口上缘移动，1点处的涡量得不到补充，分布减少，3点处的涡量分布增多，因此1点附近压强增大，3点周边压强减小，此时涡在孔壁下缘声源大声压作用下，继续向开口上缘移动。

 图 9 t=0.75 T时刻涡量-压强云图 Fig. 9 Vorticity-pressure contours of t=0.75 T

t=T时刻xOy切面上涡量-压强分布云图如图10所示。此时在腔体下缘的涡量分布达到较小值，1点附近压强达到较大值，而在开口上缘3点出的涡量分布达到最大值，附近压强达到最小值，与t=0时刻一致。此时由于上缘涡量分布集中，涡结构运动产生的压力脉动在腔体后缘作为声源产生较大声压，随着声波向前传播，对涡结构移动产生排挤，致使由开口前缘向孔后壁迁移的涡向后迁移的同时向开口下缘移动，从而进入下一个涡结构运动周期。

 图 10 t=1 T时刻涡量-压强云图 Fig. 10 Vorticity-pressure contours of t=T

2.2 受力分析

 图 11 各采集点压力功率谱 Fig. 11 Exciting force power spectral density of measurement points

 图 2 局部开口深腔示意图 Fig. 2 The model of deep cavity with local hole

 图 5 监测点压强时间序列 Fig. 5 Pressure-time diagram of measurement points
2.3 声场分析

 ${f_n} = \frac{{{c_0}}}{2}\sqrt {{{\left( {\frac{{{n_1}}}{L}} \right)}^2} + {{\left( {\frac{{{n_2}}}{B}} \right)}^2} + {{\left( {\frac{{{n_3}}}{H}} \right)}^2}}{\text{。}}$ (7)

Rossiter JE[14]最早对矩形开口腔体绕流振荡机理进行研究，并给出自持振荡频率预测半经验公式：

 ${f_n} = \frac{{{U_\infty }}}{{{L_{hole}}}}\frac{{n - \alpha }}{{{M_a} + 1/{k_c}}}\text{。}$ (8)

3 结　语

1）根据仿真得到一个周期内空腔内部各个时刻的涡量、压强分布云图，首次对孔后壁不同监测点脉动压力变化的周期、相位异同之处进行监测分析，用涡上（下）运动—碰撞发声—涡下（上）运动—碰撞发声—涡上（下）运动的涡-声反馈模型解释孔腔流噪声发声机理。

2）对各个采集点的压强功率谱密度进行对比分析，得出局部开孔深腔的各个部位对声场能量的贡献量不同，其中开孔后壁的贡献量最大。

3）将计算结果与Rossiter经验公式的计算结果进行对比，验证了仿真结果的准确性。

 [1] LIGHTHILL M J. On sound generated aerodynamically. I. general theory[J]. Proceedings of the Royal Society A, 1952, 211(1107): 564-587. DOI:10.1098/rspa.1952.0060 [2] POWELL A. Theory of vortex sound[J]. Journal of the Acoustical Society of America, 1964, 36(1): xiv, 216. [3] HOWE M S. Mechanism of sound generation by low Mach number flow over a wall cavity[J]. Journal of Sound & Vibration, 2004, 273(1-2): 103-123. [4] 杨党国, 李建强, 梁锦敏. 基于CFD和气动声学理论的空腔自激振荡发声机理[J]. 空气动力学学报, 2010, 28(6): 724-730. YANG Dang-guo, LI Jian-qiang, LIANG Jin-min. Sound generation induced by self-sustained oscillations inside cavities based on CFD and aeroacoustic theory[J]. ACTA Aeroacoustic Sinica, 2010, 28(6): 724-730. DOI:10.3969/j.issn.0258-1825.2010.06.019 [5] M G, A R. The effect of flow oscillations on cavity drag[J]. Journal of Fluid Mechanics, 1987, 177(-1): 193-226. [6] 张楠, 沈泓萃, 朱锡清, 等. 基于大涡模拟和Kirchhoff积分方法的孔腔流动发声机理分析[J]. 船舶力学, 2011, 15(4): 427-434. ZHANG Nan, SHEN Hong-Cui, ZHU Xi-qing, et al. Analysis of the mechanism of cavity flow induced noise with large eddy simulation and Kirchhoff method integral[J]. Journal of Ship Mechanics, 2011, 15(4): 427-434. DOI:10.3969/j.issn.1007-7294.2011.04.015 [7] 王玉, 王树新, 刘玉红. 刚性壁面三维陷落腔涡流噪声机理研究[J]. 船舶力学, 2012(11): 1321-1328. WANG Yu, WANG Shu-xin, LIU Yu-hong. Research on turbulent flow noise mechanism of 3D cavity[J]. Journal of Ship Mechanics, 2012(11): 1321-1328. [8] 徐俊, 唐科范, 张旭. 基于数值模拟的孔腔水动噪声机理及其控制研究[J]. 水动力学研究与进展A辑, 2014, 29(05): 618-629. XU Jun, TANG Ke-fan, ZHANG Xu. Study on mechanism and reduction of hydro-acoustical noise induced by flow over an open cavity based on numerical simulation[J]. Chinese Journal of Hydrodynamics, 2014, 29(05): 618-629. [9] 高岩, 沈琪, 俞孟萨. 弹性腔流激耦合共振及声辐射机理研究[J]. 船舶力学, 2016, 20(8): 1036-1044. GAO Yan, SHEN Qi, YU Meng-sa. A mechanism study on coupling resonance and acoustic radiation of elastic cavity induced by flow[J]. Journal of Ship Mechanics, 2016, 20(8): 1036-1044. DOI:10.3969/j.issn.1007-7294.2016.08.013 [10] 陈灿, 吴方良, 李环, 等. 不可压缩空腔流振荡模式和声学特性研究[C]//全国水动力学研讨会. 2014. CHEN Can, WU Fang-liang, LI Huan, et al. Investigation on the oscillation mode and the acoustic characteristics of incompressible cavity flow[C]// National Symposium on Hydrodynamics, 2014. [11] YUAN Guoqing, JIANG Hongkang, HUA Hongxing. Hydroacoustic analysis of open cavity subsonic flow based on multiple parameter numerical models[J]. Journal of Hydrodynamics, 2015, 27(5): 668-678. DOI:10.1016/S1001-6058(15)60529-7 [12] SAROHIA V. Experimental investigation of oscillations in flows shallow cavities[J]. Aiaa Journal, 1977, 15(7): 984-991. DOI:10.2514/3.60739 [13] 张强. 气动声学基础[M]. 北京: 国防工业出版社, 2012. [14] ROSSITER JE. Wind tunnel experiments on the flow over rectangular cavities at subsonic and transonic speeds[R]. Aeronautical Research Council Reports and Memoranda, 1964.