﻿ 船用燃气轮机进气管道声辐射特性计算与分析
 舰船科学技术  2023, Vol. 45 Issue (12): 82-88    DOI: 10.3404/j.issn.1672-7619.2023.12.015 PDF

Calculation and analysis of acoustic radiation characteristics of marine gas turbine intake ducts
ZHANG Xiao-hai
The Eighth Military Representative Office of Naval Equipment Department in Shanghai Area, Shanghai 200011, China
Abstract: Most of the studies on the noise of intake and exhaust system of power plant focus on the sound radiation of intake and exhaust pipe ports, and few studies focus on the sound radiation of the pipe wall itself. In this paper, based on analytical and numerical calculation methods, we analyze the sound radiation at the inlet and the radiation field in the cabin caused by the vibration of the pipe wall under the excitation of the gas turbine noise source. The study shows the following conclusions. Increasing the pipe size and wall thickness can reduce the cabin noise caused by the pipe wall. Without control measures, the noise in the adjacent cabin of the inlet pipe can be as high as 89 dBA. Adopting acoustic cladding on the pipe wall can effectively reduce the radiation noise in the cabin.
Key words: gas turbine     pipe wall sound radiation     noise control
0 引　言

Allen[6]引用的1个非常简单的公式计算管道声辐射，但该方法只在高频下取得比较可靠的结果，无法用于低频管道噪声的预测。Cummings[7-8]针对低频范围内矩形管道声辐射的管壁传递损失计算问题提出了wave solution的计算方法，并且和实验结果吻合良好。在更高频率范围内，Guthrie[9]和Cummings[10]等学者通过实验和解析等方法均观察到，当管道内存在高阶模态的声传播时，管壁的传递损失曲线呈现以斜率为 $3{\rm{dB}}/{\rm{octave}}$ 的增加规律。

1 简单管道声辐射解析估算

 ${L}_{w,out}={L}_{w,in}+10\mathrm{log}\left(\frac{S}{A}\right)-T{L}_{out} 。$

 图 1 wave solution方法计算模型 Fig. 1 wave solution method calculation model

 ${k}_{i}=\frac{2{\text{π}} f}{c}，$
 $K=\frac{12(1-{\sigma }^{2})}{E{h}^{3}}，$
 ${\gamma }^{4}={\omega }^{2}mK 。$

 ${\alpha }_{1}=\sqrt{{\gamma }^{2}-{k}_{x}^{2}}，$
 ${\alpha }_{2}=\sqrt{{\gamma }^{2}+{k}_{x}^{2}}。$

 $\begin{split} D\left(x,y\right)=&\Biggr[{A}_{1}\mathrm{cos}\left({\alpha }_{1}y\right)+{A}_{2}\mathrm{sin}\left({\alpha }_{1}y\right)+{A}_{3}\mathrm{cosh}\left({\alpha }_{2}y\right)+\\ &{A}_{4}\mathrm{sinh}\left({\alpha }_{2}y\right)+\frac{K{P}_{0}}{{k}_{x}^{4}-{\gamma }^{4}}\Biggr]{e}^{-i{k}_{x}x}。\end{split}$

xz平面平行的管壁在y方向上的振动：

 $\begin{split} D\left(x,z\right)=&\Biggr[{B}_{1}\mathrm{cos}\left({\alpha }_{1}z\right)+{B}_{2}\mathrm{sin}\left({\alpha }_{1}z\right)+{B}_{3}\mathrm{cosh}\left({\alpha }_{2}z\right)+\\ &{B}_{4}\mathrm{sinh}\left({\alpha }_{2}z\right)+\frac{K{P}_{0}}{{k}_{x}^{4}-{\gamma }^{4}}\Biggr]{e}^{-i{k}_{x}x} ，\end{split}$
 $\begin{split} Y\left(y\right)=&{A}_{1}\mathrm{cos}\left({\alpha }_{1}y\right)+{A}_{2}\mathrm{sin}\left({\alpha }_{1}y\right)+{A}_{3}\mathrm{cosh}\left({\alpha }_{2}y\right)+\\ &{A}_{4}\mathrm{sinh}\left({\alpha }_{2}y\right)+\frac{K{P}_{0}}{{k}_{x}^{4}-{\gamma }^{4}} ，\end{split}$
 $\begin{split}Z\left(z\right)=&B_{1}\mathrm{cos}\left({\alpha }_{1}z\right)+{B}_{2}\mathrm{sin}\left({\alpha }_{1}z\right)+{B}_{3}\mathrm{cosh}\left({\alpha }_{2}z\right)+\\ &{B}_{4}\mathrm{sinh}\left({\alpha }_{2}z\right)+\frac{K{P}_{0}}{{k}_{x}^{4}-{\gamma }^{4}}，\end{split}$
 $\begin{split} {Y}'\left(y\right)=&{-A}_{1}{\alpha }_{1}\mathrm{sin}\left({\alpha }_{1}y\right)+{A}_{2}{\mathrm{\alpha }}_{1}\mathrm{cos}\left({\alpha }_{1}y\right)+\\ &{A}_{3}{\alpha }_{2}\mathrm{sinh}\left({\alpha }_{2}y\right)+{A}_{4}{\mathrm{\alpha }}_{2}\mathrm{cossh}\left({\alpha }_{2}y\right) ，\end{split}$
 $\begin{split} {Z}'\left(y\right)=&{-B}_{1}{\alpha }_{1}\mathrm{sin}\left({\alpha }_{1}z\right)+{B}_{2}{\mathrm{\alpha }}_{1}\mathrm{cos}\left({\alpha }_{1}z\right)+\\ &{B}_{3}{\alpha }_{2}\mathrm{sinh}\left({\alpha }_{2}z\right)+{B}_{4}{\mathrm{\alpha }}_{2}\mathrm{cossh}\left({\alpha }_{2}z\right)，\end{split}$
 ${M}_{y}\left(x,y\right)=-\frac{1}{K}\left(\frac{{\partial }^{2}}{\partial {y}^{2}}+\frac{{\partial }^{2}}{\partial {x}^{2}}\right)D(x,y)，$
 $\begin{split} {M}_{y}\left(x,y\right)=&-\frac{1}{K}\Biggr\{{-A}_{1}{\mathrm{\alpha }}_{1}^{2}\mathrm{cos}\left({\alpha }_{1}y\right)-{A}_{2}{\mathrm{\alpha }}_{1}^{2}\mathrm{sin}\left({\alpha }_{1}y\right)+\\ &{A}_{3}{\mathrm{\alpha }}_{2}^{2}\mathrm{cosh}\left({\alpha }_{2}y\right)+{A}_{4}{\mathrm{\alpha }}_{2}^{2}\mathrm{sinh}\left({\alpha }_{2}y\right)+\\ &{k}_{x}^{2}\Biggr[{A}_{1}\mathrm{cos}\left({\alpha }_{1}y\right)+{A}_{2}\mathrm{sin}\left({\alpha }_{1}y\right)+{A}_{3}\mathrm{cosh}\left({\alpha }_{2}y\right)+\\ &{A}_{4}\mathrm{sinh}\left({\alpha }_{2}y\right)+\frac{K{P}_{0}}{{k}_{x}^{4}-{\gamma }^{4}}\Biggr]\Biggr\}{e}^{-i{k}_{x}x}，\end{split}$
 $\begin{split} {M}_{z}\left(x,z\right)=&-\frac{1}{K}\Biggr\{{-B}_{1}{\mathrm{\alpha }}_{1}^{2}\mathrm{cos}\left({\alpha }_{1}z\right)-{B}_{2}{\mathrm{\alpha }}_{1}^{2}\mathrm{sin}\left({\alpha }_{1}z\right)+\\ &{B}_{3}{\mathrm{\alpha }}_{2}^{2}\mathrm{cosh}\left({\alpha }_{2}z\right)+{B}_{4}{\mathrm{\alpha }}_{2}^{2}\mathrm{sinh}\left({\alpha }_{2}z\right)+\\ &{k}_{x}^{2}[{B}_{1}\mathrm{cos}\left({\alpha }_{1}z\right)+{B}_{2}\mathrm{sin}\left({\alpha }_{1}z\right)+{B}_{3}\mathrm{cosh}\left({\alpha }_{2}z\right)+\\ &{B}_{4}\mathrm{sinh}\left({\alpha }_{2}z\right)+\frac{K{P}_{0}}{{k}_{x}^{4}-{\gamma }^{4}}]\Biggr\}{e}^{-i{k}_{x}x}。\end{split}$

 $\left\{\begin{array}{l}Y\left(0\right)=0,Y\left(0\right)=0,Y\left(0\right)=0,Y\left(0\right)=0，\\ {Y}'\left(0\right)={Z}'\left(0\right),{M}_{y}\left(0\right)={M}_{z}\left(0\right)，\\ {Y}'\left(\dfrac{a}{2}\right)=0,{Z}'\left(\dfrac{b}{2}\right)=0。\end{array}\right.$
 $Y\left(0\right)=0，$
 $\begin{split} {A}_{1}\mathrm{cos}\left({\alpha }_{1}0\right)+&{A}_{2}\mathrm{sin}\left({\alpha }_{1}0\right)+{A}_{3}\mathrm{cosh}\left({\alpha }_{2}0\right)+\\ &{A}_{4}\mathrm{sinh}\left({\alpha }_{2}0\right)=-\frac{K{P}_{0}}{{k}_{x}^{4}-{\gamma }^{4}}。\end{split}$
 $Y\left(a\right)=0 ，$
 $\begin{split}{A}_{1}\mathrm{cos}\left({\alpha }_{1}a\right)+&{A}_{2}\mathrm{sin}\left({\alpha }_{1}a\right)+{A}_{3}\mathrm{cosh}\left({\alpha }_{2}a\right)+\\ &{A}_{4}\mathrm{sinh}\left({\alpha }_{2}a\right)=-\frac{K{P}_{0}}{{k}_{x}^{4}-{\gamma }^{4}} 。\end{split}$
 $Z\left(0\right)=0 ，$
 $\begin{split} {B}_{1}\mathrm{cos}\left({\alpha }_{1}0\right)+&{B}_{2}\mathrm{sin}\left({\alpha }_{1}0\right)+{B}_{3}\mathrm{cosh}\left({\alpha }_{2}0\right)+\\ &{B}_{4}\mathrm{sinh}\left({\alpha }_{2}0\right)=-\frac{K{P}_{0}}{{k}_{x}^{4}-{\gamma }^{4}}。\end{split}$
 $Z\left(b\right)=0 ，$
 $\begin{split} {B}_{1}\mathrm{cos}\left({\alpha }_{1}b\right)+&{B}_{2}\mathrm{sin}\left({\alpha }_{1}b\right)+{B}_{3}\mathrm{cosh}\left({\alpha }_{2}b\right)+\\ &{B}_{4}\mathrm{sinh}\left({\alpha }_{2}b\right)=-\frac{K{P}_{0}}{{k}_{x}^{4}-{\gamma }^{4}} 。\end{split}$
 ${Y}'\left(0\right)={-Z}'\left(0\right)or{Y}'\left(0\right)+{Z}'\left(0\right)=0 ，$
 $\begin{split}{-A}_{1}{\alpha }_{1}\mathrm{sin}\left({\alpha }_{1}0\right)+&{A}_{2}{\mathrm{\alpha }}_{1}\mathrm{cos}\left({\alpha }_{1}0\right)+{A}_{3}{\alpha }_{2}\mathrm{sinh}\left({\alpha }_{2}0\right)+\\ &{A}_{4}{\mathrm{\alpha }}_{2}\mathrm{cossh}\left({\alpha }_{2}0\right){-B}_{1}{\alpha }_{1}\mathrm{sin}\left({\alpha }_{1}0\right)+\\ &{B}_{2}{\mathrm{\alpha }}_{1}\mathrm{cos}\left({\alpha }_{1}0\right)+{B}_{3}{\alpha }_{2}\mathrm{sinh}\left({\alpha }_{2}0\right)+\\ &{B}_{4}{\mathrm{\alpha }}_{2}\mathrm{cossh}\left({\alpha }_{2}0\right)=0 ，\end{split}$
 ${Y}'\left(\frac{a}{2}\right)=0，$
 $\begin{split} &{-A}_{1}{\alpha }_{1}\mathrm{sin}\left(\frac{{\alpha }_{1}a}{2}\right)+{A}_{2}{\mathrm{\alpha }}_{1}\mathrm{cos}\left(\frac{{\alpha }_{1}a}{2}\right)+\\ &{A}_{3}{\alpha }_{2}\mathrm{sinh}\left(\frac{{\alpha }_{2}a}{2}\right)+{A}_{4}{\mathrm{\alpha }}_{2}\mathrm{cossh}\left(\frac{{\alpha }_{2}a}{2}\right)=0\end{split} ，$
 ${Z}'\left(\frac{b}{2}\right)=0 ，$
 $\begin{split}&{-B}_{1}{\alpha }_{1}\mathrm{sin}\left(\frac{{\alpha }_{1}b}{2}\right)+{B}_{2}{\mathrm{\alpha }}_{1}\mathrm{cos}\left(\frac{{\alpha }_{1}b}{2}\right)+\\ &{B}_{3}{\alpha }_{2}\mathrm{sinh}\left(\frac{{\alpha }_{2}b}{2}\right)+{B}_{4}{\mathrm{\alpha }}_{2}\mathrm{cossh}\left(\frac{{\alpha }_{2}b}{2}\right)=0，\end{split}$
 ${M}_{y}\left(0\right)={M}_{x}\left(0\right)，$
 $\begin{split} -&A_{1}{\mathrm{\alpha }}_{1}^{2}\mathrm{cos}\left({\alpha }_{1}0\right)-{A}_{2}{\mathrm{\alpha }}_{1}^{2}\mathrm{sin}\left({\alpha }_{1}0\right)+{A}_{3}{\mathrm{\alpha }}_{2}^{2}\mathrm{cosh}\left({\alpha }_{2}0\right)+\\ &{A}_{4}{\mathrm{\alpha }}_{2}^{2}\mathrm{sinh}\left({\alpha }_{2}0\right)+{k}_{x}^{2}[{A}_{1}\mathrm{cos}\left({\alpha }_{1}0\right)+{A}_{2}\mathrm{sin}\left({\alpha }_{1}0\right)+\\ &{A}_{3}\mathrm{cosh}\left({\alpha }_{2}0\right)+{A}_{4}\mathrm{sinh}\left({\alpha }_{2}0\right)]={-B}_{1}{\mathrm{\alpha }}_{1}^{2}\mathrm{cos}\left({\alpha }_{1}0\right)-\\ &{B}_{2}{\mathrm{\alpha }}_{1}^{2}\mathrm{sin}\left({\alpha }_{1}0\right)+{B}_{3}{\mathrm{\alpha }}_{2}^{2}\mathrm{cosh}\left({\alpha }_{2}0\right)+\\ &{B}_{4}{\mathrm{\alpha }}_{2}^{2}\mathrm{sinh}\left({\alpha }_{2}0\right)+{k}_{x}^{2}[{B}_{1}\mathrm{cos}\left({\alpha }_{1}0\right)+\\ &{B}_{2}\mathrm{sin}\left({\alpha }_{1}0\right)+{B}_{3}\mathrm{cosh}\left({\alpha }_{2}0\right)+{B}_{4}\mathrm{sinh}\left({\alpha }_{2}0\right)] 。\end{split}$

 $\begin{split} {\bar {\beta }_{y}}=&\frac{i\omega {\rho }_{i}{c}_{i}}{a{P}_{0}}\Biggr[\frac{{A}_{1}}{{\alpha }_{1}}\mathrm{sin}\left({\alpha }_{1}a\right)-\frac{{A}_{2}}{{\alpha }_{1}}\mathrm{cos}\left({\alpha }_{1}a\right)+\frac{{A}_{3}}{{\alpha }_{2}}\mathrm{sinh}\left({\alpha }_{2}a\right)+\\ &\frac{{A}_{4}}{{\alpha }_{2}}\mathrm{cossh}\left({\alpha }_{2}a\right)+\frac{{A}_{2}}{{\alpha }_{1}}-\frac{{A}_{4}}{{\alpha }_{2}}\Biggr]+\frac{i\omega {\rho }_{i}{c}_{i}K}{{k}_{x}^{4}-{\gamma }^{4}}，\end{split}$
 $\begin{split} {\bar{\beta }_{z}}=&\frac{i\omega {\rho }_{i}{c}_{i}}{b{P}_{0}}\Biggr[\frac{{B}_{1}}{{\alpha }_{1}}\mathrm{sin}\left({\alpha }_{1}b\right)-\frac{{B}_{2}}{{\alpha }_{1}}\mathrm{cos}\left({\alpha }_{1}b\right)+\frac{{B}_{3}}{{\alpha }_{2}}\mathrm{sinh}\left({\alpha }_{2}b\right)+\\ &\frac{{B}_{4}}{{\alpha }_{2}}\mathrm{cossh}\left({\alpha }_{2}b\right)+\frac{{B}_{2}}{{\alpha }_{1}}-\frac{{B}_{4}}{{\alpha }_{2}}\Biggr]+\frac{i\omega {\rho }_{i}{c}_{i}K}{{k}_{x}^{4}-{\gamma }^{4}} 。\end{split}$

 $\bar{\beta }=\frac{a{\bar{\beta }_{y}}+b{\bar{\beta }_{y}}}{a+b}。$

 ${k}_{x}={k}_{i}\sqrt{1-\frac{iL\bar{\beta }}{{k}_{1}S}} 。$

 ${C}_{r}=-\frac{1}{\text{π} }\mathrm{arctan}\left(\frac{\text{π} }{6}l{k}_{x}\left(1-\frac{{k}_{e}}{{k}_{x}}\right)\right)+0.5 。$

 ${c}_{x}=\frac{2\text{π} f}{{k}_{x}} 。$

 $TL=10\mathrm{log}\left(\frac{ab{\rho }_{i}{c}_{i}}{{C}_{r}{k}_{i}{\rho }_{e}{c}_{x}\left|a{\bar{\beta }_{y}}+b{\bar{\beta }_{y}}\right|}\right) 。$

 图 2 不同厚度下的壁面辐射声压级 Fig. 2 Radiated sound pressure levels for different thicknesses

 图 3 不同管道截面下的壁面辐射声压级 Fig. 3 Radiated sound pressure levels for different pipe sections

wave solution方法可以在设计之初给出管壁辐射声压的解析估算结果，但该方法也存在以下问题：

2 燃气轮机进气管道声辐射数值计算

 图 4 燃气轮机进气管路计算模型 Fig. 4 Calculation model of gas turbine intake pipeline

 图 5 燃气轮机进气噪声源与百叶窗处辐射噪声对比 Fig. 5 Comparison of gas turbine intake noise sources and radiated noise at louvers

 图 6 频率为31.5 Hz时声压级分布 Fig. 6 Sound pressure level distribution at 31.5 Hz

 图 7 频率为125 Hz时声压级分布 Fig. 7 Sound pressure level distribution at a frequency of 125 Hz

 图 8 频率为500 Hz时声压级分布 Fig. 8 Sound pressure level distribution at a frequency of 500 Hz

 图 9 频率为2000 Hz时声压级分布 Fig. 9 Sound pressure level distribution at a frequency of 2000 Hz

 图 10 频率为8000 Hz时声压级分布 Fig. 10 Sound pressure level distribution at a frequency of 8000 Hz

 图 11 不同频率下舱室声压级大小 Fig. 11 Cabin sound pressure level at different frequencies

3 燃机进气管道声辐射控制措施

 图 12 不同厚度吸声材料的传递损失 Fig. 12 Transmission loss of sound absorbing materials with different thicknesses

4 结　语

1）对于船用燃机进气管道而言，由于其噪声源激励幅值高、管道尺寸大，这导致管壁声激振动引起的二次辐射噪声不容忽视。

2）解析估算表明：随着板厚的增加，管外辐射声压逐渐降低。随着管道尺寸的减小，壁面外的辐射声压级会增大。对于本文研究的高度、宽带均为2.56 m的大尺寸进气管段，管道壁面取6 mm以上才可使进气消声器和燃气轮机之间的管道辐射噪声降低到75 dBA以下。

3）数值计算表明，对燃气轮机进气管道低频声衰减起主要作用的是进气集箱，其内部较大的空腔结构相当于一个膨胀腔消声器，阻止了进气噪声向舷外传播。当频率高于500 Hz以后，随着频谱的增加，消声器中吸声材料的高频吸声特性逐渐体现。经过进气集箱和消声器的双重降噪后，进气噪声得到了衰减。距离燃机进气百叶窗1 m处的总声压级降低至76.8 dBA。但在管道表面未采取控制措施的情况下，舱室内监测点的总噪声平均声压级可达到89 dBA。

4）依据声学包覆的隔声特性以及舱室环境要求可知，进气管道的声学包覆厚度为40mm时，可使该船燃机进气管道相邻舱室内的管道辐射噪声降低到75 dBA以下。

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