基于边界元法的管道内声传播问题研究

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摘要

近些年来，噪声污染的问题已经受到广泛关注。管道作为大型机械设备的重

要连接部件，同时也是机械设备向外部环境辐射噪声的重要途径。本文通过在抗

性消声管道自身结构上进行声学设计，分析扩张腔长度、起始位置、扩张度、扩

张段进出口倒角形式、扩张段形式、最大扩张截面位置等管道几何参数对其声波

在各种管道内的传播规律和消声特性的影响，为管路消声器设计提供参考依据。

本文主要研究工作和结论如下：

1. 首先本文完成了一个能够运用到管道内声传播问题的边界元程序，同时对

其进行了验证及网格无关性分析，结果表明最大网格尺寸小于最小波长的 1/6 时，

由网格带来的计算误差将降至 1%。

2. 利用边界元程序分析了扩张段长度、起始位置、扩张度对声传播和消声特

性的影响。研究表明：扩张管长度为入射声波波长四分之一的奇数倍时，管内声

压分布相近，且传递损失最大；为四分之一波长的偶数倍时，声传播特性也相同，

且传递损失几乎为 0。扩张段起始位置不影响传递损失，但透射声压会随着入射

波波长的一半周期性出现峰值。在一定入射波频率范围内，扩张段长度增加，最

大传递损失基本不变，出现最大消声频率数目增多；随着扩张度增加，最大消声

特性提升。

3. 基于本文的边界元程序分析了倒角形式、扩张段形式及最大扩张截面位置

对单腔扩张管消声特性的影响。本文分析的两种倒角形式对传递损失影响不大，

最大消声频率稍有偏移。相比原型扩张管，圆弧过渡扩张管最大传递损失下降了

0.85dB，直线过渡扩张管下降了 1.75dB。对最大扩张截面位置 Ld/Lc=0、1/4、1/2、

3/4、1的直线过渡扩张管分析表明，最大扩张截面的位置对传递损失的影响关于

扩张段中心成对称关系。并且在远离扩张段中心时，整个频段内综合消声特性最

佳，但第一阶最大消声频率下的传递损失最小。

4. 本文对第二腔长度（Le）与第一腔（Lc）比为 0.5、0.75、1、1.5、2的串

联双腔扩张管消声特性分析表明，串联双腔扩张管最大传递损失大于两个单腔最

大传递损失之和。在 1000Hz 以下的低频区内，双腔管最大消声频率数量为两个

单腔最大消声频率数之和；在高于 1000Hz 的中频区内，双腔的传递损失普遍大

于任意单腔管的传递损失，且传递损失峰值出现在两个单腔管传递损失相同的频

率下，而传递损失谷值出现在任意一个单腔的通过频率下，双腔通过频率通常一

定为两个单腔共同的通过频率。当第一腔长度固定时，Le/Lc<1 时的传递损失最大

值普遍比 Le/Lc>1 时高 1~2dB。

5. 最后本文基于 LabVIEW 测试平台，设计了不同扩张度（m=2.56、4、6.25）

下单腔扩张管插入损失的实验，对比了相同监测点的声压级。结果表明，扩张度

最大的管道插入损失最大为 4.789dB；扩张度最小的插入损失为 0.468dB。

关键词：管道边界元扩张管传递损失消声特性频率

ABSTRACT

In recent years, noise pollution has been widely concerned. Pipes play a

significant role as interconnecting pieces in large mechanical equipments, which are

also important paths for noise radiation to the external environment. In this paper,

certain geometric factors of pipes are studied for sound propagation law and

attenuation characteristics, including the length of expansion chamber, the starting

expansion position, expansion ratio, chamfering, forms of expansion chamber and

maximum expansion positions, which provide references to the design of pipe mufflers.

The main research work and conclusions are as follows:

1. A calculator program based on boundary element method is completed with

validation and grid independence analysis. Results show that while the maximum grid

size is reduced to 1/6 of minimum wavelength, the calculation error from grids drop to

1%.

2. The effect of the length of the expansion chamber, the starting expansion

position and expansion ratio on sound propagation and attenuation characteristics is

analyzed. Numerical results indicate that distributions of sound pressures along the

centerline in pipes are similar with the largest transmission loss when the lengths of

expansion chambers are odd times of quarter wavelength. So are the pipes of integer

times with transmission loss close to 0. The starting expansion position has nothing to

do with transmission loss, but transmission sound pressures change cyclically with half

of the wavelength. In a certain frequency range, the increase of lengths of expansion

chambers doesn’t influence the maximum transmission loss but more maximum

noise-reducing frequencies occurs, and larger expansion ratios improve the maximum

transmission loss.

3. Expansion pipes with different chamfering, forms and maximum expansion

positions are researched based on the program. Results indicate that chamfering has

little influence on attenuation characteristics, only cause a little excursion of the

maximum noise-reducing frequency. Compared to the prototype, the maximum

transmission loss drops by 0.85dB with circular transition, while it drops by 1.75dB

with straight-line transition. The maximum expansion positions (Ld/Lc=0, 1/4, 1/2, 3/4,

1) with straight-line transition are analyzed, which indicate that the same

characteristics occur with the symmetrical maximum expansion position. In the whole

frequency domain, it makes the best comprehensive attenuation characteristics, while

the worst at the first maximum noise-reducing frequency.

4. Results for double expansion pipes (Le/Lc=0.5, 0.75, 1, 1.5, 2) in series, where

Le stands for the lengths of second expansion chambers (Lc stands for the first) ,

manifest that maximum transmission loss is larger than the sum of the two single

pipes’. When the frequency is lower than 1000Hz, the number of maximum

noise-reducing frequencies is equal to the amount of the two single pipes’. When the

frequency is higher than 1000Hz, transmission loss is generally larger than any one of

the two single pipes’, peaks occur at the frequencies when both of the single pipes

reach the same transmission loss, valleys occur at the passing frequencies of any one of

the two single pipes, the passing frequencies occur at the corporate ones of the two

single pipes. With the same first expansion chamber, when the second chambers are

larger than the first, the maximum transmission losses are generally higher by 1~2dB

than those are shorter.

5. The SPL of the same monitoring point outside the expansion pipes are

measured, which are designed with different expansion ratios(m=2.56, 4, 6.25), by an

insertion loss experiment based on LabVIEW. Experimental results indicate that the

pipe with the biggest expansion ratio has insertion loss 4.789dB in maximum, while

the pipe with the smallest expansion ratio has the minimum insertion loss 0.468dB.

Keywords: pipes, BEM, expansion pipes, transmission loss,

attenuation characteristics, frequency

摘要

ABSTRACT

第一章绪论 ................................................................................................................ 1

§1.1 课题来源及意义 ........................................................................................... 1

§1.2 国内外研究现状 ........................................................................................... 2

§1.2.1 边界元方法应用的研究进展 .............................................................. 2

§1.2.2 管道内声传播问题的研究进展 .......................................................... 4

§1.2.3 边界元法在管道内声学问题的应用 ................................................... 5

§1.3 本文研究内容 ............................................................................................... 6

第二章声学边界元基本理论 ..................................................................................... 8

§2.1 声传播控制方程 ........................................................................................... 8

§2.2 Dirac-



函数 ................................................................................................... 8

§2.3 基本解的形式 ............................................................................................... 9

§2.4 格林公式..................................................................................................... 10

§2.5 亥姆霍兹方程基本解 ................................................................................. 11

§2.6 边界积分方程 ............................................................................................. 12

§2.6.1 待求点 M在声学计算域内 ............................................................... 13

§2.6.2 待求点 M在光滑的声学边界上 ....................................................... 14

§2.6.3 待求点 M在不光滑的声学边界上 ................................................... 14

§2.6.4 亥姆霍兹边界积分方程 .................................................................... 14

§2.7 边界积分方程的离散与求解 ...................................................................... 15

§2.7.1 不同单元划分方法............................................................................ 15

§2.7.2 边界积分方程的离散 ........................................................................ 17

§2.7.3 边界矩阵方程的求解 ........................................................................ 19

§2.7.4 声学边界条件的确定 ........................................................................ 20

§2.8 声学边界元方法的程序设计 ...................................................................... 21

§2.9 声学性能评价指标 ..................................................................................... 22

§2.10 本章小结 ................................................................................................... 24

第三章单一入射频率下管道声传播特性研究 ........................................................ 25

§3.1 管道声学边界元计算程序的运用 .............................................................. 25

§3.1.1 边界元程序的验证............................................................................ 25

§3.1.2 计算模型及边界条件 ........................................................................ 26

§3.1.3 网格无关性分析 ............................................................................... 27

§3.2 收缩管道的声传播特性 .............................................................................. 27

§3.2.1 收缩段长度 Lc/



的影响 .................................................................... 28

§3.2.2 收缩段起始位置 L1/L 的影响 ........................................................... 30

§3.2.3 收缩段收缩度 H/h 的影响 ................................................................ 31

§3.3 扩张管道声传播特性 ................................................................................. 32

§3.3.1 扩张段长度 Lc/



的影响 .................................................................... 33

§3.3.2 扩张段起始位置 L1/L 的影响 ........................................................... 35

§3.3.3 扩张段扩张度 R2/r2（H/h）的影响 .................................................. 36

§3.4 本章小结..................................................................................................... 38

第四章不同入射频率下扩张管消声特性研究 ........................................................ 39

§4.1 单腔扩张管消声特性研究 .......................................................................... 39

§4.1.1 单腔扩张管边界元程序验证 ............................................................ 39

§4.1.2 不同入射声波频率下单腔扩张管的消声特性 ................................. 40

§4.2 不同类型单腔扩张管消声特性研究 ........................................................... 43

§4.2.1 扩张段进出口倒角的影响 ................................................................ 44

§4.2.2 扩张段形式的影响............................................................................ 45

§4.2.3 最大扩张截面位置的影响 ................................................................ 46

§4.3 双腔扩张管消声特性研究 .......................................................................... 49

§4.3.1 串联双腔扩张管消声特性 ................................................................ 50

§4.3.2 第二个单腔长度的影响 .................................................................... 51

§4.3.3 双腔先后顺序的影响 ........................................................................ 53

§4.4 本章小结..................................................................................................... 54

第五章扩张管声传播实验研究 ............................................................................... 55

§5.1 噪声测试台 ................................................................................................. 55

§5.1.1 测试环境 ........................................................................................... 55

§5.1.2 测试系统 ........................................................................................... 55

§5.1.3 实验仪器及装置 ............................................................................... 56

§5.1.4 测试步骤 ........................................................................................... 57

§5.2 实验注意事项 ............................................................................................. 58

§5.3 实验结果及分析 ......................................................................................... 59

§5.4 本章小结..................................................................................................... 61

第六章结论与展望 ................................................................................................... 62

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摘要：

摘要近些年来，噪声污染的问题已经受到广泛关注。管道作为大型机械设备的重要连接部件，同时也是机械设备向外部环境辐射噪声的重要途径。本文通过在抗性消声管道自身结构上进行声学设计，分析扩张腔长度、起始位置、扩张度、扩张段进出口倒角形式、扩张段形式、最大扩张截面位置等管道几何参数对其声波在各种管道内的传播规律和消声特性的影响，为管路消声器设计提供参考依据。本文主要研究工作和结论如下：1.首先本文完成了一个能够运用到管道内声传播问题的边界元程序，同时对其进行了验证及网格无关性分析，结果表明最大网格尺寸小于最小波长的1/6时，由网格带来的计算误差将降至1%。2.利用边界元程序分析了扩张段长度、起始位置、扩...

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