双层微穿孔管消声器传声损失理论计算与分析

.作者:张孟浩 左曙光 相龙洋 胡佳杰
.来源期刊:中南大学学报(自然科学版)2015年第2期
.中文关键字:平面波理论;双层微穿孔管消声器;传声损失;膨胀腔厚度
.英文关键字:plane wave theory; double-layer micro-perforated muffler; transmission loss; thickness of expansion cavity
.中文摘要:基于一维平面波理论和微穿孔结构吸声理论,推导双层微穿孔管消声器传声损失理论模型,并将理论计算值与三维有限元声学仿真结果进行对比,利用消声器传声损失理论公式,对比双层和单层微穿孔管消声器的传声损失,分析内外层膨胀腔厚度对双层微穿孔管消声器声学特性的影响。研究结果表明:双层微穿孔管消声器在中低频的传声损失要大于单层微穿孔管消声器;增加内外层膨胀腔的厚度,可以提高双层微穿孔管消声器的消声特性;当双层膨胀腔总厚度固定,外层膨胀腔厚度大时,消声器在中低频的声学性能更好。
.英文摘要:The transmission loss theoretical model of double-layer micro-perforated muffler was proposed based on one-dimensional plane wave theory and acoustic theory of micro-perforated panel. The calculated values were compared with the three-dimensional finite element model (FEM) acoustic simulation results. According to the transmission loss theoretical formulas of muffler, the transmission loss of double-layer micro-perforated muffler was contrasted with that of single-layer. The influence of inner and outer expansion cavities on the transmission loss of double-layer micro-perforated muffler was analyzed. The results show that the transmission loss of double-layer micro-perforated muffler is bigger than that of single-layer micro-perforated muffler in low and medium frequency. The acoustic characteristic of double-layer micro-perforated muffler is improved by increasing the thickness of both inner and outer expansion cavities. When the total thickness of inner and outer expansion cavities is fixed, the acoustic characteristic of muffler is good in low and medium frequency with a bigger thickness of outer expansion cavity.
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DOI: 10.11817/j.issn.1672-7207.2015.02.019

双层微穿孔管消声器传声损失理论计算与分析

张孟浩,左曙光,相龙洋,胡佳杰

(同济大学 新能源汽车工程中心,上海,201804)

摘要:基于一维平面波理论和微穿孔结构吸声理论,推导双层微穿孔管消声器传声损失理论模型,并将理论计算值与三维有限元声学仿真结果进行对比,利用消声器传声损失理论公式,对比双层和单层微穿孔管消声器的传声损失,分析内外层膨胀腔厚度对双层微穿孔管消声器声学特性的影响。研究结果表明:双层微穿孔管消声器在中低频的传声损失要大于单层微穿孔管消声器;增加内外层膨胀腔的厚度,可以提高双层微穿孔管消声器的消声特性;当双层膨胀腔总厚度固定,外层膨胀腔厚度大时,消声器在中低频的声学性能更好。

关键词:平面波理论;双层微穿孔管消声器;传声损失;膨胀腔厚度

中图分类号:TB535.2             文献标志码:A         文章编号:1672-7207(2015)02-0505-07

Transmission loss theoretical calculation and analysis of double-layer micro-perforated muffler

ZHANG Menghao, ZUO Shuguang, XIANG Longyang, HU Jiajie

(New Energy Vehicle Engineering Centre, Tongji University, Shanghai 201804, China)

Abstract: The transmission loss theoretical model of double-layer micro-perforated muffler was proposed based on one-dimensional plane wave theory and acoustic theory of micro-perforated panel. The calculated values were compared with the three-dimensional finite element model (FEM) acoustic simulation results. According to the transmission loss theoretical formulas of muffler, the transmission loss of double-layer micro-perforated muffler was contrasted with that of single-layer. The influence of inner and outer expansion cavities on the transmission loss of double-layer micro-perforated muffler was analyzed. The results show that the transmission loss of double-layer micro-perforated muffler is bigger than that of single-layer micro-perforated muffler in low and medium frequency. The acoustic characteristic of double-layer micro-perforated muffler is improved by increasing the thickness of both inner and outer expansion cavities. When the total thickness of inner and outer expansion cavities is fixed, the acoustic characteristic of muffler is good in low and medium frequency with a bigger thickness of outer expansion cavity.

Key words: plane wave theory; double-layer micro-perforated muffler; transmission loss; thickness of expansion cavity

微穿孔板吸声结构具有高声阻和低声抗的特点,因而具有良好的吸声效果。其吸声理论的正确性已得到学者们的验证,并被广泛采用[1-5]。微穿孔板具有清洁、无污染及不受材料限制的优点,近年来被制作成管结构,应用于消声器结构。由于双层微穿孔板结构的吸声效果要比单层微穿孔板结构的更好,学者们开始利用双层微穿孔管消声器进行消声,并取得良好的降噪效果[6]。目前,国内外均没有直接计算微穿孔管消声器声学特性的理论公式,只是通过微穿孔板结构的吸声理论来设计消声器[7-8]。而微穿孔板吸声系数并不能很好地说明微穿孔管消声器的声学特性。因此,有必要提出微穿孔管消声器声学特性的理论模型,进行消声器的结构设计。微穿孔管消声器与穿孔管消声器消声原理类似,只是结构的声阻抗不同。因此,微穿孔管消声器声学特性计算可以参考穿孔管消声器的计算方法,并结合微穿孔板声阻抗理论。对于穿孔管消声器声学特性的理论计算,Munjal等[9-12]已对此进行了推导和阐述,季振林[13-14]也对直通穿孔管消声器的声学特性进行了分析。而目前学者们针对的穿孔管消声器都是单层结构,双层穿孔管消声器声学特性的理论计算却未见相关文献。本文作者结合一维平面波理论和微穿孔板吸声理论,推导了双层微穿孔管消声器的声学特性理论公式,并进行消声器的三维有限元仿真。将理论计算与声学仿真结果进行对比,分析了双层微穿孔管消声器的声学性能,为双层微穿孔管消声器的设计提供了理论依据。

1  理论模型

图1所示为双层微穿孔管消声器的结构,由2层微穿孔管结构和膨胀腔组成。消声器膨胀腔部分长度为L,两端内插管长度分别为la和lb,内外层穿孔管和膨胀腔内径分别为d1,d2和d0;内外层微穿孔管穿孔率分别为Pa和Pb

图1  双层微穿孔管消声器结构示意图

Fig. 1  Schematic diagram of structure of double-layer micro-perforated muffler

声传递矩阵法的基础是一维平面波理论,因此假设平面波在微穿孔管消声器内传播,且整个过程是绝热的。

根据流体力学质量守恒和动量守恒定律,在内层微穿孔管内,有连续性方程和运动方程

          (1)

             (2)

同样在外层微穿孔管内,有

   (3)

            (4)

在膨胀腔内,有

       (5)

            (6)

其中:p1和u1分别为内层微穿孔管内声压和质点振速;p1a和u1a分别为外层微穿孔管内声压和质点振速;p2a和u2a为膨胀腔内声压和质点振速;v1为空气由内层微穿孔管流向外层微穿孔管的速度;v2为空气由外层微穿孔管流向膨胀腔的速度;ρ为声波传播过程中空气密度;ρ0为静态空气密度;t为时间。

由绝热过程,有

               (7)

其中:c0为声速。

双层微穿孔板的相对声阻抗率分别为

            (8)

,可得

        (9)

根据微穿孔板结构吸声理论,式(8)中微穿孔板相对声阻抗率z1和z2可通过下式求出[1]

               (10)

        (11)

   (12)

其中:z为声阻抗率;r和m分别为微穿孔板的声阻和声抗;d为穿孔直径;b为板厚;p为穿孔率;k为波数。

把式(7)与式(9)代入式(1)~(6),整理得

      (13)

式中:

由式(13)可得

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