Transmission Loss Characteristics of Dual Cavity Impedance Composite Mufflers for Non-Planar Wave Cavity Resonance

Abstract

In conventional gasoline automobiles, the engine powers the air conditioning system and engine noise can somewhat mask the noise and vibration of the air conditioning system. In pure electric vehicles, however, the absence of an engine makes the air conditioning system’s noise more noticeable, concentrated in a limited frequency range at constant speeds. As a result, aerodynamic noise from the air conditioning system is a primary noise source in electric vehicles. Pipeline silencers are the main method for reducing this noise. The current silencer design uses plane wave acoustic theory but when cavity modal resonance occurs, the transmission loss error is relatively high. This article addresses the issue of non-planar wave cavity resonance, studying the cavity modal of a muffler using the finite element method to reveal the transmission loss under cavity mode resonance. A dual cavity expansion structure of an impedance composite muffler is proposed, with sound-absorbing materials placed in the cavity to enhance acoustic performance. The analysis of the transmission loss characteristics of the impedance composite muffler provides a theoretical basis for noise control in pure electric vehicle air conditioning systems.

1. Introduction

The protection of the ecological environment has become crucial due to the worsening environmental pollution crisis [1,2,3]. Creating new energy vehicles is vital to combat climate change [4]. Pure electric vehicles, supported by advancements in battery technology and charging infrastructure, are rapidly gaining market acceptance [5,6]. Reducing vibration and noise levels in these vehicles is essential for addressing market concerns and enhancing driving comfort [7]. In conventional gasoline cars, the engine powers the air conditioning system [8], masking its noise and vibration [9]. In contrast, pure electric vehicles lack an engine to mask this noise [10], making the air conditioning system’s noise more noticeable [11], especially when idling. Reducing this noise is therefore necessary [12]. Numerous factors contribute to noise from electric vehicle air conditioning systems [13]. The primary sources are aerodynamic noise from the blower blades contacting the air [14], turbulence noise from unstable gas flow in intricate air ducts [15], and mechanical and electromagnetic noise from blowers and compressors [16]. The interaction of the stator and rotor causes vibrations that generate electromagnetic noise, while the dynamic imbalance of spinning components causes mechanical noise [17]. These noises can negatively impact interior environmental quality and driving comfort by allowing sound waves to travel through the air conditioning ducts [18]. The muffler is an effective means to suppress the propagation of pipeline sound and reduce the noise of the air conditioning pipeline system.

Li [19] covered rectangular pipes with materials designed to resemble thin sheet networks for sound absorption. The peak attenuation frequency of the muffler was found to be exactly related to the square root of the material’s Young’s modulus and the thin sheet’s width by modifying the geometric parameters and structural arrangement of the sound-absorbing materials. By examining the pore network model of porous ceramic walls in automobile exhaust channel filters, Yamamoto [20] investigated the connection between a material’s microstructure and noise reduction properties. A resistive muffler reduces noise well in the mid-to-high frequency range and when airflow resistance is minimal but it performs poorly in the low frequency region. Resistance silencers diminish noise by altering the acoustic impedance rather than by directly absorbing sound energy. In order to lessen the amount of sound energy that is released into space, a sudden change in the cross-section of an air duct or an adjacent resonant cavity is typically used to induce resonance of the elastic vibration system inside the resonant cavity or to cause reflection, interference, and other phenomena of a certain frequency sound wave transmitted by the air duct at the sudden change in cross-section. Piana [21] established a numerical calculation model for the transmission loss of a combined muffler based on experimental data and coupled four expansion chamber silencing units in series with resonance chamber silencing units. In the context of labyrinth acoustic resonators [22], Xiao [23] achieved wideband noise reduction characteristics spanning from 660 Hz to 1200 Hz by embedding four circular labyrinth resonant cavities around the airflow channel, employing a coiling approach. With the objective of constructing a maze-type acoustic metamaterial air duct muffler that could decrease noise by 10 dB in the frequency range of 230 Hz to 816 Hz, Qi [24] integrated a resonant cavity with a spatial maze microstructure. Based on a compact assembly slot-type Helmholtz silencer, Nguyen [25] built a double-layer subwavelength noise reduction structural unit that is capable of decreasing noise by over 30 dB in the working frequency region without affecting ventilation. Overall, a reasonable noise reduction result may be obtained in a certain frequency range by modifying the adversarial muffler’s structural characteristics; however, this method is not applicable to scenarios with an extended frequency range. For the purpose of achieving wideband sound absorption capability from 640 Hz to 1410 Hz while guaranteeing smooth ventilation ducts, Gao [26] implemented an inventive technique of inserting sound-absorbing materials into the inner wall of the expansion chamber muffler. The micro-perforated plate muffler combines the features of a resonant and resistive muffler. A broader noise reduction frequency range is produced by the tiny microporous structure’s improved sound resistance. Simultaneously, the absorption peak’s frequency is controlled by the cavity construction, which enhances the noise reduction effect. By altering the porosity of perforated materials, Panggabean [27] conducted a preliminary investigation on the noise reduction properties of perforated silencers in vehicle HVAC systems. Villau [28] established an ecologically friendly double-layer micro-perforated material muffler that may achieve stronger noise reduction characteristics under smaller-sized circumstances by combining the acoustic reflection expansion chamber with dissipative micro-perforated components. In the context of Helmholtz acoustic resonators [29], by creatively combining a Helmholtz silencer with a perforated plate construction, Zhang [30] was able to achieve excellent results in terms of the reduction in low-frequency sound noise. The three primary methods for managing noise are reducing noise sources, restricting noise spread, and enhancing receiver protection [31,32].

The aforementioned indicates that pipeline muffler research has advanced significantly. Nonetheless, the majority of current research discloses the noise reduction capabilities and sound propagation properties of mufflers by focusing on the plane wave theory-based transmission loss prediction model. The study effort has taken factors that impact noise reduction performance into consideration, such as the shape of the pipeline cross-section and the installation of sound-absorbing materials. In actuality, there is a cavity resonance mode in expansion-type mufflers because, when the frequency rises, the sound wave in the muffler pipeline is not a perfect plane wave. It is obvious that the plane wave-based transmission loss model of pipeline mufflers is unable to accurately represent the muffler performance. Consequently, the acoustic cavity mode of the expansion muffler will be analyzed using the finite element approach in this article in order to uncover the transmission loss underneath its acoustic cavity resonance. Using a sound pressure level diagram, investigate the acoustic properties of a short-cavity expansion muffler and suggest a dual-cavity composite pipeline muffler construction. Potential engineering uses for this research include noise control in air conditioning pipes. The article is organized as follows. The research is summarized in Section 4 and covers the following topics: Section 2 examines the transmission losses and acoustic resonance modes of pipeline mufflers and Section 3 examines the acoustic model, resonant modes, and the impact of sound-absorbing materials on the noise reduction performance of a dual cavity composite air duct muffler.

2. Acoustic Performance Evaluation Indicators for an Expandable Duct Silencing System

2.1. Acoustic Performance Evaluation Indicators of Noise Reduction Systems

The noise reduction objectives that the air conditioning duct noise reduction system must accomplish in different frequency bands are determined by the acoustic performance indicators. Indicators for assessing acoustic performance that are often employed are noise reduction, transmission loss, and insertion loss. Transmission loss can reflect the acoustic performance of silencers and this study mainly evaluates the acoustic performance of silencers from the perspective of transmission loss.

(1)

Transmission loss caused by cross-sectional mutation

In perfect circumstances, sound waves will travel an unending distance without interference when they travel through a steady unchanging medium. However, sound transmission will be impeded when the propagation medium shifts or the air duct’s cross-section abruptly changes. A portion of the incident sound wave is transmitted, which keeps on traveling through the air duct, while the remaining portion is reflected back, establishing a reflected sound wave, as shown in Figure 1.

The calculation formula for the acoustic impedance $Z$ of the air duct is

$$Z=S\rho u$$

(1)

The formula involves $S$, representing the air duct’s cross-sectional area, its unit is m²; $\rho$, denoting the medium’s density, its unit is kg/m³, and $u$, representing the sound waves’ velocity, its unit is m/s. The sound pressure $p_{tr}$ of the transmitted sound wave is equal to the total of the incident wave sound pressure $p_{in}$ and the reflected wave sound pressure $p_{re}$ at the point where the cross-section of the air duct changes because the pressure is equal on both sides of the cross-section.

$$p_{in}+p_{re}=p_{tr}$$

(2)

Furthermore, the volumetric velocity at every location in the air duct is equal when sound waves flow through it. Consequentially, the volume velocities of the two sound waves on the left add up to the volume velocities on the right side of the cross-section.

$$S_1{\displaystyle \frac{p_{in}}{z_1}}-S_1{\displaystyle \frac{p_{re}}{z_1}}=S_2{\displaystyle \frac{p_{tr}}{z_2}}$$

(3)

The acoustic impedances of the two mediums are represented in the formula as $z_1={\rho }_1{u}_1$ and $z_2={\rho }_2{u}_2$. Equation (2) may be combined to modify the previous equation to

$${\displaystyle \frac{z_1\left(p_{in}+p_{re}\right)}{S_1\left(p_{in}-p_{re}\right)}}={\displaystyle \frac{z_2}{S_2}}$$

(4)

The ratio of the sound pressure amplitude $p_{re}$ of the incoming wave to the amplitude $p_{in}$ of the reflected wave is known as the reflection coefficient $R$. When we replace it in the previous equation, we receive the following benefits:

$$R={\displaystyle \frac{p_{re}}{p_{in}}}={\displaystyle \frac{S_1{z}_2-S_2{z}_1}{S_1{z}_2+S_2{z}_1}}$$

(5)

The ratio of the incoming wave’s sound pressure amplitude $p_{in}$ to the transmitted wave’s amplitude $p_{tr}$ is known as the transmission coefficient (T). It may be produced by inserting it into Equations (2) and (4) as follows:

$$T={\displaystyle \frac{p_{tr}}{p_{in}}}={\displaystyle \frac{2S_1{z}_2}{S_1{z}_2+S_2{z}_1}}$$

(6)

The ratio of the incident sound power $W_{in}$ to the reflected sound power $W_{re}$ is commonly referred to as the sound power’s reflection coefficient, or $R_w$.

$$R_w={\displaystyle \frac{W_{re}}{W_{in}}}={\displaystyle \frac{S_1{p}_{re}{u}_{re}}{S_1{p}_{in}{u}_{in}}}=R^2$$

(7)

The ratio of the incident sound power $W_{in}$ to the transmitted sound power $W_{tr}$ is known as the sound power transfer coefficient, or $T_w$.

$$T_w={\displaystyle \frac{W_{tr}}{W_{in}}}={\displaystyle \frac{S_2{p}_{tr}{u}_{tr}}{S_1{p}_{in}{u}_{in}}}={\displaystyle \frac{S_2{z}_1}{S_1{z}_2}}{T}^2$$

(8)

$R_w+T_w=1$ Respect the principle of energy conservation. The transmission loss may be computed using the following formula in the absence of a reflected sound wave at the muffler’s outlet:

$$TL=L_{W_{in}}-L_{W_{tr}}=10\lg \left|{\displaystyle \frac{W_{in}}{W_{tr}}}\right|$$

(9)

The incident sound power level and incident sound power at the air duct muffler’s inlet are represented by the formula’s $L_{W_{in}}$ and $W_{in}$ their units are dB and W, respectively, while the transmitted sound power level and transmitted sound power at the air duct muffler’s outlet are represented by $L_{W_{tr}}$ and $W_{tr}$, respectively. Equation (8) may be substituted to determine that

$$TL=10\lg \left|{\displaystyle \frac{1}{T_w}}\right|$$

(10)

It is undisputed that the air duct silencing system’s transmission loss is independent of the noise source and only depends on the muffler’s structural characteristics.

In general, insertion loss is favored as the silencing system’s acoustic performance assessment index when assessing its acoustic performance. Although the insertion loss measuring technique is rather straightforward, it presents some challenges for simulation prediction since it necessitates a thorough analysis of the impacts of the sound radiation impedance at the outlet, air duct attenuation impedance, and sound source impedance. Studying the muffler’s noise reduction effect can provide an approximation of the acoustic performance of the duct muffler system, as the transmission loss is mostly connected to the muffler’s structural features. The insertion loss is equal to the transmission loss when the noise source and the air duct silencing system’s output are both non-reflective sound waves. The transmission loss and noise reduction level of the air duct muffler are equivalent when the acoustic impedance of the inlet and outlet ends are the same.

(2)

Transmission loss of expansion muffler based on plane waves

An example of a resistance muffler is an expansion chamber air duct muffler, which has a primary chamber and air ducts attached to both sides of it. Its effortless processing and straightforward structure are among its qualities. The expansion chamber’s $S_2$ cross-sectional area is greater than the air duct muffler’s $S_1$ and $S_3$ intake and outlet ends combined. With the help of this function, the expansion chamber duct muffler reduces noise by reflecting and interfering with sound waves by expanding and contracting the duct section, as shown in Figure 2.

The expansion chamber duct muffler’s one-dimensional transmission loss (TL) may be computed using the following formula:

$$TL=10\lg \left[1+{\displaystyle \frac{1}{4}}{\left({\displaystyle \frac{1}{m}}-m\right)}^2{\sin }^2\left(kL\right)\right]$$

(11)

The expansion ratio is given by the formula $m=S_2/S_1$, while the wave number, which is based on the sound wave’s frequency, is determined by $k=2\pi /\lambda$. Figure 3 depicts the transmission loss curve with frequency variation when the expansion chamber duct muffler’s length $L$ is 20 cm.

From the graph, it is clear that the expansion chamber duct muffler’s transmission loss curve exhibits periodic variations. As frequency increases, the transmission loss also exhibits periodic oscillations between 0 and the maximum value. Furthermore, the amplitude of transmission loss is proportional to the expansion ratio $m$ while the expansion chamber’s length remains constant. The expansion chamber muffler’s noise reduction increases with increasing $m$. Reducing the cross-sectional size of the air duct $S_1$ or raising the cross-sectional area of the expansion chamber $S_2$ are two ways to raise the expansion ratio $m$. As demonstrated by Figure 4, the frequency corresponding to the amplitude of the transmission loss will fluctuate while the expansion ratio m is constant. The amplitude of the transmission loss stays constant.

2.2. Transmission Loss of Expansion Mufflers Based on the Acoustic Finite Element Method

The COMSOL Multiphysics 6.2 software’s acoustic module can evaluate the acoustic performance of expansion chamber duct silencers in as realistic a scenario as possible by utilizing the Acoustic Finite Element Method (AFEM) to model and simulate acoustic problems. It can also visualize the distribution of sound fields and multiple physical fields. Using an estimated sound pressure function, the AFEM approach first discretizes the muffler’s acoustic model into a finite number of non-overlapping linked tiny pieces. Approximate solutions for all elements make up the solution in the whole computational domain, given suitable boundary conditions. Establishing a geometric model of the air duct muffler, defining material parameters, adding boundary conditions, creating grids, setting solver settings, and post-processing the results are all steps in the simulation calculation process that COMSOL Multiphysics uses to finish the air duct muffler. The material used is a porous elastic material with a flow resistance of 1500 Pa·s/m³.

Table 1. Structural parameters of expansion chamber air duct mufflers.

Structural Parameters	Value
Cross-sectional area of air duct cavity	$286 {\mathrm{cm}}^2$
Dilated chamber cross-sectional area	$656 {\mathrm{cm}}^2$
Expansion ratio $m$	2.29
Chamber length $L$	$25 \mathrm{cm}$

displays the structural characteristics of the expansion room air conditioning duct muffler.

As shown in Figure 5a, create a three-dimensional model of the expansion chamber duct muffler. The incident sound wave at the inlet and the transmitted sound wave at the outlet are approximately defined as plane wave radiation, with the direction of the sound wave being perpendicular to the cross-section of the air duct.

As illustrated in Figure 5b, remove the hollow portion of the air duct, designate its substance as air, and divide the grid. Determining the right element types and grid sizes throughout the grid partitioning process is essential to increasing the efficiency of the solution. In general, simulation findings are more accurate the finer the network quality but this comes at a higher computing cost. As a result, a free tetrahedral mesh was selected as the mesh element type and an empirical formula was used to determine the mesh element’s maximum value, or $M_{max}$. The number of Degrees of Freedom (DoFs) of the finite element model are 24,824 and the number of elements is 40,708.

$$M_{max}={\displaystyle \frac{c}{5f_{max}}}$$

(12)

In the formula, $c$ is the speed of sound, its unit is m/s, and $f_{max}$ is the maximum solution frequency, its unit is Hz.

Designate the surfaces as hard sound field boundaries, except the entrance and outflow. In line with reality, the rigid sound field border prevents sound waves from transmitting or absorbing any sound energy. The expansion chamber duct muffler’s inlet and outlet ends have the same acoustic impedance in an ideal gas environment. Thus, the noise reduction amount may be used to compute the expansion chamber duct muffler’s transmission loss. The one-dimensional theoretical calculation data and the acoustic finite element simulation values for the expansion chamber duct muffler’s transmission loss in the frequency range of 0 Hz to 1500 Hz are displayed in Figure 6.

Figure 7 illustrates how the theoretical calculation value of the expansion chamber duct muffler’s transmission loss is extremely compatible with the findings of the simulation calculations in the frequency range of 0–975 Hz. The variation between the theoretical calculation values and the simulation calculation findings, however, steadily rises within the frequency range of 975–1500 Hz, with a notable peak occurring between 1200 and 1350 Hz. The acoustic performance of the expansion chamber duct muffler is further analyzed by taking into consideration the sound pressure level amplitude cloud map.

The sound pressure level of the expansion chamber duct muffler exhibits a strip-like distribution in the mid-to-low frequency range of 0–975 Hz, as demonstrated by cloud Figure 7, with regard to the sound pressure level amplitude. This suggests that sound travels in the form of plane waves. The sound pressure level distribution of the expansion chamber duct muffler grows to be more complex in the mid-to-high frequency range of 975–1500 Hz, corresponding to the one-dimensional transmission loss calculation of the expansion chamber muffler, which is momentarily consistent with the acoustic finite element simulation calculation. Sound pressure levels display a distinct rapid distribution at 1350 Hz, suggesting non-planar wave propagation. The acoustic properties of the expansion chamber muffler can no longer be reliably predicted using the one-dimensional transmission loss calculation strategy. However, it can be predicted that the acoustic characteristics of the expansion chamber muffler are related to the expansion ratio and the length of the expansion chamber.

2.3. Experimental Verification of Transmission Loss of Mufflers

Experiments on the expansion chamber duct muffler’s noise reduction performance were carried out in order to confirm the correctness of the simulation results. In Figure 8, the experimental concept is displayed. First, to reduce the impact of background noise, the noise frequency range is adjusted using computer software and signal-to-noise ratio testing is carried out. The speaker is then controlled to produce noise signals upstream of the impedance tube by adjusting the amplitude of the noise signal by employing a power amplifier. Ultimately, the transmission loss test results were computed by gathering the incident and reflected sound wave signals at the front and back ends of the expansion chamber duct muffler using four pre-calibrated microphones.

In this test, the air duct cavity section was set to a square of $5 \mathrm{cm} \times 5 \mathrm{cm}$, the expansion chamber cavity section was set to a square of $11.2 \mathrm{cm} \times 11.2 \mathrm{cm}$, the expansion ratio $m$ was 4.8, and the cavity length $L$ was $2 \mathrm{cm}$ in order to better adapt the expansion chamber muffler to the square impedance tube. The testing apparatus is depicted in Figure 9.

The test findings are displayed in Figure 10, where it is evident that the results of the acoustic finite element simulation computation are compatible with the trend of the transmission loss test value of the expansion chamber duct muffler with frequency variation. The transmission loss test’s peak value is lower than the simulation’s result and its peak frequency moves toward lower frequencies as a result. This is the consequence of the test sample being constructed from iron sheets and cardboard that have been joined. The expansion chamber’s radial mode is not well aroused due to manufacturing flaws and the construction itself and the modal frequency also exhibits some degree of fluctuation. The test findings’ noise reduction features, on the other hand, deviate considerably from the one-dimensional transmission loss calculation model and are generally in line with the simulation results. This shows that the one-dimensional transmission loss calculation model is only appropriate in cases with longer cavity lengths and verifies the viability of the acoustic finite element simulation analysis approach.

This suggests that the acoustic finite element model of the air conditioning duct muffler may be more accurately computed and fitted to the real world using the COMSOL Multiphysics acoustic module. Furthermore, studies have shown that the expansion chamber air duct muffler has a good noise reduction effect. Additionally, while maintaining the expansion chamber’s cross-sectional area, a smaller chamber length L can enhance the noise reduction performance of the expansion chamber noise reduction unit.

3. Acoustic Analysis of Dual Cavity Composite Duct Mufflers

3.1. Acoustic Finite Element Model of Dual Cavity Composite Duct Mufflers

As illustrated in Figure 11, the dual chamber composite air duct muffler is composed of two expansion chamber silencing devices. One of the expansion chamber sound-absorbing units, which has a cavity length of $L_1$ of $5 \mathrm{cm}$ and a cross-sectional area of $S_1$, is vacant. The other expansion chamber has a cavity length of $L_2$ of 10 cm, a cross-sectional area of $S_2$, and is filled with porous material that absorbs sound.

The cross-sectional area of the duct $S_0$ stays constant at 286 ${\mathrm{cm}}^2$, the dual chamber composite muffler’s total length L stays constant at 25 $\mathrm{cm}$, the cross-sectional area of the two expansion chambers $S_1=S_2=656{ \mathrm{cm}}^2$, and the expansion ratio $m_1=m_2=2.29$. These values are used to compare the acoustic performance of the expansion chamber duct muffler. The acoustic properties of the expansion chamber air duct muffler may be efficiently enhanced by packing the chamber with porous materials that absorb sound waves. Sound waves may be absorbed by porous materials that transform them into thermal energy [33,34]. This lowers noise levels by minimizing sound waves’ reflection and propagation. The goal of choosing $L_1<L_2$ is to obtain greater attenuation peaks by making use of a short cavity expansion chamber’s non-planar wave attenuation properties. The transmission loss results of an acoustic finite element simulation for a dual cavity composite duct muffler operating in the frequency range of 0 Hz to 1500 Hz are displayed in Figure 12.

The dual chamber composite air duct muffler has a more notable noise reduction impact than the expansion chamber muffler under the same expansion ratio ($m$), as can be seen in the picture. At least a 5 dB increase in transmission loss occurs in the frequency range of 650 Hz to 1250 Hz. Its noise reduction impact may be enhanced by at least 10 dB, particularly in the frequency range of 850 Hz to 1000 Hz and 1125 Hz to 1200 Hz. Furthermore, a peak in noise reduction was noted at around 1175 Hz. Further investigation into the dual chamber composite duct muffler’s acoustic performance will be carried out, taking into consideration the sound pressure level cloud map:

The expansion chamber sound-absorbing device, in the absence of any additional materials, has good resistance qualities based on the sound pressure level cloud map in Figure 13. The expansion chamber has a rather high and focused sound pressure level in the frequency range of 650 Hz to 1175 Hz, which suggests that there are a lot of reflected sound waves occurring at these frequencies. The distribution of sound pressure levels becomes more complicated as the frequency increases. Non-planar waves began to form around 1125 Hz and at 1175 Hz a distinct longitudinal distribution and the phenomenon of sound pressure backflow were seen. Furthermore, the sound-absorbing equipment with an expansion chamber and other sound-absorbing materials has strong resistance features. The sound pressure level close to the sound-absorbing material is comparatively low, with a good sound absorption effect in the 850 Hz to 1500 Hz range, as can be seen from the sound pressure level cloud map. The distribution of sound pressure levels throughout the whole muffler is quite consistent, as can be seen from the sound pressure level cloud map at 1375 Hz, and the twin chamber muffler’s sound reduction effect exhibits a local valley around this frequency. In terms of noise reduction, the twin-chamber composite air duct muffler possesses resistance and structural features. Within the broad frequency range of 650 Hz to 1500 Hz, it has a good noise reduction impact but as frequency increases, so does transmission loss.

3.2. Impact of Sound-Absorbing Materials on the Acoustic Performance of Dual Chamber Silencers

The expansion chamber duct muffler may efficiently absorb the energy of incident sound waves by adding porous materials that absorb sound. Furthermore, porous structures aid in distributing the direction of sound wave propagation, preventing sound waves from reflecting and concentrating. This can greatly lower the efficiency with which sound waves propagate across space, which in turn lowers the noise level, particularly in a particular frequency band where the effect of noise reduction is most pronounced. Using the COMSOL Multiphysics platform, acoustic finite element models of the dual chamber muffler and the dual chamber sound-absorbing muffler are built based on the model of the dual chamber composite air duct muffler, depicted in Figure 14.

Two expansion chamber sound-absorbing units make up the dual chamber sound-absorbing muffler (Figure 14a); however, both expansion chambers are packed with porous sound-absorbing materials. Figure 14b depicts the dual chamber silencer; neither of the two expansion chamber silencing devices has any material inside of it. The structural characteristics of the two expansion cavity silencing units are kept constant in order to compare the acoustic performance with the dual cavity composite muffler. The transmission loss calculations for dual chamber sound absorption silencers and dual chamber silencers in the frequency range of 0 to 1500 Hz are displayed in the accompanying Figure 15.

Figure 15 illustrates how dual-chamber silencers and dual-chamber composite silencers have comparable noise reduction properties in the broad frequency range of 450 Hz to 1100 Hz. This suggests that the resistance muffler’s capability to reflect sound waves is primarily responsible for reducing noise levels within this frequency range. Nevertheless, there was a noticeable variation in the twin chamber muffler’s noise reduction effectiveness beginning at 1125 Hz. Lower noise reduction troughs were seen in the frequency range of 1300 Hz to 1400 Hz, whereas two noise reduction peaks were seen at 1150 Hz and 1200 Hz. Examine the twin chamber muffler in more detail by taking into account the peak and valley noise reduction sound pressure level cloud map.

The sound pressure level distribution of the dual chamber muffler is similar to that of the dual chamber composite muffler at 650 Hz, which indicates that the first expansion chamber silencing unit is primarily responsible for controlling the noise in this frequency band. This can be observed by comparing the sound pressure level cloud map of the dual chamber composite muffler in Figure 13. On the other hand, the sound pressure level cloud maps of the two chambers before and following the dual-chamber muffler exhibit a longitudinal strip distribution beginning at 1100 Hz. The second expansion chamber noise reduction unit’s excited radial mode exhibits superior noise reduction features, whereas the first expansion chamber’s noise reduction impact is diminished. There are two noise reduction peaks at 1150 Hz and 1200 Hz. The sound pressure level distribution is quite consistent at 1300 Hz, making the twin chamber muffler’s sound reduction effect less noticeable. In conclusion, the acoustic performance of dual-chamber silencers exhibits notable changes when compared to dual-chamber composite silencers. Specifically, there are lower noise reduction troughs and narrower noise reduction frequency bands collectively, with a broader frequency distribution of noise reduction amplitude.

Dual-cavity composite mufflers and dual-cavity sound absorption mufflers are compared using the same analytical technique, as shown in Figure 13 and Figure 16. The comparison research results shown in Figure 15 make it clear that the twin-cavity sound-absorbing muffler has superior resistance and noise reduction capabilities. It has a more persistent sound absorption effect in the broad frequency range of 725 Hz to 1500 Hz. To assess the dual cavity sound-absorbing muffler’s effectiveness even more, sound pressure level cloud maps at frequencies of 525 Hz, 725 Hz, 1050 Hz, and 1200 Hz were selected for examination.

Figure 17 illustrates how the sound wave is attenuated to different degrees after going through two expansion chamber absorption units. There is a blocky distribution of low sound pressure levels, particularly around 1000 Hz, which is more important, especially near porous sound-absorbing materials. The first expansion chamber absorption unit’s ability to reduce noise starts to diminish around 1275 Hz, while the second expansion chamber absorption unit’s ability to do so is noticeably more effective. All things considered, twin-cavity sound absorption silencers offer more consistent sound reduction properties than dual-cavity composite silencers. However, the maximum transmission loss of the local frequency band noise reduction peak can only reach 15 dB due to the absence of resistance noise reduction units.

3.3. The Influence of Parameters on the Acoustic Performance of Dual Cavity Composite Silencers

Dual chamber composite duct mufflers provide more steady broadband noise reduction properties as compared to dual chamber mufflers and dual chamber sound absorption mufflers. Based on the dual chamber composite air duct muffler model in Figure 11, examine the effects of the expansion ratio $m_1$ and the length of the expansion chamber $L_1$ of the first expansion chamber silencing unit on the dual chamber composite air duct muffler in order to determine the relationship between structural parameters and acoustic characteristics of the muffler.

The expansion ratio $m_1$ should not be chosen too greatly because of the coordination between the air conditioning duct and other parts. The expansion ratios of 1.62, 1.94, and 2.29 were obtained by increasing the thickness by 4 cm, 6 cm, and 8 cm based on the initial air duct size. It is evident from the data displayed in Figure 18a that the expansion ratio significantly affects the muffler’s acoustic performance. The peak frequency range of the dual cavity composite muffler changes toward lower frequencies as the expansion ratio $m_1$ develops and the peak noise reduction in the muffler increases in addition. This is because the expansion chamber’s radial mode is activated, beginning at around 1000 Hz. The frequency corresponding to the radial mode is also lower when the length of the expansion chamber $L_1$ is constant because the bigger the expansion ratio $m_1$, the smaller the ratio between the length of the expansion chamber $L_1$ and the cross-sectional diameter $D_1$.

The acoustic properties of a dual chamber muffler with chamber lengths of 2.5 cm, 5 cm, and 7.5 cm and the first expansion chamber silencing unit are displayed in Figure 18b. The figure illustrates how the length of the cavity affects the peak frequency band of the dual cavity composite air duct muffler; however, it has very little effect on the noise reduction amplitude.

The expansion ratio $m_2$ and the chamber length $L_2$ were modified and the transmission loss was computed, taking into consideration the impact of the structural characteristics of the second expansion chamber absorption unit on the acoustic performance of the muffler. Figure 18c,d displays the outcomes. The figure illustrates how the sound reduction amplitude of the dual chamber composite muffler is somewhat influenced by the expansion ratio of the sound-absorbing expansion chamber sound-absorbing unit $m_2$. The cavity is filled with more sound-absorbing material as the expansion ratio rises, which enhances the sound absorption effect in the mid-to-high frequency range. Conversely, the dual cavity composite muffler’s noise reduction amplitude is mostly unaffected by the cavity length $L_2$ but is affected in a specific frequency region.

Finally, an investigation is conducted into how the muffler’s acoustic performance is affected by the distance $L_0$ between its two expansion chamber silencing components. The dual chamber composite duct muffler’s transmission loss is computed by considering $L_0$ to be 5 cm, 10 cm, and 15 cm, according to Figure 18e. The diagram’s results indicate that the peak noise reduction in the muffler is somewhat influenced by the distance $L_0$ between the two expansion cavity silencing units. The peak noise reduction rises with an increase in $L_0$.

To sum up, the total noise reduction performance of a dual chamber composite air duct muffler is influenced to variable degrees by its characteristics. The length of the cavities $L_1$ and $L_2$ has some influence on the peak frequency; the spacing between the two chambers $L_0$ and the expansion ratio $m_2$ of the second section of the noise reduction unit also have some influence on the peak noise reduction. In particular, the expansion ratio $m_1$ of the first expansion chamber silencing unit has a significant impact on the peak and peak frequency of silencing.

4. Conclusions

The acoustic properties of duct silencers under ideal gas circumstances were examined in this work. A thorough study of the air conditioning duct silence system’s design needs was conducted based on the noise characteristics of the vehicle air conditioning system. It is essential to first fulfill the acoustic performance assessment indicators of air duct silencers before developing them. Using the COMSOL Multiphysics software, an acoustic finite element model of the expansion chamber duct muffler was created based on this information. Research has contributed to the following conclusions:

(1) An expansion cavity’s cross-sectional area may be maintained while achieving improved noise reduction performance with a shorter cavity length.

(2) A dual chamber composite air duct muffler structure was proposed, which has both resistive and reactive noise reduction characteristics and exhibits a superior noise reduction effect than expansion chamber silencers. The structural parameters of the double-cavity composite duct muffler exert varying degrees of influence on its overall muffling performance. In particular, the expansion ratio of the initial muffling unit exerts a more pronounced influence on the peak muffling value and peak frequency. The cavity lengths exert a certain influence on the peak frequency, while the spacing between the two cavities and the expansion ratio of the second muffling unit also exert a certain degree of influence on the peak muffling value.

(3) Dual-chamber sound-absorbing silencers feature more consistent noise reduction characteristics than dual-chamber composite silencers.

This article does not yet assess the whole performance of air conditioning duct silencing systems in conjunction with their flow field characteristics; instead, it mainly concentrates on the acoustic features of these systems under ideal gas circumstances. As a result, by integrating the properties of their flow fields, further study on the acoustic performance of silencing devices may be undertaken.