Analysis for effect of pores on acoustic performance of reactive muffler

Abstract

The major source of noise pollution was an internal combustion engine. Henceforth, the design of the engine exhaust system was a tough challenge for automotive industries. The mufflers have been used to moderate the exhaust noise from the engine to the neighboring atmosphere. So in domestic as well as the industrial application, it is required to reduce noise levels to prevent human hazards. The performance of muffler is measured in terms of transmission loss. The transmission loss of reactive muffler is depending on its geometry. This article describes the effects of pores at the inlet pipe and outlet pipe of the reactive muffler on its performance capacity at a target frequency. It is found that the muffler performance is dependent on the number and position of pores. The single chamber and double chamber reactive mufflers are used for the study. The numerical analysis is performed by COMSOL Multiphysics software. The numerical analysis result of the different models of the muffler is compared with experimental analysis. The purpose of the study is to investigate the effect of pores in inlet and outlet pipe to maximize the TL at the target frequency of reactive muffler.

Keywords

Reactive muffler noise transmission loss pores target frequency impedance tube

Introduction

The muffler is an integral part of the engine exhaust system to attenuate the noise intensity which helps to decrease human hazards. It is required to moderate the noise level through any internal modifications or using any external devices which reduces noise level. The sound pressure level is measured in the decibels (dB). The sound pressure level should not exceed 140 dB to avoid permanent hearing loss. Transmission loss (TL) is known as the difference between the sound power or sound pressure level at the termination with and without a muffler. Various finite element method tools such as Ricardo wave and COMSOL Multiphysics are used to an investigation of an acoustic performance of the muffler. Generally, the muffler performance depends upon the number of baffle plates and the number of pores on inlet and outlet pipes. The principle of working of a muffler is either to absorb the sound waves emitted by the engine or canceling the waves of each other. There are two types of mufflers, namely, dissipative and reactive muffler and are extensively used. The numerical analysis method is used to assess the diverse muffler design alternates at lower frequencies.¹ Ahmed Elsayed et al.² are studied the influence of baffle size on muffler TL and backpressure. They found that the TL is enhanced by more than 40% by decreasing the baffle spacing. They also observed that due to the increase in the number of holes in baffles, the backpressure is decreased.

Hakan Arslan et al.³ have measured the performance of gun mufflers. They found that the rise in the number of baffles with an appropriate position of the baffle, the sound TL is also increased. Chinna Rao et al.⁴ have demonstrated an applied methodology to design, develop, and corroborate reactive muffler for the exhaust system, which helped to reduce the product development cycle time and validation time. Xiang et al.⁵ proposed a multi-chamber micro-perforated muffler with adaptable TL to reduce the blower noise.

They found that the proposed muffler is effective to reduce the both wide band noise and narrow band noise. Chao et al.⁶ have explained the application of parametric optimization techniques for acoustic performance analysis of the reactive mufflers. They found that by using the optimization technique, the Nelder Mead algorithm can minimize the pressure drop and maximize the TL with the given weight factor.

In recent years, extensive design and development of mufflers were done. Mostafa et al.^7–9 focused on the experimental investigation to obtain TL with different cross-section areas of a muffler. The material of the muffler does not affect more on the sound attenuation. But the selection of muffler material is important as it is related to heat dissipation. So materials are reviewed for better performance.^10,11

The transfer matrix approach and boundary element method are used for muffler performance analysis. The TL versus frequencies graphs are represented with the help of MATLAB software.^12–14 Zhang et al.¹⁵ developed a split stream rushing muffler to understand the effect of airflow resistivity on the performance of muffler. They found that split-stream rushing muffler can successfully decrease the exhaust airflow velocity through the muffler and exhaust backpressure.

This study focused to investigate the acoustic performance of different models of the reactive muffler with pores in inlet and outlet pipes using COMSOL Multiphysics software.

Reactive muffler

Reactive muffler generally uses the principle of cancelation of sound waves to reduce the engine noise. It consists of the baffle plates with inlet and outlet pipes. Sound waves are circulated through the expansion chamber as shown in Figure 1. To obtain multiple chambers, the baffle plate is used for partition of muffler.

Figure 1.

Reactive muffler.

Design of reactive muffler

The muffler design is based on the engine output. From engine output, the target frequency of noise reduction is calculated. This target frequency is the basis of the design of mufflers. The reactive muffler is categorized by controlling lower frequencies, that is, below 1000 Hz. The reactive muffler under study is designed for the internal combustion engine having four cylinders of volume of 200 cc and speed of rotation is 6000 rpm. The fundamental target frequency of the pulsating noise can be obtained by the following equation

f = \frac{(N \cdot S)}{120} Hz \dots

(1)

Where N is number of cylinders and S is engine speed. For the given engine, the target frequencies obtained are 200 Hz and 600 Hz. From the target frequency, dimensions of the required muffler are calculated. Due to space limitations, the one design that gives more TL with less volume will be the best design for the muffler.^5–7 For the analysis purpose single chamber and double chamber, reactive mufflers with pores and without pores are considered. Figure 2 shows double chamber muffler with pores. The basic dimension of muffler under study is as given in Table 1.

Figure 2.

Double chamber muffler with pores.

Table 1.

Dimensions of the muffler.

Entity	Dimension (mm)
Diameter of shell	150
Length of shell	250
Thickness of shell	2
Inlet pipe diameter	50
Outlet pipe diameter	50
Diameter of pore	4

Cad modeling

The present study considers six different types of models of reactive muffler by applying topology optimization concept.¹⁶ Various models with different configurations are drawn in CATIA software. Different muffler models with a single chamber and the double chamber for the same expansion volume are shown in Table 2. Up till now, the effect of pores on backpressure is studied extensively. The effect of pores on TL for mufflers with a single expansion chamber is also explored. But the effect of pores on TL for muffler with double expansion chamber is not much explored. The research under study majorly focuses on the effect of pore on TL for mufflers with a double expansion chamber.

Table 2.

Muffler model geometry.

Model	Name of model	Model	Name of model
Model 1	Single chamber	Model 4	Double chamber
Model 2	Single chamber with pores	Model 5	Double chamber with pores
Model 3	Single chamber with optimize pores	Model 6	Double chamber with optimize pores

Optimization

In this optimal design study, initially nine different models of single expansion chamber muffler are considered for Taguchi analysis. Taguchi analysis is used for design optimization. The three factors and three levels used for single expansion chamber are shown in Table 3. At pore diameter 4 mm, the TL is found maximum. Hence, 4 mm is the chosen middle level for Taguchi analysis. Similarly, 12.68% and 240 mm are the middle levels of porosity and perforated pipe length for Taguchi optimization.

Table 3.

Factors and levels.^1–20

Factors	Level 1	Level 2	Level 3
Diameter(mm)	3	4	5
Porosity (%)	8.19	12.68	16.89
Perforated pipe length(mm)	230	240	250

By using design optimization three factors with three levels, L9 orthogonal array are prepared. The objective is to get maximum TL.

From the Taguchi analysis of single expansion chamber, the S/N graph optimum level obtained for diameter, porosity, and perforated pipe length are 4 mm, 16.89%, and 250 mm, respectively. Similarly from the Taguchi analysis of double expansion chamber, the S/N graph optimum level obtained for diameter, porosity, and perforated pipe length are 4 mm, 11.26%, and 250 mm, respectively.

To investigate the effect of pores on TL, all these six models are analyzed by using the pores optimization concept.¹⁷ The perforated tubing properties for different reactive muffler model are as shown in Table 4.

Table 4.

Perforated tubing properties for different muffler.

Perforated model type	Hole diameter (mm)	Hole spacing along length(mm)	Hole spacing radial (mm)	Hole pattern	Tube thickness (mm)	Porosity (%)
Model 1	No pores	--	--	--	1	00
Model 2	4	10	19.625	Circular	1	12.28
Model 3	4	10	13.08	Circular	1	16.89
Model 4	No pores	--	--	--	1	00
Model 5	4	10	19.625	Circular	1	8.19
Model 6	4	10	13.08	Circular	1	11.26

By using Taguchi optimization technique, the best optimized model of single expansion chamber and double expansion chamber is obtained. These models are further used for numerical analysis. The performance analysis of the two optimized models is compared with two non-optimized model and two models with no pores. To avoid the repetitive work, only six models are used for numerical analysis. To observe the prominent effect of pores along with baffle plate, the mufflers with double expansion chamber mufflers are analyzed.

Numerical analysis

In this research, finite element approach is used to calculate TL of the muffler. The three-dimensional finite element analysis of the muffler is carried out in COMSOL Multiphysics software¹⁸ with no fluid structure interaction. Transmission loss is calculated directly in COMSOL using the acoustic power at the inlet and outlet of the muffler. COMSOL predicts result by taking the incident and transmitted sound power for surfaces at inlet and outlet, respectively. The frequency range considered for the investigation is 100–1000 Hz which includes the target frequencies. The speed of sound is taken as 343 m s⁻¹ and density of air is taken as 1.2 Kg·m⁻³.

Finite element analysis of the three-dimensional muffler is carried out in COMSOL Multiphysics. To perform numerical analysis in COMSOL, various steps are used. The initial pressure acoustic, frequency domain (acpr.) model environment is selected. Then import the geometry of the muffler from the CATIA software. Later on, global definition is used to set acoustic environment with pressure as a variable. Air as the material is selected in this case. Material properties such as air density and velocity are used. For the boundary condition, the complete area of a muffler is treated as a sound hard boundary except for the inlet and outlet surface. It will restrict the flow of gases into the model, and gases will flow by guiding the internal structure. Inlet and outlet are exempted to allow entry and exit of gas flow.

For meshing, tetrahedral elements are used. For the better result, the element size is taken as 10 elements per wavelength. By applying the preprocessing requisites, the 3D model is analyzed to determine the TL.

The 3D model is analyzed by the run simulation step using start and stop value for the interested frequency range. After the run simulation, by using post processing, the graph of TL versus frequency is drawn.

Results and discussion

The simulation of different reactive muffler models is carried out under the normal operating conditions in COMSOL Multiphysics software using the air properties. The single chamber and double chamber mufflers are used for analysis.

Single chamber

The acoustic performance analysis of Model 1, Model 2, and Model 3 is performed. The CAD model of a single chamber reactive muffler is as shown in Figure 3(a). The sound pressure distribution for all models of the muffler with a single chamber is obtained by COMSOL Multiphysics software and is shown in Figure 3(b) to (d).

Figure 3.

Finite element analysis analysis of single chamber mufflers.

Double chamber

The acoustic performance analysis of Model 4, Model 5, and Model 6 is performed. The CAD model of double chamber reactive muffler is as shown in Figure 4(a). The sound pressure distribution for all models of the muffler with a double chamber is obtained by COMSOL Multiphysics software and is shown in Figure 4(b) to (d).

Figure 4.

Finite element analysis analysis of double chamber mufflers.

The acoustic performance analysis of all models of the muffler with a single chamber and the double chamber is performed by using COMSOL Multiphysics software. The COMSOL Multiphysics software simulation result is expressed in terms of graph of TL versus frequencies. The simulation result of a single chamber muffler is as shown in Figure 5. To analyze the effect of pores on TL, the graph of TL versus frequency for Model 1, Model 2, and Model 3 is expressed in Excel format.

Figure 5.

Transmission loss versus frequency for Single chamber muffler.

The Figure 6 shows the COMSOL Multiphysics software simulation result of the double chamber muffler for Model 6

Figure 6.

Transmission loss versus frequency for Model 6.

The simulation result of double chamber muffler is as shown in Figure 7. To analyze the effect of pores on TL, the graph of TL versus frequency for Model 4, Model 5, and Model 6 is expressed in Excel format.

Figure 7.

Transmission loss versus frequency for Double chamber muffler.

Simulation is carried out to optimize the muffler design to increase the TL. From Figures 5 and 7, the TL (dB) of different models of the reactive muffler at target frequencies 200 Hz and 600 Hz is tabulated in Table 5.

Table 5.

Transmission loss (dB).

Muffler type	Muffler model	Transmission loss (dB)
Muffler type	Muffler model	Target frequency 200 Hz	Target frequency 600 Hz
Single chamber	Model 1	4	5.5
	Model 2	5	6.5
	Model 3	5.5	7
Double chamber	Model 4	7.5	10
	Model 5	8	12
	Model 6	10	13

From Table 5, it is observed that for the same volume of expansion, the TL increases due to pores as compared to muffler without pores. It is also observed that the TL is increased in double chamber muffler due to the addition of one baffle plate as compared to a single chamber muffler.

Experimental analysis

The TL of mufflers is measured by standard experimental setup. Figure 8 shows the setup for experimental analysis. It consists of a noise generation system, noise propagation system, and noise measurement system. The major components of setup are impedance tube, multichannel Fast Fourier Transfer Analyzer [BSWA-MC3242], 1/4” prepolarized free-field measurement microphones [BSWA MPA 416 ], power amplifier [PA50], and sound source[ AU-35].

Figure 8.

Experimental setup.

The experimental analysis is performed as per ISO 10534-2 standard¹⁹ to obtain the TL. The experimental analysis is performed using the two-load method. The two-load method is based on the transfer matrix approach. The TL of muffler can obtain by four-pole equations from the four positions of microphones using the transfer matrix method.

For experimental investigations, the impedance tube with 100 mm diameter is used. This impedance tube allows frequency range of 63 Hz–1800 Hz. The experiment is performed for frequency range of 100–1000 Hz.

Comparison of numerical and experimental analysis result

The BSWA VA-Lab 4 software is used for data analysis.²⁰ The VA-Lab 4 software directly gives the graph of TL versus frequency. Figure 9 shows the comparison of TL curve of muffler Model 6 obtained by numerical analysis and experimental analysis. The blue line curve shows the TL obtained by numerical analysis, while red line curve shows the TL obtained by experimental analysis. The TL by numerical analysis at 200 Hz is 10 dB and at 600 Hz is 13 dB, while the TL calculated using experimental analysis at 200 Hz is 11.9 dB and at 600 Hz is 15 dB. The percentage error calculated is 15% which shows that the experimental results obtained are in good agreement with the numerical analysis results.

Figure 9.

Comparison of numerical and experimental analysis of muffler Model 6.

Conclusion

A reactive muffler system has been analyzed numerically to study especially the effect of pores on TL. In the present work, six different models of the reactive muffler are analyzed by using COMSOL Multiphysics software. It is observed that due to pores, the TL of Model 2 and Model 3 is increased as compared to muffler Model 1. It is also observed that due to pores and one baffle plate, the TL of Model 5 and Model 6 is increased as compared to muffler Model 4. To maximize the TL, the porosity of muffler pipe plays an important role.

It is observed that as the porosity of the pipe increases, the TL increases. It is found that at frequency 600 Hz in single expansion chamber, TL is increased by 27.2% due to pores whereas in double expansion chamber, TL is increased by 30% due to pores and baffle plate. It is due the fact that as the porosity increases, the back pressure decreases. The decrease in back pressure causes the increase in TL. The pores in the pipe generate outlet flow with less turbulence intensity which reduces noise level. From Figure 7 the graph of TL versus frequency, the TL for muffler Model 6 is found maximum as compared to all other reactive muffler models. The minor deviation in numerical results from experimental results may be ascribed to poor surface finish quality of impedance tube and leakage of sound from the impedance tube. The TL at target frequencies of muffler Model 6 results obtained by numerical analysis is well corroborated with experimental analysis.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Pravin P Hujare

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