Numerical investigation for acoustic performance improvement of a forklift exhaust muffler with the influence of flow and temperature fields

Abstract

In order to improve the acoustic performance of an internal combustion forklift exhaust muffler, this paper considered the influence of air flow and temperature, based on the flow field analysis theory, the exhaust muffler’s fluid domain model at the highest engine speed was established, that is, the complex flow and temperature fields were numerically simulated with a computational fluid dynamics (CFD) model, and the acoustic calculation was carried out by the finite element mothod (FEM), obtaining the velocity and temperature cloud maps and transmission loss curve. In addition, according to the simulation results, the improvement strategy towards intake pipe structural parameters was proposed. Numerical simulations indicate that for the improved exhaust muffler, flow eddy regions are obviously decreased, temperature gradient distribution is uniform, the transmission loss in most frequency bands and the overall sound attenuation effect are improved, which will lay a technical foundation for future physical application and multi-field coupling research.

Keywords

Internal combustion forklift exhaust muffler flow and temperature fields structural improvement acoustic performance

Introduction

As a common industrial handling vehicle, with the continuous development of society, the radiation sound power level of the internal combustion forklift has been strictly controlled and decreased to meet the decibel limit requirement.¹ Related studies show that engine exhaust noise is one of the main noise sources in a forklift, and the most common way to reduce the exhaust noise is by installing a muffler in exhaust pipeline system, which can effectively attenuate or prevent sound transmission.^2,3 And thus designing exhaust muffler with fine acoustic performance is an important measure to reduce forklift radiated noise.

In the actual working conditions, when the high-velocity and high-temperature air flow discharged by the engine passes through the exhaust muffler, very complex flow and temperature fields are formed, which leads to the high cost of research using experimental methods, and analytical methods such as transfer matrix are difficult to solve the acoustic properties. Therefore, the numerical simulation of exhaust muffler characteristics based on finite element method (FEM) has become an indispensable research means.^4–6 In recent years, three-dimensional finite volume method has been widely applied, because it can overcome the imprecision defect of one-dimensional plane wave theory in the calculation of high frequency band, and can make up for the limited application range of two-dimensional finite element. The interaction between the flow fields inside exhaust muffler can be simulated to the greatest extent using the method of computational fluid dynamics (CFD). Relevant studies have proved that the application of CFD can well solve complex actual flow field problems.^7–11 For instance, Mann et al. adopted CFD to simulate the airflow noise generated in exhaust muffler and completed measurements in a semi-anechoic chamber, and the consistency between the simulation and the experimental results verified the feasibility by CFD in the optimization design of airflow noise.¹²

CFD analysis can give full consideration to muffler’s complexity structure, as well as the resulting turbulence and dissipation effects, and more accurately simulate the actual working conditions, which provides convenience for the numerical calculation in flow field and temperature field of exhaust muffler. However, for the simulation analysis of muffler acoustic performance under the highest speed condition, simplifying the flow field and temperature field in the muffler, or only considering the influence of the single factor of air flow and temperature, may produce large errors.⁵ This is due to the inside small hole structure and mutant pipe cross section easily produce complex and uneven flow fields, resulting in eddy current noise, and increasing internal temperature causes changes in airflow density and characteristic impedance with a result of affecting the acoustic propagation characteristics.⁶ Therefore, it is a new exploratory work to consider the influence of both high speed and high temperature flow field in the process of improving the acoustic performance of exhaust muffler.

At present, the combination of CFD simulation and acoustic calculation has gradually become a trend in the research on fluid dynamics and acoustics.^13–16 For example, Guo and Fan applied CFD and LMS Virtual. Lab Acoustics software to research the influence of gas flow and temperature on the acoustic performance of a car perforated muffler, and took the flow field calculation results as finite element boundary conditions to simulate muffler internal sound field and obtain transmission loss curve.⁶ On the basis of the above numerical simulation methods, aiming at the problem of excessive exhaust noise of an internal combustion forklift at the highest speed, in this paper, the CFD model of internal muffler flow field under the highest-speed working condition is established and simulated using Fluent software, and the transmission loss of muffler is calculated by LMS Virtual. According to the numerical calculation results, a new structural design scheme for the targeted exhaust muffler is explored and proposed to numerically improve its acoustic performance.

Internal structure and parameters

The internal structures of the targeted exhaust muffler studied in this paper are illustrated in Figure 1. Detailed components are as follows: ① intake pipe (its right end is closed); ② perforated pipe in the front of ①; ③ second chamber; ④ perforated pipe in the back of ①; ⑤ third chamber; ⑥ transition pipe; ⑦ perforated pipe in ⑥; ⑧ first chamber; ⑨ exhaust pipe. Obviously, the exhaust muffler has three chambers inside and is connected through the intake, transition and exhaust pipes, in which the second chamber forms two resonant silencing structures with intake front perforation and transition pipe perforation, respectively.

Figure 1.

Internal structures of the forklift exhaust muffler.

The working principle of the exhaust muffler is described below: engine exhaust gas enters from the left intake of ① and flows in two forms: one part of gas passes through the resonance chamber composed of ② and ③, and the other gas enters the large expansion chamber ⑤ through the pore structure ④ at the right end of ①; after complex and irregular movements, the gas in ⑤ goes through the right end of ⑥ and enters the resonant silencing chamber composed of ⑦ and ③, then flows from the left end of ⑥ into the small expansion chamber ⑧, and eventually exhales waste gas into the outside atmosphere from the right side of ⑨.

It can be seen that three typical structures are applied to the forklift exhaust muffler, which are: 1) small hole muffler structure, such as components of ②, ④ and ⑦; 2) expansion chamber muffler structure, for example, ⑤ and ⑧; 3) resonant silencing structure, such as ③ and ②, or ③ and ⑦. The main structural parameters related to the forklift exhaust muffler in this case are listed in Table 1.

Table 1.

Main structural parameters of the forklift exhaust muffler.

Internal structure	Parameter	Internal structure	Parameter
Small hole diameter	4.5 mm	Expansion chamber diameter	200 mm
Small hole spacing	8 mm	Exhaust pipe diameter	45 mm
Small hole number in ②	20	Expansion chamber length in ⑧	100 mm
Small hole number in ④	120	Resonant chamber length in ③	45 mm
Small hole number in ⑦	100	Expansion chamber length in ⑤	165 mm

Flow field simulation and results

As mentioned above, the exhaust muffler works in a high-velocity and high-temperature airflow environment, and the flow velocity and temperature factors of the internal airflow can influence muffler acoustic performance to some extent. The air flow in the exhaust muffler is actually a complex problem of fluid flow and heat exchange. And based on the following assumptions, the flow state of exhaust muffler can be regarded as turbulence with incompressibility, and it also follows physics laws such as mass conservation, momentum convergence and energy conservation. The following focus is on the control theory, finite element modeling and numerical calculation of airflow and heat exchange in the internal structure of exhaust muffler based on CFD.^4,5,17–19

Standard k-ε turbulence equation

In general, turbulence model is used to calculate and analyze the fluid with irregular motion, and what needs to be proposed is that the k-ε standard turbulence model has become the most widely applied numerical simulation method because the turbulent kinetic energy dissipation rate is more consistent with the actual fluid flow characteristics, in which the turbulent kinetic energy equation of k is expressed as follows

{ρ (u \nabla) k = \nabla [(μ + \frac{μ_{T}}{σ_{k}}) \nabla k] + P}_{k} - ρ ε

(1)

And the dissipation rate equation of ε or turbulent kinetic energy is described as

{ρ (u \nabla) ε = \nabla [(μ + \frac{μ_{T}}{σ_{ε}}) \nabla ε] + C}_{ε 1} \frac{ε}{k} P_{k} - C_{ε 2} ρ \frac{ε^{2}}{k}

(2)

Where

μ

is the dynamic viscosity, and turbulent dynamic viscosity is

μ_{T} = ρ C_{μ} \frac{k^{2}}{ε}, p_{k} = μ_{T} [\nabla u : (\nabla u + {(\nabla u)}^{T})]

;

σ_{k}

and

σ_{ε}

stand for the turbulent Prandtl numbers of k and ε, respectively, which represents relative values of heat diffusion and momentum in the fluid.

In general, the turbulence model parameters are taken as $C_{ε 1} = 1.44, C_{ε 2} = 1.92, C_{μ} = 0.09, σ_{k} = 1$ and $σ_{ε} = 1.3$ .

Basic governing equation for heat transfer

During the operation of exhaust muffler, there are two basic heat transfer forms generally involved: heat conduction and heat convection. Due to the action of air flow, the temperature distribution on the exhaust muffler surface is not uniform, and the heat conduction phenomenon often occurs. Theoretically, the heat flow at unit time through unit area can be expressed for heat conduction by the heat flow density q.

q = \frac{Q}{A} = - λ_{s} \frac{\partial T}{\partial x}

(3)

Where Q stands for transmission rate; A represents heat conductivity area;

λ_{s}

is the fixed thermal conductivity of solid materials;

\partial T / \partial x

is a temperature gradient and the minus sign indicates the opposite direction between heat transfer and temperature gradient.

Thermal convection often occurs in exhaust muffler, mainly between internal walls and gases, and it is forced convection heat exchange. The basic convective heat exchange law satisfies the Newtonian cooling formula, which is calculated as

Q = α A' Δ T = α A' T_{s} - T_{f} |

(4)

Where

Δ T

represents temperature difference; T_s and T_f are the temperatures of wall and fluid, respectively;

A^{'}

is the area of convective heat transfer;

α

is the convective heat transfer coefficient.

The calculation of heat Q in formula (4) mainly depends on the convection heat exchange coefficient. For the forced convection heat exchange between muffler inner wall and gas, the value is determined based on the fluid heat convection in a circular straight pipe, and its calculation formula is described below.

α_{f} = 0.023 \frac{λ_{f}}{d} {(\frac{μ d ρ}{μ})}^{0.8} {(\frac{μ c_{p}}{λ_{f}})}^{0.4}

(5)

Where parameter meanings are described as:

λ_{f}

stands for fluid thermal conductivity; d is the pipe radius through which the fluid passes; c_p represents fluid fixed pressure specific heat.

Flow field simulation and calculation results

The Fluent module in ANSYS software was applied to model and analyze flow velocity and temperature fields in the exhaust muffler fluid domain. After free meshing and refinement for the three-dimensional model of the fluid domain, the standard k-ε equation turbulence model was used to simulate air flow. In addition, SIMPLE is the solution algorithm; the working medium is regarded as in-compressible air.

According to tests in relevant reports,^4,5 the inlet temperature in the exhaust muffler at the highest speed is 503 K, and corresponding thermal and physical properties of dry air are shown in Table 2.

Table 2.

Air physical properties at 503K.

T/K	$ρ$ /kg·m⁻³	$μ$ /N·s·m⁻²	c_p/KJ·(kg·⁰C)⁻¹	$λ$ /10⁻² W·(m·⁰C)⁻¹
503	0.702	2.7	1.033	4.13

When setting the inlet boundary conditions, it is need to enter the fluid initial velocity v, and according to the data and research given by the engine manufacturer, the maximum engine rotational speed is 2625 r/min, and the inlet boundary parameters for flow field simulation are listed in Table 3.

Table 3.

Parameters for inlet boundary.

v/m·s⁻¹	T/K	k/m²·s⁻²	ε/m²·s⁻³
100	503	21.01	5257.4

As the exhaust pipe is connected with outside air, the ambient pressure is set as a outlet boundary condition, so the reference pressure relative to atmospheric pressure is 0 Pa and the temperature is 300 K; structural material is Q235a, and the wall surface is a fixed boundary condition. Considering that the actual inner wall may hinder gas flow to some extent, the wall roughness is set to 0.5.

After the boundary conditions were set, the standard k-ε turbulence calculation model was selected, and then energy equations were activated. When the calculation reached convergence, the velocity and temperature distributions of exhaust muffler on interface 1 (B-B) connecting the circle centers O₁ and O₂ in Figure 1, which is a axial section through intake and middle transition pipes, and the interface 2 (C-C) connecting the circle centers O₂ and O₃, also a axial section through middle transition and exhaust pipes, were obtained, as illustrated in Figures 2 and 3, respectively.

Figure 2.

Flow filed distribution maps inside the original exhaust muffler.

Figure 3.

Temperature distribution maps inside the original exhaust muffler.

As can be seen from Figure 2, after gas enters the intake pipe ① at 100 m/s, a part of gas flows into the large expansion chamber ⑤ at an average velocity of about 90 m/s from right-most holes, and the gas in ⑤ flows into the transition pipe ⑥ after moving; the other part of gas flows into the closed end of intake pipe, resulting in a back-flow due to resistance. After passing through the intake pipe pore structure ②, the back-flow flows into the resonant chamber ③ at about 50 m/s, and then flows into the transition pipe through the pore structure ⑦. The two parts of gas enter the small expansion chamber ⑧ at a velocity of about 140 m/s through intersection in transition pipe, and the incoming gas flows into the exhaust pipe ⑨ along the wall after being dispersed. Moreover, the velocity distribution in each region of internal flow field is quite uneven, and there are a large range of eddy currents in the first, second and third chambers, mainly appearing in the regions near middle separator and between intake pipe and transition pipe.

Figure 3 demonstrates that large temperature changes occur in each area of the exhaust muffler, and the temperature inside intake pipe ① is the highest, and temperature gradually decreases as gas flows, leading to a large temperature gradient. The gas temperature of the intake pipe is basically maintained at 500 K, away from intake pipe, gas temperature of roughly 490 K, and close to the wall, temperature is relatively low; as gas flows into the resonant chamber ③, it is seen that gas temperature distributions are uneven, and their temperatures are about around 470 K–490 K. Large temperature gradient changes in the third chamber ⑤ due to differences in airflow velocity distribution characteristics. The gases from the large expansion and resonant chambers enter the transition pipe ⑥, forming a uniform temperature distribution whose temperature is about 490 K; the gas flows into the small expansion chamber ⑧ along the transition pipe and drops to about 480K, and eventually flows into the exhaust pipe ⑨ with uniform temperature distribution.

Acoustic performance analysis

The above physical characteristics of the velocity field and temperature field are basically consistent with the internal flow field analysis in Reference⁵, and the next work is, considering the influence of airflow and temperature factors, to calculate the transmission loss of the targeted forklift exhaust muffler by the acoustic simulation software of LMS Virtual. Lab for evaluating its acoustic performance.^20–22 The transmission loss indicates the difference between the incident sound power level L_Wi at inlet and the transmitted sound power level L_Wt at outlet, which reflects a inherent property of muffler component, that is, it is not affected by sound source and external environment, only related to the muffler itself. The calculation formula is expressed as

T L = L_{W_{i}} - L_{W_{t}} = 10 \lg | \frac{W_{i}}{W_{t}} | = 10 \lg | \frac{S_{i} p_{i}^{2}}{S_{t} p_{t}^{2}} |

(6)

Where W_i and W_t respectively represent inlet incident sound power and outlet transmitted sound power with the unit of W; p_i and p_t are the incident sound pressure at inlet and the transmitted sound pressure at outlet, Pa; S_i and S_t stand for the cross-sectional areas at the inlet and outlet of exhaust muffler, respectively, m².

The original muffler model in ANSYS module was saved as x_t format, and the acoustic mesh model was established by STAR-CCM+. When the NAS file was imported into LMS Virtual. Lab, the expected mesh was divided and its growth index was set as 1.2. The input analysis frequency range was 20 Hz–2000 Hz, and finally the calculated transmission loss curve of the forklift exhaust muffler was obtained and shown in Figure 4.

Figure 4.

Transmission loss curve of the original exhaust muffler.

Figure 4 states clearly that the original exhaust muffler in this case has three transmission loss peaks at about 570 Hz, 1200 Hz and 2000 Hz, but there are three distinct muffling lows at 250 Hz–270 Hz in low frequency, 850 Hz–950 Hz in medium frequency and 1400 Hz–1600 Hz in high frequency, and their transmission losses are below 20 dB. In general, the smaller the value of transmission loss, the worse the acoustic performance of exhaust muffler. Therefore, it can be concluded that the current muffler needs to be adjusted in the structural parameters to further improve its acoustic performance.

Structural and acoustic performance improvements

According to the analysis results of the above flow field, temperature field and acoustic performance, after several structural improvements and simulation tests, it is proposed to increase the distance and number of small holes in the intake pipe and expand the end part length in the intake pipe to reduce the formation of internal gas eddy currents and uneven temperature gradient distribution. Consequently, the determined structure parameters improved include: the hole spacing of perforated pipe ④ was increased from 8 mm to 11.5 mm and in corresponding hole number from 120 to 200; the small hole number in the perforated pipe ② was added to 60; and furthermore, the perforated pipe length ④ was increased by 50 mm.

Structural improvements were completed on the three-dimensional model of the original exhaust muffler, and the mesh was re-divided in Fluent software, and the same boundary conditions were set as before. After the convergence, the same interface 1 and interface 2 were selected to analyze the internal flow velocity and temperature fields of the improved exhaust muffler. Consequently, the calculation results are illustrated in Figures 5 and 6.

Figure 5.

Flow filed distribution maps inside the improved exhaust muffler.

Figure 6.

Temperature distribution maps inside the improved exhaust muffler.

As can be seen from Figure 5, because the number of intake pipe holes is increased, the injection flow around the holes is more uniform and smaller, and the flow velocity from the intake pipe holes is about 85 m/s. In addition, the velocity distribution in the small expansion chamber ⑧ is similar to that before the improvement. It flows into the exhaust pipe ⑨ through some complex movements, resulting in a variety of inlet velocity distribution in exhaust pipe, with a maximum velocity of 150 m/s, which is about 20 m/s lower than before, and finally gas is discharged into the atmosphere at 100 m/s. It is worth noting that eddy currents formed in the improved exhaust muffler is significantly reduced, with a few concentrated in the intake and exhaust pipe openings and small holes, which means decreasing eddy current noise sources.

The improved exhaust muffler exhibits multiple temperature gradient distributions in the large expansion chamber ⑤, as illustrated in Figure 6, but the temperature distributions in the transition pipe ⑥ at 490 K and small expansion chamber ⑧ around 470 K–480 K are relatively uniform, and finally, the exhaust gas is discharged into the atmosphere at a temperature of 470 K. Overall, the area temperature in the improved exhaust muffler is reduced by about 10 K–25 K.

Similarly, the acoustic performance of the improved exhaust muffler was analyzed by FEM, in which mesh division, boundary conditions and operation process were consistent with the above section. After calculation and convergence, the improved transmission loss curve of targeted exhaust muffler is obtained, as shown in Figure 7.

Figure 7.

Transmission loss curve of the improved exhaust muffler.

Comparing with Figures 4 and 7, the following conclusions can be intuitively drawn: the maximum transmission loss of the improved exhaust muffler is 97.42 dB, which occurs in the frequency range of 1130 Hz–1248 Hz, 2.97 dB higher than 94.45 dB at 570 Hz before the improvement in Figure 4. Although the transmission loss at 570 Hz is weakened before the improvement, it is worth pointing out that the three curve troughs of transmission loss in Figure 4 are increased from 5.16 dB to 28.9 dB as a whole. Therefore, it can be concluded that the acoustic performance of the improved exhaust muffler is significantly optimized.

Conclusions and future work

The exhaust muffler is an important component of the internal combustion forklift, and its silencing effect is directly related to vehicle noise radiation level, thus improving its acoustic performance is one of the main aspects of NVH. When the engine is working at the highest speed, radiated noise decibel of exhaust muffler is the largest, and its acoustic performance can be affected by internal high-velocity air flow and high temperature factors.

Taking the forklift exhaust muffler under the highest speed working condition as a research case, this paper theoretically analyzes the control equations of internal gas flow and heat exchange, completes boundary parameter setting, grid division and numerical solution of three-dimensional CFD model using Fluent, and obtains velocity and temperature cloud maps of internal fluid domains. It is found that the distributions of flow velocity and temperature fields are not uniform, the velocity mainly changes greatly at the inlet and exit pipes, and the temperature gradually decreases from intake pipe, transition pipe to exhaust pipe. In particular, the internal eddy currents are concentrated near the small holes of the intake pipe. The transmission loss curve of the original exhaust muffler is obtained through LMS Virtual. Lab software and indicates that there are three significant muffling lows below 20 dB. Based on the numerical calculation results, exhaust muffler internal structures are improved, and simultaneously the same flow field simulation and the acoustic calculation are carried out to obtain the following conclusions: gas flow velocity and temperature inside the improved exhaust muffler are reduced, and the transmission loss peak and three troughs are improved by 2.97 dB and 23.74 dB, respectively, indicating that the new exhaust muffler has a better acoustic performance, which provides an improvement basis for the actual structure design and test in the future, and then lays a key technical foundation for reducing the radiated noise decibel of the target internal combustion forklift. What’s more, it is a new direction to investigate fluid-solid and multi-physical field coupling to further reveal the influence mechanism of air flow and temperature on transfer loss.

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) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The work was supported by National Natural Science Foundation of China (12004136), Natural Science Foundation of Xiamen City (3502Z20206024), and Science and Technology Project for High-level Talents (YKJ22017R, YKJ22014R).

ORCID iD

Enlai Zhang

References

Zhang

Zhuo

Hou

, et al. Comprehensive annoyance modeling of forklift sound quality based on rank score comparison and multi-fuzzy analytic hierarchy process. Appl Acous 2021; 173: 107705.

Zhang

Hou

Zhuo

, et al. A noise reduction method for forklift based on numerical separation and spectrum analysis of main noise sources. Revista Internacional de Metodos Numericos para Calculo y Diseno en Ingenieria 2020; 36(4): 47.

Zhang

Hou

Xin

, et al. Noise reduction of a tractor exhaust tailpipe with bionic convex textures. Noise Contr Eng J 2019; 67(5): 363–372.

You

Wang

, et al. Numerical analysis of the flow and temperature fields inside an internal combustion forklift exhaust muffler. J Zhejiang Univer Technol 2017; 45(2): 142–146.

Wang

You

Weng

, et al. Improvement of internal combustion forklift exhaust muffler considering the influence of flow and temperature fields. J Mech & Electri Eng 2016; 33(8): 944–949.

Guo

Fan

. Acoustic attenuation performance of perforated tube silencer based on computational fluid dynamics results. J Mech Eng 2017; 53(1): 79–85.

Liu

Zheng

Hao

, et al. A computational fluid dynamics approach for full characterization of muffler without and with exhaust flow. Phys Fluid 2020; 32: 067114–067116.

Chatterjee

. Computational fluid dynamic analysis of the exhaust gas flow through absorptive and reactive mufflers: some case studies. Pro Insti Mech Eng Part D- J Automob Eng 2017; 231(11): 1568–1588.

Liu

Zheng

Hao

, et al. A time-domain simulation method to predict insertion loss of a dissipative muffler with exhaust flow. Phys Fluid 2021; 33(6): 067114.

10.

Guhan

CPO

Arthanareeswaran

Varadarajan

, et al. Exhaust system muffler volume optimization of light commercial vehicle using CFD simulation. Mat Today-Proc 2018; 5(2): 8471–8479.

11.

Chen

Huang

. Acoustic impedance of perforated plates in the presence of fully developed grazing flow. J Sound Vibra 2020; 485: 115547.

12.

Mann

Nair

Gill

Birschbach

, et al. Flow Noise Predictions for Single Cylinder Engine-Mounted Muffler Using a Lattice Boltzmann Based Method, SAE Int. J. Engines. 10(4):2067-2076, 2017. DOI: 10.4271/2017-01-1797

13.

Seruga

Hansenne

Haesen

, et al. Durability prediction of EN 1.4512 exhaust mufflers under thermomechanical loading. Int J Mech Sci 2014; 84: 199–207.

14.

Hou

Zhang

, et al. Case study: numerical study of the noise reduction characteristics of corrugated perforated pipe mufflers. Noise Contr Eng J 2022; 70(1): 16–36.

15.

Mohamad

Karoly

Zelentsov

, et al. Investigation of perforated tube configuration effect on the performance of exhaust mufflers with mean flow based on three-dimensional analysis. Arc Acousti 2021; 46(3): 561–566.

16.

Zheng

, et al. Effects of structural parameters on transmission loss of diesel engine muffler and analysis of prominent structural parameters. Appl Acous 2021; 173: 107686.

17.

Goktepeli

Atmaca

Cakan

. Investigation of heat transfer augmentation between the ribbed plates via taguchi approach and computational fluid dynamics. J Therm Sci 2020; 29(3): 647–666.

18.

Ngo

Phu

. Computational fluid dynamics analysis of the heat transfer and pressure drop of solar air heater with conic-curve profile ribs. J Therm Analy Calorim 2020; 139(5): 3235–3246.

19.

Zhao

Liu

, et al. A computational fluid dynamics - discrete element-immersed boundary method for Cartesian grid simulation of heat transfer in compressible gas-solid flow with complex geometries. Phys Fluid 2020; 32(10): 103306.

20.

Jena

Panigrahi

. Numerically estimating acoustic transmission loss of a reactive muffler with and without mean flow. Measurement 2017; 109: 168–186.

21.

Munjal

. Tuning a two-chamber muffler for wide-band transmission loss. Int J Acous Vib 2020; 25(2): 248–253.

22.

Shi

, et al. Thermal and acoustic performance of silencing heat exchanger for engine waste heat recovery. Appl Therm Eng 2022; 201: 117711.