New Research Article An Investigation of Acoustic Attenuation...
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Research Article An Investigation of Acoustic Attenuation Performance of Silencers with Mean Flow Based on Three-Dimensional Numerical Simulation Wei Fan and Li-Xin Guo School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, China Correspondence should be addressed to Li-Xin Guo; [email protected] Received 28 June 2015; Revised 18 September 2015; Accepted 27 September 2015 Academic Editor: M. I. Herreros Copyright © 2016 W. Fan and L.-X. Guo. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Transmission loss (TL) is oſten used to evaluate the acoustic attenuation performance of a silencer. In this work, a three-dimensional (3D) finite element method (FEM) is employed to calculate the TL of some representative silencers, namely, circular expansion chamber silencer and straight-through perforated pipe silencer. In order to account for the effect of mean flow that exists inside the silencer, the 3D FEM is used in conjunction with the Computational Fluid Dynamics (CFD) simulation of the flow field. More concretely, the 3D mean flow field is computed by firstly using CFD, and then the obtained mean flow data are imported to an acoustic solution undertaken using FEM. e data transfer between the two steps is accomplished by mesh mapping. e results presented demonstrate good agreement between present TL predictions and previously published experimental and numerical works. Also, the details of the flow inside the silencers may be studied. Furthermore, the effect of mean flow velocity on acoustic attenuation performance of the silencers is investigated. It is concluded that for the studied silencers, in general, increasing flow velocity increases the TL and decreases the resonance peaks. 1. Introduction It is common for silencing devices to be used to attenu- ate exhaust noise generated by vehicles and various fluid machines. It is well known that the silencer is always accom- panied with mean gas flow in practical application. Many studies, including theoretical and experimental methods, had been conducted to investigate the acoustic attenuation performance of the silencer with mean flow during the past years [1–5]. With the rapid development of high-performance computers, recent years have seen an increasing interest in adopting 3D numerical methods to predict silencer perfor- mance. Generally speaking, two kinds of numerical methods are available, namely, time-domain method [6–8] based on the nonlinear fluid dynamic model and frequency-domain method based on the linear acoustic model. e frequency- domain method mainly includes boundary element method (BEM) [9–11] and finite element method (FEM). FEM was initially applied to predict the acoustic per- formance of mufflers by Young and Crocker [12]. Due to restrictions in computational resources, most of previously published applications of FEM had been limited to two- dimensional analyses with simplified boundary conditions. However, realistic silencer geometries oſten exhibit 3D fea- tures; hence these analyses tend to be less accurate when deal- ing with complex geometries. As mentioned before, with the ever-increasing computational speed and memory capacity of the computer in recent years, more applications of 3D FEM can be found in the literature. For example, Mehdizadeh and Paraschivoiu [13] implemented a comprehensive 3D FEM to assess TL of a packed muffler and a parallel baffle silencer with nonhomogeneous domain in the absence of mean flow, and the success of the 3D finite element modeling encouraged extending the application of the FEM to more complex cases. Kang and Ji [14] adopted 3D FEM to study the acoustic length correction of duct extension into a cylindrical chamber and examined the effect of chamber geometry on the acoustic length correction. Ge et al. [15] applied 3D FEM to predict the acoustic attenuation characteristics of complex perforated Hindawi Publishing Corporation Shock and Vibration Volume 2016, Article ID 6797593, 12 pages http://dx.doi.org/10.1155/2016/6797593
Transcript of New Research Article An Investigation of Acoustic Attenuation...
Research ArticleAn Investigation of Acoustic AttenuationPerformance of Silencers with Mean Flow Based onThree-Dimensional Numerical Simulation
Wei Fan and Li-Xin Guo
School of Mechanical Engineering and Automation Northeastern University Shenyang 110819 China
Correspondence should be addressed to Li-Xin Guo lxguomailneueducn
Received 28 June 2015 Revised 18 September 2015 Accepted 27 September 2015
Academic Editor M I Herreros
Copyright copy 2016 W Fan and L-X Guo This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited
Transmission loss (TL) is often used to evaluate the acoustic attenuation performance of a silencer In this work a three-dimensional(3D) finite element method (FEM) is employed to calculate the TL of some representative silencers namely circular expansionchamber silencer and straight-through perforated pipe silencer In order to account for the effect of mean flow that exists insidethe silencer the 3D FEM is used in conjunction with the Computational Fluid Dynamics (CFD) simulation of the flow field Moreconcretely the 3D mean flow field is computed by firstly using CFD and then the obtained mean flow data are imported to anacoustic solution undertaken using FEM The data transfer between the two steps is accomplished by mesh mapping The resultspresented demonstrate good agreement between present TL predictions and previously published experimental and numericalworks Also the details of the flow inside the silencers may be studied Furthermore the effect of mean flow velocity on acousticattenuation performance of the silencers is investigated It is concluded that for the studied silencers in general increasing flowvelocity increases the TL and decreases the resonance peaks
1 Introduction
It is common for silencing devices to be used to attenu-ate exhaust noise generated by vehicles and various fluidmachines It is well known that the silencer is always accom-panied with mean gas flow in practical application Manystudies including theoretical and experimental methodshad been conducted to investigate the acoustic attenuationperformance of the silencer with mean flow during the pastyears [1ndash5]With the rapid development of high-performancecomputers recent years have seen an increasing interest inadopting 3D numerical methods to predict silencer perfor-mance Generally speaking two kinds of numerical methodsare available namely time-domain method [6ndash8] based onthe nonlinear fluid dynamic model and frequency-domainmethod based on the linear acoustic model The frequency-domain method mainly includes boundary element method(BEM) [9ndash11] and finite element method (FEM)
FEM was initially applied to predict the acoustic per-formance of mufflers by Young and Crocker [12] Due to
restrictions in computational resources most of previouslypublished applications of FEM had been limited to two-dimensional analyses with simplified boundary conditionsHowever realistic silencer geometries often exhibit 3D fea-tures hence these analyses tend to be less accurate when deal-ing with complex geometries As mentioned before with theever-increasing computational speed andmemory capacity ofthe computer in recent years more applications of 3D FEMcan be found in the literature For example Mehdizadeh andParaschivoiu [13] implemented a comprehensive 3D FEM toassess TL of a packed muffler and a parallel baffle silencerwith nonhomogeneous domain in the absence of mean flowand the success of the 3Dfinite elementmodeling encouragedextending the application of the FEM to more complex casesKang and Ji [14] adopted 3D FEM to study the acoustic lengthcorrection of duct extension into a cylindrical chamber andexamined the effect of chamber geometry on the acousticlength correction Ge et al [15] applied 3D FEM to predictthe acoustic attenuation characteristics of complex perforated
Hindawi Publishing CorporationShock and VibrationVolume 2016 Article ID 6797593 12 pageshttpdxdoiorg10115520166797593
2 Shock and Vibration
l1
l
Dd
(a)l
Dd
(b)
Figure 1 Geometries of the silencers considered (a) circle expansion chamber silencer and (b) straight-through perforated pipe silencer
pipe silencers with the help of perforate impedance modelsFurthermore the effects of perforation length and porosityon the acoustic performance are investigated Chaitanya andMunjal [16] used 3D FEM analysis to investigate the effectof wall thickness of the inletoutlet duct on end correctionand their predictions are validated by comparing themwith experimental data In order to improve the acousticattenuation performance of an exhaust muffler in 175 series ofagriculture diesel engine Fu et al [17] established a 3Dmodelfor the muffler and then employed commercial finite elementsoftware package to calculate the TL and their predictionsshowed very close agreement with experimental data
In the aforementioned works the applications of FEMmainly focus on predictingTL in silencerswithoutmean flowOf course FEM is capable of considering the effect of meanflow by assuming that the acoustic field is superimposedover the decoupled mean flow but this mean flow must beimported from an external steady flow computation that isoften performed by a simplified potential-flow approach [1819] in previous works In this paper to acquire amore realisticflow distribution inside the silencer the CFD simulationwith proper turbulence model which is extremely useful indetermining the flow distribution and commonly used foranalyzing themean flow performance [6 8 20ndash22] is utilizedto perform the external steady flow computation via commer-cial software ANSYS FLUENT 145 After finishing the CFDcomputation themean flow data are used as an input into theacoustic field and then an acoustic response analysis is car-ried out using FEMvia commercial software LMSVirtualLab110 Finally the TL with the effect of mean flow is calculated
2 Method
21 Silencer Modeling In present work the circle expansionchamber silencer with extended inlet used in [23] and threestraight-through perforated pipe silencers used in [24] areconsidered Also the published experimental data from theseauthors are used as a basis for comparison of the numericalresults presented in this paper Figure 1 shows the 3Dgeometries of the silencers considered here and their precisedimensions are given in Table 1 where 119889ℎ and 120590 denote thediameter of the orifice on the perforated pipe and the porosityrespectively
Table 1 Dimensions for the silencers considered (unit mm)
Silencer 119863 119889 119897 1198971 119889ℎ 120590 ()Expansion chamber 108 40 208 52 mdash mdashPerforated pipe 1 (1198751) 110 32 200 mdash 4 47Perforated pipe 2 (1198752) 110 32 200 mdash 6 90Perforated pipe 3 (1198753) 110 32 200 mdash 8 147
Tetrahedral mesh is chosen to discretize the computa-tional field of the silencer due to its high flexibility Twodifferent meshes namely CFD mesh and acoustic mesh willbe used for the solution of mean flow and acoustic problemsrespectively For the expansion chamber silencer the elementsizes of CFD and acoustic meshes are 4mm and 8mmrespectively and the CFD mesh is composed of 131111 nodesand 406204 elements the acousticmesh is composed of 51972nodes and 35807 elements For the straight-through perfo-rated pipe silencer whose geometry is relatively complex thecomputational model is split into several parts to generatemesh individually in order to decrease computational costAn element size of 2mm is used for the perforation area inboth CFD and acoustic meshes and the element sizes for therest of the two meshes are 4mm and 10mm respectivelyTake silencer 1198752 as an example the CFD mesh is composedof 206827 nodes and 1142767 elements the acoustic mesh iscomposed of 668038 nodes and 479644 elements
Figures 2(a) and 3(a) show the generated CFD meshwhich is fine and dense and the mesh near to the wallsis densified further in order to resolve the boundary layerCompared with the CFD mesh the acoustic mesh shown inFigures 2(b) and 3(b) is coarse and thin But it should be notedthat to ensure computational accuracy the maximum size ofthe acoustic mesh must meet the following formulation [25]
119871 le119888
6119891max (1)
where 119888 is the speed of sound and 119891max is the maximumfrequency of interest The maximum achieved frequencyof acoustic mesh can be calculated directly in VirtualLaband it is found that the maximum achieved frequencies ofgenerated acoustic meshes for the studied silencers are all
Shock and Vibration 3
(a) (b)
Figure 2 Geometry of meshes for the expansion chamber silencer (a) CFD mesh and (b) acoustic mesh
(a) (b)
Figure 3 Geometry of meshes for the straight-through perforated pipe silencer (a) CFD mesh and (b) acoustic mesh
above 3500Hz well over the maximum frequency of interest(3000Hz) Therefore the accuracy of acoustic computationcan be ensured
22 Prediction of TL In the CFD steady flow computationthe data type used is double precision the solver imple-mented is a pressure-based implicit solver SIMPLEC pres-sure-velocity coupling algorithm is chosenwith second-orderscheme for spatial discretisation and the realizable 119896-epsilonturbulence model is employed [26] The fluid material isair with the density conforming to the ideal gas law Theboundary conditions consist of the following (i) amass-flow-inlet with constant mass flux (ii) a pressure-outlet with con-stant static pressure in this case 0 Pa relative to one standardatmospheric pressure and (iii) a series of walls assumed tobe stationary with no slip and adiabatic After convergenceof the CFD computation the flow velocity data are exportedinto format CGNS (CFD General Notation System) andthen imported to the acoustic field to serve as a mean flowboundary condition of the acoustic response analysis (iethe mean flow field is superimposed over the acoustic field)Note that the purpose of using this CFD simulation is toobtain a more realistic and detailed flow velocity distributioninside the silencers rather than to consider the viscous effectof mean flow on sound propagation as the full time-domainCFD method [7 8] conducts
The data transfer between acoustic and mean flow prob-lems is accomplished by mesh mapping function that Vir-tualLab provides Because there is no one-to-one correspon-dence between nodes of generated CFD and acoustic meshesan appropriate mapping algorithm should be employed Inthis paperMaximum Distance Algorithm [27] which is oftenapplied to set a mesh mapping between two meshes withdifferent density of nodes is employed and this algorithmincludes two necessary parameters (i) number of nodes (119873)it is the maximum number of nodes from the source mesh(CFDmesh) that is considered for mapping with one node ofthe target mesh (acoustic mesh) and (ii) maximum distance(119877) only the nodes of the source mesh lying inside a spherewith radius 119877 centered at the node of target mesh are takeninto account 119873 closest to a given source node are used totransfer data to the target node The data value assigned tothe target node is a weighted average of the value at the 119873source nodes The weights are [27]
119882119894 =1119889119894
sum119873
119894=1(1119889119894)
(2)
The transferred value on the target node is then
VTarget =sum119873
119894=1(VSource119894
119889119894)
sum119873
119894=1(1119889119894)
(3)
4 Shock and Vibration
x = 0
pincpref
ptrapout
Anechoic endpin in
Figure 4 Theory for TL calculation
where 119889119894 is the distance between source node and target nodeand VSource is the value of source node The 119873 and 119877 couldbe given automatically when CFD and acoustic meshes areintroduced to the data transfer module in VirtualLab herewe calculate directly using the defaults
After finishing the data transfer the acoustic responseanalysis is performed with 10Hz spacing using FEM For thesound field inside the silencer the governing formulation isHelmholtz equation as [13]
nabla2119901 + 1198962119901 = 0 (4)
where119901 is the acoustic pressure 119896 is thewave number definedas 119896 = 120596119888 120596 is the angular frequency and 119888 is the speed ofsound Galerkinrsquos method of weighted residuals is applied to(4) and the acoustic finite element formulation [28] is formed
([119872] minus 1198962[119875]) 119901 = minus119895120588120596 119865 (5)
where [119872] and [119875] are the inertia and stiffness matrices ofthe element 119901 is the vector of acoustic pressure at all nodesof the system 120588 is the density of the medium and 119865 is theforcing vector at all nodes of the system At the inlet of thesilencer a unit velocity of 119906in = 1ms is imposed and theoutlet is defined to be an anechoic end by setting an AnechoicEndDuct Property inVirtualLab In order tomodel the effectof mean flow on sound propagation themean flow boundarycondition is set on the inlet [27] Applying these boundaryconditions and solving (5) may obtain the sound pressure atall nodes of the system And then the TL is determined by[8] Consider
TL = 20 log10[(
119860 in119860out
)
12 10038161003816100381610038161003816100381610038161003816
119901inc119901tra
10038161003816100381610038161003816100381610038161003816] (6)
where 119860 in and 119860out are the cross-sectional areas of the inletand outlet of the silencer respectively 119901inc is the acousticpressure of incident wave at the inlet of the silencer and119901tra is the acoustic pressure of transmitted wave at the outletof the silencer However it should be pointed out that theresults obtained using FEM are acoustic pressure at the inletand outlet (119901in and 119901out) which include the acoustic pressureof reflective wave (119901ref ) as shown in Figure 4 where 119909represents the coordinate of the point along the silencer axisTherefore (6) should be further deduced to build the rela-tionship between 119901in 119901out and 119901inc 119901tra
In the frequency range of interest for silencer analysisthese acoustic pressure waves typically travel through the
0 1
2 34
0
2
4
6
8
10
12
67 8910 12
Velo
city
-mag
nitu
de
11
(ms
)
Figure 5 Counters of velocity-magnitude for the expansion cham-ber silencer with inlet flow velocity of V = 102ms
9376833472936251520941673125208410420000 Tu
rbul
ence
kin
etic
ener
gy (J
kg)
Figure 6 Counters of turbulent kinetic energy for the expansionchamber silencer with inlet flow velocity of V = 102ms
inlet and outlet pipes as planewaves [17]When thewave trav-els in an inviscid moving medium the 1D wave formulationis [29]
1205972119901
1205971199052+ 2119881
1205972119901
120597119909120597119905+ (1198812minus 1198882)1205972119901
1205971199092= 0 (7)
where 119881 is the flow velocity of the medium Solving (7) withthe corresponding boundary and initial conditions in thetime-domain gives 119901 as a function of time and space [13] Byassuming a time-harmonic solution for the acoustic pressure(ie assuming that the time dependence takes an exponentialform) (7) is solved to obtain the acoustic pressure at the inletwhich is written as
119901in = (119901inc119890minus119895119896119909(1+119872)
+ 119901ref119890+119895119896119909(1minus119872)
) 119890119895120596119905 (8)
where 119901ref is the acoustic pressure of reflective wave at theinlet and119872 is the mean flow Mach number defined as 119881 =
119872119888 The particle velocity at the inlet also satisfies the samewave formulation and one can write
119906in =1
120588119888(119901inc119890
minus119895119896119909(1+119872)minus 119901ref119890
+119895119896119909(1minus119872)) 119890119895120596119905 (9)
where 120588119888 represents the characteristic impendence of themedium at the inlet As mentioned before there are 119909 = 0
Shock and Vibration 5
37
28
19
9
0
Velo
city
-vec
tor (
ms
)
(a) Velocity-vector
73
55
36
18
0
Velo
city
-vec
tor (
ms
)
(b) Velocity-vector
38
28
19
9
0
Velo
city
-vec
tor (
ms
)
(c) Velocity-vector
Figure 7 Velocity-vectors for the straight-through perforated pipe silencers (a) silencer1198751119872 = 01 (b) silencer1198752119872 = 02 and (c) silencer1198753119872 = 01
39701352923088326473220641765513246883744280019
Turb
ulen
ce k
inet
icen
ergy
(Jk
g)
(a) Turbulence kinetic energy
16721814864713007611150692935743645579437223186520082
Turb
ulen
ce k
inet
icen
ergy
(Jk
g)
(b) Turbulence kinetic energy
617005486048019411793433827498206571381769760136
Turb
ulen
ce k
inet
icen
ergy
(Jk
g)
(c) Turbulence kinetic energy
Figure 8 Counters of turbulent kinetic energy for the straight-through perforated pipe silencers (a) silencer 1198751119872 = 01 (b) silencer 1198752119872 = 02 and (c) silencer 119875
3119872 = 01
and 119906in = 1ms at the inlet and with neglecting ldquo119890119895119908119905rdquo item(8) and (9) reduce to
119901in = 119901inc + 119901ref
119906in =1
120588119888(119901inc minus 119901ref) = 1
(10)
which yield
119901inc =119901in + 120588119888
2 (11)
In addition the outlet is defined to be an anechoic end (iethe acoustic pressure of reflective wave at the outlet is 0) sothere is
119901tra = 119901out (12)
6 Shock and Vibration
200
180
160
140
120
100
80
60
Acou
stic p
ress
ure l
evel
(dB)
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
InletOutlet
Figure 9 Acoustic pressure level for the inlet and outlet of the expansion chamber silencer with inlet flow velocity of V = 102ms200
180
160
140
120
100
80
Acou
stic p
ress
ure l
evel
(dB)
InletOutlet
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
(a)
200
180
160
140
120
100
80
Acou
stic p
ress
ure l
evel
(dB)
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
InletOutlet
(b)200
180
160
140
120
100
80
Acou
stic p
ress
ure l
evel
(dB)
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
InletOutlet
(c)Figure 10 Acoustic pressure level for the inlet and outlet of the straight-through perforated pipe silencers (a) silencer 1198751 119872 = 01 (b)silencer 119875
2119872 = 02 and (c) silencer 119875
3119872 = 01
Shock and Vibration 7
50
60
40
30
20
10
0
TL (d
B)
Published experimental dataFEMPredicted by literature [23]
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
Figure 11 Measured and predicted TL for the expansion chamber silencer with inlet flow velocity of V = 102ms
Substituting (11) and (12) into (6) yields
TL = 10 log10[(119901in + 120588119888)
2
41199012out
119860 in119860out
]
= 10 log10((119901in + 120588119888) (119901in + 120588119888)
4119901out119901out
119860 in119860out
)
(13)
It should be noted that the obtained acoustic pressure is infrequency-domain and therefore has a complex value In thispaper the temperature and density of the medium (air) are119879 = 288K and 120588 = 1225 kgm3 respectively and the speedof sound in air is 119888 = 340ms
3 Results and Discussion
31 Validation of the 3D Numerical Method Following thecalculation steps stated in Section 22 CFD steady flowcomputation is performed first Figure 5 shows the computedvelocity contours on the axial cutting plane of the expansionchamber silencer with extended inlet it is found that thevelocity distribution is uneven The flow velocity in the inletand outlet pipes are higher than that in the chamber and thesudden section area change enhances the turbulent kineticenergy as shown in Figure 6 Figure 7 shows the veloc-ity-vectors for the three straight-through perforated pipesilencers with a mean flow Mach number of 119872 = 01 or02 Flow circulations can be observed in the rear part of thechamber and the velocity in the pipe is much higher thanthat in the orifices and chamber Moreover the magnitudeand direction of cross-flow velocity through the perforationsare different along the axial direction In addition under theaction of pressure difference between the chamber and perfo-rated pipe the gas flows into the chamber through the orificesand then flows back again into the pipe which enhancesthe turbulent kinetic energy near the orifices as shown in
Figure 8 Generally speaking the flow velocity distributionsinside the studied silencers are anisotropic and nonuniformand the gas flow is accompanied with turbulence
After importing the mean flow data to the acoustic fieldby mesh mapping acoustic response analysis is performedto acquire acoustic pressure at the inlet and outlet as shownin Figures 9 and 10 To validate the accuracy of the 3Dnumerical method published experimental and numericalresults for the studied silencers are comparedwith the presentpredictions
Figure 11 compares the TL results for the expansionchamber silencer with extended inlet from numerical andexperimental methodsThe present predictions agree reason-ably well with the experimental data in the frequency range ofinterest Some deviation from the measurements is observedfor example near the resonance peak This discrepancy maybe attributed to the fact that (i) the medium viscous effectsand wall thickness are neglected in the FEM calculation and(ii) flow noise generated inside the silencer is neglected inthe simulation but the noise is included in the experimentsFurthermore the present FEM results are compared withthe numerical results from literature [23] One can see thatthe present FEM yields better results between the predictedTL curves That is because the method employed in theliterature neglects the turbulence inside the silencer and usesthe simplified mean flow velocity In contrast the presentstudy may acquire more detailed distribution of mean flowthrough the CFD steady flow computation with the properturbulence model
In Figure 12 a comparison between the present predic-tions and measurements shows a good agreement in generalbetween TL results obtained for the three straight-throughperforated pipe silencers studied here However it is foundthat the present predicted TL values are slightly less thanthose measured This is because the influence of mean flowon the sound propagation in the silencer can be explained as
8 Shock and Vibration
50
40
30
20
10
00 500 1000 1500 2000 2500 3000
Frequency (Hz)
TL (d
B)
Published experimental dataFEMPredicted by literature [24]
(a)
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
50
40
30
20
10
0
TL (d
B)
Published experimental dataFEMPredicted by literature [24]
(b)
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
50
40
30
20
10
0
TL (d
B)
Published experimental dataFEMPredicted by literature [24]
(c)
Figure 12 Measured and predicted TL for the straight-through perforated pipe silencers (a) silencer 1198751119872 = 01 (b) silencer 1198752119872 = 02and (c) silencer 1198753119872 = 01
the convective and dissipative effects [7] and the convectiveeffect can be considered by importing the decouple meanfrom an external steady flow computation to the acousticfield but the dissipative effect of medium viscous (especiallyin the orifices) which can cause sound energy loss and thusincrease TL is not included in the FEM calculation just likethe conventional frequency-domain method At present lotsof studies such as [24] mainly focus on applying mathe-matical modeling of perforate impedance to calculate andanalyze the acoustic attenuation performance of perforatedpipe silencer In the absence of mean flow the acousticperformance of the silence can be accurately predicted withthe help of perforate impedance models However when
mean flow is present rigorous mathematical modeling ofthe mechanisms that determine the perforate impedance isextremely difficult Therefore most of current impedancemodels considering the mean flow effect are empirical Incontrast although there is a lack of consideration of meanflow dissipative effect on sound propagation in present FEMby decoupling the problems this method avoids complexmathematical calculation and it is accessible and easy to useFurthermore the predicted results presented are not badTherefore it is valuable for predicting the acoustic attenuationperformance of perforated pipe silencer
At present with the development of computer perfor-mance the full time-domain CFD method such as that
Shock and Vibration 9
00
500 1000 1500 2000 2500 3000
Frequency (Hz)
TL (d
B)10
20
30
40
50
60
= 0
= 30ms = 60ms
Figure 13 Effect of flow velocity on TL of the expansion chamber silencer
performed in [8] has also attracted the interest of researchersThe main advantage of this method is that the dissipativeeffect of medium viscous could be better represented How-ever compared with the present method the main problemwhen using the time-domain CFD method is the CPU timeconsumed during the transient flow computation due tothe fact that long upstream and downstream pipes typicallyexceeding 15 times the length of the silencer are requiredto capture isolated incident and transmitted signals and thetime window (record length of data) must be long enoughto capture the entire pressure signals Moreover when meanflow is present the CFD transient flow computation needs tobe run twice (with and without impulse signal) Additionallyit can be seen from [8] that the TL curves calculated by thetime-domain CFD method are not smooth and have somesawteeth This is because the time-domain CFD method isa simulation of the process of an impulse technique [30]for measuring silencer acoustic performance and thereforethe predicted TL curves are easy to fluctuate like thoseobtained from the impulse technique Middelberg et al [31]investigated the effect of mesh size on TL obtained from thetime-domain CFD method and they found that for higherfrequencies the coarse mesh would influence the accuracy ofsolution due to the inability of the mesh to resolve the wave-length with a sufficient number of points and introducedthe artificial numerical dissipation Therefore the mesh sizefor the time-domain CFD method should be small enoughto avoid high-frequency dissipation As mentioned in Sec-tion 21 two different meshes CFD mesh and acoustic meshare used for the solution of the mean flow and acousticproblems when employing present method Compared withthe mesh used in the time-domain CFDmethod the require-ments of the CFD mesh for the steady flow computation inpresent method are much reduced [32] but it should be finerthan the acoustic mesh
32 Effect of Mean Flow on Silencer Acoustic Attenuation Per-formance Two main effects of mean flow on silencer acous-tic performance can be distinguished one is to affect thesound propagation in the silencer (stated in Section 31) Theother is to induce aerodynamic noise due to turbulence Insilencers the typical mean flow Mach number is below 03[33] and the aerodynamic noise is considered to be weakTherefore the aerodynamic noise is neglected in this work
Figure 13 shows that the predicted TL curves of theexpansion chamber silencer with the flow velocity variedbetween 0ms and 60ms It is observed that the shape ofTL curve with mean flow is much similar to that withoutmean flow The presence of mean flow increases the TLat most frequencies and decreases the resonance peak andTL increases further as flow velocities increase Figure 14shows the effect of mean flow on TL of the straight-throughperforated pipe silencers with different flow velocities It canbe seen from these pictures that the mean flow has littleinfluence on the acoustic attenuation in the plane wave rangeand leads to complex variation of TL curves in the non-plane wave Overall except that the presence of mean flowremarkably decreases resonance peak the acoustic attenu-ation performance of the straight-through perforated pipesilencers increases at most frequencies as flow velocity isincreased especially at higher frequencies
4 Conclusions
In this paper a 3D numerical method is employed to inves-tigate the acoustic attenuation performance of a circularexpansion chamber silencer with extended inlet and threestraight-through perforated pipe silencers in the presence ofmean flow By decoupling the problem the linear acousticsare away from the mean flow computation CFD and FEM
10 Shock and Vibration
= 0
= 30ms = 60ms
00
500 1000 1500 2000 2500 3000
Frequency (Hz)
TL (d
B)
10
20
30
40
50
(a)
= 0
= 30ms = 60ms
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
0
TL (d
B)
10
20
30
40
50
(b)
= 0
= 30ms = 60ms
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
0
TL (d
B)
10
20
30
40
50
(c)
Figure 14 Effect of flow velocity on TL of the straight-through perforated pipe silencers (a) silencer 1198751 (b) silencer 1198752 and (c) silencer 1198753
are employed to perform the steady flow computation andacoustic response analysis respectively The data transferis accomplished by mesh mapping A comparison betweenpresent results and previously published experimental andnumerical results indicates that the present 3D numericalmethod is capable of delivering reasonable predictions Themajor advantage of present method is that it is accessible andeasy to use and avoids complexmathematical calculationwiththe help of simulation software especially for the perforatedpipe silencer while the major drawback of this method liesin the considerable computational effort and cost that arerequired to acquire a complete and accurate solution in the3D calculations
Furthermore the TL of studied silencers with differentflow velocities is calculated It is concluded that the presenceof mean flow decreases the resonance peak and increases theacoustic attenuation at most frequencies for the expansionchamber silencer For the straight-through perforated pipesilencer mean flow has little influence on the acoustic atten-uation in the plane wave range and remarkably decreasesthe resonance peak and increases the acoustic attenuation athigher frequencies
Conflict of Interests
The authors declare that there is no conflict of interests withregard to this study and the publication of this paper
Shock and Vibration 11
Acknowledgments
The authors are grateful for the grants from National NaturalScience Foundation of China (51275082 11272273) Funda-mental Research Fund of Central Universities (N130403009)Research Fund for Doctoral Program of Higher Education(20100042110013) and Program for Liaoning InnovativeResearch Team in University (LT2014006)
References
[1] M G Prasad and M J Crocker ldquoInsertion loss studies onmodels of automotive exhaust systemsrdquo Journal of the AcousticalSociety of America vol 70 no 5 pp 1339ndash1344 1981
[2] M L Munjal and P T Thawani ldquoOn the transfer matrix for auniform tube with a moving mediumrdquo Journal of Sound andVibration vol 91 no 4 pp 597ndash599 1983
[3] K Narayana Rao and M L Munjal ldquoExperimental evaluationof impedance of perforates with grazing flowrdquo Journal of Soundand Vibration vol 108 no 2 pp 283ndash295 1986
[4] Y H Kim S H Kim B D Lim and Y K Kwak ldquoExperimentalstudy of acoustic characteristics of expansion chamber withmean flowsrdquo KSME Journal vol 2 no 2 pp 125ndash132 1988
[5] Y Auregan and M Leroux ldquoFailures in the discrete modelsfor flow duct with perforations an experimental investigationrdquoJournal of Sound andVibration vol 265 no 1 pp 109ndash121 2003
[6] A Broatch XMargot A Gil and F DDenia ldquoACFD approachto the computation of the acoustic response of exhaustmufflersrdquoJournal of Computational Acoustics vol 13 no 2 pp 301ndash3162005
[7] Z L Ji H S Xu and Z X Kang ldquoInfluence of mean flowon acoustic attenuation performance of straight-through per-forated tube reactive silencers and resonatorsrdquo Noise ControlEngineering Journal vol 58 no 1 pp 12ndash17 2010
[8] C Liu and Z-L Ji ldquoComputational fluid dynamics-basednumerical analysis of acoustic attenuation and flow resistancecharacteristics of perforated tube silencersrdquo Journal of Vibrationand Acoustics vol 136 no 2 Article ID 021006 11 pages 2014
[9] H-D Ju S-B Lee and Y-B Park ldquoTransmission loss estima-tion of splitter silencer using multi-domain BEMrdquo Journal ofMechanical Science and Technology vol 21 no 12 pp 2073ndash2081 2007
[10] Z L Ji ldquoBoundary element acoustic analysis of hybrid expan-sion chamber silencers with perforated facingrdquo EngineeringAnalysis with Boundary Elements vol 34 no 7 pp 690ndash6962010
[11] C Jiang T W Wu M B Xu and C Y R Cheng ldquoBEMmodeling of mufflers with diesel particulate filters and catalyticconvertersrdquoNoise Control Engineering Journal vol 58 no 3 pp243ndash250 2010
[12] C I J Young and M J Crocker ldquoPrediction of transmissionloss in mufflers by the finite element methodrdquo Journal of theAcoustical Society of America vol 57 no 1 pp 144ndash148 1975
[13] O Z Mehdizadeh and M Paraschivoiu ldquoA three-dimensionalfinite element approach for predicting the transmission loss inmufflers and silencers with no mean flowrdquo Applied Acousticsvol 66 no 8 pp 902ndash918 2005
[14] Z Kang and Z Ji ldquoAcoustic length correction of duct extensioninto a cylindrical chamberrdquo Journal of Sound and Vibration vol310 no 4-5 pp 782ndash791 2008
[15] Y S GeH B Zhang Y R Zhang JW Tan XM Zhang andXK Han ldquoAn analysis on 3D acoustic performance of automotiveexhaust mufflerrdquo Automotive Engineering vol 28 no 1 pp 51ndash55 2006 (Chinese)
[16] P Chaitanya and M L Munjal ldquoEffect of wall thickness on theend corrections of the extended inlet and outlet of a double-tuned expansion chamberrdquo Applied Acoustics vol 72 no 1 pp65ndash70 2011
[17] J Fu W Chen Y Tang W H Yuan G M Li and Y Li ldquoMod-ification of exhaust muffler of a diesel engine based on finiteelement method acoustic analysisrdquo Advances in MechanicalEngineering vol 7 no 4 11 pages 2015
[18] K S Peat ldquoEvaluation of four-pole parameters for ducts withflow by the finite element methodrdquo Journal of Sound andVibration vol 84 no 3 pp 389ndash395 1982
[19] X R Wang and Z L Ji ldquoBoundary element analysis of four-pole parameters and transmission loss of silencers with flowrdquoChinese Journal of Computational Physics vol 24 no 6 pp 717ndash724 2007 (Chinese)
[20] N Gil-Negrete A Rivas and J Vinolas ldquoPredicting thedynamic behaviour of hydrobushingsrdquo Shock andVibration vol12 no 2 pp 91ndash107 2005
[21] S N Panigrahi and M L Munjal ldquoBackpressure considera-tions in designing of cross flow perforated-element reactivesilencersrdquo Noise Control Engineering Journal vol 55 no 6 pp504ndash515 2007
[22] A J Torregrosa P Fajardo A Gil and R Navarro ldquoDevelop-ment of non-reflecting boundary condition for application in3D computational fluid dynamics codesrdquo Engineering Applica-tions of Computational Fluid Mechanics vol 6 no 3 pp 447ndash460 2012
[23] C-NWang ldquoAboundary element analysis for simple expansionsilencers with mean flowrdquo Journal of the Chinese Institute ofEngineers vol 23 no 4 pp 529ndash536 2000
[24] S-H Lee and J-G Ih ldquoEmpirical model of the acousticimpedance of a circular orifice in grazing mean flowrdquo Journalof the Acoustical Society of America vol 114 no 1 pp 98ndash1132003
[25] F L Zhan and J W Xu VirtualLab Acoustics Simulation fromEntry to Master Northwestern Polytechnical University PressXian China 2013 (Chinese)
[26] ANSYS Inc ANSYS FLUENT 145 in Workbench Userrsquos GuideANSYS Inc New York NY USA 2012
[27] LMS International NV LMS VirtualLab Online Help11-SL2LMS International N V Leuven Belgium 2013
[28] C Liu Z L Ji and Z Fang ldquoNumerical analysis of acousticattenuation and flow resistance characteristics of double expan-sion chamber silencersrdquo Noise Control Engineering Journal vol61 no 5 pp 487ndash499 2013
[29] M L Munjal Acoustic of Ducts and Mufflers Wiley New YorkNY USA 2014
[30] R Singh and T Katra ldquoDevelopment of an impulse techniquefor measurement of muffler characteristicsrdquo Journal of Soundand Vibration vol 56 no 2 pp 279ndash298 1978
[31] J M Middelberg T J Barber S S Leong K P Byrne andE Leonardi ldquoCFD analysis of the acoustic and mean flowperformance of simple expansion chamber mufflersrdquo in Pro-ceedings of theASME InternationalMechanical EngineeringCon-gress and Exposition pp 151ndash156 Anaheim Calif USA Novem-ber 2004
12 Shock and Vibration
[32] B K Gardner A Mejdi F Mendonca and D Copley ldquoUsingCFD flow fields to inform acoustic finite element models ofcomplex mufflers with thermal and flow effectsrdquo in Proceedingsof the 44th International Congress and Exposition on NoiseControl Engineering Paper 15-665 San Francisco Calif USAAugust 2015
[33] E Dokumaci ldquoEffect of sheared grazing mean flow on acoustictransmission in perforated pipe mufflersrdquo Journal of Sound andVibration vol 283 no 3ndash5 pp 645ndash663 2005
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Shock and Vibration
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International Journal of
2 Shock and Vibration
l1
l
Dd
(a)l
Dd
(b)
Figure 1 Geometries of the silencers considered (a) circle expansion chamber silencer and (b) straight-through perforated pipe silencer
pipe silencers with the help of perforate impedance modelsFurthermore the effects of perforation length and porosityon the acoustic performance are investigated Chaitanya andMunjal [16] used 3D FEM analysis to investigate the effectof wall thickness of the inletoutlet duct on end correctionand their predictions are validated by comparing themwith experimental data In order to improve the acousticattenuation performance of an exhaust muffler in 175 series ofagriculture diesel engine Fu et al [17] established a 3Dmodelfor the muffler and then employed commercial finite elementsoftware package to calculate the TL and their predictionsshowed very close agreement with experimental data
In the aforementioned works the applications of FEMmainly focus on predictingTL in silencerswithoutmean flowOf course FEM is capable of considering the effect of meanflow by assuming that the acoustic field is superimposedover the decoupled mean flow but this mean flow must beimported from an external steady flow computation that isoften performed by a simplified potential-flow approach [1819] in previous works In this paper to acquire amore realisticflow distribution inside the silencer the CFD simulationwith proper turbulence model which is extremely useful indetermining the flow distribution and commonly used foranalyzing themean flow performance [6 8 20ndash22] is utilizedto perform the external steady flow computation via commer-cial software ANSYS FLUENT 145 After finishing the CFDcomputation themean flow data are used as an input into theacoustic field and then an acoustic response analysis is car-ried out using FEMvia commercial software LMSVirtualLab110 Finally the TL with the effect of mean flow is calculated
2 Method
21 Silencer Modeling In present work the circle expansionchamber silencer with extended inlet used in [23] and threestraight-through perforated pipe silencers used in [24] areconsidered Also the published experimental data from theseauthors are used as a basis for comparison of the numericalresults presented in this paper Figure 1 shows the 3Dgeometries of the silencers considered here and their precisedimensions are given in Table 1 where 119889ℎ and 120590 denote thediameter of the orifice on the perforated pipe and the porosityrespectively
Table 1 Dimensions for the silencers considered (unit mm)
Silencer 119863 119889 119897 1198971 119889ℎ 120590 ()Expansion chamber 108 40 208 52 mdash mdashPerforated pipe 1 (1198751) 110 32 200 mdash 4 47Perforated pipe 2 (1198752) 110 32 200 mdash 6 90Perforated pipe 3 (1198753) 110 32 200 mdash 8 147
Tetrahedral mesh is chosen to discretize the computa-tional field of the silencer due to its high flexibility Twodifferent meshes namely CFD mesh and acoustic mesh willbe used for the solution of mean flow and acoustic problemsrespectively For the expansion chamber silencer the elementsizes of CFD and acoustic meshes are 4mm and 8mmrespectively and the CFD mesh is composed of 131111 nodesand 406204 elements the acousticmesh is composed of 51972nodes and 35807 elements For the straight-through perfo-rated pipe silencer whose geometry is relatively complex thecomputational model is split into several parts to generatemesh individually in order to decrease computational costAn element size of 2mm is used for the perforation area inboth CFD and acoustic meshes and the element sizes for therest of the two meshes are 4mm and 10mm respectivelyTake silencer 1198752 as an example the CFD mesh is composedof 206827 nodes and 1142767 elements the acoustic mesh iscomposed of 668038 nodes and 479644 elements
Figures 2(a) and 3(a) show the generated CFD meshwhich is fine and dense and the mesh near to the wallsis densified further in order to resolve the boundary layerCompared with the CFD mesh the acoustic mesh shown inFigures 2(b) and 3(b) is coarse and thin But it should be notedthat to ensure computational accuracy the maximum size ofthe acoustic mesh must meet the following formulation [25]
119871 le119888
6119891max (1)
where 119888 is the speed of sound and 119891max is the maximumfrequency of interest The maximum achieved frequencyof acoustic mesh can be calculated directly in VirtualLaband it is found that the maximum achieved frequencies ofgenerated acoustic meshes for the studied silencers are all
Shock and Vibration 3
(a) (b)
Figure 2 Geometry of meshes for the expansion chamber silencer (a) CFD mesh and (b) acoustic mesh
(a) (b)
Figure 3 Geometry of meshes for the straight-through perforated pipe silencer (a) CFD mesh and (b) acoustic mesh
above 3500Hz well over the maximum frequency of interest(3000Hz) Therefore the accuracy of acoustic computationcan be ensured
22 Prediction of TL In the CFD steady flow computationthe data type used is double precision the solver imple-mented is a pressure-based implicit solver SIMPLEC pres-sure-velocity coupling algorithm is chosenwith second-orderscheme for spatial discretisation and the realizable 119896-epsilonturbulence model is employed [26] The fluid material isair with the density conforming to the ideal gas law Theboundary conditions consist of the following (i) amass-flow-inlet with constant mass flux (ii) a pressure-outlet with con-stant static pressure in this case 0 Pa relative to one standardatmospheric pressure and (iii) a series of walls assumed tobe stationary with no slip and adiabatic After convergenceof the CFD computation the flow velocity data are exportedinto format CGNS (CFD General Notation System) andthen imported to the acoustic field to serve as a mean flowboundary condition of the acoustic response analysis (iethe mean flow field is superimposed over the acoustic field)Note that the purpose of using this CFD simulation is toobtain a more realistic and detailed flow velocity distributioninside the silencers rather than to consider the viscous effectof mean flow on sound propagation as the full time-domainCFD method [7 8] conducts
The data transfer between acoustic and mean flow prob-lems is accomplished by mesh mapping function that Vir-tualLab provides Because there is no one-to-one correspon-dence between nodes of generated CFD and acoustic meshesan appropriate mapping algorithm should be employed Inthis paperMaximum Distance Algorithm [27] which is oftenapplied to set a mesh mapping between two meshes withdifferent density of nodes is employed and this algorithmincludes two necessary parameters (i) number of nodes (119873)it is the maximum number of nodes from the source mesh(CFDmesh) that is considered for mapping with one node ofthe target mesh (acoustic mesh) and (ii) maximum distance(119877) only the nodes of the source mesh lying inside a spherewith radius 119877 centered at the node of target mesh are takeninto account 119873 closest to a given source node are used totransfer data to the target node The data value assigned tothe target node is a weighted average of the value at the 119873source nodes The weights are [27]
119882119894 =1119889119894
sum119873
119894=1(1119889119894)
(2)
The transferred value on the target node is then
VTarget =sum119873
119894=1(VSource119894
119889119894)
sum119873
119894=1(1119889119894)
(3)
4 Shock and Vibration
x = 0
pincpref
ptrapout
Anechoic endpin in
Figure 4 Theory for TL calculation
where 119889119894 is the distance between source node and target nodeand VSource is the value of source node The 119873 and 119877 couldbe given automatically when CFD and acoustic meshes areintroduced to the data transfer module in VirtualLab herewe calculate directly using the defaults
After finishing the data transfer the acoustic responseanalysis is performed with 10Hz spacing using FEM For thesound field inside the silencer the governing formulation isHelmholtz equation as [13]
nabla2119901 + 1198962119901 = 0 (4)
where119901 is the acoustic pressure 119896 is thewave number definedas 119896 = 120596119888 120596 is the angular frequency and 119888 is the speed ofsound Galerkinrsquos method of weighted residuals is applied to(4) and the acoustic finite element formulation [28] is formed
([119872] minus 1198962[119875]) 119901 = minus119895120588120596 119865 (5)
where [119872] and [119875] are the inertia and stiffness matrices ofthe element 119901 is the vector of acoustic pressure at all nodesof the system 120588 is the density of the medium and 119865 is theforcing vector at all nodes of the system At the inlet of thesilencer a unit velocity of 119906in = 1ms is imposed and theoutlet is defined to be an anechoic end by setting an AnechoicEndDuct Property inVirtualLab In order tomodel the effectof mean flow on sound propagation themean flow boundarycondition is set on the inlet [27] Applying these boundaryconditions and solving (5) may obtain the sound pressure atall nodes of the system And then the TL is determined by[8] Consider
TL = 20 log10[(
119860 in119860out
)
12 10038161003816100381610038161003816100381610038161003816
119901inc119901tra
10038161003816100381610038161003816100381610038161003816] (6)
where 119860 in and 119860out are the cross-sectional areas of the inletand outlet of the silencer respectively 119901inc is the acousticpressure of incident wave at the inlet of the silencer and119901tra is the acoustic pressure of transmitted wave at the outletof the silencer However it should be pointed out that theresults obtained using FEM are acoustic pressure at the inletand outlet (119901in and 119901out) which include the acoustic pressureof reflective wave (119901ref ) as shown in Figure 4 where 119909represents the coordinate of the point along the silencer axisTherefore (6) should be further deduced to build the rela-tionship between 119901in 119901out and 119901inc 119901tra
In the frequency range of interest for silencer analysisthese acoustic pressure waves typically travel through the
0 1
2 34
0
2
4
6
8
10
12
67 8910 12
Velo
city
-mag
nitu
de
11
(ms
)
Figure 5 Counters of velocity-magnitude for the expansion cham-ber silencer with inlet flow velocity of V = 102ms
9376833472936251520941673125208410420000 Tu
rbul
ence
kin
etic
ener
gy (J
kg)
Figure 6 Counters of turbulent kinetic energy for the expansionchamber silencer with inlet flow velocity of V = 102ms
inlet and outlet pipes as planewaves [17]When thewave trav-els in an inviscid moving medium the 1D wave formulationis [29]
1205972119901
1205971199052+ 2119881
1205972119901
120597119909120597119905+ (1198812minus 1198882)1205972119901
1205971199092= 0 (7)
where 119881 is the flow velocity of the medium Solving (7) withthe corresponding boundary and initial conditions in thetime-domain gives 119901 as a function of time and space [13] Byassuming a time-harmonic solution for the acoustic pressure(ie assuming that the time dependence takes an exponentialform) (7) is solved to obtain the acoustic pressure at the inletwhich is written as
119901in = (119901inc119890minus119895119896119909(1+119872)
+ 119901ref119890+119895119896119909(1minus119872)
) 119890119895120596119905 (8)
where 119901ref is the acoustic pressure of reflective wave at theinlet and119872 is the mean flow Mach number defined as 119881 =
119872119888 The particle velocity at the inlet also satisfies the samewave formulation and one can write
119906in =1
120588119888(119901inc119890
minus119895119896119909(1+119872)minus 119901ref119890
+119895119896119909(1minus119872)) 119890119895120596119905 (9)
where 120588119888 represents the characteristic impendence of themedium at the inlet As mentioned before there are 119909 = 0
Shock and Vibration 5
37
28
19
9
0
Velo
city
-vec
tor (
ms
)
(a) Velocity-vector
73
55
36
18
0
Velo
city
-vec
tor (
ms
)
(b) Velocity-vector
38
28
19
9
0
Velo
city
-vec
tor (
ms
)
(c) Velocity-vector
Figure 7 Velocity-vectors for the straight-through perforated pipe silencers (a) silencer1198751119872 = 01 (b) silencer1198752119872 = 02 and (c) silencer1198753119872 = 01
39701352923088326473220641765513246883744280019
Turb
ulen
ce k
inet
icen
ergy
(Jk
g)
(a) Turbulence kinetic energy
16721814864713007611150692935743645579437223186520082
Turb
ulen
ce k
inet
icen
ergy
(Jk
g)
(b) Turbulence kinetic energy
617005486048019411793433827498206571381769760136
Turb
ulen
ce k
inet
icen
ergy
(Jk
g)
(c) Turbulence kinetic energy
Figure 8 Counters of turbulent kinetic energy for the straight-through perforated pipe silencers (a) silencer 1198751119872 = 01 (b) silencer 1198752119872 = 02 and (c) silencer 119875
3119872 = 01
and 119906in = 1ms at the inlet and with neglecting ldquo119890119895119908119905rdquo item(8) and (9) reduce to
119901in = 119901inc + 119901ref
119906in =1
120588119888(119901inc minus 119901ref) = 1
(10)
which yield
119901inc =119901in + 120588119888
2 (11)
In addition the outlet is defined to be an anechoic end (iethe acoustic pressure of reflective wave at the outlet is 0) sothere is
119901tra = 119901out (12)
6 Shock and Vibration
200
180
160
140
120
100
80
60
Acou
stic p
ress
ure l
evel
(dB)
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
InletOutlet
Figure 9 Acoustic pressure level for the inlet and outlet of the expansion chamber silencer with inlet flow velocity of V = 102ms200
180
160
140
120
100
80
Acou
stic p
ress
ure l
evel
(dB)
InletOutlet
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
(a)
200
180
160
140
120
100
80
Acou
stic p
ress
ure l
evel
(dB)
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
InletOutlet
(b)200
180
160
140
120
100
80
Acou
stic p
ress
ure l
evel
(dB)
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
InletOutlet
(c)Figure 10 Acoustic pressure level for the inlet and outlet of the straight-through perforated pipe silencers (a) silencer 1198751 119872 = 01 (b)silencer 119875
2119872 = 02 and (c) silencer 119875
3119872 = 01
Shock and Vibration 7
50
60
40
30
20
10
0
TL (d
B)
Published experimental dataFEMPredicted by literature [23]
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
Figure 11 Measured and predicted TL for the expansion chamber silencer with inlet flow velocity of V = 102ms
Substituting (11) and (12) into (6) yields
TL = 10 log10[(119901in + 120588119888)
2
41199012out
119860 in119860out
]
= 10 log10((119901in + 120588119888) (119901in + 120588119888)
4119901out119901out
119860 in119860out
)
(13)
It should be noted that the obtained acoustic pressure is infrequency-domain and therefore has a complex value In thispaper the temperature and density of the medium (air) are119879 = 288K and 120588 = 1225 kgm3 respectively and the speedof sound in air is 119888 = 340ms
3 Results and Discussion
31 Validation of the 3D Numerical Method Following thecalculation steps stated in Section 22 CFD steady flowcomputation is performed first Figure 5 shows the computedvelocity contours on the axial cutting plane of the expansionchamber silencer with extended inlet it is found that thevelocity distribution is uneven The flow velocity in the inletand outlet pipes are higher than that in the chamber and thesudden section area change enhances the turbulent kineticenergy as shown in Figure 6 Figure 7 shows the veloc-ity-vectors for the three straight-through perforated pipesilencers with a mean flow Mach number of 119872 = 01 or02 Flow circulations can be observed in the rear part of thechamber and the velocity in the pipe is much higher thanthat in the orifices and chamber Moreover the magnitudeand direction of cross-flow velocity through the perforationsare different along the axial direction In addition under theaction of pressure difference between the chamber and perfo-rated pipe the gas flows into the chamber through the orificesand then flows back again into the pipe which enhancesthe turbulent kinetic energy near the orifices as shown in
Figure 8 Generally speaking the flow velocity distributionsinside the studied silencers are anisotropic and nonuniformand the gas flow is accompanied with turbulence
After importing the mean flow data to the acoustic fieldby mesh mapping acoustic response analysis is performedto acquire acoustic pressure at the inlet and outlet as shownin Figures 9 and 10 To validate the accuracy of the 3Dnumerical method published experimental and numericalresults for the studied silencers are comparedwith the presentpredictions
Figure 11 compares the TL results for the expansionchamber silencer with extended inlet from numerical andexperimental methodsThe present predictions agree reason-ably well with the experimental data in the frequency range ofinterest Some deviation from the measurements is observedfor example near the resonance peak This discrepancy maybe attributed to the fact that (i) the medium viscous effectsand wall thickness are neglected in the FEM calculation and(ii) flow noise generated inside the silencer is neglected inthe simulation but the noise is included in the experimentsFurthermore the present FEM results are compared withthe numerical results from literature [23] One can see thatthe present FEM yields better results between the predictedTL curves That is because the method employed in theliterature neglects the turbulence inside the silencer and usesthe simplified mean flow velocity In contrast the presentstudy may acquire more detailed distribution of mean flowthrough the CFD steady flow computation with the properturbulence model
In Figure 12 a comparison between the present predic-tions and measurements shows a good agreement in generalbetween TL results obtained for the three straight-throughperforated pipe silencers studied here However it is foundthat the present predicted TL values are slightly less thanthose measured This is because the influence of mean flowon the sound propagation in the silencer can be explained as
8 Shock and Vibration
50
40
30
20
10
00 500 1000 1500 2000 2500 3000
Frequency (Hz)
TL (d
B)
Published experimental dataFEMPredicted by literature [24]
(a)
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
50
40
30
20
10
0
TL (d
B)
Published experimental dataFEMPredicted by literature [24]
(b)
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
50
40
30
20
10
0
TL (d
B)
Published experimental dataFEMPredicted by literature [24]
(c)
Figure 12 Measured and predicted TL for the straight-through perforated pipe silencers (a) silencer 1198751119872 = 01 (b) silencer 1198752119872 = 02and (c) silencer 1198753119872 = 01
the convective and dissipative effects [7] and the convectiveeffect can be considered by importing the decouple meanfrom an external steady flow computation to the acousticfield but the dissipative effect of medium viscous (especiallyin the orifices) which can cause sound energy loss and thusincrease TL is not included in the FEM calculation just likethe conventional frequency-domain method At present lotsof studies such as [24] mainly focus on applying mathe-matical modeling of perforate impedance to calculate andanalyze the acoustic attenuation performance of perforatedpipe silencer In the absence of mean flow the acousticperformance of the silence can be accurately predicted withthe help of perforate impedance models However when
mean flow is present rigorous mathematical modeling ofthe mechanisms that determine the perforate impedance isextremely difficult Therefore most of current impedancemodels considering the mean flow effect are empirical Incontrast although there is a lack of consideration of meanflow dissipative effect on sound propagation in present FEMby decoupling the problems this method avoids complexmathematical calculation and it is accessible and easy to useFurthermore the predicted results presented are not badTherefore it is valuable for predicting the acoustic attenuationperformance of perforated pipe silencer
At present with the development of computer perfor-mance the full time-domain CFD method such as that
Shock and Vibration 9
00
500 1000 1500 2000 2500 3000
Frequency (Hz)
TL (d
B)10
20
30
40
50
60
= 0
= 30ms = 60ms
Figure 13 Effect of flow velocity on TL of the expansion chamber silencer
performed in [8] has also attracted the interest of researchersThe main advantage of this method is that the dissipativeeffect of medium viscous could be better represented How-ever compared with the present method the main problemwhen using the time-domain CFD method is the CPU timeconsumed during the transient flow computation due tothe fact that long upstream and downstream pipes typicallyexceeding 15 times the length of the silencer are requiredto capture isolated incident and transmitted signals and thetime window (record length of data) must be long enoughto capture the entire pressure signals Moreover when meanflow is present the CFD transient flow computation needs tobe run twice (with and without impulse signal) Additionallyit can be seen from [8] that the TL curves calculated by thetime-domain CFD method are not smooth and have somesawteeth This is because the time-domain CFD method isa simulation of the process of an impulse technique [30]for measuring silencer acoustic performance and thereforethe predicted TL curves are easy to fluctuate like thoseobtained from the impulse technique Middelberg et al [31]investigated the effect of mesh size on TL obtained from thetime-domain CFD method and they found that for higherfrequencies the coarse mesh would influence the accuracy ofsolution due to the inability of the mesh to resolve the wave-length with a sufficient number of points and introducedthe artificial numerical dissipation Therefore the mesh sizefor the time-domain CFD method should be small enoughto avoid high-frequency dissipation As mentioned in Sec-tion 21 two different meshes CFD mesh and acoustic meshare used for the solution of the mean flow and acousticproblems when employing present method Compared withthe mesh used in the time-domain CFDmethod the require-ments of the CFD mesh for the steady flow computation inpresent method are much reduced [32] but it should be finerthan the acoustic mesh
32 Effect of Mean Flow on Silencer Acoustic Attenuation Per-formance Two main effects of mean flow on silencer acous-tic performance can be distinguished one is to affect thesound propagation in the silencer (stated in Section 31) Theother is to induce aerodynamic noise due to turbulence Insilencers the typical mean flow Mach number is below 03[33] and the aerodynamic noise is considered to be weakTherefore the aerodynamic noise is neglected in this work
Figure 13 shows that the predicted TL curves of theexpansion chamber silencer with the flow velocity variedbetween 0ms and 60ms It is observed that the shape ofTL curve with mean flow is much similar to that withoutmean flow The presence of mean flow increases the TLat most frequencies and decreases the resonance peak andTL increases further as flow velocities increase Figure 14shows the effect of mean flow on TL of the straight-throughperforated pipe silencers with different flow velocities It canbe seen from these pictures that the mean flow has littleinfluence on the acoustic attenuation in the plane wave rangeand leads to complex variation of TL curves in the non-plane wave Overall except that the presence of mean flowremarkably decreases resonance peak the acoustic attenu-ation performance of the straight-through perforated pipesilencers increases at most frequencies as flow velocity isincreased especially at higher frequencies
4 Conclusions
In this paper a 3D numerical method is employed to inves-tigate the acoustic attenuation performance of a circularexpansion chamber silencer with extended inlet and threestraight-through perforated pipe silencers in the presence ofmean flow By decoupling the problem the linear acousticsare away from the mean flow computation CFD and FEM
10 Shock and Vibration
= 0
= 30ms = 60ms
00
500 1000 1500 2000 2500 3000
Frequency (Hz)
TL (d
B)
10
20
30
40
50
(a)
= 0
= 30ms = 60ms
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
0
TL (d
B)
10
20
30
40
50
(b)
= 0
= 30ms = 60ms
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
0
TL (d
B)
10
20
30
40
50
(c)
Figure 14 Effect of flow velocity on TL of the straight-through perforated pipe silencers (a) silencer 1198751 (b) silencer 1198752 and (c) silencer 1198753
are employed to perform the steady flow computation andacoustic response analysis respectively The data transferis accomplished by mesh mapping A comparison betweenpresent results and previously published experimental andnumerical results indicates that the present 3D numericalmethod is capable of delivering reasonable predictions Themajor advantage of present method is that it is accessible andeasy to use and avoids complexmathematical calculationwiththe help of simulation software especially for the perforatedpipe silencer while the major drawback of this method liesin the considerable computational effort and cost that arerequired to acquire a complete and accurate solution in the3D calculations
Furthermore the TL of studied silencers with differentflow velocities is calculated It is concluded that the presenceof mean flow decreases the resonance peak and increases theacoustic attenuation at most frequencies for the expansionchamber silencer For the straight-through perforated pipesilencer mean flow has little influence on the acoustic atten-uation in the plane wave range and remarkably decreasesthe resonance peak and increases the acoustic attenuation athigher frequencies
Conflict of Interests
The authors declare that there is no conflict of interests withregard to this study and the publication of this paper
Shock and Vibration 11
Acknowledgments
The authors are grateful for the grants from National NaturalScience Foundation of China (51275082 11272273) Funda-mental Research Fund of Central Universities (N130403009)Research Fund for Doctoral Program of Higher Education(20100042110013) and Program for Liaoning InnovativeResearch Team in University (LT2014006)
References
[1] M G Prasad and M J Crocker ldquoInsertion loss studies onmodels of automotive exhaust systemsrdquo Journal of the AcousticalSociety of America vol 70 no 5 pp 1339ndash1344 1981
[2] M L Munjal and P T Thawani ldquoOn the transfer matrix for auniform tube with a moving mediumrdquo Journal of Sound andVibration vol 91 no 4 pp 597ndash599 1983
[3] K Narayana Rao and M L Munjal ldquoExperimental evaluationof impedance of perforates with grazing flowrdquo Journal of Soundand Vibration vol 108 no 2 pp 283ndash295 1986
[4] Y H Kim S H Kim B D Lim and Y K Kwak ldquoExperimentalstudy of acoustic characteristics of expansion chamber withmean flowsrdquo KSME Journal vol 2 no 2 pp 125ndash132 1988
[5] Y Auregan and M Leroux ldquoFailures in the discrete modelsfor flow duct with perforations an experimental investigationrdquoJournal of Sound andVibration vol 265 no 1 pp 109ndash121 2003
[6] A Broatch XMargot A Gil and F DDenia ldquoACFD approachto the computation of the acoustic response of exhaustmufflersrdquoJournal of Computational Acoustics vol 13 no 2 pp 301ndash3162005
[7] Z L Ji H S Xu and Z X Kang ldquoInfluence of mean flowon acoustic attenuation performance of straight-through per-forated tube reactive silencers and resonatorsrdquo Noise ControlEngineering Journal vol 58 no 1 pp 12ndash17 2010
[8] C Liu and Z-L Ji ldquoComputational fluid dynamics-basednumerical analysis of acoustic attenuation and flow resistancecharacteristics of perforated tube silencersrdquo Journal of Vibrationand Acoustics vol 136 no 2 Article ID 021006 11 pages 2014
[9] H-D Ju S-B Lee and Y-B Park ldquoTransmission loss estima-tion of splitter silencer using multi-domain BEMrdquo Journal ofMechanical Science and Technology vol 21 no 12 pp 2073ndash2081 2007
[10] Z L Ji ldquoBoundary element acoustic analysis of hybrid expan-sion chamber silencers with perforated facingrdquo EngineeringAnalysis with Boundary Elements vol 34 no 7 pp 690ndash6962010
[11] C Jiang T W Wu M B Xu and C Y R Cheng ldquoBEMmodeling of mufflers with diesel particulate filters and catalyticconvertersrdquoNoise Control Engineering Journal vol 58 no 3 pp243ndash250 2010
[12] C I J Young and M J Crocker ldquoPrediction of transmissionloss in mufflers by the finite element methodrdquo Journal of theAcoustical Society of America vol 57 no 1 pp 144ndash148 1975
[13] O Z Mehdizadeh and M Paraschivoiu ldquoA three-dimensionalfinite element approach for predicting the transmission loss inmufflers and silencers with no mean flowrdquo Applied Acousticsvol 66 no 8 pp 902ndash918 2005
[14] Z Kang and Z Ji ldquoAcoustic length correction of duct extensioninto a cylindrical chamberrdquo Journal of Sound and Vibration vol310 no 4-5 pp 782ndash791 2008
[15] Y S GeH B Zhang Y R Zhang JW Tan XM Zhang andXK Han ldquoAn analysis on 3D acoustic performance of automotiveexhaust mufflerrdquo Automotive Engineering vol 28 no 1 pp 51ndash55 2006 (Chinese)
[16] P Chaitanya and M L Munjal ldquoEffect of wall thickness on theend corrections of the extended inlet and outlet of a double-tuned expansion chamberrdquo Applied Acoustics vol 72 no 1 pp65ndash70 2011
[17] J Fu W Chen Y Tang W H Yuan G M Li and Y Li ldquoMod-ification of exhaust muffler of a diesel engine based on finiteelement method acoustic analysisrdquo Advances in MechanicalEngineering vol 7 no 4 11 pages 2015
[18] K S Peat ldquoEvaluation of four-pole parameters for ducts withflow by the finite element methodrdquo Journal of Sound andVibration vol 84 no 3 pp 389ndash395 1982
[19] X R Wang and Z L Ji ldquoBoundary element analysis of four-pole parameters and transmission loss of silencers with flowrdquoChinese Journal of Computational Physics vol 24 no 6 pp 717ndash724 2007 (Chinese)
[20] N Gil-Negrete A Rivas and J Vinolas ldquoPredicting thedynamic behaviour of hydrobushingsrdquo Shock andVibration vol12 no 2 pp 91ndash107 2005
[21] S N Panigrahi and M L Munjal ldquoBackpressure considera-tions in designing of cross flow perforated-element reactivesilencersrdquo Noise Control Engineering Journal vol 55 no 6 pp504ndash515 2007
[22] A J Torregrosa P Fajardo A Gil and R Navarro ldquoDevelop-ment of non-reflecting boundary condition for application in3D computational fluid dynamics codesrdquo Engineering Applica-tions of Computational Fluid Mechanics vol 6 no 3 pp 447ndash460 2012
[23] C-NWang ldquoAboundary element analysis for simple expansionsilencers with mean flowrdquo Journal of the Chinese Institute ofEngineers vol 23 no 4 pp 529ndash536 2000
[24] S-H Lee and J-G Ih ldquoEmpirical model of the acousticimpedance of a circular orifice in grazing mean flowrdquo Journalof the Acoustical Society of America vol 114 no 1 pp 98ndash1132003
[25] F L Zhan and J W Xu VirtualLab Acoustics Simulation fromEntry to Master Northwestern Polytechnical University PressXian China 2013 (Chinese)
[26] ANSYS Inc ANSYS FLUENT 145 in Workbench Userrsquos GuideANSYS Inc New York NY USA 2012
[27] LMS International NV LMS VirtualLab Online Help11-SL2LMS International N V Leuven Belgium 2013
[28] C Liu Z L Ji and Z Fang ldquoNumerical analysis of acousticattenuation and flow resistance characteristics of double expan-sion chamber silencersrdquo Noise Control Engineering Journal vol61 no 5 pp 487ndash499 2013
[29] M L Munjal Acoustic of Ducts and Mufflers Wiley New YorkNY USA 2014
[30] R Singh and T Katra ldquoDevelopment of an impulse techniquefor measurement of muffler characteristicsrdquo Journal of Soundand Vibration vol 56 no 2 pp 279ndash298 1978
[31] J M Middelberg T J Barber S S Leong K P Byrne andE Leonardi ldquoCFD analysis of the acoustic and mean flowperformance of simple expansion chamber mufflersrdquo in Pro-ceedings of theASME InternationalMechanical EngineeringCon-gress and Exposition pp 151ndash156 Anaheim Calif USA Novem-ber 2004
12 Shock and Vibration
[32] B K Gardner A Mejdi F Mendonca and D Copley ldquoUsingCFD flow fields to inform acoustic finite element models ofcomplex mufflers with thermal and flow effectsrdquo in Proceedingsof the 44th International Congress and Exposition on NoiseControl Engineering Paper 15-665 San Francisco Calif USAAugust 2015
[33] E Dokumaci ldquoEffect of sheared grazing mean flow on acoustictransmission in perforated pipe mufflersrdquo Journal of Sound andVibration vol 283 no 3ndash5 pp 645ndash663 2005
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Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Shock and Vibration 3
(a) (b)
Figure 2 Geometry of meshes for the expansion chamber silencer (a) CFD mesh and (b) acoustic mesh
(a) (b)
Figure 3 Geometry of meshes for the straight-through perforated pipe silencer (a) CFD mesh and (b) acoustic mesh
above 3500Hz well over the maximum frequency of interest(3000Hz) Therefore the accuracy of acoustic computationcan be ensured
22 Prediction of TL In the CFD steady flow computationthe data type used is double precision the solver imple-mented is a pressure-based implicit solver SIMPLEC pres-sure-velocity coupling algorithm is chosenwith second-orderscheme for spatial discretisation and the realizable 119896-epsilonturbulence model is employed [26] The fluid material isair with the density conforming to the ideal gas law Theboundary conditions consist of the following (i) amass-flow-inlet with constant mass flux (ii) a pressure-outlet with con-stant static pressure in this case 0 Pa relative to one standardatmospheric pressure and (iii) a series of walls assumed tobe stationary with no slip and adiabatic After convergenceof the CFD computation the flow velocity data are exportedinto format CGNS (CFD General Notation System) andthen imported to the acoustic field to serve as a mean flowboundary condition of the acoustic response analysis (iethe mean flow field is superimposed over the acoustic field)Note that the purpose of using this CFD simulation is toobtain a more realistic and detailed flow velocity distributioninside the silencers rather than to consider the viscous effectof mean flow on sound propagation as the full time-domainCFD method [7 8] conducts
The data transfer between acoustic and mean flow prob-lems is accomplished by mesh mapping function that Vir-tualLab provides Because there is no one-to-one correspon-dence between nodes of generated CFD and acoustic meshesan appropriate mapping algorithm should be employed Inthis paperMaximum Distance Algorithm [27] which is oftenapplied to set a mesh mapping between two meshes withdifferent density of nodes is employed and this algorithmincludes two necessary parameters (i) number of nodes (119873)it is the maximum number of nodes from the source mesh(CFDmesh) that is considered for mapping with one node ofthe target mesh (acoustic mesh) and (ii) maximum distance(119877) only the nodes of the source mesh lying inside a spherewith radius 119877 centered at the node of target mesh are takeninto account 119873 closest to a given source node are used totransfer data to the target node The data value assigned tothe target node is a weighted average of the value at the 119873source nodes The weights are [27]
119882119894 =1119889119894
sum119873
119894=1(1119889119894)
(2)
The transferred value on the target node is then
VTarget =sum119873
119894=1(VSource119894
119889119894)
sum119873
119894=1(1119889119894)
(3)
4 Shock and Vibration
x = 0
pincpref
ptrapout
Anechoic endpin in
Figure 4 Theory for TL calculation
where 119889119894 is the distance between source node and target nodeand VSource is the value of source node The 119873 and 119877 couldbe given automatically when CFD and acoustic meshes areintroduced to the data transfer module in VirtualLab herewe calculate directly using the defaults
After finishing the data transfer the acoustic responseanalysis is performed with 10Hz spacing using FEM For thesound field inside the silencer the governing formulation isHelmholtz equation as [13]
nabla2119901 + 1198962119901 = 0 (4)
where119901 is the acoustic pressure 119896 is thewave number definedas 119896 = 120596119888 120596 is the angular frequency and 119888 is the speed ofsound Galerkinrsquos method of weighted residuals is applied to(4) and the acoustic finite element formulation [28] is formed
([119872] minus 1198962[119875]) 119901 = minus119895120588120596 119865 (5)
where [119872] and [119875] are the inertia and stiffness matrices ofthe element 119901 is the vector of acoustic pressure at all nodesof the system 120588 is the density of the medium and 119865 is theforcing vector at all nodes of the system At the inlet of thesilencer a unit velocity of 119906in = 1ms is imposed and theoutlet is defined to be an anechoic end by setting an AnechoicEndDuct Property inVirtualLab In order tomodel the effectof mean flow on sound propagation themean flow boundarycondition is set on the inlet [27] Applying these boundaryconditions and solving (5) may obtain the sound pressure atall nodes of the system And then the TL is determined by[8] Consider
TL = 20 log10[(
119860 in119860out
)
12 10038161003816100381610038161003816100381610038161003816
119901inc119901tra
10038161003816100381610038161003816100381610038161003816] (6)
where 119860 in and 119860out are the cross-sectional areas of the inletand outlet of the silencer respectively 119901inc is the acousticpressure of incident wave at the inlet of the silencer and119901tra is the acoustic pressure of transmitted wave at the outletof the silencer However it should be pointed out that theresults obtained using FEM are acoustic pressure at the inletand outlet (119901in and 119901out) which include the acoustic pressureof reflective wave (119901ref ) as shown in Figure 4 where 119909represents the coordinate of the point along the silencer axisTherefore (6) should be further deduced to build the rela-tionship between 119901in 119901out and 119901inc 119901tra
In the frequency range of interest for silencer analysisthese acoustic pressure waves typically travel through the
0 1
2 34
0
2
4
6
8
10
12
67 8910 12
Velo
city
-mag
nitu
de
11
(ms
)
Figure 5 Counters of velocity-magnitude for the expansion cham-ber silencer with inlet flow velocity of V = 102ms
9376833472936251520941673125208410420000 Tu
rbul
ence
kin
etic
ener
gy (J
kg)
Figure 6 Counters of turbulent kinetic energy for the expansionchamber silencer with inlet flow velocity of V = 102ms
inlet and outlet pipes as planewaves [17]When thewave trav-els in an inviscid moving medium the 1D wave formulationis [29]
1205972119901
1205971199052+ 2119881
1205972119901
120597119909120597119905+ (1198812minus 1198882)1205972119901
1205971199092= 0 (7)
where 119881 is the flow velocity of the medium Solving (7) withthe corresponding boundary and initial conditions in thetime-domain gives 119901 as a function of time and space [13] Byassuming a time-harmonic solution for the acoustic pressure(ie assuming that the time dependence takes an exponentialform) (7) is solved to obtain the acoustic pressure at the inletwhich is written as
119901in = (119901inc119890minus119895119896119909(1+119872)
+ 119901ref119890+119895119896119909(1minus119872)
) 119890119895120596119905 (8)
where 119901ref is the acoustic pressure of reflective wave at theinlet and119872 is the mean flow Mach number defined as 119881 =
119872119888 The particle velocity at the inlet also satisfies the samewave formulation and one can write
119906in =1
120588119888(119901inc119890
minus119895119896119909(1+119872)minus 119901ref119890
+119895119896119909(1minus119872)) 119890119895120596119905 (9)
where 120588119888 represents the characteristic impendence of themedium at the inlet As mentioned before there are 119909 = 0
Shock and Vibration 5
37
28
19
9
0
Velo
city
-vec
tor (
ms
)
(a) Velocity-vector
73
55
36
18
0
Velo
city
-vec
tor (
ms
)
(b) Velocity-vector
38
28
19
9
0
Velo
city
-vec
tor (
ms
)
(c) Velocity-vector
Figure 7 Velocity-vectors for the straight-through perforated pipe silencers (a) silencer1198751119872 = 01 (b) silencer1198752119872 = 02 and (c) silencer1198753119872 = 01
39701352923088326473220641765513246883744280019
Turb
ulen
ce k
inet
icen
ergy
(Jk
g)
(a) Turbulence kinetic energy
16721814864713007611150692935743645579437223186520082
Turb
ulen
ce k
inet
icen
ergy
(Jk
g)
(b) Turbulence kinetic energy
617005486048019411793433827498206571381769760136
Turb
ulen
ce k
inet
icen
ergy
(Jk
g)
(c) Turbulence kinetic energy
Figure 8 Counters of turbulent kinetic energy for the straight-through perforated pipe silencers (a) silencer 1198751119872 = 01 (b) silencer 1198752119872 = 02 and (c) silencer 119875
3119872 = 01
and 119906in = 1ms at the inlet and with neglecting ldquo119890119895119908119905rdquo item(8) and (9) reduce to
119901in = 119901inc + 119901ref
119906in =1
120588119888(119901inc minus 119901ref) = 1
(10)
which yield
119901inc =119901in + 120588119888
2 (11)
In addition the outlet is defined to be an anechoic end (iethe acoustic pressure of reflective wave at the outlet is 0) sothere is
119901tra = 119901out (12)
6 Shock and Vibration
200
180
160
140
120
100
80
60
Acou
stic p
ress
ure l
evel
(dB)
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
InletOutlet
Figure 9 Acoustic pressure level for the inlet and outlet of the expansion chamber silencer with inlet flow velocity of V = 102ms200
180
160
140
120
100
80
Acou
stic p
ress
ure l
evel
(dB)
InletOutlet
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
(a)
200
180
160
140
120
100
80
Acou
stic p
ress
ure l
evel
(dB)
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
InletOutlet
(b)200
180
160
140
120
100
80
Acou
stic p
ress
ure l
evel
(dB)
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
InletOutlet
(c)Figure 10 Acoustic pressure level for the inlet and outlet of the straight-through perforated pipe silencers (a) silencer 1198751 119872 = 01 (b)silencer 119875
2119872 = 02 and (c) silencer 119875
3119872 = 01
Shock and Vibration 7
50
60
40
30
20
10
0
TL (d
B)
Published experimental dataFEMPredicted by literature [23]
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
Figure 11 Measured and predicted TL for the expansion chamber silencer with inlet flow velocity of V = 102ms
Substituting (11) and (12) into (6) yields
TL = 10 log10[(119901in + 120588119888)
2
41199012out
119860 in119860out
]
= 10 log10((119901in + 120588119888) (119901in + 120588119888)
4119901out119901out
119860 in119860out
)
(13)
It should be noted that the obtained acoustic pressure is infrequency-domain and therefore has a complex value In thispaper the temperature and density of the medium (air) are119879 = 288K and 120588 = 1225 kgm3 respectively and the speedof sound in air is 119888 = 340ms
3 Results and Discussion
31 Validation of the 3D Numerical Method Following thecalculation steps stated in Section 22 CFD steady flowcomputation is performed first Figure 5 shows the computedvelocity contours on the axial cutting plane of the expansionchamber silencer with extended inlet it is found that thevelocity distribution is uneven The flow velocity in the inletand outlet pipes are higher than that in the chamber and thesudden section area change enhances the turbulent kineticenergy as shown in Figure 6 Figure 7 shows the veloc-ity-vectors for the three straight-through perforated pipesilencers with a mean flow Mach number of 119872 = 01 or02 Flow circulations can be observed in the rear part of thechamber and the velocity in the pipe is much higher thanthat in the orifices and chamber Moreover the magnitudeand direction of cross-flow velocity through the perforationsare different along the axial direction In addition under theaction of pressure difference between the chamber and perfo-rated pipe the gas flows into the chamber through the orificesand then flows back again into the pipe which enhancesthe turbulent kinetic energy near the orifices as shown in
Figure 8 Generally speaking the flow velocity distributionsinside the studied silencers are anisotropic and nonuniformand the gas flow is accompanied with turbulence
After importing the mean flow data to the acoustic fieldby mesh mapping acoustic response analysis is performedto acquire acoustic pressure at the inlet and outlet as shownin Figures 9 and 10 To validate the accuracy of the 3Dnumerical method published experimental and numericalresults for the studied silencers are comparedwith the presentpredictions
Figure 11 compares the TL results for the expansionchamber silencer with extended inlet from numerical andexperimental methodsThe present predictions agree reason-ably well with the experimental data in the frequency range ofinterest Some deviation from the measurements is observedfor example near the resonance peak This discrepancy maybe attributed to the fact that (i) the medium viscous effectsand wall thickness are neglected in the FEM calculation and(ii) flow noise generated inside the silencer is neglected inthe simulation but the noise is included in the experimentsFurthermore the present FEM results are compared withthe numerical results from literature [23] One can see thatthe present FEM yields better results between the predictedTL curves That is because the method employed in theliterature neglects the turbulence inside the silencer and usesthe simplified mean flow velocity In contrast the presentstudy may acquire more detailed distribution of mean flowthrough the CFD steady flow computation with the properturbulence model
In Figure 12 a comparison between the present predic-tions and measurements shows a good agreement in generalbetween TL results obtained for the three straight-throughperforated pipe silencers studied here However it is foundthat the present predicted TL values are slightly less thanthose measured This is because the influence of mean flowon the sound propagation in the silencer can be explained as
8 Shock and Vibration
50
40
30
20
10
00 500 1000 1500 2000 2500 3000
Frequency (Hz)
TL (d
B)
Published experimental dataFEMPredicted by literature [24]
(a)
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
50
40
30
20
10
0
TL (d
B)
Published experimental dataFEMPredicted by literature [24]
(b)
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
50
40
30
20
10
0
TL (d
B)
Published experimental dataFEMPredicted by literature [24]
(c)
Figure 12 Measured and predicted TL for the straight-through perforated pipe silencers (a) silencer 1198751119872 = 01 (b) silencer 1198752119872 = 02and (c) silencer 1198753119872 = 01
the convective and dissipative effects [7] and the convectiveeffect can be considered by importing the decouple meanfrom an external steady flow computation to the acousticfield but the dissipative effect of medium viscous (especiallyin the orifices) which can cause sound energy loss and thusincrease TL is not included in the FEM calculation just likethe conventional frequency-domain method At present lotsof studies such as [24] mainly focus on applying mathe-matical modeling of perforate impedance to calculate andanalyze the acoustic attenuation performance of perforatedpipe silencer In the absence of mean flow the acousticperformance of the silence can be accurately predicted withthe help of perforate impedance models However when
mean flow is present rigorous mathematical modeling ofthe mechanisms that determine the perforate impedance isextremely difficult Therefore most of current impedancemodels considering the mean flow effect are empirical Incontrast although there is a lack of consideration of meanflow dissipative effect on sound propagation in present FEMby decoupling the problems this method avoids complexmathematical calculation and it is accessible and easy to useFurthermore the predicted results presented are not badTherefore it is valuable for predicting the acoustic attenuationperformance of perforated pipe silencer
At present with the development of computer perfor-mance the full time-domain CFD method such as that
Shock and Vibration 9
00
500 1000 1500 2000 2500 3000
Frequency (Hz)
TL (d
B)10
20
30
40
50
60
= 0
= 30ms = 60ms
Figure 13 Effect of flow velocity on TL of the expansion chamber silencer
performed in [8] has also attracted the interest of researchersThe main advantage of this method is that the dissipativeeffect of medium viscous could be better represented How-ever compared with the present method the main problemwhen using the time-domain CFD method is the CPU timeconsumed during the transient flow computation due tothe fact that long upstream and downstream pipes typicallyexceeding 15 times the length of the silencer are requiredto capture isolated incident and transmitted signals and thetime window (record length of data) must be long enoughto capture the entire pressure signals Moreover when meanflow is present the CFD transient flow computation needs tobe run twice (with and without impulse signal) Additionallyit can be seen from [8] that the TL curves calculated by thetime-domain CFD method are not smooth and have somesawteeth This is because the time-domain CFD method isa simulation of the process of an impulse technique [30]for measuring silencer acoustic performance and thereforethe predicted TL curves are easy to fluctuate like thoseobtained from the impulse technique Middelberg et al [31]investigated the effect of mesh size on TL obtained from thetime-domain CFD method and they found that for higherfrequencies the coarse mesh would influence the accuracy ofsolution due to the inability of the mesh to resolve the wave-length with a sufficient number of points and introducedthe artificial numerical dissipation Therefore the mesh sizefor the time-domain CFD method should be small enoughto avoid high-frequency dissipation As mentioned in Sec-tion 21 two different meshes CFD mesh and acoustic meshare used for the solution of the mean flow and acousticproblems when employing present method Compared withthe mesh used in the time-domain CFDmethod the require-ments of the CFD mesh for the steady flow computation inpresent method are much reduced [32] but it should be finerthan the acoustic mesh
32 Effect of Mean Flow on Silencer Acoustic Attenuation Per-formance Two main effects of mean flow on silencer acous-tic performance can be distinguished one is to affect thesound propagation in the silencer (stated in Section 31) Theother is to induce aerodynamic noise due to turbulence Insilencers the typical mean flow Mach number is below 03[33] and the aerodynamic noise is considered to be weakTherefore the aerodynamic noise is neglected in this work
Figure 13 shows that the predicted TL curves of theexpansion chamber silencer with the flow velocity variedbetween 0ms and 60ms It is observed that the shape ofTL curve with mean flow is much similar to that withoutmean flow The presence of mean flow increases the TLat most frequencies and decreases the resonance peak andTL increases further as flow velocities increase Figure 14shows the effect of mean flow on TL of the straight-throughperforated pipe silencers with different flow velocities It canbe seen from these pictures that the mean flow has littleinfluence on the acoustic attenuation in the plane wave rangeand leads to complex variation of TL curves in the non-plane wave Overall except that the presence of mean flowremarkably decreases resonance peak the acoustic attenu-ation performance of the straight-through perforated pipesilencers increases at most frequencies as flow velocity isincreased especially at higher frequencies
4 Conclusions
In this paper a 3D numerical method is employed to inves-tigate the acoustic attenuation performance of a circularexpansion chamber silencer with extended inlet and threestraight-through perforated pipe silencers in the presence ofmean flow By decoupling the problem the linear acousticsare away from the mean flow computation CFD and FEM
10 Shock and Vibration
= 0
= 30ms = 60ms
00
500 1000 1500 2000 2500 3000
Frequency (Hz)
TL (d
B)
10
20
30
40
50
(a)
= 0
= 30ms = 60ms
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
0
TL (d
B)
10
20
30
40
50
(b)
= 0
= 30ms = 60ms
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
0
TL (d
B)
10
20
30
40
50
(c)
Figure 14 Effect of flow velocity on TL of the straight-through perforated pipe silencers (a) silencer 1198751 (b) silencer 1198752 and (c) silencer 1198753
are employed to perform the steady flow computation andacoustic response analysis respectively The data transferis accomplished by mesh mapping A comparison betweenpresent results and previously published experimental andnumerical results indicates that the present 3D numericalmethod is capable of delivering reasonable predictions Themajor advantage of present method is that it is accessible andeasy to use and avoids complexmathematical calculationwiththe help of simulation software especially for the perforatedpipe silencer while the major drawback of this method liesin the considerable computational effort and cost that arerequired to acquire a complete and accurate solution in the3D calculations
Furthermore the TL of studied silencers with differentflow velocities is calculated It is concluded that the presenceof mean flow decreases the resonance peak and increases theacoustic attenuation at most frequencies for the expansionchamber silencer For the straight-through perforated pipesilencer mean flow has little influence on the acoustic atten-uation in the plane wave range and remarkably decreasesthe resonance peak and increases the acoustic attenuation athigher frequencies
Conflict of Interests
The authors declare that there is no conflict of interests withregard to this study and the publication of this paper
Shock and Vibration 11
Acknowledgments
The authors are grateful for the grants from National NaturalScience Foundation of China (51275082 11272273) Funda-mental Research Fund of Central Universities (N130403009)Research Fund for Doctoral Program of Higher Education(20100042110013) and Program for Liaoning InnovativeResearch Team in University (LT2014006)
References
[1] M G Prasad and M J Crocker ldquoInsertion loss studies onmodels of automotive exhaust systemsrdquo Journal of the AcousticalSociety of America vol 70 no 5 pp 1339ndash1344 1981
[2] M L Munjal and P T Thawani ldquoOn the transfer matrix for auniform tube with a moving mediumrdquo Journal of Sound andVibration vol 91 no 4 pp 597ndash599 1983
[3] K Narayana Rao and M L Munjal ldquoExperimental evaluationof impedance of perforates with grazing flowrdquo Journal of Soundand Vibration vol 108 no 2 pp 283ndash295 1986
[4] Y H Kim S H Kim B D Lim and Y K Kwak ldquoExperimentalstudy of acoustic characteristics of expansion chamber withmean flowsrdquo KSME Journal vol 2 no 2 pp 125ndash132 1988
[5] Y Auregan and M Leroux ldquoFailures in the discrete modelsfor flow duct with perforations an experimental investigationrdquoJournal of Sound andVibration vol 265 no 1 pp 109ndash121 2003
[6] A Broatch XMargot A Gil and F DDenia ldquoACFD approachto the computation of the acoustic response of exhaustmufflersrdquoJournal of Computational Acoustics vol 13 no 2 pp 301ndash3162005
[7] Z L Ji H S Xu and Z X Kang ldquoInfluence of mean flowon acoustic attenuation performance of straight-through per-forated tube reactive silencers and resonatorsrdquo Noise ControlEngineering Journal vol 58 no 1 pp 12ndash17 2010
[8] C Liu and Z-L Ji ldquoComputational fluid dynamics-basednumerical analysis of acoustic attenuation and flow resistancecharacteristics of perforated tube silencersrdquo Journal of Vibrationand Acoustics vol 136 no 2 Article ID 021006 11 pages 2014
[9] H-D Ju S-B Lee and Y-B Park ldquoTransmission loss estima-tion of splitter silencer using multi-domain BEMrdquo Journal ofMechanical Science and Technology vol 21 no 12 pp 2073ndash2081 2007
[10] Z L Ji ldquoBoundary element acoustic analysis of hybrid expan-sion chamber silencers with perforated facingrdquo EngineeringAnalysis with Boundary Elements vol 34 no 7 pp 690ndash6962010
[11] C Jiang T W Wu M B Xu and C Y R Cheng ldquoBEMmodeling of mufflers with diesel particulate filters and catalyticconvertersrdquoNoise Control Engineering Journal vol 58 no 3 pp243ndash250 2010
[12] C I J Young and M J Crocker ldquoPrediction of transmissionloss in mufflers by the finite element methodrdquo Journal of theAcoustical Society of America vol 57 no 1 pp 144ndash148 1975
[13] O Z Mehdizadeh and M Paraschivoiu ldquoA three-dimensionalfinite element approach for predicting the transmission loss inmufflers and silencers with no mean flowrdquo Applied Acousticsvol 66 no 8 pp 902ndash918 2005
[14] Z Kang and Z Ji ldquoAcoustic length correction of duct extensioninto a cylindrical chamberrdquo Journal of Sound and Vibration vol310 no 4-5 pp 782ndash791 2008
[15] Y S GeH B Zhang Y R Zhang JW Tan XM Zhang andXK Han ldquoAn analysis on 3D acoustic performance of automotiveexhaust mufflerrdquo Automotive Engineering vol 28 no 1 pp 51ndash55 2006 (Chinese)
[16] P Chaitanya and M L Munjal ldquoEffect of wall thickness on theend corrections of the extended inlet and outlet of a double-tuned expansion chamberrdquo Applied Acoustics vol 72 no 1 pp65ndash70 2011
[17] J Fu W Chen Y Tang W H Yuan G M Li and Y Li ldquoMod-ification of exhaust muffler of a diesel engine based on finiteelement method acoustic analysisrdquo Advances in MechanicalEngineering vol 7 no 4 11 pages 2015
[18] K S Peat ldquoEvaluation of four-pole parameters for ducts withflow by the finite element methodrdquo Journal of Sound andVibration vol 84 no 3 pp 389ndash395 1982
[19] X R Wang and Z L Ji ldquoBoundary element analysis of four-pole parameters and transmission loss of silencers with flowrdquoChinese Journal of Computational Physics vol 24 no 6 pp 717ndash724 2007 (Chinese)
[20] N Gil-Negrete A Rivas and J Vinolas ldquoPredicting thedynamic behaviour of hydrobushingsrdquo Shock andVibration vol12 no 2 pp 91ndash107 2005
[21] S N Panigrahi and M L Munjal ldquoBackpressure considera-tions in designing of cross flow perforated-element reactivesilencersrdquo Noise Control Engineering Journal vol 55 no 6 pp504ndash515 2007
[22] A J Torregrosa P Fajardo A Gil and R Navarro ldquoDevelop-ment of non-reflecting boundary condition for application in3D computational fluid dynamics codesrdquo Engineering Applica-tions of Computational Fluid Mechanics vol 6 no 3 pp 447ndash460 2012
[23] C-NWang ldquoAboundary element analysis for simple expansionsilencers with mean flowrdquo Journal of the Chinese Institute ofEngineers vol 23 no 4 pp 529ndash536 2000
[24] S-H Lee and J-G Ih ldquoEmpirical model of the acousticimpedance of a circular orifice in grazing mean flowrdquo Journalof the Acoustical Society of America vol 114 no 1 pp 98ndash1132003
[25] F L Zhan and J W Xu VirtualLab Acoustics Simulation fromEntry to Master Northwestern Polytechnical University PressXian China 2013 (Chinese)
[26] ANSYS Inc ANSYS FLUENT 145 in Workbench Userrsquos GuideANSYS Inc New York NY USA 2012
[27] LMS International NV LMS VirtualLab Online Help11-SL2LMS International N V Leuven Belgium 2013
[28] C Liu Z L Ji and Z Fang ldquoNumerical analysis of acousticattenuation and flow resistance characteristics of double expan-sion chamber silencersrdquo Noise Control Engineering Journal vol61 no 5 pp 487ndash499 2013
[29] M L Munjal Acoustic of Ducts and Mufflers Wiley New YorkNY USA 2014
[30] R Singh and T Katra ldquoDevelopment of an impulse techniquefor measurement of muffler characteristicsrdquo Journal of Soundand Vibration vol 56 no 2 pp 279ndash298 1978
[31] J M Middelberg T J Barber S S Leong K P Byrne andE Leonardi ldquoCFD analysis of the acoustic and mean flowperformance of simple expansion chamber mufflersrdquo in Pro-ceedings of theASME InternationalMechanical EngineeringCon-gress and Exposition pp 151ndash156 Anaheim Calif USA Novem-ber 2004
12 Shock and Vibration
[32] B K Gardner A Mejdi F Mendonca and D Copley ldquoUsingCFD flow fields to inform acoustic finite element models ofcomplex mufflers with thermal and flow effectsrdquo in Proceedingsof the 44th International Congress and Exposition on NoiseControl Engineering Paper 15-665 San Francisco Calif USAAugust 2015
[33] E Dokumaci ldquoEffect of sheared grazing mean flow on acoustictransmission in perforated pipe mufflersrdquo Journal of Sound andVibration vol 283 no 3ndash5 pp 645ndash663 2005
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Shock and Vibration
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International Journal of
4 Shock and Vibration
x = 0
pincpref
ptrapout
Anechoic endpin in
Figure 4 Theory for TL calculation
where 119889119894 is the distance between source node and target nodeand VSource is the value of source node The 119873 and 119877 couldbe given automatically when CFD and acoustic meshes areintroduced to the data transfer module in VirtualLab herewe calculate directly using the defaults
After finishing the data transfer the acoustic responseanalysis is performed with 10Hz spacing using FEM For thesound field inside the silencer the governing formulation isHelmholtz equation as [13]
nabla2119901 + 1198962119901 = 0 (4)
where119901 is the acoustic pressure 119896 is thewave number definedas 119896 = 120596119888 120596 is the angular frequency and 119888 is the speed ofsound Galerkinrsquos method of weighted residuals is applied to(4) and the acoustic finite element formulation [28] is formed
([119872] minus 1198962[119875]) 119901 = minus119895120588120596 119865 (5)
where [119872] and [119875] are the inertia and stiffness matrices ofthe element 119901 is the vector of acoustic pressure at all nodesof the system 120588 is the density of the medium and 119865 is theforcing vector at all nodes of the system At the inlet of thesilencer a unit velocity of 119906in = 1ms is imposed and theoutlet is defined to be an anechoic end by setting an AnechoicEndDuct Property inVirtualLab In order tomodel the effectof mean flow on sound propagation themean flow boundarycondition is set on the inlet [27] Applying these boundaryconditions and solving (5) may obtain the sound pressure atall nodes of the system And then the TL is determined by[8] Consider
TL = 20 log10[(
119860 in119860out
)
12 10038161003816100381610038161003816100381610038161003816
119901inc119901tra
10038161003816100381610038161003816100381610038161003816] (6)
where 119860 in and 119860out are the cross-sectional areas of the inletand outlet of the silencer respectively 119901inc is the acousticpressure of incident wave at the inlet of the silencer and119901tra is the acoustic pressure of transmitted wave at the outletof the silencer However it should be pointed out that theresults obtained using FEM are acoustic pressure at the inletand outlet (119901in and 119901out) which include the acoustic pressureof reflective wave (119901ref ) as shown in Figure 4 where 119909represents the coordinate of the point along the silencer axisTherefore (6) should be further deduced to build the rela-tionship between 119901in 119901out and 119901inc 119901tra
In the frequency range of interest for silencer analysisthese acoustic pressure waves typically travel through the
0 1
2 34
0
2
4
6
8
10
12
67 8910 12
Velo
city
-mag
nitu
de
11
(ms
)
Figure 5 Counters of velocity-magnitude for the expansion cham-ber silencer with inlet flow velocity of V = 102ms
9376833472936251520941673125208410420000 Tu
rbul
ence
kin
etic
ener
gy (J
kg)
Figure 6 Counters of turbulent kinetic energy for the expansionchamber silencer with inlet flow velocity of V = 102ms
inlet and outlet pipes as planewaves [17]When thewave trav-els in an inviscid moving medium the 1D wave formulationis [29]
1205972119901
1205971199052+ 2119881
1205972119901
120597119909120597119905+ (1198812minus 1198882)1205972119901
1205971199092= 0 (7)
where 119881 is the flow velocity of the medium Solving (7) withthe corresponding boundary and initial conditions in thetime-domain gives 119901 as a function of time and space [13] Byassuming a time-harmonic solution for the acoustic pressure(ie assuming that the time dependence takes an exponentialform) (7) is solved to obtain the acoustic pressure at the inletwhich is written as
119901in = (119901inc119890minus119895119896119909(1+119872)
+ 119901ref119890+119895119896119909(1minus119872)
) 119890119895120596119905 (8)
where 119901ref is the acoustic pressure of reflective wave at theinlet and119872 is the mean flow Mach number defined as 119881 =
119872119888 The particle velocity at the inlet also satisfies the samewave formulation and one can write
119906in =1
120588119888(119901inc119890
minus119895119896119909(1+119872)minus 119901ref119890
+119895119896119909(1minus119872)) 119890119895120596119905 (9)
where 120588119888 represents the characteristic impendence of themedium at the inlet As mentioned before there are 119909 = 0
Shock and Vibration 5
37
28
19
9
0
Velo
city
-vec
tor (
ms
)
(a) Velocity-vector
73
55
36
18
0
Velo
city
-vec
tor (
ms
)
(b) Velocity-vector
38
28
19
9
0
Velo
city
-vec
tor (
ms
)
(c) Velocity-vector
Figure 7 Velocity-vectors for the straight-through perforated pipe silencers (a) silencer1198751119872 = 01 (b) silencer1198752119872 = 02 and (c) silencer1198753119872 = 01
39701352923088326473220641765513246883744280019
Turb
ulen
ce k
inet
icen
ergy
(Jk
g)
(a) Turbulence kinetic energy
16721814864713007611150692935743645579437223186520082
Turb
ulen
ce k
inet
icen
ergy
(Jk
g)
(b) Turbulence kinetic energy
617005486048019411793433827498206571381769760136
Turb
ulen
ce k
inet
icen
ergy
(Jk
g)
(c) Turbulence kinetic energy
Figure 8 Counters of turbulent kinetic energy for the straight-through perforated pipe silencers (a) silencer 1198751119872 = 01 (b) silencer 1198752119872 = 02 and (c) silencer 119875
3119872 = 01
and 119906in = 1ms at the inlet and with neglecting ldquo119890119895119908119905rdquo item(8) and (9) reduce to
119901in = 119901inc + 119901ref
119906in =1
120588119888(119901inc minus 119901ref) = 1
(10)
which yield
119901inc =119901in + 120588119888
2 (11)
In addition the outlet is defined to be an anechoic end (iethe acoustic pressure of reflective wave at the outlet is 0) sothere is
119901tra = 119901out (12)
6 Shock and Vibration
200
180
160
140
120
100
80
60
Acou
stic p
ress
ure l
evel
(dB)
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
InletOutlet
Figure 9 Acoustic pressure level for the inlet and outlet of the expansion chamber silencer with inlet flow velocity of V = 102ms200
180
160
140
120
100
80
Acou
stic p
ress
ure l
evel
(dB)
InletOutlet
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
(a)
200
180
160
140
120
100
80
Acou
stic p
ress
ure l
evel
(dB)
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
InletOutlet
(b)200
180
160
140
120
100
80
Acou
stic p
ress
ure l
evel
(dB)
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
InletOutlet
(c)Figure 10 Acoustic pressure level for the inlet and outlet of the straight-through perforated pipe silencers (a) silencer 1198751 119872 = 01 (b)silencer 119875
2119872 = 02 and (c) silencer 119875
3119872 = 01
Shock and Vibration 7
50
60
40
30
20
10
0
TL (d
B)
Published experimental dataFEMPredicted by literature [23]
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
Figure 11 Measured and predicted TL for the expansion chamber silencer with inlet flow velocity of V = 102ms
Substituting (11) and (12) into (6) yields
TL = 10 log10[(119901in + 120588119888)
2
41199012out
119860 in119860out
]
= 10 log10((119901in + 120588119888) (119901in + 120588119888)
4119901out119901out
119860 in119860out
)
(13)
It should be noted that the obtained acoustic pressure is infrequency-domain and therefore has a complex value In thispaper the temperature and density of the medium (air) are119879 = 288K and 120588 = 1225 kgm3 respectively and the speedof sound in air is 119888 = 340ms
3 Results and Discussion
31 Validation of the 3D Numerical Method Following thecalculation steps stated in Section 22 CFD steady flowcomputation is performed first Figure 5 shows the computedvelocity contours on the axial cutting plane of the expansionchamber silencer with extended inlet it is found that thevelocity distribution is uneven The flow velocity in the inletand outlet pipes are higher than that in the chamber and thesudden section area change enhances the turbulent kineticenergy as shown in Figure 6 Figure 7 shows the veloc-ity-vectors for the three straight-through perforated pipesilencers with a mean flow Mach number of 119872 = 01 or02 Flow circulations can be observed in the rear part of thechamber and the velocity in the pipe is much higher thanthat in the orifices and chamber Moreover the magnitudeand direction of cross-flow velocity through the perforationsare different along the axial direction In addition under theaction of pressure difference between the chamber and perfo-rated pipe the gas flows into the chamber through the orificesand then flows back again into the pipe which enhancesthe turbulent kinetic energy near the orifices as shown in
Figure 8 Generally speaking the flow velocity distributionsinside the studied silencers are anisotropic and nonuniformand the gas flow is accompanied with turbulence
After importing the mean flow data to the acoustic fieldby mesh mapping acoustic response analysis is performedto acquire acoustic pressure at the inlet and outlet as shownin Figures 9 and 10 To validate the accuracy of the 3Dnumerical method published experimental and numericalresults for the studied silencers are comparedwith the presentpredictions
Figure 11 compares the TL results for the expansionchamber silencer with extended inlet from numerical andexperimental methodsThe present predictions agree reason-ably well with the experimental data in the frequency range ofinterest Some deviation from the measurements is observedfor example near the resonance peak This discrepancy maybe attributed to the fact that (i) the medium viscous effectsand wall thickness are neglected in the FEM calculation and(ii) flow noise generated inside the silencer is neglected inthe simulation but the noise is included in the experimentsFurthermore the present FEM results are compared withthe numerical results from literature [23] One can see thatthe present FEM yields better results between the predictedTL curves That is because the method employed in theliterature neglects the turbulence inside the silencer and usesthe simplified mean flow velocity In contrast the presentstudy may acquire more detailed distribution of mean flowthrough the CFD steady flow computation with the properturbulence model
In Figure 12 a comparison between the present predic-tions and measurements shows a good agreement in generalbetween TL results obtained for the three straight-throughperforated pipe silencers studied here However it is foundthat the present predicted TL values are slightly less thanthose measured This is because the influence of mean flowon the sound propagation in the silencer can be explained as
8 Shock and Vibration
50
40
30
20
10
00 500 1000 1500 2000 2500 3000
Frequency (Hz)
TL (d
B)
Published experimental dataFEMPredicted by literature [24]
(a)
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
50
40
30
20
10
0
TL (d
B)
Published experimental dataFEMPredicted by literature [24]
(b)
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
50
40
30
20
10
0
TL (d
B)
Published experimental dataFEMPredicted by literature [24]
(c)
Figure 12 Measured and predicted TL for the straight-through perforated pipe silencers (a) silencer 1198751119872 = 01 (b) silencer 1198752119872 = 02and (c) silencer 1198753119872 = 01
the convective and dissipative effects [7] and the convectiveeffect can be considered by importing the decouple meanfrom an external steady flow computation to the acousticfield but the dissipative effect of medium viscous (especiallyin the orifices) which can cause sound energy loss and thusincrease TL is not included in the FEM calculation just likethe conventional frequency-domain method At present lotsof studies such as [24] mainly focus on applying mathe-matical modeling of perforate impedance to calculate andanalyze the acoustic attenuation performance of perforatedpipe silencer In the absence of mean flow the acousticperformance of the silence can be accurately predicted withthe help of perforate impedance models However when
mean flow is present rigorous mathematical modeling ofthe mechanisms that determine the perforate impedance isextremely difficult Therefore most of current impedancemodels considering the mean flow effect are empirical Incontrast although there is a lack of consideration of meanflow dissipative effect on sound propagation in present FEMby decoupling the problems this method avoids complexmathematical calculation and it is accessible and easy to useFurthermore the predicted results presented are not badTherefore it is valuable for predicting the acoustic attenuationperformance of perforated pipe silencer
At present with the development of computer perfor-mance the full time-domain CFD method such as that
Shock and Vibration 9
00
500 1000 1500 2000 2500 3000
Frequency (Hz)
TL (d
B)10
20
30
40
50
60
= 0
= 30ms = 60ms
Figure 13 Effect of flow velocity on TL of the expansion chamber silencer
performed in [8] has also attracted the interest of researchersThe main advantage of this method is that the dissipativeeffect of medium viscous could be better represented How-ever compared with the present method the main problemwhen using the time-domain CFD method is the CPU timeconsumed during the transient flow computation due tothe fact that long upstream and downstream pipes typicallyexceeding 15 times the length of the silencer are requiredto capture isolated incident and transmitted signals and thetime window (record length of data) must be long enoughto capture the entire pressure signals Moreover when meanflow is present the CFD transient flow computation needs tobe run twice (with and without impulse signal) Additionallyit can be seen from [8] that the TL curves calculated by thetime-domain CFD method are not smooth and have somesawteeth This is because the time-domain CFD method isa simulation of the process of an impulse technique [30]for measuring silencer acoustic performance and thereforethe predicted TL curves are easy to fluctuate like thoseobtained from the impulse technique Middelberg et al [31]investigated the effect of mesh size on TL obtained from thetime-domain CFD method and they found that for higherfrequencies the coarse mesh would influence the accuracy ofsolution due to the inability of the mesh to resolve the wave-length with a sufficient number of points and introducedthe artificial numerical dissipation Therefore the mesh sizefor the time-domain CFD method should be small enoughto avoid high-frequency dissipation As mentioned in Sec-tion 21 two different meshes CFD mesh and acoustic meshare used for the solution of the mean flow and acousticproblems when employing present method Compared withthe mesh used in the time-domain CFDmethod the require-ments of the CFD mesh for the steady flow computation inpresent method are much reduced [32] but it should be finerthan the acoustic mesh
32 Effect of Mean Flow on Silencer Acoustic Attenuation Per-formance Two main effects of mean flow on silencer acous-tic performance can be distinguished one is to affect thesound propagation in the silencer (stated in Section 31) Theother is to induce aerodynamic noise due to turbulence Insilencers the typical mean flow Mach number is below 03[33] and the aerodynamic noise is considered to be weakTherefore the aerodynamic noise is neglected in this work
Figure 13 shows that the predicted TL curves of theexpansion chamber silencer with the flow velocity variedbetween 0ms and 60ms It is observed that the shape ofTL curve with mean flow is much similar to that withoutmean flow The presence of mean flow increases the TLat most frequencies and decreases the resonance peak andTL increases further as flow velocities increase Figure 14shows the effect of mean flow on TL of the straight-throughperforated pipe silencers with different flow velocities It canbe seen from these pictures that the mean flow has littleinfluence on the acoustic attenuation in the plane wave rangeand leads to complex variation of TL curves in the non-plane wave Overall except that the presence of mean flowremarkably decreases resonance peak the acoustic attenu-ation performance of the straight-through perforated pipesilencers increases at most frequencies as flow velocity isincreased especially at higher frequencies
4 Conclusions
In this paper a 3D numerical method is employed to inves-tigate the acoustic attenuation performance of a circularexpansion chamber silencer with extended inlet and threestraight-through perforated pipe silencers in the presence ofmean flow By decoupling the problem the linear acousticsare away from the mean flow computation CFD and FEM
10 Shock and Vibration
= 0
= 30ms = 60ms
00
500 1000 1500 2000 2500 3000
Frequency (Hz)
TL (d
B)
10
20
30
40
50
(a)
= 0
= 30ms = 60ms
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
0
TL (d
B)
10
20
30
40
50
(b)
= 0
= 30ms = 60ms
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
0
TL (d
B)
10
20
30
40
50
(c)
Figure 14 Effect of flow velocity on TL of the straight-through perforated pipe silencers (a) silencer 1198751 (b) silencer 1198752 and (c) silencer 1198753
are employed to perform the steady flow computation andacoustic response analysis respectively The data transferis accomplished by mesh mapping A comparison betweenpresent results and previously published experimental andnumerical results indicates that the present 3D numericalmethod is capable of delivering reasonable predictions Themajor advantage of present method is that it is accessible andeasy to use and avoids complexmathematical calculationwiththe help of simulation software especially for the perforatedpipe silencer while the major drawback of this method liesin the considerable computational effort and cost that arerequired to acquire a complete and accurate solution in the3D calculations
Furthermore the TL of studied silencers with differentflow velocities is calculated It is concluded that the presenceof mean flow decreases the resonance peak and increases theacoustic attenuation at most frequencies for the expansionchamber silencer For the straight-through perforated pipesilencer mean flow has little influence on the acoustic atten-uation in the plane wave range and remarkably decreasesthe resonance peak and increases the acoustic attenuation athigher frequencies
Conflict of Interests
The authors declare that there is no conflict of interests withregard to this study and the publication of this paper
Shock and Vibration 11
Acknowledgments
The authors are grateful for the grants from National NaturalScience Foundation of China (51275082 11272273) Funda-mental Research Fund of Central Universities (N130403009)Research Fund for Doctoral Program of Higher Education(20100042110013) and Program for Liaoning InnovativeResearch Team in University (LT2014006)
References
[1] M G Prasad and M J Crocker ldquoInsertion loss studies onmodels of automotive exhaust systemsrdquo Journal of the AcousticalSociety of America vol 70 no 5 pp 1339ndash1344 1981
[2] M L Munjal and P T Thawani ldquoOn the transfer matrix for auniform tube with a moving mediumrdquo Journal of Sound andVibration vol 91 no 4 pp 597ndash599 1983
[3] K Narayana Rao and M L Munjal ldquoExperimental evaluationof impedance of perforates with grazing flowrdquo Journal of Soundand Vibration vol 108 no 2 pp 283ndash295 1986
[4] Y H Kim S H Kim B D Lim and Y K Kwak ldquoExperimentalstudy of acoustic characteristics of expansion chamber withmean flowsrdquo KSME Journal vol 2 no 2 pp 125ndash132 1988
[5] Y Auregan and M Leroux ldquoFailures in the discrete modelsfor flow duct with perforations an experimental investigationrdquoJournal of Sound andVibration vol 265 no 1 pp 109ndash121 2003
[6] A Broatch XMargot A Gil and F DDenia ldquoACFD approachto the computation of the acoustic response of exhaustmufflersrdquoJournal of Computational Acoustics vol 13 no 2 pp 301ndash3162005
[7] Z L Ji H S Xu and Z X Kang ldquoInfluence of mean flowon acoustic attenuation performance of straight-through per-forated tube reactive silencers and resonatorsrdquo Noise ControlEngineering Journal vol 58 no 1 pp 12ndash17 2010
[8] C Liu and Z-L Ji ldquoComputational fluid dynamics-basednumerical analysis of acoustic attenuation and flow resistancecharacteristics of perforated tube silencersrdquo Journal of Vibrationand Acoustics vol 136 no 2 Article ID 021006 11 pages 2014
[9] H-D Ju S-B Lee and Y-B Park ldquoTransmission loss estima-tion of splitter silencer using multi-domain BEMrdquo Journal ofMechanical Science and Technology vol 21 no 12 pp 2073ndash2081 2007
[10] Z L Ji ldquoBoundary element acoustic analysis of hybrid expan-sion chamber silencers with perforated facingrdquo EngineeringAnalysis with Boundary Elements vol 34 no 7 pp 690ndash6962010
[11] C Jiang T W Wu M B Xu and C Y R Cheng ldquoBEMmodeling of mufflers with diesel particulate filters and catalyticconvertersrdquoNoise Control Engineering Journal vol 58 no 3 pp243ndash250 2010
[12] C I J Young and M J Crocker ldquoPrediction of transmissionloss in mufflers by the finite element methodrdquo Journal of theAcoustical Society of America vol 57 no 1 pp 144ndash148 1975
[13] O Z Mehdizadeh and M Paraschivoiu ldquoA three-dimensionalfinite element approach for predicting the transmission loss inmufflers and silencers with no mean flowrdquo Applied Acousticsvol 66 no 8 pp 902ndash918 2005
[14] Z Kang and Z Ji ldquoAcoustic length correction of duct extensioninto a cylindrical chamberrdquo Journal of Sound and Vibration vol310 no 4-5 pp 782ndash791 2008
[15] Y S GeH B Zhang Y R Zhang JW Tan XM Zhang andXK Han ldquoAn analysis on 3D acoustic performance of automotiveexhaust mufflerrdquo Automotive Engineering vol 28 no 1 pp 51ndash55 2006 (Chinese)
[16] P Chaitanya and M L Munjal ldquoEffect of wall thickness on theend corrections of the extended inlet and outlet of a double-tuned expansion chamberrdquo Applied Acoustics vol 72 no 1 pp65ndash70 2011
[17] J Fu W Chen Y Tang W H Yuan G M Li and Y Li ldquoMod-ification of exhaust muffler of a diesel engine based on finiteelement method acoustic analysisrdquo Advances in MechanicalEngineering vol 7 no 4 11 pages 2015
[18] K S Peat ldquoEvaluation of four-pole parameters for ducts withflow by the finite element methodrdquo Journal of Sound andVibration vol 84 no 3 pp 389ndash395 1982
[19] X R Wang and Z L Ji ldquoBoundary element analysis of four-pole parameters and transmission loss of silencers with flowrdquoChinese Journal of Computational Physics vol 24 no 6 pp 717ndash724 2007 (Chinese)
[20] N Gil-Negrete A Rivas and J Vinolas ldquoPredicting thedynamic behaviour of hydrobushingsrdquo Shock andVibration vol12 no 2 pp 91ndash107 2005
[21] S N Panigrahi and M L Munjal ldquoBackpressure considera-tions in designing of cross flow perforated-element reactivesilencersrdquo Noise Control Engineering Journal vol 55 no 6 pp504ndash515 2007
[22] A J Torregrosa P Fajardo A Gil and R Navarro ldquoDevelop-ment of non-reflecting boundary condition for application in3D computational fluid dynamics codesrdquo Engineering Applica-tions of Computational Fluid Mechanics vol 6 no 3 pp 447ndash460 2012
[23] C-NWang ldquoAboundary element analysis for simple expansionsilencers with mean flowrdquo Journal of the Chinese Institute ofEngineers vol 23 no 4 pp 529ndash536 2000
[24] S-H Lee and J-G Ih ldquoEmpirical model of the acousticimpedance of a circular orifice in grazing mean flowrdquo Journalof the Acoustical Society of America vol 114 no 1 pp 98ndash1132003
[25] F L Zhan and J W Xu VirtualLab Acoustics Simulation fromEntry to Master Northwestern Polytechnical University PressXian China 2013 (Chinese)
[26] ANSYS Inc ANSYS FLUENT 145 in Workbench Userrsquos GuideANSYS Inc New York NY USA 2012
[27] LMS International NV LMS VirtualLab Online Help11-SL2LMS International N V Leuven Belgium 2013
[28] C Liu Z L Ji and Z Fang ldquoNumerical analysis of acousticattenuation and flow resistance characteristics of double expan-sion chamber silencersrdquo Noise Control Engineering Journal vol61 no 5 pp 487ndash499 2013
[29] M L Munjal Acoustic of Ducts and Mufflers Wiley New YorkNY USA 2014
[30] R Singh and T Katra ldquoDevelopment of an impulse techniquefor measurement of muffler characteristicsrdquo Journal of Soundand Vibration vol 56 no 2 pp 279ndash298 1978
[31] J M Middelberg T J Barber S S Leong K P Byrne andE Leonardi ldquoCFD analysis of the acoustic and mean flowperformance of simple expansion chamber mufflersrdquo in Pro-ceedings of theASME InternationalMechanical EngineeringCon-gress and Exposition pp 151ndash156 Anaheim Calif USA Novem-ber 2004
12 Shock and Vibration
[32] B K Gardner A Mejdi F Mendonca and D Copley ldquoUsingCFD flow fields to inform acoustic finite element models ofcomplex mufflers with thermal and flow effectsrdquo in Proceedingsof the 44th International Congress and Exposition on NoiseControl Engineering Paper 15-665 San Francisco Calif USAAugust 2015
[33] E Dokumaci ldquoEffect of sheared grazing mean flow on acoustictransmission in perforated pipe mufflersrdquo Journal of Sound andVibration vol 283 no 3ndash5 pp 645ndash663 2005
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
Shock and Vibration 5
37
28
19
9
0
Velo
city
-vec
tor (
ms
)
(a) Velocity-vector
73
55
36
18
0
Velo
city
-vec
tor (
ms
)
(b) Velocity-vector
38
28
19
9
0
Velo
city
-vec
tor (
ms
)
(c) Velocity-vector
Figure 7 Velocity-vectors for the straight-through perforated pipe silencers (a) silencer1198751119872 = 01 (b) silencer1198752119872 = 02 and (c) silencer1198753119872 = 01
39701352923088326473220641765513246883744280019
Turb
ulen
ce k
inet
icen
ergy
(Jk
g)
(a) Turbulence kinetic energy
16721814864713007611150692935743645579437223186520082
Turb
ulen
ce k
inet
icen
ergy
(Jk
g)
(b) Turbulence kinetic energy
617005486048019411793433827498206571381769760136
Turb
ulen
ce k
inet
icen
ergy
(Jk
g)
(c) Turbulence kinetic energy
Figure 8 Counters of turbulent kinetic energy for the straight-through perforated pipe silencers (a) silencer 1198751119872 = 01 (b) silencer 1198752119872 = 02 and (c) silencer 119875
3119872 = 01
and 119906in = 1ms at the inlet and with neglecting ldquo119890119895119908119905rdquo item(8) and (9) reduce to
119901in = 119901inc + 119901ref
119906in =1
120588119888(119901inc minus 119901ref) = 1
(10)
which yield
119901inc =119901in + 120588119888
2 (11)
In addition the outlet is defined to be an anechoic end (iethe acoustic pressure of reflective wave at the outlet is 0) sothere is
119901tra = 119901out (12)
6 Shock and Vibration
200
180
160
140
120
100
80
60
Acou
stic p
ress
ure l
evel
(dB)
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
InletOutlet
Figure 9 Acoustic pressure level for the inlet and outlet of the expansion chamber silencer with inlet flow velocity of V = 102ms200
180
160
140
120
100
80
Acou
stic p
ress
ure l
evel
(dB)
InletOutlet
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
(a)
200
180
160
140
120
100
80
Acou
stic p
ress
ure l
evel
(dB)
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
InletOutlet
(b)200
180
160
140
120
100
80
Acou
stic p
ress
ure l
evel
(dB)
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
InletOutlet
(c)Figure 10 Acoustic pressure level for the inlet and outlet of the straight-through perforated pipe silencers (a) silencer 1198751 119872 = 01 (b)silencer 119875
2119872 = 02 and (c) silencer 119875
3119872 = 01
Shock and Vibration 7
50
60
40
30
20
10
0
TL (d
B)
Published experimental dataFEMPredicted by literature [23]
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
Figure 11 Measured and predicted TL for the expansion chamber silencer with inlet flow velocity of V = 102ms
Substituting (11) and (12) into (6) yields
TL = 10 log10[(119901in + 120588119888)
2
41199012out
119860 in119860out
]
= 10 log10((119901in + 120588119888) (119901in + 120588119888)
4119901out119901out
119860 in119860out
)
(13)
It should be noted that the obtained acoustic pressure is infrequency-domain and therefore has a complex value In thispaper the temperature and density of the medium (air) are119879 = 288K and 120588 = 1225 kgm3 respectively and the speedof sound in air is 119888 = 340ms
3 Results and Discussion
31 Validation of the 3D Numerical Method Following thecalculation steps stated in Section 22 CFD steady flowcomputation is performed first Figure 5 shows the computedvelocity contours on the axial cutting plane of the expansionchamber silencer with extended inlet it is found that thevelocity distribution is uneven The flow velocity in the inletand outlet pipes are higher than that in the chamber and thesudden section area change enhances the turbulent kineticenergy as shown in Figure 6 Figure 7 shows the veloc-ity-vectors for the three straight-through perforated pipesilencers with a mean flow Mach number of 119872 = 01 or02 Flow circulations can be observed in the rear part of thechamber and the velocity in the pipe is much higher thanthat in the orifices and chamber Moreover the magnitudeand direction of cross-flow velocity through the perforationsare different along the axial direction In addition under theaction of pressure difference between the chamber and perfo-rated pipe the gas flows into the chamber through the orificesand then flows back again into the pipe which enhancesthe turbulent kinetic energy near the orifices as shown in
Figure 8 Generally speaking the flow velocity distributionsinside the studied silencers are anisotropic and nonuniformand the gas flow is accompanied with turbulence
After importing the mean flow data to the acoustic fieldby mesh mapping acoustic response analysis is performedto acquire acoustic pressure at the inlet and outlet as shownin Figures 9 and 10 To validate the accuracy of the 3Dnumerical method published experimental and numericalresults for the studied silencers are comparedwith the presentpredictions
Figure 11 compares the TL results for the expansionchamber silencer with extended inlet from numerical andexperimental methodsThe present predictions agree reason-ably well with the experimental data in the frequency range ofinterest Some deviation from the measurements is observedfor example near the resonance peak This discrepancy maybe attributed to the fact that (i) the medium viscous effectsand wall thickness are neglected in the FEM calculation and(ii) flow noise generated inside the silencer is neglected inthe simulation but the noise is included in the experimentsFurthermore the present FEM results are compared withthe numerical results from literature [23] One can see thatthe present FEM yields better results between the predictedTL curves That is because the method employed in theliterature neglects the turbulence inside the silencer and usesthe simplified mean flow velocity In contrast the presentstudy may acquire more detailed distribution of mean flowthrough the CFD steady flow computation with the properturbulence model
In Figure 12 a comparison between the present predic-tions and measurements shows a good agreement in generalbetween TL results obtained for the three straight-throughperforated pipe silencers studied here However it is foundthat the present predicted TL values are slightly less thanthose measured This is because the influence of mean flowon the sound propagation in the silencer can be explained as
8 Shock and Vibration
50
40
30
20
10
00 500 1000 1500 2000 2500 3000
Frequency (Hz)
TL (d
B)
Published experimental dataFEMPredicted by literature [24]
(a)
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
50
40
30
20
10
0
TL (d
B)
Published experimental dataFEMPredicted by literature [24]
(b)
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
50
40
30
20
10
0
TL (d
B)
Published experimental dataFEMPredicted by literature [24]
(c)
Figure 12 Measured and predicted TL for the straight-through perforated pipe silencers (a) silencer 1198751119872 = 01 (b) silencer 1198752119872 = 02and (c) silencer 1198753119872 = 01
the convective and dissipative effects [7] and the convectiveeffect can be considered by importing the decouple meanfrom an external steady flow computation to the acousticfield but the dissipative effect of medium viscous (especiallyin the orifices) which can cause sound energy loss and thusincrease TL is not included in the FEM calculation just likethe conventional frequency-domain method At present lotsof studies such as [24] mainly focus on applying mathe-matical modeling of perforate impedance to calculate andanalyze the acoustic attenuation performance of perforatedpipe silencer In the absence of mean flow the acousticperformance of the silence can be accurately predicted withthe help of perforate impedance models However when
mean flow is present rigorous mathematical modeling ofthe mechanisms that determine the perforate impedance isextremely difficult Therefore most of current impedancemodels considering the mean flow effect are empirical Incontrast although there is a lack of consideration of meanflow dissipative effect on sound propagation in present FEMby decoupling the problems this method avoids complexmathematical calculation and it is accessible and easy to useFurthermore the predicted results presented are not badTherefore it is valuable for predicting the acoustic attenuationperformance of perforated pipe silencer
At present with the development of computer perfor-mance the full time-domain CFD method such as that
Shock and Vibration 9
00
500 1000 1500 2000 2500 3000
Frequency (Hz)
TL (d
B)10
20
30
40
50
60
= 0
= 30ms = 60ms
Figure 13 Effect of flow velocity on TL of the expansion chamber silencer
performed in [8] has also attracted the interest of researchersThe main advantage of this method is that the dissipativeeffect of medium viscous could be better represented How-ever compared with the present method the main problemwhen using the time-domain CFD method is the CPU timeconsumed during the transient flow computation due tothe fact that long upstream and downstream pipes typicallyexceeding 15 times the length of the silencer are requiredto capture isolated incident and transmitted signals and thetime window (record length of data) must be long enoughto capture the entire pressure signals Moreover when meanflow is present the CFD transient flow computation needs tobe run twice (with and without impulse signal) Additionallyit can be seen from [8] that the TL curves calculated by thetime-domain CFD method are not smooth and have somesawteeth This is because the time-domain CFD method isa simulation of the process of an impulse technique [30]for measuring silencer acoustic performance and thereforethe predicted TL curves are easy to fluctuate like thoseobtained from the impulse technique Middelberg et al [31]investigated the effect of mesh size on TL obtained from thetime-domain CFD method and they found that for higherfrequencies the coarse mesh would influence the accuracy ofsolution due to the inability of the mesh to resolve the wave-length with a sufficient number of points and introducedthe artificial numerical dissipation Therefore the mesh sizefor the time-domain CFD method should be small enoughto avoid high-frequency dissipation As mentioned in Sec-tion 21 two different meshes CFD mesh and acoustic meshare used for the solution of the mean flow and acousticproblems when employing present method Compared withthe mesh used in the time-domain CFDmethod the require-ments of the CFD mesh for the steady flow computation inpresent method are much reduced [32] but it should be finerthan the acoustic mesh
32 Effect of Mean Flow on Silencer Acoustic Attenuation Per-formance Two main effects of mean flow on silencer acous-tic performance can be distinguished one is to affect thesound propagation in the silencer (stated in Section 31) Theother is to induce aerodynamic noise due to turbulence Insilencers the typical mean flow Mach number is below 03[33] and the aerodynamic noise is considered to be weakTherefore the aerodynamic noise is neglected in this work
Figure 13 shows that the predicted TL curves of theexpansion chamber silencer with the flow velocity variedbetween 0ms and 60ms It is observed that the shape ofTL curve with mean flow is much similar to that withoutmean flow The presence of mean flow increases the TLat most frequencies and decreases the resonance peak andTL increases further as flow velocities increase Figure 14shows the effect of mean flow on TL of the straight-throughperforated pipe silencers with different flow velocities It canbe seen from these pictures that the mean flow has littleinfluence on the acoustic attenuation in the plane wave rangeand leads to complex variation of TL curves in the non-plane wave Overall except that the presence of mean flowremarkably decreases resonance peak the acoustic attenu-ation performance of the straight-through perforated pipesilencers increases at most frequencies as flow velocity isincreased especially at higher frequencies
4 Conclusions
In this paper a 3D numerical method is employed to inves-tigate the acoustic attenuation performance of a circularexpansion chamber silencer with extended inlet and threestraight-through perforated pipe silencers in the presence ofmean flow By decoupling the problem the linear acousticsare away from the mean flow computation CFD and FEM
10 Shock and Vibration
= 0
= 30ms = 60ms
00
500 1000 1500 2000 2500 3000
Frequency (Hz)
TL (d
B)
10
20
30
40
50
(a)
= 0
= 30ms = 60ms
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
0
TL (d
B)
10
20
30
40
50
(b)
= 0
= 30ms = 60ms
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
0
TL (d
B)
10
20
30
40
50
(c)
Figure 14 Effect of flow velocity on TL of the straight-through perforated pipe silencers (a) silencer 1198751 (b) silencer 1198752 and (c) silencer 1198753
are employed to perform the steady flow computation andacoustic response analysis respectively The data transferis accomplished by mesh mapping A comparison betweenpresent results and previously published experimental andnumerical results indicates that the present 3D numericalmethod is capable of delivering reasonable predictions Themajor advantage of present method is that it is accessible andeasy to use and avoids complexmathematical calculationwiththe help of simulation software especially for the perforatedpipe silencer while the major drawback of this method liesin the considerable computational effort and cost that arerequired to acquire a complete and accurate solution in the3D calculations
Furthermore the TL of studied silencers with differentflow velocities is calculated It is concluded that the presenceof mean flow decreases the resonance peak and increases theacoustic attenuation at most frequencies for the expansionchamber silencer For the straight-through perforated pipesilencer mean flow has little influence on the acoustic atten-uation in the plane wave range and remarkably decreasesthe resonance peak and increases the acoustic attenuation athigher frequencies
Conflict of Interests
The authors declare that there is no conflict of interests withregard to this study and the publication of this paper
Shock and Vibration 11
Acknowledgments
The authors are grateful for the grants from National NaturalScience Foundation of China (51275082 11272273) Funda-mental Research Fund of Central Universities (N130403009)Research Fund for Doctoral Program of Higher Education(20100042110013) and Program for Liaoning InnovativeResearch Team in University (LT2014006)
References
[1] M G Prasad and M J Crocker ldquoInsertion loss studies onmodels of automotive exhaust systemsrdquo Journal of the AcousticalSociety of America vol 70 no 5 pp 1339ndash1344 1981
[2] M L Munjal and P T Thawani ldquoOn the transfer matrix for auniform tube with a moving mediumrdquo Journal of Sound andVibration vol 91 no 4 pp 597ndash599 1983
[3] K Narayana Rao and M L Munjal ldquoExperimental evaluationof impedance of perforates with grazing flowrdquo Journal of Soundand Vibration vol 108 no 2 pp 283ndash295 1986
[4] Y H Kim S H Kim B D Lim and Y K Kwak ldquoExperimentalstudy of acoustic characteristics of expansion chamber withmean flowsrdquo KSME Journal vol 2 no 2 pp 125ndash132 1988
[5] Y Auregan and M Leroux ldquoFailures in the discrete modelsfor flow duct with perforations an experimental investigationrdquoJournal of Sound andVibration vol 265 no 1 pp 109ndash121 2003
[6] A Broatch XMargot A Gil and F DDenia ldquoACFD approachto the computation of the acoustic response of exhaustmufflersrdquoJournal of Computational Acoustics vol 13 no 2 pp 301ndash3162005
[7] Z L Ji H S Xu and Z X Kang ldquoInfluence of mean flowon acoustic attenuation performance of straight-through per-forated tube reactive silencers and resonatorsrdquo Noise ControlEngineering Journal vol 58 no 1 pp 12ndash17 2010
[8] C Liu and Z-L Ji ldquoComputational fluid dynamics-basednumerical analysis of acoustic attenuation and flow resistancecharacteristics of perforated tube silencersrdquo Journal of Vibrationand Acoustics vol 136 no 2 Article ID 021006 11 pages 2014
[9] H-D Ju S-B Lee and Y-B Park ldquoTransmission loss estima-tion of splitter silencer using multi-domain BEMrdquo Journal ofMechanical Science and Technology vol 21 no 12 pp 2073ndash2081 2007
[10] Z L Ji ldquoBoundary element acoustic analysis of hybrid expan-sion chamber silencers with perforated facingrdquo EngineeringAnalysis with Boundary Elements vol 34 no 7 pp 690ndash6962010
[11] C Jiang T W Wu M B Xu and C Y R Cheng ldquoBEMmodeling of mufflers with diesel particulate filters and catalyticconvertersrdquoNoise Control Engineering Journal vol 58 no 3 pp243ndash250 2010
[12] C I J Young and M J Crocker ldquoPrediction of transmissionloss in mufflers by the finite element methodrdquo Journal of theAcoustical Society of America vol 57 no 1 pp 144ndash148 1975
[13] O Z Mehdizadeh and M Paraschivoiu ldquoA three-dimensionalfinite element approach for predicting the transmission loss inmufflers and silencers with no mean flowrdquo Applied Acousticsvol 66 no 8 pp 902ndash918 2005
[14] Z Kang and Z Ji ldquoAcoustic length correction of duct extensioninto a cylindrical chamberrdquo Journal of Sound and Vibration vol310 no 4-5 pp 782ndash791 2008
[15] Y S GeH B Zhang Y R Zhang JW Tan XM Zhang andXK Han ldquoAn analysis on 3D acoustic performance of automotiveexhaust mufflerrdquo Automotive Engineering vol 28 no 1 pp 51ndash55 2006 (Chinese)
[16] P Chaitanya and M L Munjal ldquoEffect of wall thickness on theend corrections of the extended inlet and outlet of a double-tuned expansion chamberrdquo Applied Acoustics vol 72 no 1 pp65ndash70 2011
[17] J Fu W Chen Y Tang W H Yuan G M Li and Y Li ldquoMod-ification of exhaust muffler of a diesel engine based on finiteelement method acoustic analysisrdquo Advances in MechanicalEngineering vol 7 no 4 11 pages 2015
[18] K S Peat ldquoEvaluation of four-pole parameters for ducts withflow by the finite element methodrdquo Journal of Sound andVibration vol 84 no 3 pp 389ndash395 1982
[19] X R Wang and Z L Ji ldquoBoundary element analysis of four-pole parameters and transmission loss of silencers with flowrdquoChinese Journal of Computational Physics vol 24 no 6 pp 717ndash724 2007 (Chinese)
[20] N Gil-Negrete A Rivas and J Vinolas ldquoPredicting thedynamic behaviour of hydrobushingsrdquo Shock andVibration vol12 no 2 pp 91ndash107 2005
[21] S N Panigrahi and M L Munjal ldquoBackpressure considera-tions in designing of cross flow perforated-element reactivesilencersrdquo Noise Control Engineering Journal vol 55 no 6 pp504ndash515 2007
[22] A J Torregrosa P Fajardo A Gil and R Navarro ldquoDevelop-ment of non-reflecting boundary condition for application in3D computational fluid dynamics codesrdquo Engineering Applica-tions of Computational Fluid Mechanics vol 6 no 3 pp 447ndash460 2012
[23] C-NWang ldquoAboundary element analysis for simple expansionsilencers with mean flowrdquo Journal of the Chinese Institute ofEngineers vol 23 no 4 pp 529ndash536 2000
[24] S-H Lee and J-G Ih ldquoEmpirical model of the acousticimpedance of a circular orifice in grazing mean flowrdquo Journalof the Acoustical Society of America vol 114 no 1 pp 98ndash1132003
[25] F L Zhan and J W Xu VirtualLab Acoustics Simulation fromEntry to Master Northwestern Polytechnical University PressXian China 2013 (Chinese)
[26] ANSYS Inc ANSYS FLUENT 145 in Workbench Userrsquos GuideANSYS Inc New York NY USA 2012
[27] LMS International NV LMS VirtualLab Online Help11-SL2LMS International N V Leuven Belgium 2013
[28] C Liu Z L Ji and Z Fang ldquoNumerical analysis of acousticattenuation and flow resistance characteristics of double expan-sion chamber silencersrdquo Noise Control Engineering Journal vol61 no 5 pp 487ndash499 2013
[29] M L Munjal Acoustic of Ducts and Mufflers Wiley New YorkNY USA 2014
[30] R Singh and T Katra ldquoDevelopment of an impulse techniquefor measurement of muffler characteristicsrdquo Journal of Soundand Vibration vol 56 no 2 pp 279ndash298 1978
[31] J M Middelberg T J Barber S S Leong K P Byrne andE Leonardi ldquoCFD analysis of the acoustic and mean flowperformance of simple expansion chamber mufflersrdquo in Pro-ceedings of theASME InternationalMechanical EngineeringCon-gress and Exposition pp 151ndash156 Anaheim Calif USA Novem-ber 2004
12 Shock and Vibration
[32] B K Gardner A Mejdi F Mendonca and D Copley ldquoUsingCFD flow fields to inform acoustic finite element models ofcomplex mufflers with thermal and flow effectsrdquo in Proceedingsof the 44th International Congress and Exposition on NoiseControl Engineering Paper 15-665 San Francisco Calif USAAugust 2015
[33] E Dokumaci ldquoEffect of sheared grazing mean flow on acoustictransmission in perforated pipe mufflersrdquo Journal of Sound andVibration vol 283 no 3ndash5 pp 645ndash663 2005
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
6 Shock and Vibration
200
180
160
140
120
100
80
60
Acou
stic p
ress
ure l
evel
(dB)
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
InletOutlet
Figure 9 Acoustic pressure level for the inlet and outlet of the expansion chamber silencer with inlet flow velocity of V = 102ms200
180
160
140
120
100
80
Acou
stic p
ress
ure l
evel
(dB)
InletOutlet
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
(a)
200
180
160
140
120
100
80
Acou
stic p
ress
ure l
evel
(dB)
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
InletOutlet
(b)200
180
160
140
120
100
80
Acou
stic p
ress
ure l
evel
(dB)
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
InletOutlet
(c)Figure 10 Acoustic pressure level for the inlet and outlet of the straight-through perforated pipe silencers (a) silencer 1198751 119872 = 01 (b)silencer 119875
2119872 = 02 and (c) silencer 119875
3119872 = 01
Shock and Vibration 7
50
60
40
30
20
10
0
TL (d
B)
Published experimental dataFEMPredicted by literature [23]
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
Figure 11 Measured and predicted TL for the expansion chamber silencer with inlet flow velocity of V = 102ms
Substituting (11) and (12) into (6) yields
TL = 10 log10[(119901in + 120588119888)
2
41199012out
119860 in119860out
]
= 10 log10((119901in + 120588119888) (119901in + 120588119888)
4119901out119901out
119860 in119860out
)
(13)
It should be noted that the obtained acoustic pressure is infrequency-domain and therefore has a complex value In thispaper the temperature and density of the medium (air) are119879 = 288K and 120588 = 1225 kgm3 respectively and the speedof sound in air is 119888 = 340ms
3 Results and Discussion
31 Validation of the 3D Numerical Method Following thecalculation steps stated in Section 22 CFD steady flowcomputation is performed first Figure 5 shows the computedvelocity contours on the axial cutting plane of the expansionchamber silencer with extended inlet it is found that thevelocity distribution is uneven The flow velocity in the inletand outlet pipes are higher than that in the chamber and thesudden section area change enhances the turbulent kineticenergy as shown in Figure 6 Figure 7 shows the veloc-ity-vectors for the three straight-through perforated pipesilencers with a mean flow Mach number of 119872 = 01 or02 Flow circulations can be observed in the rear part of thechamber and the velocity in the pipe is much higher thanthat in the orifices and chamber Moreover the magnitudeand direction of cross-flow velocity through the perforationsare different along the axial direction In addition under theaction of pressure difference between the chamber and perfo-rated pipe the gas flows into the chamber through the orificesand then flows back again into the pipe which enhancesthe turbulent kinetic energy near the orifices as shown in
Figure 8 Generally speaking the flow velocity distributionsinside the studied silencers are anisotropic and nonuniformand the gas flow is accompanied with turbulence
After importing the mean flow data to the acoustic fieldby mesh mapping acoustic response analysis is performedto acquire acoustic pressure at the inlet and outlet as shownin Figures 9 and 10 To validate the accuracy of the 3Dnumerical method published experimental and numericalresults for the studied silencers are comparedwith the presentpredictions
Figure 11 compares the TL results for the expansionchamber silencer with extended inlet from numerical andexperimental methodsThe present predictions agree reason-ably well with the experimental data in the frequency range ofinterest Some deviation from the measurements is observedfor example near the resonance peak This discrepancy maybe attributed to the fact that (i) the medium viscous effectsand wall thickness are neglected in the FEM calculation and(ii) flow noise generated inside the silencer is neglected inthe simulation but the noise is included in the experimentsFurthermore the present FEM results are compared withthe numerical results from literature [23] One can see thatthe present FEM yields better results between the predictedTL curves That is because the method employed in theliterature neglects the turbulence inside the silencer and usesthe simplified mean flow velocity In contrast the presentstudy may acquire more detailed distribution of mean flowthrough the CFD steady flow computation with the properturbulence model
In Figure 12 a comparison between the present predic-tions and measurements shows a good agreement in generalbetween TL results obtained for the three straight-throughperforated pipe silencers studied here However it is foundthat the present predicted TL values are slightly less thanthose measured This is because the influence of mean flowon the sound propagation in the silencer can be explained as
8 Shock and Vibration
50
40
30
20
10
00 500 1000 1500 2000 2500 3000
Frequency (Hz)
TL (d
B)
Published experimental dataFEMPredicted by literature [24]
(a)
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
50
40
30
20
10
0
TL (d
B)
Published experimental dataFEMPredicted by literature [24]
(b)
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
50
40
30
20
10
0
TL (d
B)
Published experimental dataFEMPredicted by literature [24]
(c)
Figure 12 Measured and predicted TL for the straight-through perforated pipe silencers (a) silencer 1198751119872 = 01 (b) silencer 1198752119872 = 02and (c) silencer 1198753119872 = 01
the convective and dissipative effects [7] and the convectiveeffect can be considered by importing the decouple meanfrom an external steady flow computation to the acousticfield but the dissipative effect of medium viscous (especiallyin the orifices) which can cause sound energy loss and thusincrease TL is not included in the FEM calculation just likethe conventional frequency-domain method At present lotsof studies such as [24] mainly focus on applying mathe-matical modeling of perforate impedance to calculate andanalyze the acoustic attenuation performance of perforatedpipe silencer In the absence of mean flow the acousticperformance of the silence can be accurately predicted withthe help of perforate impedance models However when
mean flow is present rigorous mathematical modeling ofthe mechanisms that determine the perforate impedance isextremely difficult Therefore most of current impedancemodels considering the mean flow effect are empirical Incontrast although there is a lack of consideration of meanflow dissipative effect on sound propagation in present FEMby decoupling the problems this method avoids complexmathematical calculation and it is accessible and easy to useFurthermore the predicted results presented are not badTherefore it is valuable for predicting the acoustic attenuationperformance of perforated pipe silencer
At present with the development of computer perfor-mance the full time-domain CFD method such as that
Shock and Vibration 9
00
500 1000 1500 2000 2500 3000
Frequency (Hz)
TL (d
B)10
20
30
40
50
60
= 0
= 30ms = 60ms
Figure 13 Effect of flow velocity on TL of the expansion chamber silencer
performed in [8] has also attracted the interest of researchersThe main advantage of this method is that the dissipativeeffect of medium viscous could be better represented How-ever compared with the present method the main problemwhen using the time-domain CFD method is the CPU timeconsumed during the transient flow computation due tothe fact that long upstream and downstream pipes typicallyexceeding 15 times the length of the silencer are requiredto capture isolated incident and transmitted signals and thetime window (record length of data) must be long enoughto capture the entire pressure signals Moreover when meanflow is present the CFD transient flow computation needs tobe run twice (with and without impulse signal) Additionallyit can be seen from [8] that the TL curves calculated by thetime-domain CFD method are not smooth and have somesawteeth This is because the time-domain CFD method isa simulation of the process of an impulse technique [30]for measuring silencer acoustic performance and thereforethe predicted TL curves are easy to fluctuate like thoseobtained from the impulse technique Middelberg et al [31]investigated the effect of mesh size on TL obtained from thetime-domain CFD method and they found that for higherfrequencies the coarse mesh would influence the accuracy ofsolution due to the inability of the mesh to resolve the wave-length with a sufficient number of points and introducedthe artificial numerical dissipation Therefore the mesh sizefor the time-domain CFD method should be small enoughto avoid high-frequency dissipation As mentioned in Sec-tion 21 two different meshes CFD mesh and acoustic meshare used for the solution of the mean flow and acousticproblems when employing present method Compared withthe mesh used in the time-domain CFDmethod the require-ments of the CFD mesh for the steady flow computation inpresent method are much reduced [32] but it should be finerthan the acoustic mesh
32 Effect of Mean Flow on Silencer Acoustic Attenuation Per-formance Two main effects of mean flow on silencer acous-tic performance can be distinguished one is to affect thesound propagation in the silencer (stated in Section 31) Theother is to induce aerodynamic noise due to turbulence Insilencers the typical mean flow Mach number is below 03[33] and the aerodynamic noise is considered to be weakTherefore the aerodynamic noise is neglected in this work
Figure 13 shows that the predicted TL curves of theexpansion chamber silencer with the flow velocity variedbetween 0ms and 60ms It is observed that the shape ofTL curve with mean flow is much similar to that withoutmean flow The presence of mean flow increases the TLat most frequencies and decreases the resonance peak andTL increases further as flow velocities increase Figure 14shows the effect of mean flow on TL of the straight-throughperforated pipe silencers with different flow velocities It canbe seen from these pictures that the mean flow has littleinfluence on the acoustic attenuation in the plane wave rangeand leads to complex variation of TL curves in the non-plane wave Overall except that the presence of mean flowremarkably decreases resonance peak the acoustic attenu-ation performance of the straight-through perforated pipesilencers increases at most frequencies as flow velocity isincreased especially at higher frequencies
4 Conclusions
In this paper a 3D numerical method is employed to inves-tigate the acoustic attenuation performance of a circularexpansion chamber silencer with extended inlet and threestraight-through perforated pipe silencers in the presence ofmean flow By decoupling the problem the linear acousticsare away from the mean flow computation CFD and FEM
10 Shock and Vibration
= 0
= 30ms = 60ms
00
500 1000 1500 2000 2500 3000
Frequency (Hz)
TL (d
B)
10
20
30
40
50
(a)
= 0
= 30ms = 60ms
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
0
TL (d
B)
10
20
30
40
50
(b)
= 0
= 30ms = 60ms
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
0
TL (d
B)
10
20
30
40
50
(c)
Figure 14 Effect of flow velocity on TL of the straight-through perforated pipe silencers (a) silencer 1198751 (b) silencer 1198752 and (c) silencer 1198753
are employed to perform the steady flow computation andacoustic response analysis respectively The data transferis accomplished by mesh mapping A comparison betweenpresent results and previously published experimental andnumerical results indicates that the present 3D numericalmethod is capable of delivering reasonable predictions Themajor advantage of present method is that it is accessible andeasy to use and avoids complexmathematical calculationwiththe help of simulation software especially for the perforatedpipe silencer while the major drawback of this method liesin the considerable computational effort and cost that arerequired to acquire a complete and accurate solution in the3D calculations
Furthermore the TL of studied silencers with differentflow velocities is calculated It is concluded that the presenceof mean flow decreases the resonance peak and increases theacoustic attenuation at most frequencies for the expansionchamber silencer For the straight-through perforated pipesilencer mean flow has little influence on the acoustic atten-uation in the plane wave range and remarkably decreasesthe resonance peak and increases the acoustic attenuation athigher frequencies
Conflict of Interests
The authors declare that there is no conflict of interests withregard to this study and the publication of this paper
Shock and Vibration 11
Acknowledgments
The authors are grateful for the grants from National NaturalScience Foundation of China (51275082 11272273) Funda-mental Research Fund of Central Universities (N130403009)Research Fund for Doctoral Program of Higher Education(20100042110013) and Program for Liaoning InnovativeResearch Team in University (LT2014006)
References
[1] M G Prasad and M J Crocker ldquoInsertion loss studies onmodels of automotive exhaust systemsrdquo Journal of the AcousticalSociety of America vol 70 no 5 pp 1339ndash1344 1981
[2] M L Munjal and P T Thawani ldquoOn the transfer matrix for auniform tube with a moving mediumrdquo Journal of Sound andVibration vol 91 no 4 pp 597ndash599 1983
[3] K Narayana Rao and M L Munjal ldquoExperimental evaluationof impedance of perforates with grazing flowrdquo Journal of Soundand Vibration vol 108 no 2 pp 283ndash295 1986
[4] Y H Kim S H Kim B D Lim and Y K Kwak ldquoExperimentalstudy of acoustic characteristics of expansion chamber withmean flowsrdquo KSME Journal vol 2 no 2 pp 125ndash132 1988
[5] Y Auregan and M Leroux ldquoFailures in the discrete modelsfor flow duct with perforations an experimental investigationrdquoJournal of Sound andVibration vol 265 no 1 pp 109ndash121 2003
[6] A Broatch XMargot A Gil and F DDenia ldquoACFD approachto the computation of the acoustic response of exhaustmufflersrdquoJournal of Computational Acoustics vol 13 no 2 pp 301ndash3162005
[7] Z L Ji H S Xu and Z X Kang ldquoInfluence of mean flowon acoustic attenuation performance of straight-through per-forated tube reactive silencers and resonatorsrdquo Noise ControlEngineering Journal vol 58 no 1 pp 12ndash17 2010
[8] C Liu and Z-L Ji ldquoComputational fluid dynamics-basednumerical analysis of acoustic attenuation and flow resistancecharacteristics of perforated tube silencersrdquo Journal of Vibrationand Acoustics vol 136 no 2 Article ID 021006 11 pages 2014
[9] H-D Ju S-B Lee and Y-B Park ldquoTransmission loss estima-tion of splitter silencer using multi-domain BEMrdquo Journal ofMechanical Science and Technology vol 21 no 12 pp 2073ndash2081 2007
[10] Z L Ji ldquoBoundary element acoustic analysis of hybrid expan-sion chamber silencers with perforated facingrdquo EngineeringAnalysis with Boundary Elements vol 34 no 7 pp 690ndash6962010
[11] C Jiang T W Wu M B Xu and C Y R Cheng ldquoBEMmodeling of mufflers with diesel particulate filters and catalyticconvertersrdquoNoise Control Engineering Journal vol 58 no 3 pp243ndash250 2010
[12] C I J Young and M J Crocker ldquoPrediction of transmissionloss in mufflers by the finite element methodrdquo Journal of theAcoustical Society of America vol 57 no 1 pp 144ndash148 1975
[13] O Z Mehdizadeh and M Paraschivoiu ldquoA three-dimensionalfinite element approach for predicting the transmission loss inmufflers and silencers with no mean flowrdquo Applied Acousticsvol 66 no 8 pp 902ndash918 2005
[14] Z Kang and Z Ji ldquoAcoustic length correction of duct extensioninto a cylindrical chamberrdquo Journal of Sound and Vibration vol310 no 4-5 pp 782ndash791 2008
[15] Y S GeH B Zhang Y R Zhang JW Tan XM Zhang andXK Han ldquoAn analysis on 3D acoustic performance of automotiveexhaust mufflerrdquo Automotive Engineering vol 28 no 1 pp 51ndash55 2006 (Chinese)
[16] P Chaitanya and M L Munjal ldquoEffect of wall thickness on theend corrections of the extended inlet and outlet of a double-tuned expansion chamberrdquo Applied Acoustics vol 72 no 1 pp65ndash70 2011
[17] J Fu W Chen Y Tang W H Yuan G M Li and Y Li ldquoMod-ification of exhaust muffler of a diesel engine based on finiteelement method acoustic analysisrdquo Advances in MechanicalEngineering vol 7 no 4 11 pages 2015
[18] K S Peat ldquoEvaluation of four-pole parameters for ducts withflow by the finite element methodrdquo Journal of Sound andVibration vol 84 no 3 pp 389ndash395 1982
[19] X R Wang and Z L Ji ldquoBoundary element analysis of four-pole parameters and transmission loss of silencers with flowrdquoChinese Journal of Computational Physics vol 24 no 6 pp 717ndash724 2007 (Chinese)
[20] N Gil-Negrete A Rivas and J Vinolas ldquoPredicting thedynamic behaviour of hydrobushingsrdquo Shock andVibration vol12 no 2 pp 91ndash107 2005
[21] S N Panigrahi and M L Munjal ldquoBackpressure considera-tions in designing of cross flow perforated-element reactivesilencersrdquo Noise Control Engineering Journal vol 55 no 6 pp504ndash515 2007
[22] A J Torregrosa P Fajardo A Gil and R Navarro ldquoDevelop-ment of non-reflecting boundary condition for application in3D computational fluid dynamics codesrdquo Engineering Applica-tions of Computational Fluid Mechanics vol 6 no 3 pp 447ndash460 2012
[23] C-NWang ldquoAboundary element analysis for simple expansionsilencers with mean flowrdquo Journal of the Chinese Institute ofEngineers vol 23 no 4 pp 529ndash536 2000
[24] S-H Lee and J-G Ih ldquoEmpirical model of the acousticimpedance of a circular orifice in grazing mean flowrdquo Journalof the Acoustical Society of America vol 114 no 1 pp 98ndash1132003
[25] F L Zhan and J W Xu VirtualLab Acoustics Simulation fromEntry to Master Northwestern Polytechnical University PressXian China 2013 (Chinese)
[26] ANSYS Inc ANSYS FLUENT 145 in Workbench Userrsquos GuideANSYS Inc New York NY USA 2012
[27] LMS International NV LMS VirtualLab Online Help11-SL2LMS International N V Leuven Belgium 2013
[28] C Liu Z L Ji and Z Fang ldquoNumerical analysis of acousticattenuation and flow resistance characteristics of double expan-sion chamber silencersrdquo Noise Control Engineering Journal vol61 no 5 pp 487ndash499 2013
[29] M L Munjal Acoustic of Ducts and Mufflers Wiley New YorkNY USA 2014
[30] R Singh and T Katra ldquoDevelopment of an impulse techniquefor measurement of muffler characteristicsrdquo Journal of Soundand Vibration vol 56 no 2 pp 279ndash298 1978
[31] J M Middelberg T J Barber S S Leong K P Byrne andE Leonardi ldquoCFD analysis of the acoustic and mean flowperformance of simple expansion chamber mufflersrdquo in Pro-ceedings of theASME InternationalMechanical EngineeringCon-gress and Exposition pp 151ndash156 Anaheim Calif USA Novem-ber 2004
12 Shock and Vibration
[32] B K Gardner A Mejdi F Mendonca and D Copley ldquoUsingCFD flow fields to inform acoustic finite element models ofcomplex mufflers with thermal and flow effectsrdquo in Proceedingsof the 44th International Congress and Exposition on NoiseControl Engineering Paper 15-665 San Francisco Calif USAAugust 2015
[33] E Dokumaci ldquoEffect of sheared grazing mean flow on acoustictransmission in perforated pipe mufflersrdquo Journal of Sound andVibration vol 283 no 3ndash5 pp 645ndash663 2005
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
Shock and Vibration 7
50
60
40
30
20
10
0
TL (d
B)
Published experimental dataFEMPredicted by literature [23]
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
Figure 11 Measured and predicted TL for the expansion chamber silencer with inlet flow velocity of V = 102ms
Substituting (11) and (12) into (6) yields
TL = 10 log10[(119901in + 120588119888)
2
41199012out
119860 in119860out
]
= 10 log10((119901in + 120588119888) (119901in + 120588119888)
4119901out119901out
119860 in119860out
)
(13)
It should be noted that the obtained acoustic pressure is infrequency-domain and therefore has a complex value In thispaper the temperature and density of the medium (air) are119879 = 288K and 120588 = 1225 kgm3 respectively and the speedof sound in air is 119888 = 340ms
3 Results and Discussion
31 Validation of the 3D Numerical Method Following thecalculation steps stated in Section 22 CFD steady flowcomputation is performed first Figure 5 shows the computedvelocity contours on the axial cutting plane of the expansionchamber silencer with extended inlet it is found that thevelocity distribution is uneven The flow velocity in the inletand outlet pipes are higher than that in the chamber and thesudden section area change enhances the turbulent kineticenergy as shown in Figure 6 Figure 7 shows the veloc-ity-vectors for the three straight-through perforated pipesilencers with a mean flow Mach number of 119872 = 01 or02 Flow circulations can be observed in the rear part of thechamber and the velocity in the pipe is much higher thanthat in the orifices and chamber Moreover the magnitudeand direction of cross-flow velocity through the perforationsare different along the axial direction In addition under theaction of pressure difference between the chamber and perfo-rated pipe the gas flows into the chamber through the orificesand then flows back again into the pipe which enhancesthe turbulent kinetic energy near the orifices as shown in
Figure 8 Generally speaking the flow velocity distributionsinside the studied silencers are anisotropic and nonuniformand the gas flow is accompanied with turbulence
After importing the mean flow data to the acoustic fieldby mesh mapping acoustic response analysis is performedto acquire acoustic pressure at the inlet and outlet as shownin Figures 9 and 10 To validate the accuracy of the 3Dnumerical method published experimental and numericalresults for the studied silencers are comparedwith the presentpredictions
Figure 11 compares the TL results for the expansionchamber silencer with extended inlet from numerical andexperimental methodsThe present predictions agree reason-ably well with the experimental data in the frequency range ofinterest Some deviation from the measurements is observedfor example near the resonance peak This discrepancy maybe attributed to the fact that (i) the medium viscous effectsand wall thickness are neglected in the FEM calculation and(ii) flow noise generated inside the silencer is neglected inthe simulation but the noise is included in the experimentsFurthermore the present FEM results are compared withthe numerical results from literature [23] One can see thatthe present FEM yields better results between the predictedTL curves That is because the method employed in theliterature neglects the turbulence inside the silencer and usesthe simplified mean flow velocity In contrast the presentstudy may acquire more detailed distribution of mean flowthrough the CFD steady flow computation with the properturbulence model
In Figure 12 a comparison between the present predic-tions and measurements shows a good agreement in generalbetween TL results obtained for the three straight-throughperforated pipe silencers studied here However it is foundthat the present predicted TL values are slightly less thanthose measured This is because the influence of mean flowon the sound propagation in the silencer can be explained as
8 Shock and Vibration
50
40
30
20
10
00 500 1000 1500 2000 2500 3000
Frequency (Hz)
TL (d
B)
Published experimental dataFEMPredicted by literature [24]
(a)
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
50
40
30
20
10
0
TL (d
B)
Published experimental dataFEMPredicted by literature [24]
(b)
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
50
40
30
20
10
0
TL (d
B)
Published experimental dataFEMPredicted by literature [24]
(c)
Figure 12 Measured and predicted TL for the straight-through perforated pipe silencers (a) silencer 1198751119872 = 01 (b) silencer 1198752119872 = 02and (c) silencer 1198753119872 = 01
the convective and dissipative effects [7] and the convectiveeffect can be considered by importing the decouple meanfrom an external steady flow computation to the acousticfield but the dissipative effect of medium viscous (especiallyin the orifices) which can cause sound energy loss and thusincrease TL is not included in the FEM calculation just likethe conventional frequency-domain method At present lotsof studies such as [24] mainly focus on applying mathe-matical modeling of perforate impedance to calculate andanalyze the acoustic attenuation performance of perforatedpipe silencer In the absence of mean flow the acousticperformance of the silence can be accurately predicted withthe help of perforate impedance models However when
mean flow is present rigorous mathematical modeling ofthe mechanisms that determine the perforate impedance isextremely difficult Therefore most of current impedancemodels considering the mean flow effect are empirical Incontrast although there is a lack of consideration of meanflow dissipative effect on sound propagation in present FEMby decoupling the problems this method avoids complexmathematical calculation and it is accessible and easy to useFurthermore the predicted results presented are not badTherefore it is valuable for predicting the acoustic attenuationperformance of perforated pipe silencer
At present with the development of computer perfor-mance the full time-domain CFD method such as that
Shock and Vibration 9
00
500 1000 1500 2000 2500 3000
Frequency (Hz)
TL (d
B)10
20
30
40
50
60
= 0
= 30ms = 60ms
Figure 13 Effect of flow velocity on TL of the expansion chamber silencer
performed in [8] has also attracted the interest of researchersThe main advantage of this method is that the dissipativeeffect of medium viscous could be better represented How-ever compared with the present method the main problemwhen using the time-domain CFD method is the CPU timeconsumed during the transient flow computation due tothe fact that long upstream and downstream pipes typicallyexceeding 15 times the length of the silencer are requiredto capture isolated incident and transmitted signals and thetime window (record length of data) must be long enoughto capture the entire pressure signals Moreover when meanflow is present the CFD transient flow computation needs tobe run twice (with and without impulse signal) Additionallyit can be seen from [8] that the TL curves calculated by thetime-domain CFD method are not smooth and have somesawteeth This is because the time-domain CFD method isa simulation of the process of an impulse technique [30]for measuring silencer acoustic performance and thereforethe predicted TL curves are easy to fluctuate like thoseobtained from the impulse technique Middelberg et al [31]investigated the effect of mesh size on TL obtained from thetime-domain CFD method and they found that for higherfrequencies the coarse mesh would influence the accuracy ofsolution due to the inability of the mesh to resolve the wave-length with a sufficient number of points and introducedthe artificial numerical dissipation Therefore the mesh sizefor the time-domain CFD method should be small enoughto avoid high-frequency dissipation As mentioned in Sec-tion 21 two different meshes CFD mesh and acoustic meshare used for the solution of the mean flow and acousticproblems when employing present method Compared withthe mesh used in the time-domain CFDmethod the require-ments of the CFD mesh for the steady flow computation inpresent method are much reduced [32] but it should be finerthan the acoustic mesh
32 Effect of Mean Flow on Silencer Acoustic Attenuation Per-formance Two main effects of mean flow on silencer acous-tic performance can be distinguished one is to affect thesound propagation in the silencer (stated in Section 31) Theother is to induce aerodynamic noise due to turbulence Insilencers the typical mean flow Mach number is below 03[33] and the aerodynamic noise is considered to be weakTherefore the aerodynamic noise is neglected in this work
Figure 13 shows that the predicted TL curves of theexpansion chamber silencer with the flow velocity variedbetween 0ms and 60ms It is observed that the shape ofTL curve with mean flow is much similar to that withoutmean flow The presence of mean flow increases the TLat most frequencies and decreases the resonance peak andTL increases further as flow velocities increase Figure 14shows the effect of mean flow on TL of the straight-throughperforated pipe silencers with different flow velocities It canbe seen from these pictures that the mean flow has littleinfluence on the acoustic attenuation in the plane wave rangeand leads to complex variation of TL curves in the non-plane wave Overall except that the presence of mean flowremarkably decreases resonance peak the acoustic attenu-ation performance of the straight-through perforated pipesilencers increases at most frequencies as flow velocity isincreased especially at higher frequencies
4 Conclusions
In this paper a 3D numerical method is employed to inves-tigate the acoustic attenuation performance of a circularexpansion chamber silencer with extended inlet and threestraight-through perforated pipe silencers in the presence ofmean flow By decoupling the problem the linear acousticsare away from the mean flow computation CFD and FEM
10 Shock and Vibration
= 0
= 30ms = 60ms
00
500 1000 1500 2000 2500 3000
Frequency (Hz)
TL (d
B)
10
20
30
40
50
(a)
= 0
= 30ms = 60ms
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
0
TL (d
B)
10
20
30
40
50
(b)
= 0
= 30ms = 60ms
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
0
TL (d
B)
10
20
30
40
50
(c)
Figure 14 Effect of flow velocity on TL of the straight-through perforated pipe silencers (a) silencer 1198751 (b) silencer 1198752 and (c) silencer 1198753
are employed to perform the steady flow computation andacoustic response analysis respectively The data transferis accomplished by mesh mapping A comparison betweenpresent results and previously published experimental andnumerical results indicates that the present 3D numericalmethod is capable of delivering reasonable predictions Themajor advantage of present method is that it is accessible andeasy to use and avoids complexmathematical calculationwiththe help of simulation software especially for the perforatedpipe silencer while the major drawback of this method liesin the considerable computational effort and cost that arerequired to acquire a complete and accurate solution in the3D calculations
Furthermore the TL of studied silencers with differentflow velocities is calculated It is concluded that the presenceof mean flow decreases the resonance peak and increases theacoustic attenuation at most frequencies for the expansionchamber silencer For the straight-through perforated pipesilencer mean flow has little influence on the acoustic atten-uation in the plane wave range and remarkably decreasesthe resonance peak and increases the acoustic attenuation athigher frequencies
Conflict of Interests
The authors declare that there is no conflict of interests withregard to this study and the publication of this paper
Shock and Vibration 11
Acknowledgments
The authors are grateful for the grants from National NaturalScience Foundation of China (51275082 11272273) Funda-mental Research Fund of Central Universities (N130403009)Research Fund for Doctoral Program of Higher Education(20100042110013) and Program for Liaoning InnovativeResearch Team in University (LT2014006)
References
[1] M G Prasad and M J Crocker ldquoInsertion loss studies onmodels of automotive exhaust systemsrdquo Journal of the AcousticalSociety of America vol 70 no 5 pp 1339ndash1344 1981
[2] M L Munjal and P T Thawani ldquoOn the transfer matrix for auniform tube with a moving mediumrdquo Journal of Sound andVibration vol 91 no 4 pp 597ndash599 1983
[3] K Narayana Rao and M L Munjal ldquoExperimental evaluationof impedance of perforates with grazing flowrdquo Journal of Soundand Vibration vol 108 no 2 pp 283ndash295 1986
[4] Y H Kim S H Kim B D Lim and Y K Kwak ldquoExperimentalstudy of acoustic characteristics of expansion chamber withmean flowsrdquo KSME Journal vol 2 no 2 pp 125ndash132 1988
[5] Y Auregan and M Leroux ldquoFailures in the discrete modelsfor flow duct with perforations an experimental investigationrdquoJournal of Sound andVibration vol 265 no 1 pp 109ndash121 2003
[6] A Broatch XMargot A Gil and F DDenia ldquoACFD approachto the computation of the acoustic response of exhaustmufflersrdquoJournal of Computational Acoustics vol 13 no 2 pp 301ndash3162005
[7] Z L Ji H S Xu and Z X Kang ldquoInfluence of mean flowon acoustic attenuation performance of straight-through per-forated tube reactive silencers and resonatorsrdquo Noise ControlEngineering Journal vol 58 no 1 pp 12ndash17 2010
[8] C Liu and Z-L Ji ldquoComputational fluid dynamics-basednumerical analysis of acoustic attenuation and flow resistancecharacteristics of perforated tube silencersrdquo Journal of Vibrationand Acoustics vol 136 no 2 Article ID 021006 11 pages 2014
[9] H-D Ju S-B Lee and Y-B Park ldquoTransmission loss estima-tion of splitter silencer using multi-domain BEMrdquo Journal ofMechanical Science and Technology vol 21 no 12 pp 2073ndash2081 2007
[10] Z L Ji ldquoBoundary element acoustic analysis of hybrid expan-sion chamber silencers with perforated facingrdquo EngineeringAnalysis with Boundary Elements vol 34 no 7 pp 690ndash6962010
[11] C Jiang T W Wu M B Xu and C Y R Cheng ldquoBEMmodeling of mufflers with diesel particulate filters and catalyticconvertersrdquoNoise Control Engineering Journal vol 58 no 3 pp243ndash250 2010
[12] C I J Young and M J Crocker ldquoPrediction of transmissionloss in mufflers by the finite element methodrdquo Journal of theAcoustical Society of America vol 57 no 1 pp 144ndash148 1975
[13] O Z Mehdizadeh and M Paraschivoiu ldquoA three-dimensionalfinite element approach for predicting the transmission loss inmufflers and silencers with no mean flowrdquo Applied Acousticsvol 66 no 8 pp 902ndash918 2005
[14] Z Kang and Z Ji ldquoAcoustic length correction of duct extensioninto a cylindrical chamberrdquo Journal of Sound and Vibration vol310 no 4-5 pp 782ndash791 2008
[15] Y S GeH B Zhang Y R Zhang JW Tan XM Zhang andXK Han ldquoAn analysis on 3D acoustic performance of automotiveexhaust mufflerrdquo Automotive Engineering vol 28 no 1 pp 51ndash55 2006 (Chinese)
[16] P Chaitanya and M L Munjal ldquoEffect of wall thickness on theend corrections of the extended inlet and outlet of a double-tuned expansion chamberrdquo Applied Acoustics vol 72 no 1 pp65ndash70 2011
[17] J Fu W Chen Y Tang W H Yuan G M Li and Y Li ldquoMod-ification of exhaust muffler of a diesel engine based on finiteelement method acoustic analysisrdquo Advances in MechanicalEngineering vol 7 no 4 11 pages 2015
[18] K S Peat ldquoEvaluation of four-pole parameters for ducts withflow by the finite element methodrdquo Journal of Sound andVibration vol 84 no 3 pp 389ndash395 1982
[19] X R Wang and Z L Ji ldquoBoundary element analysis of four-pole parameters and transmission loss of silencers with flowrdquoChinese Journal of Computational Physics vol 24 no 6 pp 717ndash724 2007 (Chinese)
[20] N Gil-Negrete A Rivas and J Vinolas ldquoPredicting thedynamic behaviour of hydrobushingsrdquo Shock andVibration vol12 no 2 pp 91ndash107 2005
[21] S N Panigrahi and M L Munjal ldquoBackpressure considera-tions in designing of cross flow perforated-element reactivesilencersrdquo Noise Control Engineering Journal vol 55 no 6 pp504ndash515 2007
[22] A J Torregrosa P Fajardo A Gil and R Navarro ldquoDevelop-ment of non-reflecting boundary condition for application in3D computational fluid dynamics codesrdquo Engineering Applica-tions of Computational Fluid Mechanics vol 6 no 3 pp 447ndash460 2012
[23] C-NWang ldquoAboundary element analysis for simple expansionsilencers with mean flowrdquo Journal of the Chinese Institute ofEngineers vol 23 no 4 pp 529ndash536 2000
[24] S-H Lee and J-G Ih ldquoEmpirical model of the acousticimpedance of a circular orifice in grazing mean flowrdquo Journalof the Acoustical Society of America vol 114 no 1 pp 98ndash1132003
[25] F L Zhan and J W Xu VirtualLab Acoustics Simulation fromEntry to Master Northwestern Polytechnical University PressXian China 2013 (Chinese)
[26] ANSYS Inc ANSYS FLUENT 145 in Workbench Userrsquos GuideANSYS Inc New York NY USA 2012
[27] LMS International NV LMS VirtualLab Online Help11-SL2LMS International N V Leuven Belgium 2013
[28] C Liu Z L Ji and Z Fang ldquoNumerical analysis of acousticattenuation and flow resistance characteristics of double expan-sion chamber silencersrdquo Noise Control Engineering Journal vol61 no 5 pp 487ndash499 2013
[29] M L Munjal Acoustic of Ducts and Mufflers Wiley New YorkNY USA 2014
[30] R Singh and T Katra ldquoDevelopment of an impulse techniquefor measurement of muffler characteristicsrdquo Journal of Soundand Vibration vol 56 no 2 pp 279ndash298 1978
[31] J M Middelberg T J Barber S S Leong K P Byrne andE Leonardi ldquoCFD analysis of the acoustic and mean flowperformance of simple expansion chamber mufflersrdquo in Pro-ceedings of theASME InternationalMechanical EngineeringCon-gress and Exposition pp 151ndash156 Anaheim Calif USA Novem-ber 2004
12 Shock and Vibration
[32] B K Gardner A Mejdi F Mendonca and D Copley ldquoUsingCFD flow fields to inform acoustic finite element models ofcomplex mufflers with thermal and flow effectsrdquo in Proceedingsof the 44th International Congress and Exposition on NoiseControl Engineering Paper 15-665 San Francisco Calif USAAugust 2015
[33] E Dokumaci ldquoEffect of sheared grazing mean flow on acoustictransmission in perforated pipe mufflersrdquo Journal of Sound andVibration vol 283 no 3ndash5 pp 645ndash663 2005
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
8 Shock and Vibration
50
40
30
20
10
00 500 1000 1500 2000 2500 3000
Frequency (Hz)
TL (d
B)
Published experimental dataFEMPredicted by literature [24]
(a)
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
50
40
30
20
10
0
TL (d
B)
Published experimental dataFEMPredicted by literature [24]
(b)
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
50
40
30
20
10
0
TL (d
B)
Published experimental dataFEMPredicted by literature [24]
(c)
Figure 12 Measured and predicted TL for the straight-through perforated pipe silencers (a) silencer 1198751119872 = 01 (b) silencer 1198752119872 = 02and (c) silencer 1198753119872 = 01
the convective and dissipative effects [7] and the convectiveeffect can be considered by importing the decouple meanfrom an external steady flow computation to the acousticfield but the dissipative effect of medium viscous (especiallyin the orifices) which can cause sound energy loss and thusincrease TL is not included in the FEM calculation just likethe conventional frequency-domain method At present lotsof studies such as [24] mainly focus on applying mathe-matical modeling of perforate impedance to calculate andanalyze the acoustic attenuation performance of perforatedpipe silencer In the absence of mean flow the acousticperformance of the silence can be accurately predicted withthe help of perforate impedance models However when
mean flow is present rigorous mathematical modeling ofthe mechanisms that determine the perforate impedance isextremely difficult Therefore most of current impedancemodels considering the mean flow effect are empirical Incontrast although there is a lack of consideration of meanflow dissipative effect on sound propagation in present FEMby decoupling the problems this method avoids complexmathematical calculation and it is accessible and easy to useFurthermore the predicted results presented are not badTherefore it is valuable for predicting the acoustic attenuationperformance of perforated pipe silencer
At present with the development of computer perfor-mance the full time-domain CFD method such as that
Shock and Vibration 9
00
500 1000 1500 2000 2500 3000
Frequency (Hz)
TL (d
B)10
20
30
40
50
60
= 0
= 30ms = 60ms
Figure 13 Effect of flow velocity on TL of the expansion chamber silencer
performed in [8] has also attracted the interest of researchersThe main advantage of this method is that the dissipativeeffect of medium viscous could be better represented How-ever compared with the present method the main problemwhen using the time-domain CFD method is the CPU timeconsumed during the transient flow computation due tothe fact that long upstream and downstream pipes typicallyexceeding 15 times the length of the silencer are requiredto capture isolated incident and transmitted signals and thetime window (record length of data) must be long enoughto capture the entire pressure signals Moreover when meanflow is present the CFD transient flow computation needs tobe run twice (with and without impulse signal) Additionallyit can be seen from [8] that the TL curves calculated by thetime-domain CFD method are not smooth and have somesawteeth This is because the time-domain CFD method isa simulation of the process of an impulse technique [30]for measuring silencer acoustic performance and thereforethe predicted TL curves are easy to fluctuate like thoseobtained from the impulse technique Middelberg et al [31]investigated the effect of mesh size on TL obtained from thetime-domain CFD method and they found that for higherfrequencies the coarse mesh would influence the accuracy ofsolution due to the inability of the mesh to resolve the wave-length with a sufficient number of points and introducedthe artificial numerical dissipation Therefore the mesh sizefor the time-domain CFD method should be small enoughto avoid high-frequency dissipation As mentioned in Sec-tion 21 two different meshes CFD mesh and acoustic meshare used for the solution of the mean flow and acousticproblems when employing present method Compared withthe mesh used in the time-domain CFDmethod the require-ments of the CFD mesh for the steady flow computation inpresent method are much reduced [32] but it should be finerthan the acoustic mesh
32 Effect of Mean Flow on Silencer Acoustic Attenuation Per-formance Two main effects of mean flow on silencer acous-tic performance can be distinguished one is to affect thesound propagation in the silencer (stated in Section 31) Theother is to induce aerodynamic noise due to turbulence Insilencers the typical mean flow Mach number is below 03[33] and the aerodynamic noise is considered to be weakTherefore the aerodynamic noise is neglected in this work
Figure 13 shows that the predicted TL curves of theexpansion chamber silencer with the flow velocity variedbetween 0ms and 60ms It is observed that the shape ofTL curve with mean flow is much similar to that withoutmean flow The presence of mean flow increases the TLat most frequencies and decreases the resonance peak andTL increases further as flow velocities increase Figure 14shows the effect of mean flow on TL of the straight-throughperforated pipe silencers with different flow velocities It canbe seen from these pictures that the mean flow has littleinfluence on the acoustic attenuation in the plane wave rangeand leads to complex variation of TL curves in the non-plane wave Overall except that the presence of mean flowremarkably decreases resonance peak the acoustic attenu-ation performance of the straight-through perforated pipesilencers increases at most frequencies as flow velocity isincreased especially at higher frequencies
4 Conclusions
In this paper a 3D numerical method is employed to inves-tigate the acoustic attenuation performance of a circularexpansion chamber silencer with extended inlet and threestraight-through perforated pipe silencers in the presence ofmean flow By decoupling the problem the linear acousticsare away from the mean flow computation CFD and FEM
10 Shock and Vibration
= 0
= 30ms = 60ms
00
500 1000 1500 2000 2500 3000
Frequency (Hz)
TL (d
B)
10
20
30
40
50
(a)
= 0
= 30ms = 60ms
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
0
TL (d
B)
10
20
30
40
50
(b)
= 0
= 30ms = 60ms
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
0
TL (d
B)
10
20
30
40
50
(c)
Figure 14 Effect of flow velocity on TL of the straight-through perforated pipe silencers (a) silencer 1198751 (b) silencer 1198752 and (c) silencer 1198753
are employed to perform the steady flow computation andacoustic response analysis respectively The data transferis accomplished by mesh mapping A comparison betweenpresent results and previously published experimental andnumerical results indicates that the present 3D numericalmethod is capable of delivering reasonable predictions Themajor advantage of present method is that it is accessible andeasy to use and avoids complexmathematical calculationwiththe help of simulation software especially for the perforatedpipe silencer while the major drawback of this method liesin the considerable computational effort and cost that arerequired to acquire a complete and accurate solution in the3D calculations
Furthermore the TL of studied silencers with differentflow velocities is calculated It is concluded that the presenceof mean flow decreases the resonance peak and increases theacoustic attenuation at most frequencies for the expansionchamber silencer For the straight-through perforated pipesilencer mean flow has little influence on the acoustic atten-uation in the plane wave range and remarkably decreasesthe resonance peak and increases the acoustic attenuation athigher frequencies
Conflict of Interests
The authors declare that there is no conflict of interests withregard to this study and the publication of this paper
Shock and Vibration 11
Acknowledgments
The authors are grateful for the grants from National NaturalScience Foundation of China (51275082 11272273) Funda-mental Research Fund of Central Universities (N130403009)Research Fund for Doctoral Program of Higher Education(20100042110013) and Program for Liaoning InnovativeResearch Team in University (LT2014006)
References
[1] M G Prasad and M J Crocker ldquoInsertion loss studies onmodels of automotive exhaust systemsrdquo Journal of the AcousticalSociety of America vol 70 no 5 pp 1339ndash1344 1981
[2] M L Munjal and P T Thawani ldquoOn the transfer matrix for auniform tube with a moving mediumrdquo Journal of Sound andVibration vol 91 no 4 pp 597ndash599 1983
[3] K Narayana Rao and M L Munjal ldquoExperimental evaluationof impedance of perforates with grazing flowrdquo Journal of Soundand Vibration vol 108 no 2 pp 283ndash295 1986
[4] Y H Kim S H Kim B D Lim and Y K Kwak ldquoExperimentalstudy of acoustic characteristics of expansion chamber withmean flowsrdquo KSME Journal vol 2 no 2 pp 125ndash132 1988
[5] Y Auregan and M Leroux ldquoFailures in the discrete modelsfor flow duct with perforations an experimental investigationrdquoJournal of Sound andVibration vol 265 no 1 pp 109ndash121 2003
[6] A Broatch XMargot A Gil and F DDenia ldquoACFD approachto the computation of the acoustic response of exhaustmufflersrdquoJournal of Computational Acoustics vol 13 no 2 pp 301ndash3162005
[7] Z L Ji H S Xu and Z X Kang ldquoInfluence of mean flowon acoustic attenuation performance of straight-through per-forated tube reactive silencers and resonatorsrdquo Noise ControlEngineering Journal vol 58 no 1 pp 12ndash17 2010
[8] C Liu and Z-L Ji ldquoComputational fluid dynamics-basednumerical analysis of acoustic attenuation and flow resistancecharacteristics of perforated tube silencersrdquo Journal of Vibrationand Acoustics vol 136 no 2 Article ID 021006 11 pages 2014
[9] H-D Ju S-B Lee and Y-B Park ldquoTransmission loss estima-tion of splitter silencer using multi-domain BEMrdquo Journal ofMechanical Science and Technology vol 21 no 12 pp 2073ndash2081 2007
[10] Z L Ji ldquoBoundary element acoustic analysis of hybrid expan-sion chamber silencers with perforated facingrdquo EngineeringAnalysis with Boundary Elements vol 34 no 7 pp 690ndash6962010
[11] C Jiang T W Wu M B Xu and C Y R Cheng ldquoBEMmodeling of mufflers with diesel particulate filters and catalyticconvertersrdquoNoise Control Engineering Journal vol 58 no 3 pp243ndash250 2010
[12] C I J Young and M J Crocker ldquoPrediction of transmissionloss in mufflers by the finite element methodrdquo Journal of theAcoustical Society of America vol 57 no 1 pp 144ndash148 1975
[13] O Z Mehdizadeh and M Paraschivoiu ldquoA three-dimensionalfinite element approach for predicting the transmission loss inmufflers and silencers with no mean flowrdquo Applied Acousticsvol 66 no 8 pp 902ndash918 2005
[14] Z Kang and Z Ji ldquoAcoustic length correction of duct extensioninto a cylindrical chamberrdquo Journal of Sound and Vibration vol310 no 4-5 pp 782ndash791 2008
[15] Y S GeH B Zhang Y R Zhang JW Tan XM Zhang andXK Han ldquoAn analysis on 3D acoustic performance of automotiveexhaust mufflerrdquo Automotive Engineering vol 28 no 1 pp 51ndash55 2006 (Chinese)
[16] P Chaitanya and M L Munjal ldquoEffect of wall thickness on theend corrections of the extended inlet and outlet of a double-tuned expansion chamberrdquo Applied Acoustics vol 72 no 1 pp65ndash70 2011
[17] J Fu W Chen Y Tang W H Yuan G M Li and Y Li ldquoMod-ification of exhaust muffler of a diesel engine based on finiteelement method acoustic analysisrdquo Advances in MechanicalEngineering vol 7 no 4 11 pages 2015
[18] K S Peat ldquoEvaluation of four-pole parameters for ducts withflow by the finite element methodrdquo Journal of Sound andVibration vol 84 no 3 pp 389ndash395 1982
[19] X R Wang and Z L Ji ldquoBoundary element analysis of four-pole parameters and transmission loss of silencers with flowrdquoChinese Journal of Computational Physics vol 24 no 6 pp 717ndash724 2007 (Chinese)
[20] N Gil-Negrete A Rivas and J Vinolas ldquoPredicting thedynamic behaviour of hydrobushingsrdquo Shock andVibration vol12 no 2 pp 91ndash107 2005
[21] S N Panigrahi and M L Munjal ldquoBackpressure considera-tions in designing of cross flow perforated-element reactivesilencersrdquo Noise Control Engineering Journal vol 55 no 6 pp504ndash515 2007
[22] A J Torregrosa P Fajardo A Gil and R Navarro ldquoDevelop-ment of non-reflecting boundary condition for application in3D computational fluid dynamics codesrdquo Engineering Applica-tions of Computational Fluid Mechanics vol 6 no 3 pp 447ndash460 2012
[23] C-NWang ldquoAboundary element analysis for simple expansionsilencers with mean flowrdquo Journal of the Chinese Institute ofEngineers vol 23 no 4 pp 529ndash536 2000
[24] S-H Lee and J-G Ih ldquoEmpirical model of the acousticimpedance of a circular orifice in grazing mean flowrdquo Journalof the Acoustical Society of America vol 114 no 1 pp 98ndash1132003
[25] F L Zhan and J W Xu VirtualLab Acoustics Simulation fromEntry to Master Northwestern Polytechnical University PressXian China 2013 (Chinese)
[26] ANSYS Inc ANSYS FLUENT 145 in Workbench Userrsquos GuideANSYS Inc New York NY USA 2012
[27] LMS International NV LMS VirtualLab Online Help11-SL2LMS International N V Leuven Belgium 2013
[28] C Liu Z L Ji and Z Fang ldquoNumerical analysis of acousticattenuation and flow resistance characteristics of double expan-sion chamber silencersrdquo Noise Control Engineering Journal vol61 no 5 pp 487ndash499 2013
[29] M L Munjal Acoustic of Ducts and Mufflers Wiley New YorkNY USA 2014
[30] R Singh and T Katra ldquoDevelopment of an impulse techniquefor measurement of muffler characteristicsrdquo Journal of Soundand Vibration vol 56 no 2 pp 279ndash298 1978
[31] J M Middelberg T J Barber S S Leong K P Byrne andE Leonardi ldquoCFD analysis of the acoustic and mean flowperformance of simple expansion chamber mufflersrdquo in Pro-ceedings of theASME InternationalMechanical EngineeringCon-gress and Exposition pp 151ndash156 Anaheim Calif USA Novem-ber 2004
12 Shock and Vibration
[32] B K Gardner A Mejdi F Mendonca and D Copley ldquoUsingCFD flow fields to inform acoustic finite element models ofcomplex mufflers with thermal and flow effectsrdquo in Proceedingsof the 44th International Congress and Exposition on NoiseControl Engineering Paper 15-665 San Francisco Calif USAAugust 2015
[33] E Dokumaci ldquoEffect of sheared grazing mean flow on acoustictransmission in perforated pipe mufflersrdquo Journal of Sound andVibration vol 283 no 3ndash5 pp 645ndash663 2005
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
Shock and Vibration 9
00
500 1000 1500 2000 2500 3000
Frequency (Hz)
TL (d
B)10
20
30
40
50
60
= 0
= 30ms = 60ms
Figure 13 Effect of flow velocity on TL of the expansion chamber silencer
performed in [8] has also attracted the interest of researchersThe main advantage of this method is that the dissipativeeffect of medium viscous could be better represented How-ever compared with the present method the main problemwhen using the time-domain CFD method is the CPU timeconsumed during the transient flow computation due tothe fact that long upstream and downstream pipes typicallyexceeding 15 times the length of the silencer are requiredto capture isolated incident and transmitted signals and thetime window (record length of data) must be long enoughto capture the entire pressure signals Moreover when meanflow is present the CFD transient flow computation needs tobe run twice (with and without impulse signal) Additionallyit can be seen from [8] that the TL curves calculated by thetime-domain CFD method are not smooth and have somesawteeth This is because the time-domain CFD method isa simulation of the process of an impulse technique [30]for measuring silencer acoustic performance and thereforethe predicted TL curves are easy to fluctuate like thoseobtained from the impulse technique Middelberg et al [31]investigated the effect of mesh size on TL obtained from thetime-domain CFD method and they found that for higherfrequencies the coarse mesh would influence the accuracy ofsolution due to the inability of the mesh to resolve the wave-length with a sufficient number of points and introducedthe artificial numerical dissipation Therefore the mesh sizefor the time-domain CFD method should be small enoughto avoid high-frequency dissipation As mentioned in Sec-tion 21 two different meshes CFD mesh and acoustic meshare used for the solution of the mean flow and acousticproblems when employing present method Compared withthe mesh used in the time-domain CFDmethod the require-ments of the CFD mesh for the steady flow computation inpresent method are much reduced [32] but it should be finerthan the acoustic mesh
32 Effect of Mean Flow on Silencer Acoustic Attenuation Per-formance Two main effects of mean flow on silencer acous-tic performance can be distinguished one is to affect thesound propagation in the silencer (stated in Section 31) Theother is to induce aerodynamic noise due to turbulence Insilencers the typical mean flow Mach number is below 03[33] and the aerodynamic noise is considered to be weakTherefore the aerodynamic noise is neglected in this work
Figure 13 shows that the predicted TL curves of theexpansion chamber silencer with the flow velocity variedbetween 0ms and 60ms It is observed that the shape ofTL curve with mean flow is much similar to that withoutmean flow The presence of mean flow increases the TLat most frequencies and decreases the resonance peak andTL increases further as flow velocities increase Figure 14shows the effect of mean flow on TL of the straight-throughperforated pipe silencers with different flow velocities It canbe seen from these pictures that the mean flow has littleinfluence on the acoustic attenuation in the plane wave rangeand leads to complex variation of TL curves in the non-plane wave Overall except that the presence of mean flowremarkably decreases resonance peak the acoustic attenu-ation performance of the straight-through perforated pipesilencers increases at most frequencies as flow velocity isincreased especially at higher frequencies
4 Conclusions
In this paper a 3D numerical method is employed to inves-tigate the acoustic attenuation performance of a circularexpansion chamber silencer with extended inlet and threestraight-through perforated pipe silencers in the presence ofmean flow By decoupling the problem the linear acousticsare away from the mean flow computation CFD and FEM
10 Shock and Vibration
= 0
= 30ms = 60ms
00
500 1000 1500 2000 2500 3000
Frequency (Hz)
TL (d
B)
10
20
30
40
50
(a)
= 0
= 30ms = 60ms
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
0
TL (d
B)
10
20
30
40
50
(b)
= 0
= 30ms = 60ms
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
0
TL (d
B)
10
20
30
40
50
(c)
Figure 14 Effect of flow velocity on TL of the straight-through perforated pipe silencers (a) silencer 1198751 (b) silencer 1198752 and (c) silencer 1198753
are employed to perform the steady flow computation andacoustic response analysis respectively The data transferis accomplished by mesh mapping A comparison betweenpresent results and previously published experimental andnumerical results indicates that the present 3D numericalmethod is capable of delivering reasonable predictions Themajor advantage of present method is that it is accessible andeasy to use and avoids complexmathematical calculationwiththe help of simulation software especially for the perforatedpipe silencer while the major drawback of this method liesin the considerable computational effort and cost that arerequired to acquire a complete and accurate solution in the3D calculations
Furthermore the TL of studied silencers with differentflow velocities is calculated It is concluded that the presenceof mean flow decreases the resonance peak and increases theacoustic attenuation at most frequencies for the expansionchamber silencer For the straight-through perforated pipesilencer mean flow has little influence on the acoustic atten-uation in the plane wave range and remarkably decreasesthe resonance peak and increases the acoustic attenuation athigher frequencies
Conflict of Interests
The authors declare that there is no conflict of interests withregard to this study and the publication of this paper
Shock and Vibration 11
Acknowledgments
The authors are grateful for the grants from National NaturalScience Foundation of China (51275082 11272273) Funda-mental Research Fund of Central Universities (N130403009)Research Fund for Doctoral Program of Higher Education(20100042110013) and Program for Liaoning InnovativeResearch Team in University (LT2014006)
References
[1] M G Prasad and M J Crocker ldquoInsertion loss studies onmodels of automotive exhaust systemsrdquo Journal of the AcousticalSociety of America vol 70 no 5 pp 1339ndash1344 1981
[2] M L Munjal and P T Thawani ldquoOn the transfer matrix for auniform tube with a moving mediumrdquo Journal of Sound andVibration vol 91 no 4 pp 597ndash599 1983
[3] K Narayana Rao and M L Munjal ldquoExperimental evaluationof impedance of perforates with grazing flowrdquo Journal of Soundand Vibration vol 108 no 2 pp 283ndash295 1986
[4] Y H Kim S H Kim B D Lim and Y K Kwak ldquoExperimentalstudy of acoustic characteristics of expansion chamber withmean flowsrdquo KSME Journal vol 2 no 2 pp 125ndash132 1988
[5] Y Auregan and M Leroux ldquoFailures in the discrete modelsfor flow duct with perforations an experimental investigationrdquoJournal of Sound andVibration vol 265 no 1 pp 109ndash121 2003
[6] A Broatch XMargot A Gil and F DDenia ldquoACFD approachto the computation of the acoustic response of exhaustmufflersrdquoJournal of Computational Acoustics vol 13 no 2 pp 301ndash3162005
[7] Z L Ji H S Xu and Z X Kang ldquoInfluence of mean flowon acoustic attenuation performance of straight-through per-forated tube reactive silencers and resonatorsrdquo Noise ControlEngineering Journal vol 58 no 1 pp 12ndash17 2010
[8] C Liu and Z-L Ji ldquoComputational fluid dynamics-basednumerical analysis of acoustic attenuation and flow resistancecharacteristics of perforated tube silencersrdquo Journal of Vibrationand Acoustics vol 136 no 2 Article ID 021006 11 pages 2014
[9] H-D Ju S-B Lee and Y-B Park ldquoTransmission loss estima-tion of splitter silencer using multi-domain BEMrdquo Journal ofMechanical Science and Technology vol 21 no 12 pp 2073ndash2081 2007
[10] Z L Ji ldquoBoundary element acoustic analysis of hybrid expan-sion chamber silencers with perforated facingrdquo EngineeringAnalysis with Boundary Elements vol 34 no 7 pp 690ndash6962010
[11] C Jiang T W Wu M B Xu and C Y R Cheng ldquoBEMmodeling of mufflers with diesel particulate filters and catalyticconvertersrdquoNoise Control Engineering Journal vol 58 no 3 pp243ndash250 2010
[12] C I J Young and M J Crocker ldquoPrediction of transmissionloss in mufflers by the finite element methodrdquo Journal of theAcoustical Society of America vol 57 no 1 pp 144ndash148 1975
[13] O Z Mehdizadeh and M Paraschivoiu ldquoA three-dimensionalfinite element approach for predicting the transmission loss inmufflers and silencers with no mean flowrdquo Applied Acousticsvol 66 no 8 pp 902ndash918 2005
[14] Z Kang and Z Ji ldquoAcoustic length correction of duct extensioninto a cylindrical chamberrdquo Journal of Sound and Vibration vol310 no 4-5 pp 782ndash791 2008
[15] Y S GeH B Zhang Y R Zhang JW Tan XM Zhang andXK Han ldquoAn analysis on 3D acoustic performance of automotiveexhaust mufflerrdquo Automotive Engineering vol 28 no 1 pp 51ndash55 2006 (Chinese)
[16] P Chaitanya and M L Munjal ldquoEffect of wall thickness on theend corrections of the extended inlet and outlet of a double-tuned expansion chamberrdquo Applied Acoustics vol 72 no 1 pp65ndash70 2011
[17] J Fu W Chen Y Tang W H Yuan G M Li and Y Li ldquoMod-ification of exhaust muffler of a diesel engine based on finiteelement method acoustic analysisrdquo Advances in MechanicalEngineering vol 7 no 4 11 pages 2015
[18] K S Peat ldquoEvaluation of four-pole parameters for ducts withflow by the finite element methodrdquo Journal of Sound andVibration vol 84 no 3 pp 389ndash395 1982
[19] X R Wang and Z L Ji ldquoBoundary element analysis of four-pole parameters and transmission loss of silencers with flowrdquoChinese Journal of Computational Physics vol 24 no 6 pp 717ndash724 2007 (Chinese)
[20] N Gil-Negrete A Rivas and J Vinolas ldquoPredicting thedynamic behaviour of hydrobushingsrdquo Shock andVibration vol12 no 2 pp 91ndash107 2005
[21] S N Panigrahi and M L Munjal ldquoBackpressure considera-tions in designing of cross flow perforated-element reactivesilencersrdquo Noise Control Engineering Journal vol 55 no 6 pp504ndash515 2007
[22] A J Torregrosa P Fajardo A Gil and R Navarro ldquoDevelop-ment of non-reflecting boundary condition for application in3D computational fluid dynamics codesrdquo Engineering Applica-tions of Computational Fluid Mechanics vol 6 no 3 pp 447ndash460 2012
[23] C-NWang ldquoAboundary element analysis for simple expansionsilencers with mean flowrdquo Journal of the Chinese Institute ofEngineers vol 23 no 4 pp 529ndash536 2000
[24] S-H Lee and J-G Ih ldquoEmpirical model of the acousticimpedance of a circular orifice in grazing mean flowrdquo Journalof the Acoustical Society of America vol 114 no 1 pp 98ndash1132003
[25] F L Zhan and J W Xu VirtualLab Acoustics Simulation fromEntry to Master Northwestern Polytechnical University PressXian China 2013 (Chinese)
[26] ANSYS Inc ANSYS FLUENT 145 in Workbench Userrsquos GuideANSYS Inc New York NY USA 2012
[27] LMS International NV LMS VirtualLab Online Help11-SL2LMS International N V Leuven Belgium 2013
[28] C Liu Z L Ji and Z Fang ldquoNumerical analysis of acousticattenuation and flow resistance characteristics of double expan-sion chamber silencersrdquo Noise Control Engineering Journal vol61 no 5 pp 487ndash499 2013
[29] M L Munjal Acoustic of Ducts and Mufflers Wiley New YorkNY USA 2014
[30] R Singh and T Katra ldquoDevelopment of an impulse techniquefor measurement of muffler characteristicsrdquo Journal of Soundand Vibration vol 56 no 2 pp 279ndash298 1978
[31] J M Middelberg T J Barber S S Leong K P Byrne andE Leonardi ldquoCFD analysis of the acoustic and mean flowperformance of simple expansion chamber mufflersrdquo in Pro-ceedings of theASME InternationalMechanical EngineeringCon-gress and Exposition pp 151ndash156 Anaheim Calif USA Novem-ber 2004
12 Shock and Vibration
[32] B K Gardner A Mejdi F Mendonca and D Copley ldquoUsingCFD flow fields to inform acoustic finite element models ofcomplex mufflers with thermal and flow effectsrdquo in Proceedingsof the 44th International Congress and Exposition on NoiseControl Engineering Paper 15-665 San Francisco Calif USAAugust 2015
[33] E Dokumaci ldquoEffect of sheared grazing mean flow on acoustictransmission in perforated pipe mufflersrdquo Journal of Sound andVibration vol 283 no 3ndash5 pp 645ndash663 2005
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
10 Shock and Vibration
= 0
= 30ms = 60ms
00
500 1000 1500 2000 2500 3000
Frequency (Hz)
TL (d
B)
10
20
30
40
50
(a)
= 0
= 30ms = 60ms
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
0
TL (d
B)
10
20
30
40
50
(b)
= 0
= 30ms = 60ms
0 500 1000 1500 2000 2500 3000
Frequency (Hz)
0
TL (d
B)
10
20
30
40
50
(c)
Figure 14 Effect of flow velocity on TL of the straight-through perforated pipe silencers (a) silencer 1198751 (b) silencer 1198752 and (c) silencer 1198753
are employed to perform the steady flow computation andacoustic response analysis respectively The data transferis accomplished by mesh mapping A comparison betweenpresent results and previously published experimental andnumerical results indicates that the present 3D numericalmethod is capable of delivering reasonable predictions Themajor advantage of present method is that it is accessible andeasy to use and avoids complexmathematical calculationwiththe help of simulation software especially for the perforatedpipe silencer while the major drawback of this method liesin the considerable computational effort and cost that arerequired to acquire a complete and accurate solution in the3D calculations
Furthermore the TL of studied silencers with differentflow velocities is calculated It is concluded that the presenceof mean flow decreases the resonance peak and increases theacoustic attenuation at most frequencies for the expansionchamber silencer For the straight-through perforated pipesilencer mean flow has little influence on the acoustic atten-uation in the plane wave range and remarkably decreasesthe resonance peak and increases the acoustic attenuation athigher frequencies
Conflict of Interests
The authors declare that there is no conflict of interests withregard to this study and the publication of this paper
Shock and Vibration 11
Acknowledgments
The authors are grateful for the grants from National NaturalScience Foundation of China (51275082 11272273) Funda-mental Research Fund of Central Universities (N130403009)Research Fund for Doctoral Program of Higher Education(20100042110013) and Program for Liaoning InnovativeResearch Team in University (LT2014006)
References
[1] M G Prasad and M J Crocker ldquoInsertion loss studies onmodels of automotive exhaust systemsrdquo Journal of the AcousticalSociety of America vol 70 no 5 pp 1339ndash1344 1981
[2] M L Munjal and P T Thawani ldquoOn the transfer matrix for auniform tube with a moving mediumrdquo Journal of Sound andVibration vol 91 no 4 pp 597ndash599 1983
[3] K Narayana Rao and M L Munjal ldquoExperimental evaluationof impedance of perforates with grazing flowrdquo Journal of Soundand Vibration vol 108 no 2 pp 283ndash295 1986
[4] Y H Kim S H Kim B D Lim and Y K Kwak ldquoExperimentalstudy of acoustic characteristics of expansion chamber withmean flowsrdquo KSME Journal vol 2 no 2 pp 125ndash132 1988
[5] Y Auregan and M Leroux ldquoFailures in the discrete modelsfor flow duct with perforations an experimental investigationrdquoJournal of Sound andVibration vol 265 no 1 pp 109ndash121 2003
[6] A Broatch XMargot A Gil and F DDenia ldquoACFD approachto the computation of the acoustic response of exhaustmufflersrdquoJournal of Computational Acoustics vol 13 no 2 pp 301ndash3162005
[7] Z L Ji H S Xu and Z X Kang ldquoInfluence of mean flowon acoustic attenuation performance of straight-through per-forated tube reactive silencers and resonatorsrdquo Noise ControlEngineering Journal vol 58 no 1 pp 12ndash17 2010
[8] C Liu and Z-L Ji ldquoComputational fluid dynamics-basednumerical analysis of acoustic attenuation and flow resistancecharacteristics of perforated tube silencersrdquo Journal of Vibrationand Acoustics vol 136 no 2 Article ID 021006 11 pages 2014
[9] H-D Ju S-B Lee and Y-B Park ldquoTransmission loss estima-tion of splitter silencer using multi-domain BEMrdquo Journal ofMechanical Science and Technology vol 21 no 12 pp 2073ndash2081 2007
[10] Z L Ji ldquoBoundary element acoustic analysis of hybrid expan-sion chamber silencers with perforated facingrdquo EngineeringAnalysis with Boundary Elements vol 34 no 7 pp 690ndash6962010
[11] C Jiang T W Wu M B Xu and C Y R Cheng ldquoBEMmodeling of mufflers with diesel particulate filters and catalyticconvertersrdquoNoise Control Engineering Journal vol 58 no 3 pp243ndash250 2010
[12] C I J Young and M J Crocker ldquoPrediction of transmissionloss in mufflers by the finite element methodrdquo Journal of theAcoustical Society of America vol 57 no 1 pp 144ndash148 1975
[13] O Z Mehdizadeh and M Paraschivoiu ldquoA three-dimensionalfinite element approach for predicting the transmission loss inmufflers and silencers with no mean flowrdquo Applied Acousticsvol 66 no 8 pp 902ndash918 2005
[14] Z Kang and Z Ji ldquoAcoustic length correction of duct extensioninto a cylindrical chamberrdquo Journal of Sound and Vibration vol310 no 4-5 pp 782ndash791 2008
[15] Y S GeH B Zhang Y R Zhang JW Tan XM Zhang andXK Han ldquoAn analysis on 3D acoustic performance of automotiveexhaust mufflerrdquo Automotive Engineering vol 28 no 1 pp 51ndash55 2006 (Chinese)
[16] P Chaitanya and M L Munjal ldquoEffect of wall thickness on theend corrections of the extended inlet and outlet of a double-tuned expansion chamberrdquo Applied Acoustics vol 72 no 1 pp65ndash70 2011
[17] J Fu W Chen Y Tang W H Yuan G M Li and Y Li ldquoMod-ification of exhaust muffler of a diesel engine based on finiteelement method acoustic analysisrdquo Advances in MechanicalEngineering vol 7 no 4 11 pages 2015
[18] K S Peat ldquoEvaluation of four-pole parameters for ducts withflow by the finite element methodrdquo Journal of Sound andVibration vol 84 no 3 pp 389ndash395 1982
[19] X R Wang and Z L Ji ldquoBoundary element analysis of four-pole parameters and transmission loss of silencers with flowrdquoChinese Journal of Computational Physics vol 24 no 6 pp 717ndash724 2007 (Chinese)
[20] N Gil-Negrete A Rivas and J Vinolas ldquoPredicting thedynamic behaviour of hydrobushingsrdquo Shock andVibration vol12 no 2 pp 91ndash107 2005
[21] S N Panigrahi and M L Munjal ldquoBackpressure considera-tions in designing of cross flow perforated-element reactivesilencersrdquo Noise Control Engineering Journal vol 55 no 6 pp504ndash515 2007
[22] A J Torregrosa P Fajardo A Gil and R Navarro ldquoDevelop-ment of non-reflecting boundary condition for application in3D computational fluid dynamics codesrdquo Engineering Applica-tions of Computational Fluid Mechanics vol 6 no 3 pp 447ndash460 2012
[23] C-NWang ldquoAboundary element analysis for simple expansionsilencers with mean flowrdquo Journal of the Chinese Institute ofEngineers vol 23 no 4 pp 529ndash536 2000
[24] S-H Lee and J-G Ih ldquoEmpirical model of the acousticimpedance of a circular orifice in grazing mean flowrdquo Journalof the Acoustical Society of America vol 114 no 1 pp 98ndash1132003
[25] F L Zhan and J W Xu VirtualLab Acoustics Simulation fromEntry to Master Northwestern Polytechnical University PressXian China 2013 (Chinese)
[26] ANSYS Inc ANSYS FLUENT 145 in Workbench Userrsquos GuideANSYS Inc New York NY USA 2012
[27] LMS International NV LMS VirtualLab Online Help11-SL2LMS International N V Leuven Belgium 2013
[28] C Liu Z L Ji and Z Fang ldquoNumerical analysis of acousticattenuation and flow resistance characteristics of double expan-sion chamber silencersrdquo Noise Control Engineering Journal vol61 no 5 pp 487ndash499 2013
[29] M L Munjal Acoustic of Ducts and Mufflers Wiley New YorkNY USA 2014
[30] R Singh and T Katra ldquoDevelopment of an impulse techniquefor measurement of muffler characteristicsrdquo Journal of Soundand Vibration vol 56 no 2 pp 279ndash298 1978
[31] J M Middelberg T J Barber S S Leong K P Byrne andE Leonardi ldquoCFD analysis of the acoustic and mean flowperformance of simple expansion chamber mufflersrdquo in Pro-ceedings of theASME InternationalMechanical EngineeringCon-gress and Exposition pp 151ndash156 Anaheim Calif USA Novem-ber 2004
12 Shock and Vibration
[32] B K Gardner A Mejdi F Mendonca and D Copley ldquoUsingCFD flow fields to inform acoustic finite element models ofcomplex mufflers with thermal and flow effectsrdquo in Proceedingsof the 44th International Congress and Exposition on NoiseControl Engineering Paper 15-665 San Francisco Calif USAAugust 2015
[33] E Dokumaci ldquoEffect of sheared grazing mean flow on acoustictransmission in perforated pipe mufflersrdquo Journal of Sound andVibration vol 283 no 3ndash5 pp 645ndash663 2005
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
Shock and Vibration 11
Acknowledgments
The authors are grateful for the grants from National NaturalScience Foundation of China (51275082 11272273) Funda-mental Research Fund of Central Universities (N130403009)Research Fund for Doctoral Program of Higher Education(20100042110013) and Program for Liaoning InnovativeResearch Team in University (LT2014006)
References
[1] M G Prasad and M J Crocker ldquoInsertion loss studies onmodels of automotive exhaust systemsrdquo Journal of the AcousticalSociety of America vol 70 no 5 pp 1339ndash1344 1981
[2] M L Munjal and P T Thawani ldquoOn the transfer matrix for auniform tube with a moving mediumrdquo Journal of Sound andVibration vol 91 no 4 pp 597ndash599 1983
[3] K Narayana Rao and M L Munjal ldquoExperimental evaluationof impedance of perforates with grazing flowrdquo Journal of Soundand Vibration vol 108 no 2 pp 283ndash295 1986
[4] Y H Kim S H Kim B D Lim and Y K Kwak ldquoExperimentalstudy of acoustic characteristics of expansion chamber withmean flowsrdquo KSME Journal vol 2 no 2 pp 125ndash132 1988
[5] Y Auregan and M Leroux ldquoFailures in the discrete modelsfor flow duct with perforations an experimental investigationrdquoJournal of Sound andVibration vol 265 no 1 pp 109ndash121 2003
[6] A Broatch XMargot A Gil and F DDenia ldquoACFD approachto the computation of the acoustic response of exhaustmufflersrdquoJournal of Computational Acoustics vol 13 no 2 pp 301ndash3162005
[7] Z L Ji H S Xu and Z X Kang ldquoInfluence of mean flowon acoustic attenuation performance of straight-through per-forated tube reactive silencers and resonatorsrdquo Noise ControlEngineering Journal vol 58 no 1 pp 12ndash17 2010
[8] C Liu and Z-L Ji ldquoComputational fluid dynamics-basednumerical analysis of acoustic attenuation and flow resistancecharacteristics of perforated tube silencersrdquo Journal of Vibrationand Acoustics vol 136 no 2 Article ID 021006 11 pages 2014
[9] H-D Ju S-B Lee and Y-B Park ldquoTransmission loss estima-tion of splitter silencer using multi-domain BEMrdquo Journal ofMechanical Science and Technology vol 21 no 12 pp 2073ndash2081 2007
[10] Z L Ji ldquoBoundary element acoustic analysis of hybrid expan-sion chamber silencers with perforated facingrdquo EngineeringAnalysis with Boundary Elements vol 34 no 7 pp 690ndash6962010
[11] C Jiang T W Wu M B Xu and C Y R Cheng ldquoBEMmodeling of mufflers with diesel particulate filters and catalyticconvertersrdquoNoise Control Engineering Journal vol 58 no 3 pp243ndash250 2010
[12] C I J Young and M J Crocker ldquoPrediction of transmissionloss in mufflers by the finite element methodrdquo Journal of theAcoustical Society of America vol 57 no 1 pp 144ndash148 1975
[13] O Z Mehdizadeh and M Paraschivoiu ldquoA three-dimensionalfinite element approach for predicting the transmission loss inmufflers and silencers with no mean flowrdquo Applied Acousticsvol 66 no 8 pp 902ndash918 2005
[14] Z Kang and Z Ji ldquoAcoustic length correction of duct extensioninto a cylindrical chamberrdquo Journal of Sound and Vibration vol310 no 4-5 pp 782ndash791 2008
[15] Y S GeH B Zhang Y R Zhang JW Tan XM Zhang andXK Han ldquoAn analysis on 3D acoustic performance of automotiveexhaust mufflerrdquo Automotive Engineering vol 28 no 1 pp 51ndash55 2006 (Chinese)
[16] P Chaitanya and M L Munjal ldquoEffect of wall thickness on theend corrections of the extended inlet and outlet of a double-tuned expansion chamberrdquo Applied Acoustics vol 72 no 1 pp65ndash70 2011
[17] J Fu W Chen Y Tang W H Yuan G M Li and Y Li ldquoMod-ification of exhaust muffler of a diesel engine based on finiteelement method acoustic analysisrdquo Advances in MechanicalEngineering vol 7 no 4 11 pages 2015
[18] K S Peat ldquoEvaluation of four-pole parameters for ducts withflow by the finite element methodrdquo Journal of Sound andVibration vol 84 no 3 pp 389ndash395 1982
[19] X R Wang and Z L Ji ldquoBoundary element analysis of four-pole parameters and transmission loss of silencers with flowrdquoChinese Journal of Computational Physics vol 24 no 6 pp 717ndash724 2007 (Chinese)
[20] N Gil-Negrete A Rivas and J Vinolas ldquoPredicting thedynamic behaviour of hydrobushingsrdquo Shock andVibration vol12 no 2 pp 91ndash107 2005
[21] S N Panigrahi and M L Munjal ldquoBackpressure considera-tions in designing of cross flow perforated-element reactivesilencersrdquo Noise Control Engineering Journal vol 55 no 6 pp504ndash515 2007
[22] A J Torregrosa P Fajardo A Gil and R Navarro ldquoDevelop-ment of non-reflecting boundary condition for application in3D computational fluid dynamics codesrdquo Engineering Applica-tions of Computational Fluid Mechanics vol 6 no 3 pp 447ndash460 2012
[23] C-NWang ldquoAboundary element analysis for simple expansionsilencers with mean flowrdquo Journal of the Chinese Institute ofEngineers vol 23 no 4 pp 529ndash536 2000
[24] S-H Lee and J-G Ih ldquoEmpirical model of the acousticimpedance of a circular orifice in grazing mean flowrdquo Journalof the Acoustical Society of America vol 114 no 1 pp 98ndash1132003
[25] F L Zhan and J W Xu VirtualLab Acoustics Simulation fromEntry to Master Northwestern Polytechnical University PressXian China 2013 (Chinese)
[26] ANSYS Inc ANSYS FLUENT 145 in Workbench Userrsquos GuideANSYS Inc New York NY USA 2012
[27] LMS International NV LMS VirtualLab Online Help11-SL2LMS International N V Leuven Belgium 2013
[28] C Liu Z L Ji and Z Fang ldquoNumerical analysis of acousticattenuation and flow resistance characteristics of double expan-sion chamber silencersrdquo Noise Control Engineering Journal vol61 no 5 pp 487ndash499 2013
[29] M L Munjal Acoustic of Ducts and Mufflers Wiley New YorkNY USA 2014
[30] R Singh and T Katra ldquoDevelopment of an impulse techniquefor measurement of muffler characteristicsrdquo Journal of Soundand Vibration vol 56 no 2 pp 279ndash298 1978
[31] J M Middelberg T J Barber S S Leong K P Byrne andE Leonardi ldquoCFD analysis of the acoustic and mean flowperformance of simple expansion chamber mufflersrdquo in Pro-ceedings of theASME InternationalMechanical EngineeringCon-gress and Exposition pp 151ndash156 Anaheim Calif USA Novem-ber 2004
12 Shock and Vibration
[32] B K Gardner A Mejdi F Mendonca and D Copley ldquoUsingCFD flow fields to inform acoustic finite element models ofcomplex mufflers with thermal and flow effectsrdquo in Proceedingsof the 44th International Congress and Exposition on NoiseControl Engineering Paper 15-665 San Francisco Calif USAAugust 2015
[33] E Dokumaci ldquoEffect of sheared grazing mean flow on acoustictransmission in perforated pipe mufflersrdquo Journal of Sound andVibration vol 283 no 3ndash5 pp 645ndash663 2005
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
12 Shock and Vibration
[32] B K Gardner A Mejdi F Mendonca and D Copley ldquoUsingCFD flow fields to inform acoustic finite element models ofcomplex mufflers with thermal and flow effectsrdquo in Proceedingsof the 44th International Congress and Exposition on NoiseControl Engineering Paper 15-665 San Francisco Calif USAAugust 2015
[33] E Dokumaci ldquoEffect of sheared grazing mean flow on acoustictransmission in perforated pipe mufflersrdquo Journal of Sound andVibration vol 283 no 3ndash5 pp 645ndash663 2005
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
