Recently, research on new techniques for dissipative mufflers in dealing with the higher frequencies has been addressed. However, the shape optimization of hybrid mufflers in reducing broadband noise within a constrained space as well as a pressure-drop limit which are both concerned with the necessity of operation and system venting in practical engineering work was rarely tackled. Therefore, this study will not only analyze the sound transmission loss (STL) of a space-constrained multichamber hybrid muffler but also optimize the best design shape under a specified pressure drop. In this paper, the generalized decoupling technique and plane wave theory used to solve the coupled acoustical problem of perforated mufflers with/without sound absorbing material are presented. The four-pole system matrix used to evaluate acoustic performance is also introduced in conjunction with a genetic algorithm (GA). A numerical case for eliminating a broadband venting noise emitted from a pressure relief valve using four kinds of hybrid mufflers is also introduced. To verify the reliability of the GA optimization, optimal noise abatement for a pure tone (1000 Hz) is exemplified. Before the GA operation can be carried out, the accuracy of the mathematical models need to be checked using the experimental data. The optimal result in eliminating broadband noise reveals that the overall noise reductions with respect to various mufflers under a maximal allowable pressure drop of 100 Pa can achieve 62.6, 54.8, 32.3 and 87.8 dB. Consequently, the approach used for the optimal design of the multichamber hybrid mufflers under space and back pressure constrained conditions is indeed easy and quite effective.

References

References
1.
Morse
,
P. M.
, 1939, “
Transmission of Sound Inside Pipes
,”
J. Acoust. Soc. Am.
,
11
, pp.
205
210
.
2.
Scott
,
R. A.
, 1946, “
The Propagation of Sound Between Walls of Porous Material
,”
Proc. Phys. Soc.
,
58
, pp.
358
368
.
3.
Ko
,
S. H.
, 1975, “
Theoretical Analyses of Sound Attenuation in Acoustically Lined Flow Ducts Separated by Porous Splitters (Rectangular, Annular and Circular Ducts), Propagation of Sound between Walls of Porous Material
,”
J. Sound Vib.
,
39
, pp.
471
487
.
4.
Cummings
,
A.
, and
Chang
,
I. J.
, 1987, “
Internal Mean Flow Effects on the Characteristics of Bulk-Reacting Liners in Circular Ducts
,”
Acustica
,
64
, pp.
169
178
.
5.
Cummings
,
A.
, and
Chang
,
I. J.
, 1988, “
Sound Attenuation of a Finite Length Dissipative Flow Duct Silencer With Internal Mean Flow in the Absorbent
,”
J. Sound Vib.
,
127
, pp.
1
17
.
6.
Peat
,
K. S.
, 1991, “
A Transfer-Matrix for an Absorption Silencer Element
,”
J. Sound Vib.
,
146
, pp.
353
360
.
7.
Wang
,
C. N.
, 1992, “
The Application of Boundary Element Method in the Noise Reduction Analysis for the Automotive Mufflers
,” Ph.D. thesis, Taiwan University, Taiwan.
8.
Munjal
,
M. L.
, 2003, “
Analysis and Design of Pod Silencers
,”
J. Sound Vib.
,
262
, pp.
497
507
.
9.
Xu
,
M. L.
,
Selamet
,
A.
,
Lee
,
I. J.
, and
Huff
,
N. T.
, 2004, “
Sound Attenuation in Dissipative Expansion Chambers
,”
J. Sound Vib.
,
272
, pp.
1125
1133
.
10.
Selamet
,
A.
,
Lee
,
I. J.
,
Ji
,
Z. L.
, and
Huff
,
N. T.
, 2001, “
Acoustic Attenuation Performance of Perforated Concentric Absorbing Silencers
,” SAE Noise and Vibration Conference and Exposition, 2001-01-1435.
11.
Selamet
,
A.
,
Lee
,
I. J.
, and
Huff
,
N. T.
, 2003, “
Acoustic Attenuation of Hybrid Silencers
,”
J. Sound Vib.
,
262
, pp.
509
527
.
12.
Chang
,
Y. C.
, and
Chiu
,
M. C.
, 2008, “
Shape Optimization of One-Chamber Perforated Plug/Non-plug Mufflers by Simulated Annealing Method
,”
Int. J. Numer. Methods Eng.
,
74
, pp.
1592
1620
.
13.
Chiu
,
M. C.
, 2010, “
Optimal Design of Multi-Chamber Mufflers Hybridized With Perforated Intruding Inlets and Resonated Tube Using Simulated Annealing
,”
ASME J. Vib. Acoust.
,
132
, p.
054503
.
14.
Elnady
,
T.
,
Abom
,
M.
, and
Allam
,
S.
, 2010, “
Modeling Perforates in Mufflers Using Two-Ports
,”
ASME J. Vib. Acoust.
,
132
, p.
061010
.
15.
Chiu
,
M. C.
, 2010, “
Shape Optimisation of Multi-Chamber Mufflers With Plug-inlet Tube on a Venting Process by Genetic Algorithms
,”
Appl. Acoust.
,
71
, pp.
495
505
.
16.
Chiu
,
M. C.
, and
Chang
,
Y. C.
, 2008, “
Numerical Studies on Venting System With Multi-chamber Perforated Mufflers by GA Optimization
,”
Appl. Acoust.
,
69
(
11
), pp.
1017
1037
.
17.
Lee
,
I. J.
, 2005, “
Acoustic Characteristics of Perforated Dissipative and Hybrid Silencers
,” Ph.D. Thesis, Ohio State University.
18.
Chang
,
Y. C.
,
Yeh
,
L. J.
,
Chiu
,
M. C.
, and
Lai
,
G. J.
, 2005, “
Shape Optimization on Constrained Single-Layer Sound Absorber by Using GA Method and Mathematical Gradient Methods
,”
J. Sound Vib.
,
286
(
4–5
), pp.
941
961
.
19.
Holland
,
J.
, 1975,
Adaptation in Natural and Artificial System
,
University of Michigan Press
,
Ann Arbor
.
20.
Jong
,
D.
, 1975, “
An Analysis of the Behavior of a Class of Genetic Adaptive Systems
,” Ph.D. Thesis, University of Michigan, Ann Arbor.
21.
Chang
,
Y. C.
,
Yeh
,
L. J.
, and
Chiu
,
M. C.
, 2004, “
Numerical Studies on Constrained Venting System With Side Inlet/Outlet Mufflers by GA Optimization
,”
Acta Acustica United Acustica
,
90
(
1
), pp.
1
11
.
22.
Munjal
,
M. L.
, 1987,
Acoustics of Ducts and Mufflers With Application to Exhaust and Ventilation System Design
,
Wiley
,
New York
.
23.
Bie
,
D. A.
, and
Hansen
,
C. H.
, 1988,
Engineering Noise Control: Theory and Practice
,
Unwin Hyman
,
London
.
24.
Panigrahi
,
S. N.
, and
Munjal
,
M. L.
, 2007, “
Backpressure Considerations in Designing of Cross Flow Perforated-Element Reactive Silencers
,”
Noise Control Eng. J.
,
55
(
6
), pp.
504
515
.
25.
Munjal
,
M. L.
,
Krishnan
,
K.
, and
Reddy
,
M. M.
, 1993, “
Flow-Acoustic Perforated Element Mufflers With Application to Design
,”
Noise Control Eng. J.
,
40
(
1
), pp.
159
167
.
26.
Sullivan
,
J. W.
, and
Crocker
,
M. J.
, 1978, “
Analysis of Concentric Tube Resonators Having Unpartitioned Cavities
,”
J. Acoust. Soc. Am.
,
64
, pp.
207
215
.
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