A one-dimensional finite difference numerical method is applied for the simulation of sound attenuation in reactive silencers placed in an impedance tube configuration. This time-domain approach solves the nonlinear fundamental balance equations of mass, momentum and energy, and the equation of state. The temporal solution is first converted to the frequency domain by the Fast Fourier Transform, which is then processed by the two-microphone technique to yield transmission loss. Results are presented for the attenuation of acoustic disturbances in four basic configurations including the expansion chamber, Helmholtz resonator, quarter-wave resonator and Herschel-Quincke tube. A comparison to available experimental data and linearized acoustic theory shows excellent agreement for silencers with both anechoic and echoic terminations.

1.
Astley
R. J.
, and
Eversman
W.
,
1983
, “
Finite Element Formulations for Acoustical Radiation
,”
Journal of Sound and Vibration
, Vol.
88
, No.
1
, pp.
47
64
.
2.
Brebbia, C. A., 1991, Boundary Element Methods in Acoustics, Computational Mechanics Publishers.
3.
Chapman
M.
,
1981
, “
FRAM—Nonlinear Damping Algorithms for the Continuity Equation
,”
Journal of Computational Physics
, Vol.
44
, No.
1
, pp.
84
103
.
4.
Chapman, M., Novak, J. M., and Stein, R. A., 1982, “Numerical Modeling of Inlet and Exhaust Flows in Multi-Cylinder Internal Combustion Engines,” Flows in Internal Combustion Engines, T. Uzkan, ed., ASME WAM.
5.
Chung
J. Y.
, and
Blaser
D. A.
,
1980
, “
Transfer Function Method of Measuring In-duct Acoustic Properties, I: Theory II: Experiment
,”
Journal of the Acoustical Society of America
, Vol.
64
, No.
3
, pp.
907
913
.
6.
Craggs
A.
,
1976
, “
A Finite Element Method for Damped Acoustic Systems: An Application to Evaluate the Performance of Reactive Mufflers
,”
Journal of sound and Vibration
, Vol.
48
, No.
3
, pp.
377
392
.
7.
Crowley
W. P.
,
1967
, “
Second-Order Numerical Advection
,”
Journal of Computational Physics
, Vol.
1
, pp.
471
484
.
8.
Davis, Jr., D. D., Stokes, G. M., Moore, D., and Stevens, Jr., G. L., 1954, “Theoretical and Experimental Investigation of Mufflers with Comments on Engine-Exhaust Muffler Design,” National Advisory Committee for Aeronautics Report No. 1192.
9.
Dickey, N. S., 1992, “A Nonlinear Computational Simulation of Acoustic Silencers,” Master’s thesis. The University of Nebraska-Lincoln.
10.
Eriksson, L. J., 1978, “An Analytical Model for Exhaust System Design,” SAE 780472.
11.
Eriksson
L. J.
,
1980
, “
Higher Order Mode Effects in Circular Ducts and Expansion Chambers
,”
Journal of the Acoustical Society of America
, Vol.
68
, No.
2
, pp.
545
550
.
12.
Levine
H.
, and
Schwinger
J.
,
1948
, “
On the Radiation of Sound from an Unflanged Circular Pipe
,”
Physical Review
, Vol.
73
, No.
4
, pp.
383
406
.
13.
Morse, P. M., 1981, Vibration and Sound, Acoustical Society of America.
14.
Munjal, M. L., 1987, Acoustics of Ducts and Mufflers, John Wiley & Sons.
15.
Peat
K. S.
,
1983
, “
A Note on One-Dimensional Acoustic Elements
,”
Journal of Sound and Vibration
, Vol.
88
, No.
4
, pp.
572
575
.
16.
Pierce, A. D., 1989, Acoustics, Acoustical Society of America.
17.
Ross
D. F.
,
1981
, “
A Finite Element Analysis of Perforated Component Acoustic Systems
,”
Journal of Sound and Vibration
, Vol.
79
, No.
1
, pp.
133
143
.
18.
Sahasrabudhe
A. D.
,
Munjal
M. L.
, and
Anantha Ramu
S.
,
1992
, “
Design of Expansion Chamber Mufflers Incorporating 3-D Effects
,”
Noise Control Engineering Journal
, Vol.
38
, No.
1
, pp.
27
38
.
19.
Selamet, A., 1982, “Noise Control and Silencers in Hydraulic and Aerodynamic Systems,” Master’s thesis, Technical University of Istanbul.
20.
Stewart
G. W.
,
1928
, “
The Theory of the Herschel-Quincke Tube
,”
Physical Review
, Vol.
31
, No.
4
, pp.
696
698
.
21.
Stewart, G. W., and Lindsay, R. B., 1930, Acoustics, D. Van Nostrand.
22.
Young
C. J.
, and
Crocker
M. J.
,
1975
, “
Prediction of Transmission Loss in Mufflers by the Finite-Element Method
,”
Journal of the Acoustical Society of America
, Vol.
57
, No.
1
, pp.
144
148
.
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