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Research Papers

Determination of Transmission Loss in Slightly Distorted Circular Mufflers Using a Regular Perturbation Method

[+] Author and Article Information
Subhabrata Banerjee

Department of Mechanical Science
and Engineering,
University of Illinois at Urbana-Champaign,
1206 West Green Street,
Urbana, IL 61801
e-mail: banerje6@illinois.edu

Anthony M. Jacobi

Department of Mechanical Science
and Engineering,
University of Illinois at Urbana-Champaign,
1206 West Green Street,
Urbana, IL 61801
e-mail: a-jacobi@illinois.edu

Contributed by the Noise Control and Acoustics Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received May 5, 2013; final manuscript received November 26, 2013; published online January 15, 2014. Assoc. Editor: Lonny Thompson.

J. Vib. Acoust 136(2), 021013 (Jan 15, 2014) (15 pages) Paper No: VIB-13-1148; doi: 10.1115/1.4026209 History: Received May 05, 2013; Revised November 26, 2013

A perturbation-based approach is implemented to study the sound attenuation in distorted cylindrical mufflers with various inlet/outlet orientations. Study of the transmission loss (TL) in mufflers requires solution of the Helmholtz equation. Exact solutions are available only for a limited class of problems where the method of separation of variables can be applied across the cross section of the muffler (e.g., circular, rectangular, elliptic sections). In many practical situations, departures from the regular geometry occur. The present work is aimed at formulating a general procedure for determining the TL in mufflers with small perturbations on the boundary. Distortions in the geometry have been approximated by Fourier series expansion, thereby, allowing for asymmetric perturbations. Using the method of strained parameters, eigensolutions for a distorted muffler are expressed as a series summation of eigensolutions of the unperturbed cylinder having similar dimensions. The resulting eigenvectors, being orthogonal up to the order of truncation, are used to define a Green's function for the Helmholtz equation in the perturbed domain. Assuming that inlet and outlet ports of the muffler are uniform-velocity piston sources, the Green's function is implemented to obtain the velocity potential inside the muffler cavity. The pressure field inside the muffler is obtained from the velocity potential by using conservation of linear momentum. Transmission loss in the muffler is derived from the averaged pressure field. In order to illustrate the method, TL of an elliptical muffler with different inlet/outlet orientations is considered. Comparisons between the perturbation results and the exact solutions show excellent agreement for moderate (0.4∼0.6) eccentricities.

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References

Figures

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Fig. 1

Schematic of an arbitrary enclosed space (Ω).∂Si represents the boundary surfaces of the domain.

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Fig. 9

Locus of the pressure nodes for the (2,1) and the (0,2) even modes: ABCDE, A'B'C'D'E' are the pressure nodal lines for the (2,1) mode; BFDD'F'B'B is the pressure nodal circle for the (0,2) mode

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Fig. 12

Transmission loss characteristics at different chamber lengths (L) for the concentric-inlet-offset-outlet chamber configuration; the outlet port is located at the intersection of the (2,1) and the (0,2) pressure node

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Fig. 13

Radial distance δ and angular position θ of the point of intersection of the (2,1), and (0,2) even modes

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Fig. 7

Cross section view of even mode shapes of ellipse with eccentricity, e=0.6. Solid curve, perturbation solution; short-dashed curve, exact solution.

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Fig. 8

Variation of the nondimensional radial wavenumber with eccentricity for various even order modes

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Fig. 10

Locus of the (2,1) pressure nodal point on the major-axis of the ellipse as a function of eccentricity

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Fig. 11

Transmission loss characteristics at different chamber lengths (L) for the concentric-inlet-offset-outlet chamber configuration; the outlet port is located at the (2,1) pressure node on the major-axis

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Fig. 2

Schematic diagram of elliptical mufflers with different inlet/outlet configurations: (a) concentric chamber muffler, (b) concentric-inlet-offset-outlet muffler, (c) reversing chamber muffler, and (d) end-inlet-side-outlet muffler

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Fig. 3

Transmission loss characteristics at different eccentricities (e) and chamber lengths (L) for concentric chamber configuration. Solid curve, perturbation solution; short-dashed curve, exact solution.

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Fig. 4

Transmission loss characteristics at different eccentricities (e) and chamber lengths (L) for concentric-inlet-offset-outlet chamber configuration. Solid curve, perturbation solution; short-dashed curve, exact solution.

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Fig. 5

Transmission loss characteristics at different eccentricities (e) and chamber lengths (L) for reversing chamber configuration. Solid curve, perturbation solution; short-dashed curve, exact solution.

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Fig. 6

Transmission loss characteristics at different eccentricities (e) and chamber lengths (L) for EISO chamber configuration. Solid curve, perturbation solution; short-dashed curve, exact solution.

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