Research Papers

Modeling of Thermoacoustic Resonators With Nonuniform Medium and Boundary Conditions

[+] Author and Article Information
Konstantin I. Matveev1

School of Mechanical and Materials Engineering, Washington State University, Pullman, WA 99164-2920matveev@wsu.edu

Sungmin Jung

School of Mechanical and Materials Engineering, Washington State University, Pullman, WA 99164-2920


Corresponding author.

J. Vib. Acoust 133(3), 031012 (Mar 31, 2011) (7 pages) doi:10.1115/1.4003200 History: Received April 30, 2010; Revised September 07, 2010; Published March 31, 2011; Online March 31, 2011

The subject of this paper is modeling of low-amplitude acoustic fields in enclosures with nonuniform medium and boundary conditions. An efficient calculation method is developed for this class of problems. Boundary conditions, accounting for the boundary-layer losses and movable walls, are applied near solid surfaces. The lossless acoustic wave equation for a nonuniform medium is solved in the bulk of the resonator by a finite-difference method. One application of this model is for designing small thermoacoustic engines. Thermoacoustic processes in the regular-geometry porous medium inserted in resonators can be modeled analytically. A calculation example is presented for a small-scale thermoacoustic engine coupled with an oscillator on a flexing wall of the resonator. The oscillator can be used for extracting mechanical power from the engine. A nonuniform wall deflection may result in a complicated acoustic field in the resonator. This leads to across-the-stack variations of the generated acoustic power and local efficiency of thermoacoustic energy conversion.

Copyright © 2011 by American Society of Mechanical Engineers
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Figure 1

Schematics of (a) classical standing-wave thermoacoustic engine and (b) low-aspect-ratio engine with electroacoustic transformer

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Figure 2

(a) Part of numerical grid. (b) Magnified view of a zone near rigid surface.

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Figure 3

(a) Geometry of a 2D thermoacoustic engine with flexing wall on the left boundary. (b) Given mean temperature profile at y=0.

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Figure 4

Model validation results. (a) Constant-temperature lossy resonator. Solid lines, analytical solution; points, 2D numerical solution. (b) Resonator with linear temperature variation. Solid lines, solution of 1D wave equation with thermoviscous functions (Eq. 8); points, 2D numerical solution. Re and Im symbols indicate the real and imaginary parts of solutions, respectively.

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Figure 5

((a) and (b)) Dimensional and normalized critical temperature difference. ((c) and (d)) Dimensional and normalized frequency of the engine at the sound onset. Solid line, M/Mg=25; dashed line, M/Mg=5; dotted line, M/Mg=1.

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Figure 6

Complex amplitudes of ((a) and (b)) acoustic pressure normalized by mean pressure and ((c) and (d)) x-component of acoustic velocity normalized by maximum velocity at flexing wall. Velocities inside stack are averaged over pore cross sections.

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Figure 7

(a) Normalized flux of acoustic power produced in the stack. (b) Local stack-based thermoacoustic efficiency. Solid line, H/L=0.5; dashed line, H/L=1.0; and dotted line, H/L=1.5.

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Figure 8

Calculated thermomechanical efficiency. Solid line, P=0.1 W/m; dashed line, P=1.0 W/m; and dotted line, P=10 W/m.




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