Theoretical treatments of thermoacoustics have been reported for stacks with circular pore and parallel plate geometries. A general linear formulation is developed for gas-filled thermoacoustic elements such as heat exchangers, stacks, and tubes having pores of arbitrary cross-sectional geometry. For compactness in the following, F represents the functional form of the transverse variation of the longitudinal particle velocity. Generally, F is a function of frequency, pore geometry, the response functions and transport coefficients of the gas used, and the ambient value of the gas density. Expressions are developed for the acoustic temperature, density, particle velocity, pressure, heat flow, and work flow from knowledge of F. Heat and work flows are compared in the short stack approximation for stacks consisting of parallel plates, circular, square, and equilateral triangular pores. In this approximation, heat and work flows are found to be greatest for the parallel plate stack geometry. Pressure and specific acoustic impedance translation theorems are derived to simplify computation of the acoustical field quantities at all points within a thermoacoustic engine. Relations with capillary-pore-based porous media models are developed.

Thermoacoustic heat engines can be used to produce sound from heat and to transport heat using sound. The air-filled prime mover studied is a quarter wavelength resonator that produces sound at nominally 115 Hz for a temperature difference of AT--176 K. Specific acoustic impedance at the mouth of the prime mover was measured as a function of the temperature difference between the hot and cold heat exchangers. The real part of the impedance changes sign for sufficiently large temperature differences, indicating the possibility of sound production. The theoretically predicted radiation impedance of an open pipe was compared to the measured impedance curves. The operating point was confirmed from the intersection of these experimental and theoretical impedance curves. These measurements allow for analysis of the prime mover as a sound source as discussed in a recent theoretical paper [T. B. Gabrielson, J. Acoust. Soc. Am. 90, 2628-2636 ( 1991 ) ].

An atmospheric sound wave can couple with the poroelastic ground, resulting in ground (or seismic) motion. This is the phenomenon of acoustic to seismic coupling. Microphones are used to measure the sound pressure level at the surface and geophones are used to measure the resulting seismic motion at or below the surface. The seismic:acoustic transfer function (SATF) characterizes a particular site. SATF measurements are reported as a function of the angle of incidence of the sound wave for frequencies 15 Hz to 1 kHz. The angle of incidence varied from 50° to 80°, and normal incidence. Surface vertical and radial-horizontal geophones were used. In addition six vertical geophones at depth intervals of 10 cm, starting at 10 cm, were used. A seismic p-wave survey indicated a first layer depth of 44 cm having a wave velocity of 159 m/s overlying a layer of velocity 379 m/s. This gives a critical angle of incidence of 65°. It was anticipated and confirmed that the SATF would increase in magnitude for certain frequency bands as the angle of incidence approached and passed over the critical angle. Comparisons of experimental results and multilayered elastic and poroelastic media theory will be addressed as time permits. [Work supported by ONR.]

Thermoacoustic heat engines can be used to produce sound from heat and to transport heat using sound. The air-filled prime mover studied is a quarter wavelength resonator that produces sound at nominally 116 Hz for a temperature difference of ΔT=176 K. Specific acoustic impedance at the mouth of the prime mover was measured as a function of the temperature difference between the hot and cold heat exchangers. The real part of the impedance changes sign for sufficiently large temperature differences, indicating the possibility of sound production. The theoretical expression for radiation impedance of an open pipe was overlaid on the impedance curves. The operating point was confirmed from the intersection of experimental and theoretical impedance curves. The stability curve was computed for a helium-filled prime mover as a function of the ambient pressure, P0, for the first two modes. The first mode has a minimum ΔT=154.6 K for P0=173 kPa and the second mode for ΔT=455.4 K for P0=200 kPa. The resonant frequencies of these modes are approximately 310 and 610 Hz. The quality factor, which characterizes the exponential decay or initial exponential growth of an initial perturbation, was computed as a function of ΔT at fixed P0=173 kPa for ΔT well in excess of the onset temperature. [Work supported by ONR.]

Wave propagation in poroelastic materials has applications ranging from ground motion induced by atmospheric sound to thermoacoustic heat engines. Bass was involved with research in this entire continuum, including both basic and applied problems. This paper will especially cover the wave propagation formulation of thermoacoustics as it was applied by Bass and others to understand and predict the behavior of thermoacoustic prime movers. Some recollections of Bass as a statesman, scientist, and enjoyable character to be with will be presented. My first meeting with Bass and some of his guidance will also be discussed.