Standing wave analysis of a thermoacoustic prime mover below onset of self-oscillation

A standing wave analysis of a thermoacoustic prime mover is presented. The analysis, motivated by Swift [G. W. Swift, 'Thermoacoustic engines,' J. Acoust. Soc. Am. 84, 1145-1180 (1988)], assumes that the acoustic pressure and velocity can be described in terms of a standing wave throughout the prime mover. Because the analysis is not limited by either the small boundary layer or short stack approximations, it is more general than Swift's short stack, boundary layer approach. However, it is not as general as a fully numerical approach. The results of the analysis compare well to measurements of the quality factor of the first three longitudinal modes of a helium- filled prime mover below onset of self-oscillation. An analysis is presented of the sensitivity of the calculations to experimental errors and to various assumptions regarding the temperature distribution in the prime mover stack. It is concluded that, in most cases, using reasonable, simplifying assumptions regarding the temperature distribution produces acceptable results.