Thermoacoustic oscillation around a plate in a nonlinear standing wave field

A stack of plates is a most basic and important component of thermoacoustic engines and thermoacoustic refrigerators. Analysis of thermoacoustic oscillation around a plate is a basis of analysis of the mechanism of these machines, but only the works in a linear standing wave field were published. On the other hand, it is shown from some experiments that the thermoacoustic efficiencies of these machines will be increased in the nonlinear standing wave field, but any quantitative result has not been found yet. In this paper a numerical simulation of thermoacoustic oscillation around a plate in a standing wave tube where the sound-pressure level of the sources is from 90 to 170 dB has been presented in order to discuss the nonlinear effects quantitatively. Two conclusions have been obtained: (1) thermoacoustic efficiencies are increased with the increase of the source slowly below 150 dB, moderately from 150 to 160 dB, and rapidly above 160 dB. (2) There exists a rule of multiplying growth of high-order harmonics of oscillation temperature level, which is very similar to the rule of multiplying growth of high-order harmonics of oscillation sound-pressure level in a nonlinear standing wave tube.