Investigation of harmonic generation in thermoacoustic engines

Abstract

One factor limiting the efficiency of thermoacoustic engines and refrigerators is the generation of harmonics. Not only do thermoviscous losses increase in relation to the generation of higher frequencies, but the stack is not designed to optimize thermoacoustic processes at these frequencies. We describe here a semi-analytical investigation of nonlinear effects associated with harmonic generation. The approach is based on a regular perturbation expansion of the acoustical quantities, combined with the assumptions and methodology underlying the linear theory developed by Rott. At first order, Rott’s equations for the pressure and particle velocity are obtained and solved numerically. The second-order system consists of Rott’s equations for the second harmonic driven by a forcing function containing products of the first-order solutions. The goal is to solve the third-order system, given by Rott’s equations for the fundamental driven by products of the first- and second-order solutions, to determine the nonlinear correction to the fundamental component. The investigation was not completed at the time of writing, and we therefore present here the intermediate results for second-harmonic generation. These results provide partial explanations of how harmonic generation influences thermoacoustics. [Work supported by ONR and ARL:UT IR&D.]