Acoustic waveform dependence on resonator shape in thermoacoustic engines

Abstract

At high amplitudes, sound fields in thermoacousic refrigerators and prime movers are rich in harmonics and possess nonsinusoidal waveforms. In empty cylindrical resonators the natural frequencies are equidistant, the pressure waveforms are sawtooth in appearance, and they dissipate considerable energy at the shocks. Noncylindrical resonators possess nonequidistant natural frequency spectra that impede harmonic generation and reduce losses. The relative phases of the harmonics also depend on the natural frequency spectrum, mainly the relation of the second harmonic to the closest natural frequency, which usually corresponds to the second mode. Pressure waveforms are U shaped when the second harmonic is greater than this natural frequency, sawtooth when the second harmonic coincides with the natural frequency, and inverted-U shaped when the second harmonic is less than the natural frequency. These phenomena are illustrated by results of numerical calculations performed with a 2-D nonlinear model that approximates a thermoacoustic engine consisting of a stack in a resonator with varying cross section. Both pressure and particle velocity waveforms are presented at different locations in resonators of different shapes, possessing correspondingly different natural frequency spectra. Attention is devoted especially to waveforms near and inside the stack. [Work supported by ONR.]