STABILITY ANALYSIS OF A HELIUM-FILLED THERMOACOUSTIC ENGINE

Spontaneous acoustic oscillations may occur in a sealed tube when an applied temperature gradient is larger than the temperature gradient associated with an acoustic standing wave in the tube. Work flow is the net acoustic power produced in the stack minus the net dissipated energy per cycle elsewhere. Instability occurs when the net work flow becomes a positive quantity. Recent theoretical results have shown that the thermoacoustic gain as well as the thermal and viscous losses can be expressed in terms of a thermoviscous dissipation function. The onset temperature and resonance frequency for a helium-filled thermoacoustic engine was computed using these theoretical results and measured as a function of the ambient pressure yielding stability and resonance frequency curves in good agreement. Expressions are derived using a short stack approximation for the optimal stack location and the onset temperature difference. These expressions are experimentally validated and are useful in searching for stack geometries that minimize the temperature difference across the stack necessary to deliver a given acoustic power.