STABILITY ANALYSIS OF A HELIUM-FILLED THERMOACOUSTIC ENGINE

Spontaneous acoustic oscillations may occur in a sealed tube when an a pplied temperature gradient is larger than the temperature gradient as sociated with an acoustic standing wave in the tube. Work flow is the net acoustic power produced in the stack minus the net dissipated ener gy per cycle elsewhere. Instability occurs when the net work flow beco mes a positive quantity. Recent theoretical results have shown that th e 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 thermoacousti c engine was computed using these theoretical results and measured as a function of the ambient pressure yielding stability and resonance fr equency curves in good agreement. Expressions are derived using a shor t stack approximation for the optimal stack location and the onset tem perature difference. These expressions are experimentally validated an d are useful in searching for stack geometries that minimize the tempe rature difference across the stack necessary to deliver a given acoust ic power.