Description of the thermoacoustic mechanism via a pressure - volume diagram
The mechanism that drives thermoacoustic oscillation is similar to that which drives a piston engine. In an idealized piston engine, work is done on a gas as it is compressed isentropically from states 1 to 2 (blue compression line). From 2 to 3, the gas combusts at fixed volume, releasing heat and raising its pressure further. From 3 to 4, the gas does work as it expands isentropically (blue expansion line). More work is done by the gas during the expansion phase than is done on it during the compression phase, leading to a net conversion of heat to work given by the area within the cycle on the pressure-volume diagram. In thermoacoustics, an acoustic wave replaces the piston and a continuous flame replaces the periodically-ignited gas. The acoustic wave independently (i) perturbs this flame and (ii) compresses and expands the gas around the flame. If the perturbed flame releases more heat than average during instants of higher local pressure, then, through the same mechanism as the piston engine, more work is done by the gas during the acoustic expansion phase than is done on it during the acoustic compression phase (red cycle). If this work is not dissipated then the oscillation amplitude grows and the system is thermoacoustically unstable (orange spiral).
Credit: Matthew Juniper