To predict a thermoacoustic engine's limit cycle from its impedance measurement

Thermoacoustic engines are self-oscillating systems converting thermal energy into acoustic waves. Recent studies on such engines highlight much nonlinear effects responsible for the engine’s saturation, leading to a limit cycle, which can be stable or not. Those effects however, are not sufficiently known, even with today knowledges, to accurately predict a limit cycle oscillations amplitude. This work suggests a new approach, based on acoustic impedance measurement at large forcing amplitudes, to predict the limit amplitude in steady state for a given engine. This method allows one to predict an engine’s saturation amplitude without studying in detail its intern geometry. In the case of a quarter wave length engine, its input impedance can easily be obtained from an impedance sensor for example. Increasing the speaker’s forcing leads to a nonlinear impedance depending on the acoustic field amplitude. Once measured, this function contains information such as the limit cycle amplitude, its stability and t...