This paper deals with the prediction of the frequency and the amplitude of selfsustained oscillations generated in thermoacoustic prime movers, which are compared to measurements. A specially designed, high amplitude, acoustic impedance sensor was developed to perform measurements of the input impedance of a thermoacoustic core, as a function of the heating power supplied to the device, of the frequency, and of the amplitude of acoustic forcing. Those measurements can then be used to predict the spontaneous generation of acoustic oscillations and their saturation up to a steady-state. Those predictions were successful for various acoustic loads connected to the thermoacoustic core. Moreover, the measurements of acoustic impedance as a function of the amplitude of acoustic oscillations are compared to a model based on the linear thermoacoustic theory, and this comparison provides insights into the processes controlling the saturation of acoustic oscillations. The experimental procedure described in this paper can also have practical value, since it provides an empirical way, in principle, to optimize the coupling between the thermoacoustic core and the load, so that the potential eciency of thermoacoustic energy conversion is maximized. a) Electronic
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 the engine’s efficiency depending on parameters as the applied heating and stack’s position. In the case of a standing wave prime mover, this study shows first results obtained from this method. Later on, this work should lead to steady state predictions for any, unknown, given engine.
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