Prediction of limit cycle amplitudes in thermoacoustic engines by means of impedance measurements

Abstract

This paper deals with the prediction of the frequency and the amplitude of self-sustained 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 efficiency of thermoacoustic energy conversion is maximized.