Theoretical prediction of the onset of thermoacoustic instability from the experimental transfer matrix of a thermoacoustic core.

The aim of this paper is to propose a method to predict the onset conditions of the thermoacoustic instability for various thermoacoustic engines. As an accurate modeling of the heat exchangers and the stack submitted to a temperature gradient is a difficult task, an experimental approach for the characterization of the amplifying properties of the thermoacoustic core is proposed. An experimental apparatus is presented which allows to measure the transfer matrix of a thermoacoustic core under various heating conditions by means of a four-microphone method. An analytical model for the prediction of the onset conditions from this measured transfer matrix is developed. The experimental data are introduced in the model and theoretical predictions of the onset conditions are compared with those actually observed in standing-wave and traveling-wave engines. The results show good agreement between predictions from the model and experiments.