Simplified Modeling of a Thermo-acousto-electric Engine Forced by an External Sound Source

Introduction Thermoacoustic wave-generators are usually designed and optimized using software tools [1, 2] based on the linear thermoacoustic theory. These tools enable to predict the operating point of a thermoacoustic engine from the balance between the thermoacoustic amplification process and the numerous nonlinear effects saturating wave amplitude growth, the latter effects being very difficult to describe properly. A non exhaustive list of these effects includes (apart from the thermoacoustic heat pumping accompanying wave amplification) different kinds of streaming, nonlinear acoustic propagation or aerodynamical and thermal entrance effects. These nonlinear effects are responsible for both dissipation of acoustic power and perturbations of the temperature field in the thermoacoustic core, that work together to limit the overall performances of thermal-to-acoustic conversion. Therefore, the development of adequate simulation tools is still needed to describe the high level of complexity of the processes involved above the onset of thermoacoustic instability. Direct numerical simulation seems to be the only way to reproduce quantitatively the effects mentioned above, but it is still limited by large computation times inherent to the complicated physics and multiple time and space scales involved in the description of thermoacoustic engines. Simplified analytical models can help in getting a deeper physical insight about the processes involved, but they are also based on substantial approximations. In this study, we use a simplified modeling of thermoacoustic engines to help understanding recent experimental observations dealing with the external forcing of thermoacoustic oscillations [3–5].