Time-domain modelling: Combining ESM and a finite-difference method for thermoacoustic devices

Thermoacoustic devices are today mainly simulated using frequency-domain methods. Contrary to frequency-domain methods, time-domain methods may include non-linear effects and time-varying boundary conditions. However, time-domain modelling of thermoacoustic devices is computationally expensive, due to large differences in geometric length scales and time scales. The primary aim of this paper has been to model thermoacoustic devices with computational efficiency by using two different methods. The acoustic field outside the stack, based on the assumption of plane waves, is modelled using the efficient Equivalent Source Method (ESM), whereas the complex acoustic field in the stack is modelled using a finite-difference model. In a previous paper of the authors, ESM and a finite-difference model have been combined to model acoustic wave propagation, though thermal effects and heat flow to the stack plate were excluded. In this paper, however, these effects are included. The performance of the model is studied and compared to linear thermoacoustic theory. The proposed model may provide a useful tool for studying time-varying acoustic fields and temperature distributions in thermoacoustic devices