A nonlinear model of thermoacoustic devices

Abstract

This paper presents a nonlinear, time-domain model of thermoacoustic devices based on cross-sectional averaged equations. Heat transfer perpendicular to the device axis--which lies at the core of thermoacoustic effects--is modeled in a novel and more realistic way. Heat conduction in the solid surfaces surrounding the fluid medium is included. Contrary to the previous versions of this model [Watanabe et al., J. Acoust. Soc. Am. 102, 3484-3496 (1997)], the present version does not require artificial damping and is numerically robust. The model performance is illustrated on several examples: a prime mover, an externally driven thermoacoustic refrigerator, and a combined prime mover/refrigerator system.

Simplified account of Rayleigh streaming for the description of nonlinear processes leading to steady state sound in thermoacoustic engines

“…That is the reason why the development of adequate simulation tools is still needed to describe the evolution of acoustic wave amplitude after the onset of thermoacoustic instability. On the one hand, direct numerical simulation [12][13][14][15] 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 the multiple time and space scales involved in the description of thermoacoustic engines. On the other hand, analytical models are often based on substantial approximations, but one can be motivated by the development of some phenomenological approach aiming at reproducing qualitatively the experiments in order to get deeper understanding of the operation of thermoacoustic engines.…”

“…They took into account the influence of various nonlinear effects such as minor losses at the edges of the stack, higher harmonics generation, heat pumping by acoustic waves, and heat convection by the so-called Gedeon streaming [20]. It is worth noting that only a few papers [9,13,14,19] provide direct comparisons of calculated transient regimes with experimental data, and to our knowledge, most of the complicated effects mentioned above cannot be reproduced by the models, even for the simplest thermoacoustic oscillators which can be built, like the Sondhaus tube or the socalled thermoacoustic laser [21].…”

Nonlinear temperature field near the stack ends of a standing-wave thermoacoustic refrigerator

“…Models relying on this approximation neglect the contribution of longitudinal gradients of temperature oscillations to the convective heat flux along the stack. However, when longitudinal gradients of temperature oscillations are not neglected, analytical models by Gusev et al [9,10] and numerical models by Karpov and Prosperetti [12] showed that, near the ends of a thermoacoustic stack, the thermal field is nonlinear. This was further validated by direct numerical simulations [7,14,15].…”

Modeling of thermoacoustic systems using the nonlinear frequency domain method

“…(1c), because we have added an extra term corresponding to axial conduction. As stated by Karpov et al, 9 this term is only important near walls. The reason for adding this term is explained in Appendix A.…”