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

The nonlinear temperature field in the vicinity of the stack of a standing-wave thermoacoustic refrigerator is investigated both theoretically and experimentally. First, the problem is addressed theoretically by a one-dimensional nonlinear model that predicts the generation of thermal harmonics near the ends of the stack. The model relies on a relaxation-time approximation to describe transverse heat transfer between the stack walls and the working fluid. It extends a previous model proposed by [Gusev et al., Thermal wave harmonics generation in the hydrodynamical heat transport in thermoacoustics, J. Acoust. Soc. Am. 109 (2001) pp. 84–90], by including the effect of axial conduction on temperature fluctuations. Second, the nonlinear temperature field is investigated experimentally. The amplitude of temperature fluctuations behind the stack at the fundamental frequency and second harmonic are measured using cold-wire anemometry. The measurements rely on a procedure recently developed by the authors that allows a full correction of the thermal inertia of the sensor. Experimental results are in good agreement with the predictions of the model. The generation of thermal harmonics behind the stack is thus validated. The influence of the Péclet number on the thermal field, which depends on the diffusivity of the working fluid and on the acoustic frequency and pressure level, is also demonstrated.