The improvement of the thermal coupling between the stack of a thermoacoustic refrigerator and the heat exchangers is necessary to achieve high-efficiency and stable operation. Heat transport by the thermoacoustic effect depends on both the velocity and temperature fields. Inside the stack, it can be described by the linear theory of thermoacoustics. However, departures from linear behaviours are expected near the edges of the stack and in the heat-exchangers due to the generation of vorticity and temperature harmonics. The present work focuses on the experimental characterization of temperature harmonics near the edges of a thermoacoustic stack. Experiments are conducted in an 18cm-long resonator operated with air at atmospheric pressure at the resonance frequency of approximately 464Hz. Drive ratios up to 3% are achieved, which corresponds to temperature oscillation amplitudes up to 2.5K. Temperature measurements are performed using a novel procedure recently proposed by Berson et al., Rev. Sci. Instrum. 81, 015102 (2010). The instantaneous temperature is measured with a cold wire operated by a Constant-Current Anemometer (CCA). In addition, we record the output signal of the same wire, under the same flow conditions — which is made possible by the periodicity of the acoustic wave — and operated in the heated mode by a Constant-Voltage Anemometer (CVA). During post-processing, the thermal inertia of the cold wire operated with the CCA is corrected using the CVA signal. This procedure does not require any physical properties of the wire such as the diameter. In addition, it does not require the knowledge of a heat-transfer/velocity relationship for the wire. This is all the most important for thermoacoustic systems since no such relationship is available in oscillating flows. Results validate the generation of temperature harmonics near the stack edges. The spatial distributions of the first and second harmonic amplitudes are compared with a one-dimensional model. The model is an extension of an analytical model from the literature [Gusev et al., J. of Sound and Vibration 235, (2000)] that takes into account axial conduction. Experimental results show an excellent qualitative agreement with the model and demonstrate the importance of axial conduction on the nonlinear thermal field behind the stack.

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