Resonance conditions of the air column in a thermoacoustic refrigerator

Among the refrigerating fluids compatible with the environment and which do not present problems of safety appears the air, ideal as regards the safety of both as regards the availability and cost. The air is used as a refrigerant since the beginning of refrigeration applications. It presents the ODP and GWP indices equal to zero, but its use has always been penalized by the low energy performance of the Brayton-Joule inverse cycle, compared to vapor compression cycles so as to exclude its use in air conditioning systems of buildings. A cooling system with acoustic resonator uses the direct conversion of mechanical work, associated with the wave propagation, in a transfer of heat from a heat source at low temperature to a source at a higher temperature. One problem in the use of an acoustic resonator is the realization and the position of the heat exchanger within the resonant volume of air. With regard to the position in a thermoacoustic tube resonator, it is mandatory to preliminarily know what the conditions of the resonant air column are, since it gets excited by an outside power source, whose form and position determine the resonance conditions. In the present paper, a simple model is presented and the definition of an effective length of the resonating tube of a thermoacoustic refrigerator is properly given. Few data are also given relative to the temperature difference obtained in a specific experimental case.