Addition of a series spring to a lumped element model of a novel thermoacoustic refrigerator

Abstract

A lumped element model is introduced for an “in-line” traveling-wave thermoacoustic refrigerator, based on a recent patent by Backhaus and Keolian [US Pat. No. 7,908,856 (22 Mar 2011)]. This model couples three electro-mechanical motors to the acoustical domain using a flexure sealed piston. Results of this lumped-element model were found to be in good agreement with a DELTAEC model. Since large displacements result in flexure fatigue, the addition of a series spring between the motor and piston was evaluated to reduce flexure seal displacement while matching the optimum load impedance. The assignment of the correct dynamic mass of the series spring when both the motor and flexure ends of the spring are moving has not been addressed previously in the literature. To determine the two effective masses required at each end of the spring, the spring is discretized into a large number of elements and is converted into a simplified circuit model to assign values to lumped-element components. These values depend upon an initial knowledge of both end velocity magnitudes and phases. This enables an iterative solution for the effective spring masses since velocities need to be known for effective masses to be determined and vice versa. [Work supported by the Applied Research Laboratory and the U.S. Department of Energy.]