An Endoreversible Model for the Regenerators of Vuilleumier Refrigerators

Abstract

We introduce a reduced-order endoreversible model of a Vuilleumier refrigerator for waste heat recovery. Based on the Vuilleumier cycle, in this refrigerator a working gas is alternately displaced between three subsystems that are in thermal contact with external heat reservoirs. Regarding refrigeration performance, very crucial components of the Vuilleumier machine are its two regenerators. For obtaining a sufficiently accurate model of the Vuilleumier machine, it is hence essential to incorporate a proper description of the regenerators. This can be achieved by using one-dimensional continuum models, e.g. with a finite volume approach, which brings about a large number of degrees of freedom and significant numerical effort. As opposed to that, the model presented in this paper utilizes a novel modeling ansatz for the regenerators that reduces the number of degrees of freedom per regenerator to three. It leads to a considerable reduction in numerical effort and computation time and is hence predestined for applications like design and control optimizations. For an exemplary set of design parameters and operational conditions, we validate the model against a detailed finite volume model of the regenerators in order to work out limitations and perspectives.