Abstract
We present a novel class of reduced-order regenerator models that is based on Endoreversible Thermodynamics. The models rest upon the idea of an internally reversible (perfect) regenerator, even though they are not limited to the reversible description. In these models, the temperatures of the working gas that alternately streams out on the regenerator’s hot and cold sides are defined as functions of the state of the regenerator matrix. The matrix is assumed to feature a linear spatial temperature distribution. Thus, the matrix has only two degrees of freedom that can, for example, be identified with its energy and entropy content. The dynamics of the regenerator is correspondingly expressed in terms of balance equations for energy and entropy. Internal irreversibilities of the regenerator can be accounted for by introducing source terms to the entropy balance equation. Compared to continuum or nodal regenerator models, the number of degrees of freedom and numerical effort are reduced considerably. As will be shown, instead of the obvious choice of variables energy and entropy, if convenient, a different pair of variables can be used to specify the state of the regenerator matrix and formulate the regenerator’s dynamics. In total, we will discuss three variants of this endoreversible regenerator model, which we will refer to as ES, EE, and EEn-regenerator models.
Highlights
In order to furnish an alternative perspective on regenerators and to provide the tools required for model development, we start with introducing the basic mindset and notation of Endoreversible Thermodynamics
We developed three variants of an endoreversible model for thermal regenerators, referred to as ES-regenerator, EE-regenerator, and EEn-regenerator models
The models are based on the notion of an internally reversible regenerator, which was defined as a subsystem that internally conserves both energy and entropy
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. In Stirling and Vuilleumier machines, for example, the regenerators usually consist of a porous metal structure that is called a matrix It is periodically passed by alternating hot and cold flows of working gas, sometimes termed hot and cold blows. The applicability of the modeling approach via regenerator effectiveness is usually limited to technical configurations with heat exchangers providing approximately constant inflow temperatures for the regenerator. Craun and Bamieh [19,20,21] applied model order reduction techniques aiming at the provision of regenerator models that constitute suitable tradeoffs for optimal control problems They succeeded in reducing the computational effort significantly while still achieving good accordance with the temperature dynamics of the original model for different engine speeds. In order to furnish an alternative perspective on regenerators and to provide the tools required for model development, we start with introducing the basic mindset and notation of Endoreversible Thermodynamics
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