An Endoreversible Model for the Regenerators of Vuilleumier Refrigerators

Paul, Raphael; Khodja, Abdellah; Hoffmann, Karl Heinz

doi:10.5541/ijot.877687

Cited by 8 publications

(5 citation statements)

References 43 publications

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“…Numerical validations of the developed endoreversible regenerator models were performed against finite volume regenerator models. For the EEn-regenerator model, such validations were carried out for Stirling and Vuilleumier machines in parallel research works [52][53][54]. Despite its significantly fewer degrees of freedom and reduced numerical effort, the EEn-regenerator model provided good approximations to the results obtained with the much more detailed finite volume models.…”

Section: Discussionmentioning

confidence: 99%

“…The comparison showed a good accordance of the models regarding entropy production rates related with single irreversibilities, as well as power and efficiency. Furthermore, in [54], a numerical validation of the EEn-regenerator model with internal irreversibilities was conducted for a Vuilleumier refrigerator. The numerical validation was here also performed against a finite volume regenerator model.…”

Section: Validationmentioning

confidence: 99%

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A Class of Reduced-Order Regenerator Models

Paul

Hoffmann

2021

Energies

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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.

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Section: Discussionmentioning

confidence: 99%

Section: Validationmentioning

confidence: 99%

A Class of Reduced-Order Regenerator Models

Paul

Hoffmann

2021

Energies

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“…It captures the effects of regeneration in the form of an irreversible interaction. For more elaborate models see [55,56].…”

Section: The Regeneratorsmentioning

confidence: 99%

Optimized Cooling Power of a Vuilleumier Refrigerator with Limited Regeneration

et al. 2021

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Vuilleumier refrigerators provide cooling power by utilizing a heat source at temperatures above the ambient. This is particularly helpful in situations where waste heat is available and other power sources are limited. Vuilleumier refrigerators come in different technical configurations; here we analyze the thermodynamic performance of a configuration utilizing two displacer pistons with integrated regenerators. More specifically, we optimize the cooling power by optimizing the piston movement for a range of operation speeds. The optimization is based on the AS motion class for cyclic dynamics and uses an endoreversible model for the refrigerator. Our focus is on the influence of the regeneration extent present, and we find performance gains of about 17% for high regeneration extent and of about 28% for lower regeneration extent.

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“…In case a more detailed description of the regenerators is required that still leads to relatively low numerical effort and few degrees of freedom, the endoreversible regenerator models developed and validated in [ 27 , 60 ] can be applied.…”

Section: Thermodynamic Modeling Of a Vuilleumier Refrigeratormentioning

confidence: 99%

Cooling Cycle Optimization for a Vuilleumier Refrigerator

Paul

Khodja

Fischer

et al. 2021

Entropy

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Vuilleumier refrigerators are a special type of heat-driven cooling machines. Essentially, they operate by using heat from a hot bath to pump heat from a cold bath to an environment at intermediate temperatures. In addition, some external energy in the form of electricity can be used as an auxiliary driving mechanism. Such refrigerators are, for example, advantageous in situations where waste heat is available and cooling power is needed. Here, the question of how the performance of Vuilleumier refrigerators can be improved is addressed with a particular focus on the piston motion and thus the thermodynamic cycle of the refrigerator. In order to obtain a quantitative estimate of the possible cooling power gain, a special class of piston movements (the AS motion class explained below) is used, which was already used successfully in the context of Stirling engines. We find improvements of the cooling power of more than 15%.

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An Endoreversible Model for the Regenerators of Vuilleumier Refrigerators

Cited by 8 publications

References 43 publications

A Class of Reduced-Order Regenerator Models

A Class of Reduced-Order Regenerator Models

Optimized Cooling Power of a Vuilleumier Refrigerator with Limited Regeneration

Cooling Cycle Optimization for a Vuilleumier Refrigerator

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