The Rate-Controlled Constrained-Equilibrium Approach to Far-From-Local-Equilibrium Thermodynamics
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Beretta-2012-The Rate-Controlled.pdf
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Author(s)
Beretta, Gian Paolo
Janbozorgi, Mohammad
Metghalchi, Hameed
Keck, James C.
Date Issued
January 2012
Journal
Entropy
Publisher
MDPI AG
Citation
Beretta, Gian Paolo et al. “The Rate-Controlled Constrained-Equilibrium Approach to Far-From-Local-Equilibrium Thermodynamics.” Entropy 14.2 (2012): 92–130. Web. 3 May 2012. © 2012 MDPI AG
Version
Final published version
Abstract
The Rate-Controlled Constrained-Equilibrium (RCCE) method for the description of the time-dependent behavior of dynamical systems in non-equilibrium states is a general, effective, physically based method for model order reduction that was originally developed in the framework of thermodynamics and chemical kinetics. A generalized mathematical formulation is presented here that allows including nonlinear constraints in non-local equilibrium systems characterized by the existence of a non-increasing Lyapunov functional under the system’s internal dynamics. The generalized formulation of RCCE enables to clarify the essentials of the method and the built-in general feature of thermodynamic consistency in the chemical kinetics context. In this paper, we work out the details of the method in a generalized mathematical-physics framework, but for definiteness we detail its well-known implementation in the traditional chemical kinetics framework. We detail proofs and spell out explicit functional dependences so as to bring out and clarify each underlying assumption of the method. In the standard context of chemical kinetics of ideal gas mixtures, we discuss the relations between the validity of the detailed balance condition off-equilibrium and the thermodynamic consistency of the method. We also discuss two examples of RCCE gas-phase combustion calculations to emphasize the constraint-dependent performance of the RCCE method.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
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Creative Commons Attribution 3.0
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DOI of Published Version
https://doi.org/10.3390/e14020092
