Rate-controlled constrained equilibrium: Formulation and application to nonpremixed laminar flames

Jones, W.P.; Rigopoulos, Stelios

doi:10.1016/j.combustflame.2005.03.008

Cited by 67 publications

(62 citation statements)

References 9 publications

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“…For the purpose of an implementation of the method, also an alternative method has been proposed [53] and implemented [34,50,54,74] which, instead of the direct integration of the rate-equations for the constraint-potentials, solves the dual problem in terms of an implicit set of rate equations for the constraint-potentials γ i . A general advantage of this method is the reduction by n c (from n c + n x to n x ) of the number of implicit equations that need to be solved during the integration.…”

Section: Rate Equations For the Constraint-potentialsmentioning

confidence: 99%

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The Rate-Controlled Constrained-Equilibrium Approach to Far-From-Local-Equilibrium Thermodynamics

Beretta

Keck

Janbozorgi

et al. 2012

Entropy

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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.

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Section: Rate Equations For the Constraint-potentialsmentioning

confidence: 99%

“…It has also formed the basis for Close Parallel Inertial Manifold (CPIM) [50] and Inertial Constrained-Equilibrium Pre-Image Curve (ICE-PIC) [51]. The method has been later developed and applied by several others, see e.g., [34,35,50,[52][53][54][55][56][57][58][59].…”

Section: Introductionmentioning

confidence: 99%

The Rate-Controlled Constrained-Equilibrium Approach to Far-From-Local-Equilibrium Thermodynamics

Beretta

Keck

Janbozorgi

et al. 2012

Entropy

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“…A different view on RCCE has been adopted by other researchers [23], [21]: RCCE can instead be viewed as a method for developing reduced mechanisms consisting of single species, similar to the conventional mechanisms derived by QSSA and PE. In that point of view, the RCCE constraints simply correspond to the leading species in QSSA and PE while the remaining species are what would be called 'steady state' species in a conventional reduced mechanism.…”

Section: Introductionmentioning

confidence: 99%

“…It is thus clear that a number of different viewpoints on RCCE exist in the literature. The present article is the latest in a series of works [23], [21], [46], [33] [9] that aim to formulate and employ RCCE as an alternative to QSSA and PE, in order to compute the dynamics of the chemical system on the constrained equilibrium manifold. The latter is a manifold defined by a set of algebraic equations (shown in Sec.…”

Section: Introductionmentioning

confidence: 99%

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A methodology for derivation of RCCE-reduced mechanisms via CSP

Koniavitis

Rigopoulos

Jones

2017

Combustion and Flame

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Reduced Flame Kinetics Via Rate-Controlled Constrained Equilibrium

Rigopoulos

2006

Computational Science – ICCS 2006

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The dynamical evolution of a chemically reacting system is governed by the equations of chemical kinetics, which exhibit a wide range of time scales thus giving rise to stiff equations. In the ratecontrolled constrained equilibrium method (RCCE), the dynamical evolution of the system is governed by the kinetics of the species associated with the slower timescales (kinetically controlled), while the remaining species are calculated via a constrained minimisation of the Gibbs free energy of the mixture. This permits the derivation of a general set of differential-algebraic equations, which apply to any reduced system given a particular selection of kinetically controlled species. In this paper, it is shown how the differential-algebraic formulation of RCCE can be derived from first principles, in the form of an extension of the computation of chemical equilibrium via miminisation of the free energy. Subsequently, RCCE is employed to reduce a comprehensive combustion mechanism and to calculate the burning velocity of premixed H2-O2 and CH4-air flames under a range of pressures and equivalence ratios.

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Rate-controlled constrained equilibrium: Formulation and application to nonpremixed laminar flames

Cited by 67 publications

References 9 publications

The Rate-Controlled Constrained-Equilibrium Approach to Far-From-Local-Equilibrium Thermodynamics

The Rate-Controlled Constrained-Equilibrium Approach to Far-From-Local-Equilibrium Thermodynamics

A methodology for derivation of RCCE-reduced mechanisms via CSP

Reduced Flame Kinetics Via Rate-Controlled Constrained Equilibrium

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