Mathematically reduced reaction mechanisms applied to adiabatic flat hydrogen/air flames

Eggels, Rlgm; Goey, de Lph Philip

doi:10.1016/0010-2180(94)00108-5

Cited by 62 publications

(20 citation statements)

References 3 publications

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“…Only the diffusion term contains a component pointing out of the manifold, which must be projected. Although the eigenvector projection is mathematically the only correct one, other (simplified) projection techniques have been used successfully [14,23,24].…”

Section: Implementation Of Fgm's In a Reacting-flow Codementioning

confidence: 99%

“…The dimension of the look-up table is determined by the number of controlling variables which is needed to describe the slow chemical processes. For simple fuels like CO/H 2 mixtures, two controlling variables are sufficient [13,14]. However, for an accurate reproduction of the burning velocity of premixed methane/air flames at least three degrees of freedom are needed [15].…”

Section: Introductionmentioning

confidence: 99%

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Modelling of Premixed Laminar Flames using Flamelet-Generated Manifolds

Oijen¹,

Goey²

2000

Combustion Science and Technology

690

264

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In order to reduce the computational cost of flame simulations, several methods have been developed during the last decades, which simplify the description of the reaction kinetics. Most of these methods are based on partial-equilibrium and steady-state assumptions, assuming that most chemical processes have a much smaller time scale than the flow time scale. These assumptions, however, give poor approximations in the 'colder' regions of a flame, where transport processes are also important.The method presented here, can be considered as a combination of two approaches to simplify flame calculations, i.e. a flamelet and a manifold approach. The method, to which we will refer as the Flamelet-Generated Manifold (FGM) method, shares the idea with flamelet approaches that a multi-dimensional flame may be considered as an ensemble of one-dimensional flames. The implementation, however, is typical for manifold methods: a low-dimensional manifold in composition space is constructed, and the thermo-chemical variables are stored in a database which can be used in subsequent flame simulations. In the FGM method a manifold is constructed using one-dimensional flamelets. Like in other manifold methods, the dimension of the manifold can be increased to satisfy a desired accuracy. Although the method can be applied to different kinds of flames, only laminar premixed flames are considered here.Since the major parts of convection and diffusion processes are present in one-dimensional flamelets, the FGM is more accurate in the 'colder' zones of premixed flames than methods based on local chemical equilibria. Therefore, less controlling variables are sufficient to represent the combustion process. Test results of one and two-dimensional premixed methane/air flames show that detailed computations are reproduced very well with a FGM consisting of only one progress variable apart from the enthalpy to account for energy losses.

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Section: Implementation Of Fgm's In a Reacting-flow Codementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Modelling of Premixed Laminar Flames using Flamelet-Generated Manifolds

Oijen¹,

Goey²

2000

Combustion Science and Technology

690

264

View full text Add to dashboard Cite

show abstract

“…Refinements, applications, and evaluations of the ILDM method against direct numerical simulations can be found in Refs. [1][2][3][4]11,12,37,39,42,47,58,[68][69][70]73,[86][87][88].…”

Section: Many Chemical Reaction Mechanisms In Combustionmentioning

confidence: 99%

Asymptotic analysis of two reduction methods for systems of chemical reactions

Kaper

2002

Physica D: Nonlinear Phenomena

132

127

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This paper concerns two methods for reducing large systems of chemical kinetics equations, namely, the method of intrinsic low-dimensional manifolds (ILDMs) due to Maas and Pope [Combust. Flame 88 (1992) Chem. Phys. 93 (1990) 1072. Both methods exploit the separation of fast and slow reaction time scales to find low-dimensional manifolds in the space of species concentrations where the long-term dynamics are played out. The asymptotic expansions of these manifolds (ε ↓ 0, where ε measures the ratio of the reaction time scales) are compared with the asymptotic expansion of M ε , the slow manifold given by geometric singular perturbation theory. It is shown that the expansions of the ILDM and M ε agree up to and including terms of O(ε); the former has an error at O(ε 2 ) that is proportional to the local curvature of M 0 . The error vanishes if and only if the curvature is zero everywhere. The iterative method generates, term by term, the asymptotic expansion of M ε . Starting from M 0 , the ith application of the algorithm yields the correct expansion coefficient at O(ε i ), while leaving the lower-order coefficients invariant. Thus, after applications, the expansion is accurate up to and including the terms of O(ε ). The analytical results are illustrated on a planar system from enzyme kinetics (Michaelis-Menten-Henri) and a model planar system due to Davis and Skodje.

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“…However, not all timescales are equally important. This is substantiated by a number of publications [6,16,31], where time scale analysis was performed for different combustion systems looking at the reaction path in composition space. It was found that the reaction path in composition space is embedded in a low-dimensional manifold, which can be described by a small number of variables.…”

Section: A Generic System Of Controlling Variablesmentioning

confidence: 99%

Inclusion of Preferential Diffusion in Simulations of Premixed Combustion of Hydrogen/Methane Mixtures with Flamelet Generated Manifolds

Swart

Bastiaans

Oijen

et al. 2010

Flow Turbulence Combust

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In this paper we study the possibility to account for preferential diffusion effects in lean turbulent premixed flames in numerical predictions with reduced chemistry. We studied the situation when hydrogen is added to methane at levels of 20% and 40% by volume in the fuel, at lean combustion (φ = 0.7) with air. The base case of pure methane was used as a reference. In this case preferential diffusion effects are negligible. First the sensitivity of the mass burning rate to flame stretch was investigated, in one dimensional computations with detailed chemistry, to set reference values. Then the framework of the Flamelet Generated Manifolds (FGM) was used to construct an adequate chemical method to take preferential diffusion into account, without the need for using detailed chemistry. To that end a generalization of the method was presented in which five controlling variables are required. For this system, proper transport equations and effective Lewis numbers where derived. In practice not all five variables are necessary to include and as a first step we limited the amount in the numerical tests in this study to two controlling variables. The method was then tested in configurations in which there was an interaction of coherent vortices and turbulence with flames. It was demonstrated that a minimum of two controlling variables is needed to account for the changed mass burning rate as function of stretch and curvature. It was shown that one-dimensional FGM as well as one-step Arrhenius kinetics can not describe this relation.

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Mathematically reduced reaction mechanisms applied to adiabatic flat hydrogen/air flames

Cited by 62 publications

References 3 publications

Modelling of Premixed Laminar Flames using Flamelet-Generated Manifolds

Modelling of Premixed Laminar Flames using Flamelet-Generated Manifolds

Asymptotic analysis of two reduction methods for systems of chemical reactions

Inclusion of Preferential Diffusion in Simulations of Premixed Combustion of Hydrogen/Methane Mixtures with Flamelet Generated Manifolds

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