The global relaxation redistribution method for reduction of combustion kinetics

Kooshkbaghi, Mahdi; Frouzakis, Christos E.; Chiavazzo, Eliodoro; Boulouchos, Konstantinos; Karlin, Iliya V.

doi:10.1063/1.4890368

Cited by 11 publications

(4 citation statements)

References 48 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Finally, in addition to using the SQEM reduced description directly, the manifold can be iteratively refined to construct slow invariant manifolds (e.g., Method of Invariant Grid , and the algorithm proposed in ref ).…”

Section: Discussionmentioning

confidence: 99%

“…The quasi-equilibrium manifold has been proposed in the literature for species reconstruction (manifold extension) for states far from equilibrium and for determining the manifold boundaries. 17,18 The spectral quasi-equilibrium manifold (SQEM) uses the left eigenvectors of the Jacobian at equilibrium corresponding to the smallest in absolute value eigenvalues (slowest directions) to construct QEMs. The SQEM has previously been employed only as an initial manifold which was subsequently refined iteratively toward the SIM.…”

Section: Introductionmentioning

confidence: 99%

“…To cover the entire admissible space with a uniform reduced model, one should find a way to extend the manifold. The quasi-equilibrium manifold has been proposed in the literature for species reconstruction (manifold extension) for states far from equilibrium and for determining the manifold boundaries. , …”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Spectral Quasi-Equilibrium Manifold for Chemical Kinetics

et al. 2016

Self Cite

View full text Add to dashboard Cite

The Spectral Quasi-Equilibrium Manifold (SQEM) method is a model reduction technique for chemical kinetics based on entropy maximization under constraints built by the slowest eigenvectors at equilibrium. The method is revisited here and discussed and validated through the Michaelis-Menten kinetic scheme, and the quality of the reduction is related to the temporal evolution and the gap between eigenvalues. SQEM is then applied to detailed reaction mechanisms for the homogeneous combustion of hydrogen, syngas, and methane mixtures with air in adiabatic constant pressure reactors. The system states computed using SQEM are compared with those obtained by direct integration of the detailed mechanism, and good agreement between the reduced and the detailed descriptions is demonstrated. The SQEM reduced model of hydrogen/air combustion is also compared with another similar technique, the Rate-Controlled Constrained-Equilibrium (RCCE). For the same number of representative variables, SQEM is found to provide a more accurate description.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Spectral Quasi-Equilibrium Manifold for Chemical Kinetics

et al. 2016

Self Cite

View full text Add to dashboard Cite

show abstract

“…3. The relaxation redistribution method (RRM), which is discussed in the papers and books of Chiavazzo et al, see [55][56][57][58][59], is based on the construction of accurate discrete approximations of slow invariant manifolds. The ideas are based on two steps:…”

Section: Alternative Modern Systematic Model Reduction Methods Of Mulmentioning

confidence: 99%

General Principles

Geiser¹

2015

Multicomponent and Multiscale Systems

View full text Add to dashboard Cite

In the general principle, we give an overview of the recently used methods and schemes to solve multicomponent and multiscale systems. While multicomponent systems are evolution equations based on each single species, which are coupled with the other species, e.g. with reaction-, diffusion-processes, multiscale systems are evolution equations based on different scales for each species, e.g. macroscopicor microscopic scale. We give the general criteria for practically performing the different splitting and multiscale methods, such that a modification to practical applications of the splitting schemes to a real-life problem can be done. Multicomponent SystemsIn the following, we deal with multicomponent systems. Multicomponent systems concentrate on disparate components in the underlying multiscale models, while they can be coupled by linear or nonlinear functions or differential systems, e.g. reactions or transport phenomena. Often, also different scales are important to resolve to understand the interactions of the different components. Here, we have to apply multicomponent schemes that are also related to disparate spatial and timescales to resolve such complexities, see algorithmic ideas of multicomponent problems in [1].In the following sections, we concentrate on modelling or algorithmical aspects of multicomponent systems for the following applications:• Multicomponent flows, see [2,3].• Multicomponent transport, see [1,4].We simulate the flow and transport systems based on their interactions with the different components. Hence, we allow to study weakly or strongly coupled components in the underlying modelling equation systems. Multicomponent FlowsThe class of multicomponent flows can be defined as a mixture of different chemical species on a molecular level, which are flown with the same velocity and temperature, The modelling of such behaviours is important in engineering, e.g. reactor design (Chemical vapour deposition reactors, see [6]) in chemical engineering. Such processes are very complex, while different physical processes occur, e.g. injection, heating, mixturing, homogeneous and heterogeneous chemistry and further, see [7].In the following, we present some typical problems in multicomponent flow problems:• Ionized Species, e.g. plasma problems, see [4].• Combustion of oil, coal or natural gas, see [8].• Chemical reaction processes in chemical engineering, see [6,9,10].• Atmospheric pollution, see [11].Remark 1.1 In the different applications, the term multiphase flow is often used. Here, we define multiphase flows where the phases are immiscible and not chemically related, see [2,12]. So each phase has a separately defined volume fraction and velocity field. Therefore, also the conservation equations for the flow of each species and their interchange between the phases are different from the multicomponent flow. Here, one is taken into account to define a common pressure field, while each phase is related to the gradient of this field and its volume fraction, see [13]. The applications a...

show abstract