Slow Manifold Structure in Explosive Kinetics. 1. Bifurcations of Points-at-Infinity in Prototypical Models

Creta, Francesco; Adrover, Alessandra; Cerbelli, Stefano; Valorani, Mauro; Giona, Massimiliano

doi:10.1021/jp0636064

Cited by 10 publications

(26 citation statements)

References 41 publications

(79 reference statements)

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“…The branching factor a takes values a > 1 to mimic branching propagation. A suitable non dimensionalization of Williams' model has been proposed in [21]. The three non dimensional ODEs that describe the kinetics of the model (1) are…”

Section: The Branched-chain Reactions Isothermal Williams Modelmentioning

confidence: 99%

Dynamical system analysis of ignition phenomena using the Tangential Stretching Rate concept

Valorani

Paolucci

Martelli

et al. 2015

Combustion and Flame

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We analyze ignition phenomena by resorting to the stretching rate concept formerly introduced in the study of dynamical systems. We construct a Tangential Stretching Rate (TSR) parameter by combining the concepts of stretching rate with the decomposition of the local tangent space in eigen-modes. The main feature of the TSR is its ability to identify unambiguously the most energetic scale at a given space location and time instant. The TSR depends only on the local composition of the mixture, its temperature and pressure. As such, it can be readily computed during the post processing of computed reactive flow fields, both for spatially homogeneous and in-homogenous systems.\ud \ud Because of the additive nature of the TSR, we defined a normalized participation index measuring the relative contribution of each mode to the TSR. This participation index to the TSR can be combined with the mode amplitude participation Index of a reaction to a mode – as defined in the Computational Singular Perturbation (CSP) method – to obtain a direct link between a reaction and TSR. The reactions having both a large participation index to the TSR and a large CSP mode amplitude participation index are those contributing the most to both the explosive and relaxation regimes of a reactive system. This information can be used for both diagnostics and for the simplification of kinetic mechanisms.\ud \ud We verified the properties of the TSR with reference to three nonlinear planar models (one for isothermal branched-chain reactions, one for a non-isothermal, one-step system, and for non-isothermal branched-chain reactions), to one planar linear model (to discuss issues associated with non-normality), and to test problems involving hydro-carbon oxidation kinetics.\ud \ud We demonstrated that the reciprocal of the TSR parameter is the proper characteristic chemical time scale in problems involving multi-step chemical kinetic mechanisms, because (i) it is the most relevant time scale during both the explosive and relaxation regimes and (ii) it is intrinsic to the kinetics, that is, it can be identified without the need of any ad hoc assumption

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Section: The Branched-chain Reactions Isothermal Williams Modelmentioning

confidence: 99%

Dynamical system analysis of ignition phenomena using the Tangential Stretching Rate concept

Valorani

Paolucci

Martelli

et al. 2015

Combustion and Flame

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“…B in a well-stirred jacketed reactor: [29]. This model problem is aimed at illustrating the operating characteristics of the GScheme.…”

Section: A Planar Ode Modelmentioning

confidence: 99%

The G-Scheme: A framework for multi-scale adaptive model reduction

Valorani

Paolucci

2009

Journal of Computational Physics

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“…While such construction has been done for small two-dimensional model systems, 3,4 the present work offers the first construction of a SIM for a realistic detailed kinetics system of greater than two dimensions. We note that here dimensionality refers to the dimension of the composition space and not to the ordinary spatial dimension, as the systems we consider have no spatial inhomogeneity.…”

Section: Introductionmentioning

confidence: 99%

Calculation of Slow Invariant Manifolds for Reactive Systems

Al-Khateeb

Powers

Paolucci

et al. 2009

47th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition

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One-dimensional slow invariant manifolds for dynamical systems arising from modeling unsteady, isothermal, isochoric, spatially homogeneous, closed reactive systems are calculated. The technique is based on global analysis of the composition space of the reactive system. The identification of all the system's finite and infinite critical points plays a major role in calculating the system's slow invariant manifold. The slow invariant manifolds are constructed by calculating heteroclinic orbits which connect appropriate critical points to the critical point which corresponds to the unique stable physical critical point of chemical equilibrium. The technique is applied to small and large detailed kinetics mechanisms for hydrogen combustion.

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Slow Manifold Structure in Explosive Kinetics. 1. Bifurcations of Points-at-Infinity in Prototypical Models

Cited by 10 publications

References 41 publications

Dynamical system analysis of ignition phenomena using the Tangential Stretching Rate concept

Dynamical system analysis of ignition phenomena using the Tangential Stretching Rate concept

The G-Scheme: A framework for multi-scale adaptive model reduction

Calculation of Slow Invariant Manifolds for Reactive Systems

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