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Diffusive-thermal instabilities in premixed flames: Stepwise ignition-temperature kinetics

Published on May 1, 2015in Combustion and Flame4.12
· DOI :10.1016/j.combustflame.2015.01.006
I. Brailovsky10
Estimated H-index: 10
(TAU: Tel Aviv University),
Peter V. Gordon8
Estimated H-index: 8
(University of Akron)
+ 1 AuthorsGregory I. Sivashinsky29
Estimated H-index: 29
(TAU: Tel Aviv University)
Abstract
Abstract This study is motivated by the observation that in combustion of hydrogen–oxygen/air and ethylene–oxygen mixtures the global activation energy appears to be high at low enough temperatures and low at high enough temperatures, reflecting the complex nature of the underlying chemistry. Stability analysis of a uniformly propagating planar premixed flame controlled by a stepwise ignition-temperature kinetics (representing the activation energy temperature-dependence) is carried out. It is shown that, for all its schematic nature, the diffusive-thermal model based on the ignition-temperature kinetics reproduces quite successfully the basic features of both cellular and pulsating instabilities typical of low and high Lewis number mixtures.
  • References (26)
  • Citations (5)
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References26
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#1Vadim N. Kurdyumov (Complutense University of Madrid)H-Index: 19
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Last. A. V. Kolobov (FIAN: Lebedev Physical Institute)H-Index: 8
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Abstract Axisymmetric and non-axisymmetric gasless flames propagating in a narrow cylindrical sample of an energetic material are considered. The work is focused on the impact of radiative heat-losses from the outer surface of the slab on the flame structure and stability. A typical C-shaped response curve is found with two different flame velocities in the case of axisymmetric flames where the slowest velocity represents an unstable solution. Global linear stability analysis of such flames is p...
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#1Angel Sánchez (Charles III University of Madrid)H-Index: 35
#2Forman A. Williams (UCSD: University of California, San Diego)H-Index: 54
Abstract The current increasing interest in hydrogen utilization and increasing understanding of hydrogen combustion motivate this review of flammability characteristics of hydrogen. The intent is to present a thorough and self-contained tutorial that covers the existing fundamental knowledge in a uniform and concise manner. The presentation begins with an up-dated exposition of the elementary chemical mechanism of hydrogen oxidation, including the latest chemical-kinetic results, with evaluated...
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#1Alvin Bayliss (NU: Northwestern University)H-Index: 25
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We consider the use of step-functions to model Arrhenius reaction terms for traveling wave solutions to combustion problems. We develop a methodology by which the Arrhenius reaction rate term is replaced by a suitably normalized step-function. The resulting model introduces interior interfaces and allows the conservation equations for energy and species to be solved explicitly within the subdomains bounded by the interfaces. The problem can then be reduced to a small number of nonlinear algebrai...
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Abstract Lean premixed hydrogen/air flames are characterized by subunity Lewis numbers and the strong influence of thermal-diffusive instability in addition to the omnipresent hydrodynamic instability caused by thermal expansion. Such intrinsically unstable flames acquire cellular structures that modify significantly their propagation dynamics. In this paper, numerical simulations with detailed chemistry and transport are used to study premixed hydrogen/air flames at an equivalence ratio of ϕ = ...
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#1Grunde JomaasH-Index: 13
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The development of pulsating instability in expanding spherical premixed flames was experimentally studied, leading to the observation and quantification of spiral waves and target patterns over the flame surfaces in rich hydrogen-air, rich hydrogen-oxygen, and lean butane-oxygen-helium mixtures at elevated pressures. The transition boundary to instability was found to agree well with the Sivashinsky criterion, Ze(Le−1)>4(1+3)≈10.9, provided that local values are used in the evaluation of the Ze...
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#1M. Kuznetsov (KIT: Karlsruhe Institute of Technology)H-Index: 16
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The authors present experimental studies of the deflagration-to-detonation transition (DDT) in tubes with smooth and rough walls in stoichiometric hydrogen-oxygen and ethylene-oxygen mixtures. On the basis of experimental evidence, it is shown that formation of the preheat zone, where reaction is chemically frozen, promotes the transition to detonation if temperature and width of the preheat zone are above certain critical values. A sequence of high-speed Schlieren records permits an accurate de...
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A linear stability of freely propagating, adiabatic premixed flames is investigated in the context of a thermal-diffusive or constant density model, together with a simple two-step chain-branching model of the chemistry. This study considers the case of realistic, finite activation energy of the chain-branching step, and emphasis is on comparing with previous high activation energy asymptotic results. It is found that for realistic activation energies, a pulsating instability is absent in regime...
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The foundations of a relatively simple two-step kinetic scheme for flame chemistry are outlined, involving a model chain branching process that should adopt the activation temperature of a rate-limiting branching reaction in order to offer a broad approximation for hydrocarbon flames. A model energetic intermediate reactant then acts as a buffer between fuel consumption and the release of heat, as the intermediate is converted into products through a completion reaction step. By taking the rate ...
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#1Grunde Jomaas (Princeton University)H-Index: 13
#2Chung King Law (Princeton University)H-Index: 81
Last. J. K. Bechtold (NJIT: New Jersey Institute of Technology)H-Index: 13
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The instant of transition to cellularity of centrally ignited, outwardly propagating spherical flames in a reactive environment of fuel-oxidizer mixture, at atmospheric and elevated pressures, was experimentally determined using high-speed schlieren imaging and subsequently interpreted on the basis of hydrodynamic and diffusional-thermal instabilities. Experimental results show that the transition Peclet number, Pe c = R c /l L , assumes an almost constant value for the near-equidiffusive acetyl...
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Cited By5
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Abstract We study in a strip of R 2 a combustion model of flame propagation with stepwise temperature kinetics and zero-order reaction, characterized by two free interfaces, respectively the ignition and the trailing fronts. The latter interface presents an additional difficulty because the non-degeneracy condition is not met. We turn the system to a fully nonlinear problem which is thoroughly investigated. When the width l of the strip is sufficiently large, we prove the existence of a critical...
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Abstract In this paper we analyze the stability of the traveling wave solution for an ignition-temperature, first-order reaction model of thermal-diffusional combustion, in the case of high Lewis numbers ( Le > 1 ). In contrast to conventional Arrhenius kinetics where the reaction zone is infinitely thin, the reaction zone for stepwise temperature kinetics is of order unity. The system of two parabolic PDEs is characterized by a free interface at which ignition temperature Θ i is reached. We tur...
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ABSTRACTAn analytical model was developed for the study of nonadiabatic flame propagation and quenching in binary mixtures of independently reacting fuels. Despite its simple formulation, in which step-wise reactions start at an externally imposed ignition temperature and proceed at a constant rate, the model reproduces the well-known regimes of dual-front propagation: front separation, control, and merging. The results indicate that, depending on the relative concentration of the fuels, the two...
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Abstract With a freely expanding unwrinkled spherical flame as an example, it is shown that deflagration-to-detonation transition in unconfined gaseous systems is possible, provided the flame is close to its propagability threshold and the deficient reactant Lewis number is not too small. The transition is triggered by the thermal runaway induced by positive feedback between the accelerating flame and the flame-driven pressure build-up. A possible way to account for the impact of wrinkling is di...
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In this paper we consider an ignition-temperature zero-order reaction model of thermo-diffusive combustion. This model describes the dynamics of thick flames, which have recently received considerable attention in the physical and engineering literature. The model admits a unique (up to translations) planar travelling wave solution. This travelling wave solution is quite different from those usually studied in combustion theory. The main qualitative feature of this travelling wave is that it has...
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#1Tarek Echekki (NCSU: North Carolina State University)H-Index: 20
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