Critical Conditions for Thermal Explosion with Reactant Consumption

Babushok, Valeri I.; Gol’dshtein, Vladimir; Sobolev, Vladimir

doi:10.1080/00102209008951613

Cited by 38 publications

(36 citation statements)

References 4 publications

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“…The critical regime separating the basic types of the regimes, slow and relaxation, was modelled with the help of the integral manifolds of variable stability. This approach was used in [13][14][15][16][17][18][19][20][21][22][23] for modelling of the critical phenomena in chemical systems.…”

Section: Resultsmentioning

confidence: 99%

Study of Oscillatory Processes in the One Model of Electrochemical Reactor

Firstova

Shchepakina

2016

Collection of Selected Papers of the II International Conference on Information Technology and Nanotechnology

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Section: Resultsmentioning

confidence: 99%

Study of Oscillatory Processes in the One Model of Electrochemical Reactor

Firstova

Shchepakina

2016

Collection of Selected Papers of the II International Conference on Information Technology and Nanotechnology

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“…What cause the ignition is the fact that the temperature is increase. The maximum temperature rise of the slow reaction is 1 + 2β + O(γ) taking the I 1 trajectory as critical one (Babushok, Goldshtein, & Sobolev, 1990). The critical trajectory determines the critical value of the parameter α = α cr , i.e., the thermal explosion limit.…”

Section: Application Of Mim To Thermal Explosion Fast and Slow Invarmentioning

confidence: 99%

“…This case is important for diesel where the evaporation time of the droplets and the values of gas temperature, fuel concentration and droplet radii can be estimated before explosion. Analysis of critical conditions for thermal explosion process requires different approximations (Babushok, Gol'dshtein, & Sobolev, 1990). Using this approximation one can rewrite the energy equation and the mass equation in non-dimensional form as:…”

Section: The Delay Time In the Model Of Thermal Explosion Of A Gas MImentioning

confidence: 99%

“…In this paper we use, in addition to different numerical methods, the geometric asymptotic method (Method of Integral Manifolds, MIM) which suggested by Bogolubov, and Mitropolsky (1974), Zadiraka, (1957), as a basic tools for the analysis of SPS system of ordinary differential equations. The MIM method has been successfully applied to the problem of combustion (for example, Babushok, Gol'dshtein, & Sobolev, 1990;Babushok, Gol'dshtein, Romanov, & Babkin, 1992;McIntosh, Gol'dshtein, Goldfarb, & Zinoviev, 1998;Goldfarb, Gol'dshtein, Kuzmenko, & Sazhin, 1999). The main idea…”

Section: Introductionmentioning

confidence: 99%

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Mathematical Modelling of Spray Combustion-Numerical and Analytical Analysis with application to Engineering Science

Nave¹,

Ajadi²,

Gol’dshtein³

2016

APR

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In the present paper we applied two well-known analytical method to the problem of thermal explosion of monodisperse and polydisperse fuel spray. The methods are the method of integral manifold (MIM) and the homotopy analysis method (HAM). The MIM method used as a basic tools for the analysis of SPS system of ordinary differential equations which means that the physical/ mathematical model should contain a small parameter in the governing equations. The HAM is always valid no matter whether there exist small physical parameters or not in contrast to the classical perturbation methods which requires the existence of a small parameter in the system (in general this is not the case). According to the theory of HAM, the convergence and the rate of solution series are dependent on the convergent control parameter ℏ. This means that this parameter gives one a convenient way to adjust and to control the convergent region of the solutions. γ (conventional parameter of Semenov's theory of thermal explosion), the final dimensionless adiabatic temperature of the thermally insulated system after explosion. This parameter is small compared with unity for most gaseous mixture due to the high exothermicity and activation energy of the chemical reactionwhere ϵ d is the emissivity of the droplet surface ϵ 1,2 dimensionless parameters, introduced for the first time (Gol'dshtein, Goldfarb, Shreiber, & Zinoviev, 1996) and describe the relations between the thermo physical properties of the gas and liquid phases

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“…The investigation of the autoignition process has been carried out by many authors, see for instance [3][4][5][6][7][8][9][10][11][12] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Critical phenomena in a model of fuel's heating in a porous medium

Shchepakina¹

2015

Collection of Selected Papers of the I International Conference on Information Technology and Nanotechnology

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Abstract. The autoignition of flammable liquid in an inert porous medium are studied. In this paper we concentrated on the critical case which is concerned with the phenomenon of delayed loss of stability in the dynamical model. The realizability conditions for the critical regime are obtained. It is shown that critical regime is modelled by a canard − a trajectory of slow-fast system, which first move near the stable part of the slow invariant manifold, then move near the unstable part of it.Keywords: ignition, critical phenomenon, canard, invariant manifold, delayed loss of stability.Citation: Shchepakina E.A. Critical phenomena in a model of fuel's heating in a porous medium.

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Critical Conditions for Thermal Explosion with Reactant Consumption

Cited by 38 publications

References 4 publications

Study of Oscillatory Processes in the One Model of Electrochemical Reactor

Study of Oscillatory Processes in the One Model of Electrochemical Reactor

Mathematical Modelling of Spray Combustion-Numerical and Analytical Analysis with application to Engineering Science

Critical phenomena in a model of fuel's heating in a porous medium

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