Quenching and propagation of combustion fronts in porous media

Gordon, Peter V.

doi:10.4310/cms.2006.v4.n2.a9

Cited by 9 publications

(11 citation statements)

References 11 publications

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“…In the new variables S, R and Y and after rescaling spacial coordinates ∆ → (1 − λ ε )∆, the system (2.1) takes the form [21] …”

Section: Reductions Of the Modelmentioning

confidence: 99%

Recent Mathematical Results on Combustion in Hydraulically Resistant Porous Media

Gordon

2007

Math. Model. Nat. Phenom.

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Abstract. Gaseous detonation is a phenomenon with very complicated dynamics which has been studied extensively by physicists, mathematicians and engineers for many years. Despite many efforts the problem is far from a complete resolution. Recently the theory of subsonic detonation that occurs in highly resistant porous media was proposed in [4]. This theory provides a model which is realistic, rich and suitable for a mathematical study. In particular, the model is capable of describing the transition from a slowly propagating deflagration wave to the fast detonation wave. This phenomena is known as a deflagration to detonation transition and is one of the most challenging issues in combustion theory. In this paper we will present some recent mathematical results concerning initiation of reaction in porous media, existence and uniqueness of traveling fronts, quenching and propagation.

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“…In the new variables S, R and Y and after rescaling spacial coordinates ∆ → (1 − λ ε )∆, the system (2.1) takes the form [21] …”

Section: Reductions Of the Modelmentioning

confidence: 99%

Recent Mathematical Results on Combustion in Hydraulically Resistant Porous Media

Gordon

2007

Math. Model. Nat. Phenom.

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Section: Introductionmentioning

confidence: 99%

“…The study of propagation of a flame is of relevance in different theoretical and applied scopes, from life sciences to physics. One of the most discussed model to describe the flame propagation (see (Gordon, 2006) and (Gordon, 2007) for some mathematical analyses about solutions) is given as follows:where T¯ represents a normalized temperature, Y¯ shows the concentration of defective impulse (related with the deficiency of reactants), P¯ denotes the flame pressure, normalΣ(trueT¯) indicates the reaction rate in normalized form, γ 1 > 1 refers to the ratio of specific heat constants, Le denotes the Lewis number and ϵ 1 is the ratio between the specific heat and the thermal diffusivity. The partially linearized equation (1.1) provides the conservation of energy, equation (1.2) indicates the continuity and state equations while the evolution of the reactants, in terms of the defective impulse, is given in (1.3).…”

Section: Introductionmentioning

confidence: 99%

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Analysis and profiles of solution for a highly nonlinear model of pressure driven flame propagation in nonhomogeneous medium

Rahman

Palencia

2023

MMMS

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PurposeThis article aims to study a model of flame propagation in a nonhomogeneous medium with a p-Laplacian operator. The intention with such operator is to model the effects of slow and fast diffusion, that can appear in a nonhomogeneous media, depending on the pressure driven conditions. In addition, the authors introduce a general form in the reaction term, that introduces the flame chemical kinetics.Design/methodology/approachTo introduce the governing equations, the authors depart from previously reported models in flame propagation, but the authors consider a new modeling approach based on a p-Laplacian operator.FindingsThe authors provide evidences of regularity and uniqueness of solutions. Afterward, the authors introduce profiles of stationary solutions based on the definition of a Hamiltonian for the newly discussed model. Eventually, the authors obtain exponential profiles solutions with the help of a scaling, that transforms the model into a nonlinear Hamilton–Jacobi equation.Originality/valueThe new model has not been previously reported in the literature. The authors consider that the mathematical properties of a p-laplacian (in particular the property known as finite propagation) is of inherent interest to model pressure drive flames with slow or fast diffusion. Indeed, the authors’ approach has the value of providing an operator that can fit better to model flame propagation. In addition, the authors introduce a general form of chemical kinetics, to make the authors’ model further general.

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“…We start with a very convenient reformulation of the problem. Following [5], we introduce new functions, u and v, related to P and T by the following linear transformation, In terms of new functions, after rescaling x → (1 − µ) 1/2 x, we obtain the following system which is equivalent to (1.1),…”

Section: Introductionmentioning

confidence: 99%

KPP type flame fronts in porous media

Ghazaryan

Gordon

2008

Nonlinearity

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In this paper we study the model of pressure-driven flames in porous media proposed by Brailovsky et al (1997 Combust. Sci. Technol. 124 145-65). We show that, under the assumption of first order reaction with linear reaction kinetics (quadratic nonlinearity), the model admits a family of positive travelling wave solutions. Moreover, under the same assumption, we prove that propagation of disturbances in the system is fully determined by the rate of decay of the initial data at infinity. We also give an upper bound of the burning rate in the case of arbitrary chemical kinetics bounded by linear function.

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Quenching and propagation of combustion fronts in porous media

Cited by 9 publications

References 11 publications

Recent Mathematical Results on Combustion in Hydraulically Resistant Porous Media

Recent Mathematical Results on Combustion in Hydraulically Resistant Porous Media

Analysis and profiles of solution for a highly nonlinear model of pressure driven flame propagation in nonhomogeneous medium

KPP type flame fronts in porous media

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