Non-adiabatic combustion waves for general Lewis numbers: wave speed and extinction conditions

McIntosh, Andy C.; Weber, R. O.; Mercer, G. N.

doi:10.1017/s1446181100013638

Cited by 16 publications

(14 citation statements)

References 12 publications

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“…which agrees with the results of [7,8] in the limit of large β. Note that a similar expression for the front speed was first found in [6].…”

Section: Travelling Wave Solutionsupporting

confidence: 93%

“…Derivation of the speed estimation is given in section 3 and agrees with the results of [5,7,8]. We have compared the numerical results with the asymptotic estimation of the speed of the combustion front.…”

Section: Discussionsupporting

confidence: 69%

“…The results of [15] agree with the predictions of the MAE analysis of [5]. Previously, this problem was solved by direct integration of the governing PDE [7,8]. Previously, this problem was solved by direct integration of the governing PDE [7,8].…”

Section: Introductionsupporting

confidence: 74%

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Evans Function Stability of Combustion Waves

Mercer¹,

Sidhu²,

Weber³

et al. 2003

SIAM J. Appl. Math.

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In this paper we investigate the linear stability and properties, such as speed, of the planar travelling combustion front. The speed of the front is estimated both analytically, using the matched asymptotic expansion, and numerically, by means of the shooting and relaxation methods. The Evans function approach extended by the compound matrix method is employed to numerically solve the linear stability problem for the travelling wave solution.stability of the travelling wave and therefore allows us to continue the solution branch over a broader parameter range.As we vary the parameters of the problem, a steady propagating planar front can lose stability, giving rise to either pulsating or cellular flames [5,9]. Analytical investigation of the stability using the MAE leads to the so-called closure problem. In contrast to steady travelling waves, in this case the leading order equations depend on first order corrections, first order equations include second order terms of the asymptotic expansion, etc. In order to find the solution to the leading order problem, an infinite number of equations have to be investigated. One of the ways of overcoming this obstacle is just to truncate the expansion [1,2,3,4,5,9]. This yields a closed problem with a replacement of the Arrhenius reaction rate by a delta-function source depending on the temperature at the reaction front. The truncated model has been used extensively for the stability analysis of combustion waves [1,2,3,4]. However, the model with the delta-function source suffers from inconsistencies, as was noted in [5,9]. The inverse of the small parameter of the expansion appears explicitly in the exponential terms describing the strength of the source. In other words, temperature variations behind the front are considered to be small in the exponential terms and of leading order elsewhere.An asymptotically consistent approach was proposed in [5] for the system with the Lewis number of the order of unity. In this case the enthalpy does not change at the leading order. A closed problem was derived for the leading order temperature and the first order enthalpy. However, until recently [9], there has not been a consistent approach that treats the model with arbitrary Lewis number.In [9] a generalization of the MAE method was introduced. The coefficients in the expansions are allowed to depend on the expansion parameter. This enables the correct scaling of the temperature variations ahead of and behind the reaction zone; namely, a restriction is imposed connecting the leading order temperature in the preheat zone and the first two terms of the asymptotic expansion in the product zone. The constraint reflects the fact that small temperature variations behind the front change the leading order terms in the preheat zone. The resulting model includes equations for the leading order variables ahead of the reaction zone and for the first order temperature variations in the product zone, together with matching and boundary conditions. There is no restriction on the range of the Le...

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“…which agrees with the results of [7,8] in the limit of large β. Note that a similar expression for the front speed was first found in [6].…”

Section: Travelling Wave Solutionsupporting

confidence: 93%

Section: Discussionsupporting

confidence: 69%

See 1 more Smart Citation

Evans Function Stability of Combustion Waves

Mercer¹,

Sidhu²,

Weber³

et al. 2003

SIAM J. Appl. Math.

Self Cite

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“…The work reported here seeks to explore more fully the phenomenology of ignition and front initiation, structure and propagation in AN, regarded as a competitively reacting material, when a parallel endothermic process is also present. In this work, we have added a specific heat loss owing to water evaporation, and the results have some similarity to earlier research for combustion waves with heat loss [16,17].…”

Section: Modelling Approach and Methodologysupporting

confidence: 60%

“…which, using (4.15), may be written as 17) equivalent, when the integrals are appropriately expressed for this special case, to the more general form in equation (4.10). Overall, it is clear that if 1 − X is everywhere very small, the fraction of A going down the exothermic channel, and therefore the value of T b , are both maximized for higher values of T sat , as occurs for higher pressures.…”

Section: Theoretical Considerationsmentioning

confidence: 99%

Initiation and propagation of combustion waves with competitive reactions and water evaporation

2013

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We use a one-dimensional model to present numerical and analytical results on the propagation of combustion waves, driven by competing exothermic and endothermic chemical reactions in parallel with water evaporation. The research was motivated by the phenomenology of emulsion explosives comprising a mixture of fuel and an ammonium nitrate (AN)-water solution. An extensive programme of computational modelling has covered a range of important physical influences, particularly the water fraction and the ambient pressure, on which the endothermic effect of evaporation is critically dependent. A substantial, and not immediately obvious, influence of the evaporation, through its effect on the temperature, is on the fraction of the AN consumed, respectively, by the competing exo-and endothermic reactions, which are controlled by differing, temperature-sensitive kinetics. Self-sustaining travelling combustion waves are initiated for a wide range of parameter values. They are usually oscillatory, regular for small water content and become highly irregular, sometimes causing extinction for larger water content. The numerics are complemented by a brief theoretical analysis, which throws light on the complex and subtle interplay of the two chemical reactions and the evaporation, expressed in the form of a highly convoluted integral over the whole time and space extent of the process.

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