Boundary-value solutions of the one-dimensional laminar flame propagation equations

Wilde, Kenneth A.

doi:10.1016/0010-2180(72)90031-4

Cited by 54 publications

(16 citation statements)

References 22 publications

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“…Despite this considerable sirnfication, the analytic solution of the problem hen finite rate chemistry is included) still remains fairly intractable problem. Because of the alytic difficulties most of the results that have pea red in the literature have been based on a riety of numerical methods (see, for example, xon- Lewis, 1967;Spalding and Stephenson, 7[;Wilde, 1972;Bledjian, 1973;Margolis, 1978). Notwithstanding the abundance of numerical rls available for solving this relatively simple problem, most of the computations have failed to count for all the physical processes occurring in 83 the flames.…”

Section: N the Prediction Of Thermal Diffusion Effects In Laminar Ne-mentioning

confidence: 98%

n the Prediction of Thermal Diffusion Effects in Laminar ne-Dimensional Flames

Greenberg

1980

Combustion Science and Technology

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Section: N the Prediction Of Thermal Diffusion Effects In Laminar Ne-mentioning

confidence: 98%

n the Prediction of Thermal Diffusion Effects in Laminar ne-Dimensional Flames

Greenberg

1980

Combustion Science and Technology

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“…This stability difficulty has been known qualitatively for some time and is usually mentioned in the present context in conjunction with the problem of stiffness, or overstability (Hirschfelder et al, 1953b;Wilde, 1972). In normal circumstances, a shooting procedure would appear to be indicated.…”

Section: Nonlinear Asymptotic (\T-oo) Analysismentioning

confidence: 83%

“…In this connection, it is worthwhile to mention the recent analyses of Kapila and Matkowsky (1979) and Matalon and Ludford (1979), which have shown that a generalization of the large activation energy approach used in Sec. Wilde, 1972). However, we note that all but one of these nontrivial solutions correspond to partially burned flames, a physical situation that is not realizable for the one-step, semi-infinite premixed flame geometry analyzed in Sec.…”

Section: Introductionmentioning

confidence: 88%

Theoretical and Computational Aspects of Premixed Laminar Flames

1981

Combustion in Reactive Systems

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In this paper two aspects of burner-stabilized premixed laminar flames are considered: the effects of multiple chemical time scales on the nontrivial steady-state solution and the existence of a bifurcation phenomena which, under certain readily achievable conditions, leads to a time-oscillating solution. To study the first problem, attention is directed at the global two-step reaction mechanism v r R-*^tI 9 j^/-« p P. The general solution properties are characterized and explicit asymptotic results are obtained which show that the governing differential system admits both spatially growing and decaying solutions whose relative growth and decay rates are directly related to the disparity in reaction rates. This spatial instability causes extreme difficulties for steady-state numerical methods of the shooting type, and it is shown how the various time-dependent approaches circumvent this difficulty. The success of this latter technique rests on the stability of the nontrivial steady-state solution, which is studied by considering the one-step mechanism VJ-F+VQ®-* v p P. Utilizing large activation energy asymptotics, a linear stability analysis yields the neutral stability boundary in Lewis number/activation energy space as a function of the incoming flow velocity (or equivalently, the burned temperature). The major result is that although a steady-state adiabatic flame is likely to be stable for typical parameter values, a value of the incoming flow velocity sufficiently less than the adiabatic flame speed is destabilizing to the extent that the unstable region becomes feasible for many flames. Consequently, if all other parameters are fixed, there exists for such flames a critical value of the incoming flow velocity at which the time-asymptotic solution to the timedependent problem bifurcates from the unique nontrivial steadystate solution. The existence of a time-oscillating solution for sufficiently small incoming flow velocities is illustrated by realistic calculations of an H 2 /O 2 premixed flame utilizing the timedependent numerical technique.

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“…Most of these methods use a nonstationary approach (see, for instance, [6,8,9,16,23,24,32,36,37,39,45]). A more recent approach is to solve directly the boundary value problem ( [35], [46]). In the GAMM workshop (1981) on "Numerical Methods in Laminar Flame Propagation", some of these methods have been compared with the same chemical mechanism describing the hydrogen-air flame (see Warnatz [42]).…”

Section: O Introductionmentioning

confidence: 99%