Theory of Gaseous Combustion

Clavin, Paul; Liñán, A.

doi:10.1007/978-1-4684-8568-4_17

Cited by 28 publications

(9 citation statements)

References 45 publications

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“…A laminar premixed flame described by the classical Zel'dovich-Frank-Kamenetskii theory (Zel'dovich & Frank-Kamenetskii 1938;Zel'dovich et al 1985) is an example of such a pushed wave (van Saarloos 2003). Transition from pulled flames whose speed is controlled by processes localized to its leading edge to pushed flames was earlier explored by Aldushin, Zel'dovich & Khudyaev (1979), Zel'dovich (1980, Clavin & Liñán (1984), Sabelnikov & Lipatnikov (2015) and Sabelnikov et al (2016). Such a transition can also occur in turbulent flows.…”

Section: Leading Point Conceptmentioning

confidence: 99%

Influence of molecular transport on burning rate and conditioned species concentrations in highly turbulent premixed flames

et al. 2021

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Apparent inconsistency between (i) experimental and direct numerical simulation (DNS) data that show the significant influence of differential diffusion on the turbulent burning rate and (ii) recent complex-chemistry DNS data that indicate mitigation of the influence of differential diffusion on conditioned profiles of various local flame characteristics at high Karlovitz numbers, is explored by analysing new DNS data obtained from lean hydrogen–air turbulent flames. Both aforementioned effects are observed by analysing the same DNS data provided that the conditioned profiles are sampled from the entire computational domain. On the contrary, the conditioned profiles sampled at the leading edge of the mean flame brush do not indicate the mitigation, but are significantly affected by differential diffusion phenomena, e.g. because reaction zones are highly curved at the leading edge. This observation is consistent with a significant increase in the computed turbulent burning velocity with decreasing Lewis number, with all the results considered jointly being consonant with the leading point concept of premixed turbulent combustion. The concept is further supported by comparing DNS data obtained by allowing for preferential diffusion solely for a single species, either atomic or molecular hydrogen.

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Section: Leading Point Conceptmentioning

confidence: 99%

Influence of molecular transport on burning rate and conditioned species concentrations in highly turbulent premixed flames

et al. 2021

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“…v(x,t) == 0, the diffusion coefficient K(t) in Equation 12 is constant, K(t) == K. In this case, the reaction-diffusion equation in (10) admits travelling wave solutions representing planar flame fronts moving at the laminar flame speed SL' The solutions T(x, t) are of the form is a straightforward application of phase plane analysis for ordinary differential equations. Here we briefly describe the results of this analysis but omit the details, and refer the interested reader to Lirian and Clavin (1983) for further algebraic details. Table I summarizes the solution of the laminar flame speed problem in (16) with piecewise linear chemistry given by Equation 3, where -co < A < co and 0 < B < ca.…”

Section: The Laminar Flame Problemmentioning

confidence: 99%

Examples and Counterexamples for Huygens Principle in Premixed Combustion

Embid

Majda

Souganidis

1996

Combustion Science and Technology

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A model involving a scalar reaction-diffusion equation with piecewise linear reaction rates and linear incompressible flow fields is developed to study the validity of Huygens principle at large scales in premixed combustion. This model includes both dependence on the reaction term and the velocity field. For plane fronts aligned with the direction of expansive strain and K PP regime, theory predicts strong violation of Huygens principle chemistry, and this is shown to persist in dramatic fashion throughout the ZFK regime. even at high activation energies. If the front is aligned with a direction of compressive strain, Huygens principle yields an excellent approximation with ZFK chemistry. For a more general rotating strain flow with ZFK chemistry, the Huygens principle significantly underpredicts the large scale flame propagation velocity in consistent fashion with the example involving expansive strain. For backward reactions or at the boundary of the ZFK regime, Huygens principle is always excellent for any large scale flow geometry.

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“…The temperature of the burned region and the propagation speed of the conversion front are expressed by the following formula [21,22]:…”

Section: Steady State As a Basic Solutionmentioning

confidence: 99%

Cellular structures in solid fuel combustion

Peters

2005

Flow Turbulence Combust

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The objective of this contribution is to investigate whether the mechanism of the thermal diffusion instability in gaseous flames causing cellular flame structures also occurs during the combustion of porous solid fuel. Based on conservation for mass and energy, the relevant set of differential equations was derived. Assuming thermal equilibrium between fuel and oxidiser, a global energy equation was valid for both solid and gaseous phase. The resulting set of differential equations was discretised by the Collocation method to arrive at a system of algebraic equations. In order to investigate into cellular flame structures, an infinitesimal disturbance was superimposed onto the plane conversion front. Carrying out a linear instability analysis, yielded eigenvalues dependent on the wave number of the disturbance. A critical wave number exists below which the real part of the eigenvalues is positive, thus, indicating a regime of instability. Within this region, eigenvalues with a not-vanishing imaginary part of the eigen value existed causing cellular flame structures. However, the growth rate of disturbances was found to be small, which may explain the difficulty to investigate this phenomena experimentally.

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Theory of Gaseous Combustion

Cited by 28 publications

References 45 publications

Influence of molecular transport on burning rate and conditioned species concentrations in highly turbulent premixed flames

Influence of molecular transport on burning rate and conditioned species concentrations in highly turbulent premixed flames

Examples and Counterexamples for Huygens Principle in Premixed Combustion

Cellular structures in solid fuel combustion

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