Faisal Al-Malki

Triple-flame propagation in a parallel flow: an analytical study

We present an analytical study of triple-flame propagation in a two-dimensional mixing layer against a parallel flow. The problem is formulated within a constant density thermo-diffusive model, and solved analytically in the asymptotic limit of large activation energy of the chemical reaction for flames thin compared with their typical radius of curvature. Explicit expressions are obtained in this limit, describing the influence of the flow on the triple-flame. The results are expected to be applicable when the ratio between the flow-scale and the flame-front radius of curvature (which is mainly dictated by concentration gradients) is of order unity, or larger. When this ratio is large, as in the illustrative case of a Poiseuille flow in a porous channel considered here, the flow is found to negligibly affect the flame structure except for a change in its speed by an amount which depends on the stoichiometric conditions of the mixture. On the other hand, when this ratio is of order unity, the flow is able to significantly wrinkle the flame-front, modify its propagation speed, and shift its leading edge away from the stoichiometric line. The latter situation is investigated in the illustrative case of spatially harmonic flows. The results presented describe, in particular, how the leading-edge of the flame-front can be determined in terms of the flow amplitude A which is critical in determining the flame speed. The latter is found to depend linearly on A in the first approximation with a correction proportional to the flame thickness multiplied by , for |A| sufficiently large. The effect of varying the flow-scale on flame propagation in this context is also described, with explicit formulae provided, and interesting behaviours, such as non-monotonic dependence on the scale, identified.

Generalized flame balls

We consider generalized flame balls which correspond to stationary spherical flames with a flow of hot inert gas, either a source or a sink, at the origin. Depending on the flow, these flames can have positive, zero, or negative burning speeds, with zero speeds characterizing the Zeldovich flame balls. A full analytical description of these structures and their stability to radial perturbations is provided, using a large activation energy asymptotic approach and a thermo-diffusive approximation. The results are also complemented by a numerical study. The number and stability of the generalized flame balls are identified in various regions of the l-M-h 0 space, where l is the (reduced) Lewis number, and M and h 0 the flow rate and its enthalpy at the origin, respectively. It is typically found that, when the flow is a source, there is a maximum value of the flow rate M ax depending on l and h 0, above which no stationary solutions exist, and below which there are two solutions characterizing a small stable flame ball and a large unstable flame ball; the implications of these results to the problem of ignition by a hot inert gas stream are discussed. When the flow is a sink, however, there is typically a single unstable solution, except for sufficiently large values of the Lewis number and large negative values of M, where three flame balls exist, the medium one being stable. Finally, the relation between the flame speed, positive or negative, and the flame curvature, small or large, is discussed.

Numerical simulation of the influence of partial premixing on the propagation of partially premixed flames

This paper examines the influence of a partial premixing between the reactants prior to the reaction in a mixing layer on the structure and propagation of triple flames formed in this configuration. The problem has been mathematically formulated in the framework of the thermo-diffusive model under a single-step irreversible chemical reaction. A computational modeling and numerical simulations based on finite elements were then employed to solve the governing equations. The study has shown that the flame structure and characteristics such as its speed and maximum temperature were significantly modified in the presence of premixing. The triple flame structure were found to exhibit several changes such as the shift of the leading edge toward the combustion mixture side, the weakening of the upper premixed branch, and the increase in the flame area. It has been predicted that the premixing can substantially enhance the reactivity of the combustion mixture, but on the other hand it tends to shift the flame to the boundary which may destroy the combustion chamber.

Asymptotic analysis to the effect of temperature gradient on the propagation of triple flames

We study asymptotically in this paper the influence of the temperature gradient across the mixing layer on the propagation triple flames formed inside a porous wall channel. The study begins by formulating the problem mathematically using the thermo-diffusive model and then presents a thorough asymptotic analysis of the problem in the limit of large activation energy and thin flames. Analytical formulae for the local burning speed, the flame shape and the propagation speed in terms of the temperature gradient parameter have been derived. It was shown that varying the feed temperatures can significantly enhance the burning of the reactants up to a critical threshold, beyond which no solutions can be obtained. In addition, the study showed that increasing the temperature at the boundaries will modify the usual triple structure of the flame by inverting the upper premixed branch and extending it to the boundary, which may have great implications on the safety of the adopted combustion chambers.

Triple-flame propagation against a Poiseuille flow in a channel with porous walls

We present an essentially numerical study of triple-flame propagation in a non-strained two-dimensional mixing layer against a Poiseuille flow, within a thermo-diffusive model. The aim of the study is twofold. First, to examine the recent analytical findings derived in the asymptotic limit of infinite Zeldovich number β for flame fronts thin compared with their typical radius of curvature and to extend these to finite-values of β. Second, to gain insight into the influence of the flow on the flame in situations where the flame in not necessarily thin, as assumed analytically. The study has focused on the effect of two main non-dimensional parameters on flame propagation, namely the flow amplitude A and the flame-front thickness ε. For moderate values of A, the flow is found to have a negligible effect on the structure of the flame, while modifying its speed by an amount proportional to A, in agreement with the asymptotic findings. Two new qualitative behaviours are found however. The first is obtained for sufficiently large values of A where the flow is shown to modify the flame structure significantly for small values of ε; more precisely, the concavity of the triple-flame front is found to turn towards the unburnt gas for A larger than a critical value. This inversion of the front curvature, which cannot be captured by the infinitely-large β asymptotic study, is found to be intimately linked to the finite values of β, which are necessarily found in any realistic model or computational study. The second new behaviour, which is also obtained for small ε, is the existence of termination-points on the flame front, or flame-tips. These termination-points are shown to exist for ε ≪ 1 only if A takes on positive values of order unity or larger; in particular they are absent for thin triple-flames without the presence of a non-uniform flow field. Furthermore, several additional novel contributions are made in the present context of triple-flame interaction with a non-uniform parallel flow. These include a fairly complete description of the flame propagation regimes for a wide range of variations in A and ε. In particular, it is found that larger values of A promote combustion by increasing the ε-range of existence of ignition fronts, while a decrease in the value of A towards zero or negative values increases the ε-range of existence of extinction fronts.

Influence of transverse temperature gradient on the propagation of triple flames in porous channels

Abstract We present in this paper a numerical simulation to the problem of triple flame propagation in a porous-walls channel in the presence of a temperature gradient across the channel. The problem has been formulated using the thermo-diffusive approximation and then solved numerically using finite elements method. The study showed that temperature gradient plays a crucial role on the existence and propagation of triple flames. More precisely, the effect of temperature gradient on the flame propagation was found to: (i) cause the flame to exist only for a limited range of values of the temperature gradient parameter, (ii) establish multiplicity of solutions each of them characterizes unique combustion regimes, (iii) modifies the flame shape from the usual triple flame shape when the temperature gradient is large, and finally (iv) enhance the reactivity of the underlying mixture, but on the other hand will have serious implications on the safety of the combustion chamber.