Joel Daou

Influence of Conductive Heat-Losses on the Propagation of Premixed Flames in Channels

We study the propagation of premixed flames in two-dimensional channels accounting for heat-losses by conduction to the channel’s walls and a prescribed Poiseuille flow. A diffusive-thermal model is used and the calculations reported are based on Arrhenius-type chemistry. Attention is focused on the influence of the magnitude of heat losses, the channel width, and the mean flow velocity. Special attention is devoted to the determination of the global burning rate and to extinction conditions. Depending on the channel width we discuss two possible modes of extinction: total flame extinction brought about in narrow channels by excessive losses, and partial flame extinction near the walls of wider channels. Our predictions of the quenching distance, namely the smallest channel’s width that permits flame propagation, and the dead space in the case of partial extinction are in agreement with experimentally reported values. The sensitivity of the flame to an imposed flow, being directed either towards the fresh mixture or towards the burned gas, is examined with some details.

The role of unequal diffusivities in ignition and extinction fronts in strained mixing layers

We have studied flame propagation in a strained mixing layer formed between a fuel stream and an oxidizer stream, which can have different initial temperatures. Allowing the Lewis numbers to deviate from unity, the problem is first formulated within the framework of a thermo-diffusive model and a single irreversible reaction. A compact formulation is then derived in the limit of large activation energy, and solved analytically for high values of the Damkohler number. Simple expressions describing the flame shape and its propagation velocity are obtained. In particular, it is found that the Lewis numbers affect the propagation of the triple flame in a way similar to that obtained in the studies of stretched premixed flames. For example, the flame curvature determined by the transverse enthalpy gradients in the frozen mixing layer leads to flame-front velocities which grow with decreasing values of the Lewis numbers. The analytical results are complemented by a numerical study which focuses on preferentialdiffusion effects on triple flames. The results cover, for different values of the fuel Lewis number, a wide range of values of the Damkohler number leading to propagation speeds which vary from positive values down to large negative values.

Flame propagation in Poiseuille flow under adiabatic conditions

Abstract We describe flame propagation in a channel subject to a Poiseuille flow, within the thermo-diffusive approximation and an adiabatic context. The two-dimensional flame fronts addressed may be either assisted or opposed by the flow. The problem is characterized by two parameters, the intensity of the flow u 0 and the spatial scale ϵ. The total burning rate and the propagation speed are determined in terms of u 0 and ϵ and different distinguished regimes are described. From the results, simple criteria for flame flashback in channels are identified. Conclusions concerning the long-term evolution of an ignition kernel in the present flow are also drawn. The results may also be useful in interpreting similar features encountered in more complicated flow situations. For example, the quadratic dependence of the burning rate on u 0 for weak flow intensities, and linear dependence for larger u 0 , is similar to that of the turbulent flame speed when the latter is considered as a function of the velocity fluctuations or turbulence intensity.

Ignition and extinction fronts in counterflowing premixed reactive gases

We describe two-dimensional steady propagating flame fronts in the stagnation mixing layer between two opposed streams of the same reactive mixture, the propagation taking place in the direction perpendicular to the plane of strain. The front, which is curved by the nonuniform flow field, separates a chemically frozen region from a region with a twin-flame configuration. The front velocity is calculated in terms of the Lewis number, LeF, and the Damkohler number, Da. Da, equal to the inverse of the Karlovitz number, is defined as the ratio of the strain time to the transit time through the planar unstrained flame. For the cases corresponding to large Da, difficult to tackle numerically, analytical expressions are given, characterizing the flame shape, and the variation of the burning rate along the flame front from the nose up to the planar trailing branches. For moderately large and low values of Da, the study is carried out numerically, yielding, in particular, the propagation velocity in terms of Da, for different values of LeF. Different combustion regimes are thus described including flames propagating toward the unburnt mixture, or ignition fronts, standing flames and retreating flames, or extinction fronts. We also describe stationary cylindrical flames of finite-extent, or 2D burning spots. In particular, a critical Lewis number is found, below which negative propagation speeds do not exist while the 2D burning spots mentioned may be encountered. Typically, these exist only for sufficiently small LeF if the Da is within a range (Damin, Damax), depending on LeF. For Da , Damin, the 2D spots are quenched, whereas as Da is increased, they grow in size, tending to give birth to propagating (ignition) fronts; Damax is indeed found to be the smallest Da allowing for ignition fronts. We notice that the range of existence of the 2D spots, for a given LeF, can overlap with that of retreating (extinction) fronts, and possibly with that of 3D spots, or flame balls, in this flow. However, the 3D case is not addressed in this work.

Supercritical burning of liquid oxygen (LOX) droplet with detailed chemistry

Abstract A numerical study of the supercritical combustion of a liquid oxygen (LOX) droplet in a stagnant environment of hot hydrogen is carried out with a detailed chemistry model. Special attention is devoted to ignition process and diffusion flame structure. Ignition consists typically of the propagation of a premixed flame which is initiated in the H 2 -rich hot side. Propagation takes place in a nonhomogeneous hot environment (say 1500 K) with a considerable velocity (typically 50 ms −1 ). Despite the high temperature of the ambiance, the medium ahead of the flame can be considered as frozen during the transit time. In addition, it is found that droplets with diameter less than 1 μm vaporize before burning. A quasi-steady-like diffusion flame is then established. In this regime we observe that the D 2 law is approximately valid. In contrast to the case of a single irreversible reaction, a full chemistry model leads to a very thick flame where chemical consumption and production cover a surrounding zone about four times the instantaneous droplet radius. Reversibility of the reactions plays a determinant role in the flame structure by inducing a large near-equilibrium zone which is separated from a frozen region by a thin nonequilibrium zone. The length scale of the latter region is found to behave as the square root of the instantaneous droplet radius and a detailed analysis shows that just two elementary reactions are involved in this zone. Furthermore, the influence of several parameters is considered; temperature and pressure in the combustion chamber have a weak influence on the burning time. Influence of initial droplet radius confirms that droplet combustion is a diffusion controlled process. Chamber composition is also considered. Finally, it is shown that a precise description of the transport properties in the dense phase is not required.

Effect of volumetric heat loss on triple-flame propagation

We present a numerical study of the effect of volumetric heat loss on the propagation of triple flames in the strained mixing layer formed between two opposed streams of fuel and air. The propagation speed of the triple flame is computed for a wide range of values of two non-dimensional parameters: a normalized flame thickness e, proportional to the square root of the strain rate, and a heat-loss parameter j. It is shown that, for relatively small values of j, the propagation speed U is decreased by heat loss, and its dependence on e is similar to the adiabatic case, known in the literature; in particular, a monotonic decrease in the speed from positive to negative values is observed as e is increased. However, for j larger than a critical value, this monotonic behavior is lost. It is shown that the more complex behavior obtained is mainly associated with the fact that, in the presence of heat loss, the trailing planar diffusion flame is extinguished both for sufficiently large and sufficiently small values of the strain rate. Moreover, for sufficiently small values of e, the dependence of U on j is similar to that of the non-adiabatic planar premixed flame, with total extinction occurring for a finite positive value of U. On the other hand, for larger values of e, negative speeds, corresponding to extinction fronts, appear before total extinction is brought about by an increase in j. A summary of the main results is provided by delimiting the different combustion regimes observed in the j–e plane.

High pressure vaporization of LOX droplet crossing the critical conditions

Abstract Vaporization of liquid O2 droplet in quiescent high-temperature and high-pressure H2 gas is numerically investigated. Classical thermodynamic modeling of high pressure mixtures allows us to study the transition from subcritical to supercritical vaporization regime. It is observed that subcritical vaporization can be obtained up to pressures several times the oxygen critical pressure. Respective domain of both regimes is determined vs temperature and pressure. Border region corresponds to minimum value of droplet lifetime. This results from two cooperative phenomena: transient effect and thermodynamic property of mixtures. Sensitivity analysis additionally shows that state of art in dense fluid transport modeling yields results that should be considered accurate only as far as orders of magnitude are concerned.

The effect of heat loss on flame edges in a non-premixed counterflow within a thermo-diffusive model

We present an asymptotic study of the effect of volumetric heat loss on the propagation of triple flames in a counterflow configuration at constant density. Analytical results for the speed, the local burning rate, the shape and the extent of the flame front are derived in the asymptotic limits of weak strain rates and large activation energies and for Lewis numbers that are near unity. The results account for the combined effects of strain, heat loss, composition gradients and non-unit Lewis numbers and provide Markstein-type relationships between the local burning speed (or local flame temperature) and the local flame stretch and can be useful for future investigations in deriving such relationships in non-homogeneous non-adiabatic mixtures under more general flow conditions. The analytical predictions are complemented by and compared with numerical predictions focusing on the low strain regime and allowing for non-unit Lewis numbers. The numerical findings are found to be in good qualitative agreement with the asymptotics, both in predicting extinction (e.g. as the burning leading-front of a triple flame becomes vanishingly small) and in the dependence of the propagation speed on heat loss, strain and the Lewis numbers. Quantitative discrepancies are discussed and are found to be mainly attributable to the infinite activation energy assumption used in the asymptotics.

TRIPLE FLAMES IN MIXING LAYERS WITH NONUNITY LEWIS NUMBERS

The present paper is devoted to the study of the effects of nonunity Lewis numbers on triple-flame propagation in nonuniform mixtures. For definiteness, the case of a strained reactive mixing layer is considered. The fuel and oxidizer that are fed to the mixing layer are allowed to have different initial temperatures. Specifically, we examine how the triple flames encountered in this context are influenced by (a) the transverse gradients in the temperature and composition of the fresh reactive mixture and (b) by differential-diffusion effects. The analysis is carried for a single irreversible reaction with a large activation energy and using the thermo-diffusive model. Analytical expressions describing the flame shape, the local burning speed, and the propagation velocity of the triple flame are obtained. In particular, it is found that the Lewis numbers affect the propagation of the triple flame in a way similar to that obtained in the studies of stretched premixed flames. For example, the flame curvature determined by the transverse gradients in the frozen mixing layer leads to flame-front velocities that grow with decreasing values of the Lewis numbers.

Effects of differential diffusion on thin and thick flames propagating in channels

Flame propagation in channels and cracks is a problem of considerable interest with applications in many combustion devices and in fire hazard scenarios. In this paper, the propagation of premixed flames in two-dimensional channels of variable width with a prescribed Poiseuille flow is discussed. The main objective is to assess the effects of differential diffusion on the burning process. For both thick (narrow channels) and thin (wide channels) flames, explicit asymptotic results are obtained for the burning rate and flame shape. These are complemented with numerical calculations spanning the remaining range of moderate flame thicknesses. The results show that unlike thin flames, known to be affected by the effective Lewis number of the mixture, in narrow channels Lewis number effects are negligible. Furthermore, in wide channels, not only does the burning rate strongly depend on the Lewis number, but flame tipopening or dead-space near thewall may result in mixtures with a Lewis number sufficiently less than one.