Amable Liñán

Unsteady Effects in Droplet Evaporation and Combustion

Abstract An asymptotic analysis is presented for the problem of droplet vaporization in a stagnant atmosphere taking into account the unsteady effects in the gas phase. The ratio of the densities of the ambient gas and of the liquid is considered as a small parameter. The results of the classical quasi-steady theories are recovered in the first approximation, and corrections due to unsteady effects are obtained for the vaporization rate and for the droplet lifetime, which are found to be of the order of the square root of the density ratio The analysis is extended to cover the cases when the vaporization rate is enhanced by a fast irreversible reaction between the fuel vapor and an oxidizer in the ambient gas. While the quasi-steady theories predict the vaporization rate with relative errors of the order of the square root of the density ratio, the ratio of flame radius to droplet radius is found in many practical cases to vary significantly with time in agreement with experimental results.

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.

Flames with chain-branching/chain-breaking kinetics

A steady plane flame subject to the chain-branching/chain-breaking kinetics \[ A + X \to 2X,\quad 2X + M \to 2P + M \] is considered for a certain distinguished limit of parameter values corresponding to fast recombination. Here A is the reactant, X the radical, P the product, and M a third body. The activation energy of the production step is very large, while that of the recombination step is small and taken to be zero. These kinetics are the most attractive of the two-step schemes that have been proposed for explaining interesting phenomena not covered by one-step kinetics, and the purpose is to provide a firm foundation for exploitation of the scheme.The object is to find the “laminar-flame eigenvalue”

Ignition and extinction fronts in counterflowing premixed reactive gases

\Delta

Ignition in an unsteady mixing layer subject to strain and variable pressure

, representing the burning rate, as a function of r, which is essentially the ratio of the two reaction rates. The response function

The reduced kinetic description of lean premixed combustion

\Delta ( r )

The virtual origin as a first-order correction for the far-field description of laminar jets

is described by numerical integration and by asymptotic analysis for

Capillary rise of a liquid between two vertical plates making a small angle

r \to 0,\infty

Ignition in the viscous layer between counterflowing streams: asymptotic theory with comparison to experiments

.

Dynamical issues in combustion theory

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.