Resumen de Ignition and extinction analyses of spray diffusion flames
Daniel Martínez Ruiz
The present dissertation deals with the description of the interacting multiscale processes governing spray vaporization and combustion downstream from the near-injector atomization region in liquid-fueled burners. The analysis incorporates rationally derived simplifications based on the disparity of length and time scales present in the problem. In particular, it is shown how the disparity of the scales that – to the droplet size, interdroplet spacing, and width of the spray jets, ensures the validity of their homogenized description. The two-way coupling associated with exchanges of mass, momentum, and energy between the gas and the liquid phases is dominated by the homogenized exchanges with the gas provided collectively by the droplets, and not by the direct interaction between neighboring droplets. The resulting multicontinua formulation is used as a basis to investigate different aspects of spray combustion, including diffusion-flame structures and finite-rate effects i) The laminar coflow mixing layer separating a hot-air stream from a monodisperse spray carried by either an inert gas or air is investigated numerically and analytically in an effort to increase understanding of the ignition process leading to stabilization of high-speed spray combustion. The problem is formulated in an Eulerian framework, with the conservation equations written in the boundary-layer approximation and with a one-step Arrhenius model adopted for the chemistry description. A phenomenon that is amenable to a theoretical analysis based on activation-energy asymptotics, presented here, following earlier ideas developed in describing unsteady gaseous ignition in mixing layers. By way of contrast, when the amount of fuel vapor reaching the hot boundary is small, as is observed in the computations employing the thermochemical properties of methanol, the incipient chemical reaction gives rise to a slowly developing lean deflagration that consumes the available fuel as it propagates across the mixing layer towards the spray. The flame structure that develops downstream from the ignition point depends on the fuel considered and also on the spray carrier gas, with fuel sprays carried by air displaying either a lean deflagration bounding a region of distributed reaction or a distinct double-flame structure with a rich premixed flame on the spray side and a diffusion flame on the air side. For fuels carried by an inert gas, a trailing diffusion flame develops downstream from the ignition region, approaching at large distances a Burke-Schumann solution that can be described in terms of coupling functions, as shown in an appendix. ii) An axisymmetric opposed-jet configuration, involving a stream of hot air counterflowing against a stream of nitrogen carrying a spray of fuel droplets, is employed as a basis to address effects of droplet inertia on spray vaporization and combustion. The Reynolds numbers of the jets are assumed to be large, so that mixing of the two streams is restricted to a thin mixing layer that separates the counterflowing streams. The evolution of the droplets in their feed stream from the injection location is seen to depend fundamentally on the value of the droplet Stokes number St, defined as the ratio of the droplet acceleration time to the mixing-layer strain time close to the stagnation point. iii) The limit of large-activation energy is employed to investigate straininduced extinction of counterflow spray diffusion flames. As in the case of gaseous flames, which is treated separately in an appendix, for near-extinction conditions the flame structure is in the first approximation that corresponding to the limit of infinitely fast reaction, i.e., two outer regions of equilibrium flow separated by an infinitesimally thin reaction layer where the fuel vapor generated outside by the vaporizing droplets reacts with the oxygen of the air at a diffusion-controlled rate. The computation of the leading-order equilibrium solution, including the flame-sheet location and the associated peak temperature, fuel-consumption rate, and temperature gradients on both sides, is facilitated by the introduction of chemistry-free coupling functions that allow for general non-unity Lewis numbers of the fuel vapor. The formal analysis of the extinction regime requires consideration of the small departures from equilibrium occurring both in the thin reaction layer, whose inner structure is in the first approximation identical to that encountered in gaseous nonpremixed flames, and also in the outer regions, where the corrections are associated with the reactants leaking through the flame, whose description involves the integration of a set of coupled linear equations on each side of the flame sheet. Appropriate matching of the solution in the different regions provides expressions for the critical extinction conditions. The results of the asymptotic analysis enable strain-rate dependences on spray dilution, fuel-vapor diffusivity, and droplet inertia to be investigated.
