Dynamics of thermal ignition of spray flames in mixing layers

Conditions are identified under which analyses of laminar mixing layers can shed light on aspects of turbulent spray combustion. With this in mind, laminar spray-combustion models are formulated for both non-premixed and partially premixed systems. The laminar 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. The numerical integrations unveil two different types of ignition behaviour depending on the fuel availability in the reaction kernel, which in turn depends on the rates of droplet vaporization and fuel-vapour diffusion. When sufficient fuel is available near the hot boundary, as occurs when the thermochemical properties of heptane are employed for the fuel in the integrations, combustion is established through a precipitous temperature increase at a well-defined thermal-runaway location, 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 vapour 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. Results are calculated for the distributions of mixture fraction and scalar dissipation rate across the mixing layer that reveal complexities that serve to identify differences between spray-flamelet and gaseous-flamelet problems.

Flammability conditions for ultra-lean hydrogen premixed combustion based on flame-ball analyses

It has been reasoned that the structures of strongly cellular flames in very lean mixtures approach an array of flame balls, each burning as if it were isolated, thereby indicating a connection between the critical conditions required for existence of steady flame balls and those necessary for occurrence of self-sustained premixed combustion. This is the starting assumption of the present study, in which structures of near-limit steady sphericosym-metrical flame balls are investigated with the objective of providing analytic expressions for critical combustion conditions in ultra-lean hydrogen-oxygen mixtures diluted with N2 and water vapor. If attention were restricted to planar premixed flames, then the lean-limit mole fraction of H2 would be found to be roughly ten percent, more than twice the observed flammability limits, thereby emphasizing the relevance of the flame-ball phenomena. Numerical integrations using detailed models for chemistry and radiation show that a onestep chemical-kinetic reduced mechanism based on steady-state assumptions for all chemical intermediates, together with a simple, optically thin approximation for water-vapor radiation, can be used to compute near-limit fuel-lean flame balls with excellent accuracy. The previously developed one-step reaction rate includes a crossover temperature that determines in the first approximation a chemical-kinetic lean limit below which combustión cannot occur, with critical conditions achieved when the diffusion-controlled radiation-free peak temperature, computed with account taken of hydrogen Soret diffusion, is equal to the crossover temperature. First-order corrections are found by activation-energy asymptotics in a solution that involves a near-field radiation-free zone surrounding a spherical flame sheet, together with a far-field radiation-conduction balance for the temperature profile. Different scalings are found depending on whether or not the surrounding atmosphere contains wáter vapor, leading to different analytic expressions for the critical conditions for flame-ball existence, which give results in very good agreement with those obtained by detailed numerical computations.

Variable-density jet flows induced by concentrated sources of momentum and energy

The planar and axisymmetric variable-density flows induced in a quiescent gas by a concentrated source of momentum that is simultaneously either a source or a sink of energy are investigated for application to the description of the velocity and temperature far fields in laminar gaseous jets with either large or small values of the initial jet-to-ambient temperature ratio. The source fluxes of momentum and heat are used to construct the characteristic scales of velocity and length in the region where the density differences are of the order of the ambient density, which is slender for the large values of the Reynolds number considered herein. The problem reduces to the integration of the dimensionless boundary-layer conservation equations, giving a solution that depends on the gas transport properties but is otherwise free of parameters. The boundary conditions at the jet exit for integration are obtained by analysing the self-similar flow that appears near the heat source in planar and axisymmetric configurations and also near the heat sink in the planar case. Numerical integrations of the boundary-layer equations with these conditions give solutions that describe accurately the velocity and temperature fields of very hot planar and round jets and also of very cold plane jets in the far field region where the density and temperature differences are comparable to the ambient values. Simple scaling arguments indicate that the point source description does not apply, however, to cold round jets, whose far field region is not large compared with the jet development region, as verified by numerical integrations