J. B. Greenberg

Coupled Evaporation and Transport Effects in Counterflow Spray Diffusion Flames

Abstract A new theoretical study of counterflow spray diffusion flames is presented. The fuel is introduced into the system in the form of liquid droplets suspended homogeneously in an inert environment. Analytic solutions are developed for the entire range of injection velocities, including large rates of injection for which asymptotic expansions based on the reciprocal of the injection velocity are involved. The sensitivity of flame position and temperature to combined transport, vaporization and liquid fuel spray-related and injection rate effects is analyzed in a comprehensive study of calculated results. These results were obtained assuming an infinite chemical Damkohler number so that the flame appears as a thin front. Additional numerically computed results with finite rate chemical kinetics show that the presence of the spray of vaporizing droplets tends to make flame extinguishment easier and ignition more difficult than in the single gas-phase counterflow diffusion flame situation.

Spray Diffusion Flames with Arbitrary Initial Droplet Velocity Distributions

A model of a laminar Burke-Schumann type of diffusion flame is developed in which the fuel is supplied in the form of droplets having an arbitrary initial velocity distribution. The spray of droplets is described using a sectional approach. The governing equations are normalized and various nondimensional parameters associated with the spray and the motion of the droplets therein are identified. Analytic solutions are presented for different assumed droplet velocity distributions. Effects of droplet velocity, dimensionless drag and vaporization coefficients and spray angle parameter on flame height, width and type are illustrated in a discussion of a detailed parametric analysis based on numerous calculations.

Steady-State and Extinction Analyses of Counterflow Spray Diffusion Flames with Arbitrary Finite Evaporation Rate

We present a new analysis of the behavior of counterflow spray diffusion flames in which the droplets are permitted to evaporate at a finite rate. The effects of fuel volatility, droplet size, and liquid fuel loading on steady-state combustion and conditions for extinction are investigated. We treat instances in which (1) the flame front is located beyond the stagnation plane in the region that, in the current model, is impenetrable to fuel droplets and (2) the flame front is located in the fuel half-plane. In case (2) droplets may actually traverse the flame front, become ignited, and burn out in the heterogeneous mode. An expression is derived for the ratio of extinction conditions with droplets present to those when all the fuel is prevaporized, enabling the direct influence of the droplets to be isolated in a compact fashion.

A Simple Phenomenological Model of an Organic Gel Spray Diffusion Flame

Recent experimental evidence has revealed the unusual behavior of organic gellant-based fuel droplets that, under appropriate ambient thermal conditions, evaporate and burn in an oscillatory fashion. This peculiar phenomenon of the droplets in the gel spray is incorporated in a model of a two-dimensional spray flame. A combined analytical/numerical solution of the governing equations is utilized to examine the way in which the frequency of oscillatory evaporation (that is likely to be dependent on such factors as the droplet size, and the make-up of the droplet (i.e., gellant versus liquid fuel content)) influences the combustion field. It is shown that the frequency of evaporation of the burning gel droplets can have a profound impact on the thermal field downstream of the homogeneous spray diffusion flame front. Hot spots of individual (or clusters of) burning droplets can be created and under certain operating conditions can lead to hotter temperatures than experienced in the main homogeneous flame. This can be extremely important in realistic combustion settings in which hot spots in undesirable regions can damage the structural integrity of the chamber. Other computed results demonstrate that, in relation to the spray diffusion flames obtained using an equivalent purely liquid fuel spray, the use of a gel fuel spray can lead, under certain operating conditions, to a reduction in flame height and temperature. The latter effect is critical when considering flame extinction. These effects highlight the fact that even though gel fuel sprays may have a distinct advantage over liquid sprays in terms of their safety features it is crucial that the correct operating conditions be employed in order not to detract from attaining the desired combustion performance.

Opposed flow polydisperse spray diffusion flames: Steady state and extinction analysis

A new analysis of polydisperse opposed flow spray diffusion flames is presented. The model permits non-unity Lewis number effects for the gaseous components, as well as a finite rate of evaporation for the droplets. Combined effects of droplet loading and spray polydispersity on the characteristics of spray flames are investigated using outer region analytic solutions. Under the assumption that the droplets are in dynamic and thermal equilibrium with their surroundings it is demonstrated that spray polydispersity alone has a profound effect on flame location, temperature and the mode of combustion (homogeneous, or homogeneous and heterogeneous combustion). Conditions for flame extinction are also examined. Frequently, polydisperse sprays are described in a global fashion by relating to them as if they were comprised of single size droplets having some average diameter, such as the Sauter mean diameter or a mean diameter based on the total surface area of the spray. It is shown that this approach can be rather erroneous when flame extinction is under consideration. By comparing strain rates for extinguishment it is demonstrated that critical extinction conditions must be based on a true representation of the sprays polydispersity, otherwise errors of as much as almost 60% can ensue.

Volatilization and Burning of Pulverized Coal, with Radiation Heat Transfer Effects, in a Counter Flow Combustor

Abstract A detailed combined experimental-theoretical analysis of pulverized coal combustion in an advanced counter flow combustor is presented. The theoretical model for the coal particles enables their size evolution to be tracked. Effects of devolatilization and char reaction are included, as well as radiative heat transfer to and from coal particles, the surrounding medium and combustor walls. A zoning method is used for the radiation calculations. The interaction between the gaseous surroundings and the particles is based on theoretical and/or experimental data. Measurements made in the counterflow combustor for the gaseous phase included temperature, pressure, composition and velocity. Particle size distribution, ash and volatile matter content were also monitored for comparison with the theoretical predictions. The results indicate that, for the configuration considered, optimal particle sizes for combustion efficiency lie within the range of about 40-60 μm. Further control of efficiency can be obt...

On the behaviour of organic gel multi-size spray diffusion flames

The recently reported, experimentally observed, unusual behaviour of organic gellant-based fuel droplets which, under appropriate ambient thermal conditions, evaporate and burn in an oscillatory fashion is incorporated in a phenomenological manner in a model of a two-dimensional arbitrary multi-size spray diffusion flame. Non-unity Lewis numbers are permitted for the fuel vapour and oxidant. A combined analytical/numerical solution of the governing equations is presented and used to investigate how a sprays initial polydispersity and the frequency of oscillatory evaporation influence the combustion field. It is demonstrated that the initial droplet size distribution and the frequency of evaporation of the burning gel droplets can have an acute impact both on the homogeneous diffusion flame shape, height and width and on the thermal field downstream of the flame front. Hot spots of individual (or clusters of) burning droplets can be created and under certain operating conditions can lead to hotter temperatures than experienced in the main homogeneous flame. The intensity of these hotspots, their number and location are sensitive to spray related parameters. In realistic combustion chambers there is a danger inherent in the existence of hotspots in undesirable regions as they can damage the structural integrity. Other computed results demonstrate that, in relation to the spray diffusion flames obtained using an equivalent purely liquid fuel spray, the use of a gel fuel spray can lead, under certain operating conditions, to a reduction in flame height and temperature. The latter effect is critical when considering flame extinction.

Vaporization Damköhler Number and Enrichment Effects in Spray Diffusion Flames in an Oscillating Flow Field

The sensitivity to the vaporization Damköhler number of the behavior of a coflow laminar spray diffusion flame in an oscillating flow field is investigated. Droplet grouping induced by the host gas flow oscillations is accounted for, and its effect is described through a specially constructed model for the vaporization Damköhler number that responds to the proximity of the droplets as they cluster. A formal analytical solution is developed, and the dynamics of the spray flame front shapes and thermal fields are deduced. Computed results demonstrate how strongly the vaporization Damköhler number impacts on the type of primary homogeneous flame formed and on the possible existence of multiple flame sheets as the flow field oscillates. In addition, isolated regions of high fuel vapor concentrations are produced by fuel droplet enrichment. The presence of resulting parallel fluctuating thermal fields indicates a potential impact on undesirable pollutants production.

Propagation and extinction of an unsteady spherical spray flame front

Experimental evidence seems to indicate that the life of a laminar spherical flame front propagating through a fresh mixture of air and liquid fuel droplets can be roughly split into three stages: (1) ignition, (2) radial propagation with a smooth flame front and (3) propagation with flame front cellularization and/or pulsation. In this work, the second stage is analysed using the slowly varying flame approach, for a fuel rich flame. The droplets are presumed to vaporize in a sharp front ahead of the reaction front. Evolution equations for the flame and evaporation fronts are derived. For the former the combined effect of heat loss due to droplet vaporization and radiation plays a dominant explicit role. In addition, the structure of the evaporation front is deduced using asymptotics based on a large parameter associated with spray vaporization. Numerical calculations based on the analysis point to the way in which the spray modifies conditions for flame front extinction. Within the framework of the present simplified model the main relevant parameters turn out to be the initial liquid fuel load in the fresh mixture and/or the latent heat of vaporization of the fuel.

A numerical study of polydisperse spray flame ignition and extinction fronts in a mixing layer

A new numerical study of laminar polydisperse flame ignition and extinction fronts in a mixing layer resulting from opposed streams of fuel and oxidant is presented. Two quite different initial droplet size distributions having the same Sauter mean diameter (SMD) are considered. The phenomenon of hysteresis is found to occur for a high initial droplet load but disappears as the latter decreases. The range of strain rate values for which hysteresis is prevalent depends on the initial size distribution. For example, whilst under certain operating conditions, an extinction front may result from using one initial droplet size distribution, use of another size distribution, even having the same SMD, can exhibit hysteresis. Other features of the influence of the initial spray polydispersity are discussed in depth.