J.B. Greenberg

On the origins of spray sectional conservation equations

Abstract In this note it is demonstrated how Tambours previously discretely derived, sectional conservation equations for the description of polydisperse sprays can be deduced directly from Williamss spray equation for a droplet number density probability function. The analysis also produces a new compact integral formulation of spray source terms, involving sectional vaporization and coalescence coefficients.

Stoichiometry and polydisperse effects in premixed spray flames

An analysis of a one-dimensional liminar premixed polydisperse spray flame is presented, for the whole range of fuel rich/lean mixtures. The spray of droplets is modeled using a sectional approach, thus making it possible to account for droplet-droplet interaction within the spray. A dimensional analysis of the mathematical model for the spray flame reveals its structure as consisting of a primary evaporation zone, a preheat zone, a homogeneous reaction zone, and a postreaction zone. If droplets survive the flame they may continue to burn or evaporate in the post reaction zone, depending on the fuel vapor-to-air ratio in the homogeneous reaction zone. Detailed analytic solutions are developed and matched for each of the aforementioned zones. Computed results show that the initial size distribution of the droplets in the spray has a profound influence on the flames characteristics. Although the use of the Sauter mean diameter (SMD) may be sufficient for the treatment of monodisperse sprays it is demonstrated here that its use to characterize the average evaporation rate of polydisperse sprays may lead to erroneous results, since the local SMD may actually decrease or increase depending on the initial droplet size distribution.

An analysis of multiple flames in counterflow spray combustion

The formation and structure of multiple flames in counterflow partially premixed spray combustion is studied in a new theoretical investigation. Analytic solutions are developed for the single, double and triple homogeneous flame ensemblages, including interflame droplet vaporization and/or heterogeneous burning, that can arise in this two-phase combustion situation. In results calculated from the analytic solutions it is demonstrated that the characteristics of the spray (fuel volatility, droplet size, injected fuel vapor to liquid fuel ratio) can be the most important factors in determining which of the aforementioned combustion scenarios is applicable.

The Burke-Schumann diffusion flame revisite—With fuel spray injection

Abstract The classical Burke-Schumann diffusion flame model is reexamined assuming the fuel is introduced in the form of liquid droplets suspended homogeneously in an inert gas stream. A sectional approach and the concept of a quasimonodisperse spray is employed to compactly describe downstream changes in droplet size due to vaporization. A Damkohler-type number for vaporization is identified as one of the dimensionless parameters of the model. Analytic solutions are presented for flat and cylindrical flames, under various assumptions concerning the motion of the droplets and their gaseous environment. A detailed parametric analysis of n -decane fuel reveals that under certain circumstances the use of the spray can quite markedly effect the existence, shape, and characteristics of the diffusion flame.

On the oscillatory behavior of laminar spray diffusion flames: experiment and theory

In this study an experimental, well-controlled parametric investigation of the behavior of an oscillating Burke-Schumann type spray diffusion flame is described. It is demonstrated that these unique spray-related oscillations occur at frequencies in the range 1–5 Hz and it is established that their genesis is due to a heat and mass transfer mechanism resulting from the presence of the droplets in the system. A complementary stability analysis of a one-dimensional model problem, containing the essential features of the experimental conditions, is performed. It is found that the correct order of magnitude of oscillations is predicted by the analysis, confirming a posteriori that the model is a satisfactory paradigm for examining the observed phenomenon.

On Droplet Enhancement of the Burning Velocity of Laminar Premixed Spray Flames

The analyses of spray flames always predicted a burning velocity that was less than that of an equivalent single-phase gaseous premixed flame. This note reports a correction factor that can be applied to previously developed spray burning velocity formulae

The Burke-Schumann spray diffusion flame in a nonuniform flow field

The uniform, constant velocity profile assumption of the classical Burke-Schumann diffusion flame model is relaxed to permit more realistic duct entrance velocity profiles to be accounted for. An approximate model is formulated to include the supply of a spray of liquid fuel in the inner duct of the coflow configuration. For appropriate operating conditions (the characteristic flow time less than the characteristic vaporization time) it is shown that a fully developed parabolic velocity profile located at a short distance downstream of the inlet region provides the background flow field for the establishment of a homogeneous spray diffusion flame. The characteristic constriction of the streamlines immediately downstream of the inlet is also taken into consideration. Analytic solutions are found for the cases of negligible and notable axial diffusion. Due to difficulties that arise in the numerical calculation of the solutions, the large eigenvalues of the problem are derived asymptotically, thus enabling the full range of parametric values to be employed in predicting the spray flame characteristics. Computed results for flame shapes and heights are compared with those of a model from the literature that is based on the assumption of a uniform velocity profile. The sensitivity of the flame profiles to the initial droplet loading, the Peclet number, the vaporization Damkohler number, and the use of a parabolic velocity profile are clearly demonstrated. The net effect of the nonuniform flow field is found to be expressible in terms of a rescaling of the vaporization Damkohler number.

Flame spread over thin solid fuels in partially premixed atmospheres

Abstract Experiments on flame spread rates ( S f ) over thin solid fuels in oxidizing atmospheres to which gaseous fuel is added reveal a large increase in S f for some gaseous fuels. The most to least effective fuels tested are, in order, H 2 , CO, hydrocarbons, and NH 3 . From these experiments it is inferred that, unlike nonpremixed flame spread, the finite-rate kinetics of the gaseous fuel have a dominant influence on S f even far from extinction conditions. A simple model developed to account for the effect of the gaseous fuel on S f , while still retaining the framework of deRiss model of S f for infinite-rate kinetics of the solid fuel vapors, shows good qualitative and fair quantitative agreement with experimental data. Furthermore, it is shown that for some fuels, e.g., CO, the gaseous products of partial combustion produce a more combustible environment than the fresh atmosphere; the practical implications of this finding for modeling fires in enclosures are discussed.

A numerical model of high intensity confined hydrocarbon combustion

Abstract A computer program was developed for the solution of the set of elliptic nonlinear partial differential equations that describe turbulent reacting recirculating flows of the kind encountered inside combustion chambers. The investigation combines a two-equation model of turbulence with three global chemical reactions in a realistic combustor geometry. Fair agreement was obtained between predictions and experimental data previously measured by the authors in a high intensity combustor.

A study of stretch in premixed spray flames

Abstract The effect of stretch in polydisperse spray flames is investigated for the first time, in the context of a spherically symmetric laminar flame propagating into a mixture of fuel vapor, droplets, and air. The study reveals that, in addition to the well-known (gas) Lewis number effect, there is a pronounced effect resulting from the presence of the spray, which causes acceleration of the flame due to droplet evaporation. For mixture Lewis numbers equal to or greater than unity, the two effects combine to bring about flame acceleration. However, in mixtures having Lewis numbers less than 1, the two effects become competitive—the Lewis number effect tending to decelerate the flame, while the spray effect accelerates it. For highly volatile sprays the Lewis number effect is dominant, but for less volatile sprays the behavior is different. The relative importance of the two effects changes dynamically in time, and, beyond some instant after ignition, the spray evaporation effect is completely dominant, causing flame acceleration for any Lewis number, in sharp contrast to the behavior of an equivalent gaseous flame.