Combustion of Interacting Droplet Arrays in a Microgravity Environment

This research program involves the study of single droplets and linear arrays of droplets in weakly-buoyant and non-bouyant environments. The primary purpose of the single droplet work was to (1) provide a data base from which to compare droplet array results and (2) to correlate the effects of buoyancy on flame shape. Traditionally convective effects in droplet combustion are represented in terms of the Reynolds number, Re, for forced convection and the Grashof number, Gr, for natural convection. Typically, corrections to the burning rate constant for convective effects are written in terms of Re or Gr(exp 1). The Stefan velocity is not included in these correlations, even though from purely physical reasons, one would expect it to be important, especially at higher burning rates. The flame distortion due to convective effects is less documented quantitatively. Kumagai and Isoda do predict flame shape in natural and forced convective flow fields. Their focus, however, was to predict the actual flame dimensions. Law and co-workers used reduced pressure, high oxidizer ambients to obtain spherical flames. This implies that buoyant flows were reduced at the low pressures, as indicated by a very small Grashof number. Ross et al, however, using scaling arguments showed that reducing the pressure does not have a large effect on the magnitude of the buoyant velocity. Struk et al showed elongated flame shapes during simulated (porous sphere) droplet combustion. The elongation of the flames was due to residual gravity levels aboard the reduced gravity aircraft on which the experiments were conducted. These flame shapes, as well as some data from the literature were interpreted based on a dimensionless grouping called the sphericity parameter, Sp. Sp is the ratio of a characteristic computed buoyant velocity to the Stefan velocity at the flame front. One purpose of the droplet arrays work is to extend the database and theories that exist for single droplets into the regime where droplet interactions are important. The eventual goal being to use the results of this work as inputs to models on spray combustion where droplets seldom burn individually; instead the combustion history of a droplet is strongly influenced by the presence of the neighboring droplets. Recently, Annamali and Ryan have summarized he current status of droplet array, cloud and spray combustion. A number of simplified theories led numerical studies of droplet vaporization/combustion where multiple droplet effects are present are now available. These theories all neglect the effect of buoyancy. Experimentally, most studies to date suffer the effects of buoyancy. It is the dominant transport mechanism in the problem. Only the works of Law and co-worker and more recently by Mikami et al were performed in an environment where buoyancy effects were small. Law and co-workers were limited to high oxygen index, low pressure ambient environments since there studies were conducted in normal gravity.