A Model of Organic Gel Spray Diffusion Flames with Droplet Drag

Abstract

A new model of an organic gel spray diffusion flame is presented in which finite droplet drag is accounted for. The phenomenological onset of oscillatory droplet evaporation once the environment of the gel droplets reaches some critical temperature is incorporated in the model. A combined analytical/numerical solution of the governing equations is found. A previously reported model, in which the droplets were taken to be in dynamic equilibrium (i.e. infinite drag) with their host carrier gas, predicted that, under certain operating conditions, hot spots will appear downstream of the main homogeneous diffusion flame front. In this work the influence of finite droplet drag and the initial average velocity of the spray’s droplets on the overall thermal field were investigated. It was found that for an initial average droplet velocity less than that of the host gas (a) the homogeneous flame heights were greater than those obtained under the assumption of infinite drag, and (b) the phenomenon of postdiffusion flame hot spots was reduced. The smaller the initial average droplet velocity (and, hence, the mass flux of gel droplets) the greater was the annihilation of the hot spot manifestation. The drag coefficient was also found to have a similar effect on the diffusion flames in that the smaller the coefficient the taller the flame was. Both the aforementioned average droplet velocity and finite drag coefficient effects reflect the augmented upstream production of vapor as a result of the longer upstream residence time of the evaporating droplets. The appearance of unwanted hot spots can be critical in a combustion chamber and may even damage its structural integrity. The current model indicates that control over the gel spray’s droplet velocity field can be valuable in reducing or even eliminating such hot spots.