TRANSIENT MASS AND HEAT TRANSFER FROM A CLOUD OF VAPORIZING DROPLETS OF VARIOUS SIZE DISTRIBUTIONS: A SECTIONAL APPROACH

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Abstract
A population of vaporizing liquid droplets of a wide range of sizes suspended in a stagnant heated atmosphere is considered. Interaction between neighboring droplets is taken into account through the ‘cooling effect’ due to latent heat absorption. To avoid the dimensionality problem associated with the discrete form of droplet population balance equations, “sectional-conservation-equations” are used. Since droplets of various sizes differ in their vaporization rates, “sectional-vaporization-coefficients” are presented. New solutions for the coupled energy and sectional size distribution equations arc presented and the transient changes in droplet size distribution are analyzed. The analysis takes into account the density of the spray, the distribution of interfacial area between the phases, rates of droplet vaporization, and the properties of the surrounding vapor-gas mixture. All the above-mentioned properties of the spray and surrounding gas are combined here to form a new nondimensional group-vaporization number, which expresses the ratio of the characteristic heat of vaporization to the initial enthalpy of the surrounding gas (both, per unit volume). To illustrate the generality of this approach, solutions are presented for various values of the group vaporization number, using three types of initial droplet number distribution: uniform, symmetrical, and nonsymmetrical.