SOLUTIONS OF POLYDISPERSE SPRAY SECTIONAL EQUATIONS VIA A MULTIPLE-SCALE APPROACH: AN ANALYSIS OF A PREMIXED POLYDISPERSE SPRAY FLAME

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Abstract
New solutions are presented for polydisperse spray sectional equations. Simultaneous evaporation and coalescence processes of the spray droplets are considered. The mathematical procedure takes advantage of a multiple-scale approach in which different scales are applied to the different physical processes (convection and evaporation). Two small spray parameters are identified and used for expansion purposes. A special zonal density model is developed, thus enabling approximate analytic solutions to be extracted from the governing equations for the entire system. The method is employed to analyze adiabatic premixed polydisperse spray flames in a one-dimensional flow field. Computed results are presented for flame location versus flame velocity, the influence of droplet evaporation rate (with and without coalescence) on flame location, and the axial variation in temperature and chemical species profiles. As to the fuel spray, the evolution in droplet size distributions, for the various size sections, along the axial direction is analyzed. Finally, all analytical results are compared with numerical solutions for the governing equations, which are obtained here using a finite-differences method. The good agreement between the analytical solutions and the numerical ones indicates that a multiple-scale approach may be an important satisfactory tool for the analysis of polydisperse sprays that undergo simultaneous evaporation and coalescence processes.

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