Analysis of steady state polydisperse counterflow spray diffusion flames in the large Stokes number limit

A new mathematical analysis is presented of certain aspects of the behavior of opposed flow polydisperse spray diffusion flames within the framework of a model in which large slip is permitted between the droplets and their host surroundings. The sectional approach is used to model the polydisperse spray. Operating conditions are identified under which the inverses of sectional Stokes numbers are small spray-related parameters to be used in a perturbation analysis of the liquid phase governing equations. The steady state equations and their solutions are similar in form to the equivalent equations considered in previous work of the authors in which dynamical equilibrium of the droplets with the carrier phase was assumed. However, here there is much more mathematical complexity involved in the spray equations solution. A hybrid Eulerian–Lagrangian approach is also suggested to get an insight into the phenomenon of reversal in the motion of the droplets that has been reported in independent experimental and computational research. Computed results based on the analytical solutions up to the 1st order of approximation reveal the influence of large droplet slip on the droplets velocity field and on the spray diffusion flame’s thermal field, for which appreciable heterogeneous combustion can occur under the operating conditions considered.