Multiradii modeling of counterflow spray diffusion flames

A multiradii spray flame model is derived in a kinetic framework in which the droplets' distribution function is taken as a sum of delta products. The droplet class equations are obtained by taking moments of the Boltzmann-type spray equation. The gas-phase equations are coupled to the droplets equations through various integral sources terms. In the counterflow geometry, using a self-similar assumption, multiradii counterflow spray flame models are then obtained as exact solutions of multidimensional small Mach number governing equations. The structure of multiradii counterflow spray flames is investigated numerically. To solve the discretized system of equation, a fully coupled adaptive computation was conducted between the gas and liquid phase. The equations are discretized by using a finite difference, and highly optimized libraries were used in order to evaluate thermochemistry and transport properties. We first investigate an n-heptane counterflow monodisperse spray flame studied experimentally by Chen and Gomez. We then investigate a multiradii methanol spray flame studied experimentally by Gomez and coworkers. The multiradii approach is used in order to describe accurately the multiple size behavior, which is found to be strongly radius-dependent. Good agreement is found in both cases up to experimental uncertainties in the measured injection velocities and class number densities.