The Combustion of Linear Droplet Arrays in a Coaxial Convective Flow.

Abstract

As approximations for spray-combustion processes, a series of increasingly sophisticated numerical models has been developed to simulate the combustion of linear droplet arrays in a co-axial, convective flow. Common to all of the models is an embedded grid, developed to increase computational accuracy. The first and simplest model is potential flow model (for Re $\to$ $\infty$). The flow is assumed to be ideal and infinitely-fast kinetics (flame sheet assumption) represent the combustion. The results show that the instantaneous droplet burning rates are increased as the droplet spacing is increased, and the burning rates of droplets tend asymptotically to smaller values as the number of droplets in the array is increased. A second model, a Stokes flow model (for Re $<$ 1), is developed by using the Stokes approximation for the flow field. The results show that, owing to the lack of strong convective flow, the temperature and species contours can penetrate deeper into the flow. The third model extends the analysis to heat transfer for linear arrays of spheres at any Reynolds number, i.e. the model is based on the steady-state Navier-Stokes equations, but no combustion is considered. A more accurate flow pattern around the arrays is obtained and the predicted heat transfer and drag agree well with the experimental data in the literature. The fourth model introduces combustion into the third model through a finite-rate, one-step chemical reaction approximation. The model predicts a thick flame layer, rather than a flame sheet. For large Reynolds numbers, the results show that the downstream droplets have a higher burning rate than the leading droplets. For small Reynolds numbers, the model predicts behavior similar to that predicted with the potential and Stokes flow models. Finally, an unsteady-state model, based on the full Navier-Stokes equations, is used to study the variation in burning behavior with time. The reduction in droplet size, velocity, and spacing is included. The results show that even when the droplet spacing is significantly reduced (from 14 to 6 radii) the burning behavior of droplets is not affected.