The combustion of a linear droplet array in a convective, coaxial potential flow

Abstract

An efficient numerical scheme is introduced to describe the effects of forced convection and droplet-droplet interactions on the burning rate of a one-dimensional droplet array. The flow field is described by point sources (or sinks) superimposed on a uniform, coaxial potential flow. The strengths of the sources (or sinks) are found from the mass and heat conservation boundary conditions at the droplet surface. The resulting flow field is then used to solve the energy and species conservation equations, which are first transformed to a generalized coordinate system so that the computations can be carried out in any grid system. In this study, an improved, composite, body-fitted grid was used to solve the equations by an iterative, finite difference method to obtain the temperature (or concentration) field. Droplet pairs of equal sizes with spacings from 4 to 16 radii have been investigated for Peclet numbers from 10 to 120. The temperature distribution around the droplet array, as well as the local Nusselt number around the droplet surfaces, has been calculated. The results show qualitative agreement with analogous heat and mass transfer analyses that have appeared in the literature. Two droplets of unequal sizes and an array of up to six equal sized droplets have also been studied. This simple approach for treating the flow field allows the computation to be extended to a linear array with a large number of droplets. The numerical scheme has excellent convergence behavior, and the composite grid introduced here can also be used for more accurate, viscous flow calculations.