Model for Studying Unsteady Droplet Combustion

Abstract

The concept of a reduced boundary condition at the surface of a droplet is used to develop a theory of unsteady droplet burning. This theory utilizes a quasi-steady gas-phase assumption, which has been shown to be realistic for a wide range of droplet sizes at low pressures. The most significant consequence of the theory is that the problem of unsteady droplet burning is reduced to the solving of a single diffusion-type nonlinear partial differential equation having one of its boundary conditions determined by an algebraic function of the quasi-steady gas-phase variables. This reduced boundary condition incorporates the entire dependence of the solution on fuel characteristics, chemical kinetics, and thermal properties of the gases. An experiment is proposed for determining this boundary condition so that the nonsteady droplet combustion problem can be solved for a realistic situation. By using additional assumptions, a numerical estimate of the boundary condition has been made.