A theoretical model for the combustion of droplets in supercritical conditions and gas pockets

Abstract

Supercritical combustion of droplets is studied by means of a physical model which assumes spherical symmetry, laminar conditions, constant pressure and a zero-thickness flame. Boundary conditions at the infinity state that temperature and composition of the mixture are given and constant. Initial distributions of temperature and mass fractions of the species are given, as well as the initial conditions at the droplet surface. As combustion proceeds, droplet surface is not considered to exist as a physical boundary allowing unrestricted diffusion of species through it. With some additional simplifications for the density and t r ansport coefficients, a numerical solution of the problem is obtained. An analytical solution of the problem is also obtained by means of an asymptotic analysis. This solution applies when the initial temperature of the droplet is small as compared with the temperature of the sourounding atmosphere. It is shown that this is the most impor t ant case from the technological point of view. For this case results show that an apparent droplet exists throughout most of the process, in which its surface is characterized by an abrupt change in temperature and composition of the chemical species. Results show burning rates, combustion times, flame radius and temperature at the droplet center as function of the principal variables of the process. In particular, the square of the apparent droplet radius is a linear function of time as occurs in subcritical combustion. It is shown that combustion times are faster in supercritical conditions than in subcritical conditions with the minimum value existing at critical conditions. A numerical application is carried out for the case of oxygen droplets burning in hydrogen and a comparison is carried out between the theoretical results obtained numerically and analytically as well as with those experimentally obtained.