Supercritical liquid fuel combustion

Abstract

The process of plane one-dimensional isobaric unsteady combustion is considered for a system wherein liquid fuel and oxidizing gas are initially in different spatially uniform states. By virtue of the similarity nature of the relevant flow fields, a set of ordinary differential equations for the heat conduction flux and concentration as functions of temperature is derived, which enables us to examine the combustion characteristics at high pressures without the cumbersome task of calculating the flow fields themselves. An asymptotic analysis is made of the heat and mass transfers occuring near the gas-liquid interface which is at the critical state of the mixture. It is especially shown that, within the range of validity of the so-called local-equilibrium hypothesis and linear phenomenological relations, the mutual diffusion coefficient must vanish at the critical interface. This ensures the finiteness of the evaporation rate in the critical condition. As a plane one-dimensional version of spherical droplet combustion, the plane-symmetric combustion of a liquid fuel slab in the wet-bulb condition is analyzed on the basis of adequate formulae for estimating the material properties involved. In unsteady combustion the burning rate is not equal to the evaporation rate. The evaporation rate becomes an increasing function of the ambient gas temperature and oxygen concentration, but has a rather complicated dependence on pressure. Consistent with previous gravity-free experimental results, it attains a maximum value at a certain value of pressure above the critical pressure of fuel, and this condition is found to correspond to the case when the surface temperature becomes maximum. The burning rate, on the other hand, is almost independent of the ambient gas temperature and becomes an increasing function of the ambient oxygen concentration and pressure. In particular it is approximately proportional to the square root of pressure.