A theoretical study on the unsteady, interactive combustion of a linear fuel droplet stream

Abstract

The combustion process of a linear fuel droplet stream is analyzed by the method of matched asymptotic expansion based on an appropriate physical model. The radial change in the heat/mass transport field occurs in accordance with the scale of the initial droplet radius while the characteristic scale for the axial change is the length of the droplet array. For a long array with small droplet spacing, adjacent droplets are in a similar situation to each other so that the far field around each droplet assumes a two-dimensional nature unlike the three-dimensional nature of the single or multiple droplet combustion cases. The main difference is that the two-dimensional transport field has no steady solution. The analysis reveals that droplet interaction enhances the unsteadiness involved, through which different properties from the single droplet case emerge. The normalized droplet lifetime, which lengthens with decreased droplet spacing, may depend significantly on the ambient gas conditions, especially, the oxygen concentration and the droplet velocity relative to the gas stream. The transition from the individual to the collective combustion mode corresponds to a rapid increase in the flame radius. When the droplets travel faster than the ambient gas, the droplet lifetime increases to finally extinguish the flame at a critical relative velocity which depends on the droplet spacing. The underlying physics is the following. With decreased droplet spacing more droplets tend to consume competitively the oxygen available in a particular finite volume of the ambient gas. As a result the flame is pushed away from the droplets and the phenomenon becomes essentially unsteady because the flame can not settle down at the quasi-steady standoff distance within the droplet lifetime. Since the near field is always influenced by the far field the droplet combustion is more easily influenced by the ambient gas conditions.