The interaction between external and internal heat losses on the flame extinction of dilute sprays

Abstract

The flame extinction of a dilute spray burning in a steady, one-dimensional, low-speed, sufficiently off-stoichiometric, two-phase flow, is studied using activation energy asymptotics. A completely prevaporized burning and a partially prevaporized burning of spray are identified on the basis of a critical value of the initial droplet radius for completing the vaporization process at the flame. The heat loss mechanism is composed of the external heat loss represeted by the buck heat conduction from the system to the surrounding, and the internal heat loss associated with the droplet gasification process. The interaction between external and internal heat losses on the flame extinction of dilute sprays is generally discussed on the basis of three parameters, namely the external heat loss, the initial droplet radius, and the liquid fuel loading. For the spray burning without external heat loss, there exists a triple-valued extinction curve in a rich spray, but is no extinction occurrence in a lean spray. Introducing the external heat loss to the spray flame, results show that for a lean spray, the flame flux at extinction is first increased, then decreased, and finally approaches exp(−0.5) with increasing the droplet radius; yet the correspondingly asymptotic value of the external heat loss is slightly larger than exp(−1.0). For a rich spray, the flame flux at extinction is monotonically increased with increased initial droplet radius or decreased liquid fuel loading.