Spray flames in a one-dimensional duct of varying cross-sectional area

The influences of flame stretch, preferential diffusion and internal heat transfer on the extinction of dilute spray flames propagating in a duct with varying cross-sectional area are analyzed using activation energy asymptotics. A completely prevaporized mode and a partially prevaporized mode of flame are identified. The results show that the internal heat transfer, which is associated with the liquid fuel loading and the initial droplet size of the spray, provides internal heat loss for rich sprays but heat gain for lean sprays. The burning intensities of a lean (rich) spray is enhanced (further reduced) with increasing liquid fuel loading and decreasing initial droplet size. The positive stretch weakens a lean methanol-spray flame and rich ethanol-spray flame (Le > 1) but intensifies a rich methanol-spray flame (Le < 1). The flame stretch is found to dominate strongly the tendency towards flame extinction characterized by a C-shaped curve. However, for a rich methanol spray flame (Le < 1), an S-shaped extinction curve can be obtained if it experiences positive stretch and endures a partially prevaporized spray of a large enough fuel loading and a sufficiently large droplet size. The S-shaped curve, which differs greatly from the C-shaped one, shows that the flame extinction is governed by the internal heat loss.