Analysis of a stagnation-point premixed flame influenced by inert spray, heat loss, and non-unity Lewis number

This study investigates the effects of the Lewis number, flow stretch, internal heat loss, and external heat loss on the extinction characteristics of propane/air flames using activation-energy asymptotics. A steady, planar, premixed flame generated in a stagnation-point, two-phase flow in which the dispersed phase is simulated by a monodisperse, dilute, and chemically inert spray (water spray) is considered. A completely prevaporized spray mode and a partially prevaporized spray mode of flame propagation are identified using a critical initial droplet size rc′ that is required for the droplet to achieve complete evaporation at the premixed flame front. The internal heat loss associated with water vaporization increases with increasing liquid loading or decreasing initial droplet size. The (positive) flow stretch coupled with the Lewis number (Le) respectively weakens and intensifies the burning intensity of a lean propane/air flame (Le > 1) and a rich propane/air flame (Le < 1). Additionally, the external heat loss weakens the burning intensity and has a significant influence on the flame behavior. The results show that a Le > 1 flame can be extinguished with or without external heat loss. Flame extinction characterized by a C-shaped curve is dominated by external heat loss or the flow stretch. For a Le < 1 flame without external heat loss, no extinction occurs under the influence of flow stretch. However, a Le < 1 flame with completely prevaporized water sprays that is subjected to a small amount of flow stretch can be extinguished by external heat loss; this behavior is characterized by a C-shaped curve. A W-shaped extinction curve is mainly governed by internal heat loss. Flame extinction characterized by a W-shaped curve occurs when a Le < 1 flame with external heat loss is subjected to a positive stretch and a partially prevaporized water spray with sufficiently large liquid loading and droplet size.