The influence of preferential diffusion and stretch on the burning intensity of a curved flame front with fuel spray

Abstract

In our most recent paper on Bunsen spray flames, only a completely prevaporized mode of a normal Bunsen flame was considered; inverted Bunsen flame and droplet size effects had not been examined yet. In the present study, we consider two flame structures: normal and inverted Bunsen flames, and two spray modes: completely and partially prevaporized burning, by the method of large activation energy asymptotics. In this way, a complete parametric study of flame tip intensification or extinction (opening) can be conducted. Four parameters are used in the analysis. The first two are the droplet size and amount of liquid-fuel loading, which indicate internal heat loss for a rich spray but heat gain for a lean spray. The other two are the stretch and Lewis number (Le). Stretch is negative for a normal Bunsen flame but positive for an inverted Bunsen flame. Stretch strengthens (or weakens) the burning intensity of the Le>1 (or Le<1) normal Bunsen flame but decreases (or increases) the burning intensity of the Le>1 (or Le<1) inverted Bunsen flame. Burning intensity of the flame tip intensifies (or weakens) when the lean (or rich) spray has a smaller droplet size or a larger amount of liquid loading. For lean and rich ethanol-spray normal Bunsen flames with Le>1 or a rich methanol-spray inverted Bunsen flame with Le<1, closed-tip solutions are obtained. Conversely, stretch weakens the burning intensities of lean and rich ethanol-spray inverted Bunsen flames with Le>1, or rich methanol-spray normal Bunsen flames with Le<1, eventually leading to tip opening. Moreover, the opening becomes wider (or narrower) as the droplet size decreases or liquid loading increases for the rich (or lean) sprays. Note that for lean ethanol-spray normal (or inverted) Bunsen flame with Le>1, if liquid loading is large enough and droplet size is sufficiently small, there exists flame transition from normal (or inverted) Bunsen through planar to inverted cone (or normal Bunsen) flame. Finally, the critical value of droplet size, at which there exists a planar flame rather than a normal (or an inverted) Bunsen flame, increases with increasing liquid loading.