The influence of droplet grouping on a Burke-Schumann spray diffusion flame in an oscillating flow field

A new mathematical analysis of a laminar Burke-Schumann type of spray diffusion flame in an oscillating flow field is presented within a framework in which mild slip is permitted between the droplets and their host surroundings. A perturbation analysis using a small Stokes number is used for solving the liquid phase governing equations. The effect of droplet grouping in the oscillatory flow field is accounted for by constructing an appropriate model for the vaporization Damkohler number. A formal analytical solution is developed for the Schwab-Zeldovitch parameter through which instantaneous flame front shapes are found. Computed results based on the solution expose the strong impact that the phenomenon of droplet grouping can have on flame characteristics such as flame height, shape and type (over- or under-ventilated). Despite the models simplicity its predictions offer an opening insight into the mechanisms prevalent in more complex spray-combustion situations in which droplet grouping may occur.