Abstract
A theoretical investigation of the influence of a standing wave flow-field on the dynamics of a laminar two-dimensional spray diffusion flame is presented for the first time. The mathematical analysis permits mild slip between the droplets and their host surroundings. For the liquid phase, the use of a small Stokes number as the perturbation parameater enables a solution of the governing equations to be developed. Influence of the standing wave flow-field on droplet grouping is described by a specially constructed modification of the vaporization Damkohler number. Instantaneous flame front shapes are found via a solution for the usual Schwab–Zeldovitch parameter. Numerical results obtained from the analytical solution uncover the strong bearing that droplet grouping, induced by the standing wave flow-field, can have on flame height, shape, and type (over- or under-ventilated) and on the existence of multiple flame fronts.
Highlights
IntroductionThe efficiency of spray systems in combustion engineering systems relies strongly on the dynamics of the liquid droplets, and among other things, their tendency to form groups
The efficiency of spray systems in combustion engineering systems relies strongly on the dynamics of the liquid droplets, and among other things, their tendency to form groups.This grouping tendency has an influence on their evaporation, the drag force applied on them, and on their final settling point
The effect of droplet grouping was incorporated into the model
Summary
The efficiency of spray systems in combustion engineering systems relies strongly on the dynamics of the liquid droplets, and among other things, their tendency to form groups. This grouping tendency has an influence on their evaporation, the drag force applied on them, and on their final settling point. There are a number of previous works in the literature relevant to the study of single streams of monodisperse droplets. In his classical text, Lamb [4] considers the case of two spheres moving in the line of their centers. Happel and Pfeffer [5]
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