The effect of droplet spacing on spray and group combustion

Formulations of the governing equations for burning air/fuel spray mixtures are discussed. The subsystem of equations describing liquid properties are formulated in three ways: Eulerian description, Lagrangian description, and probabilistic or distribution function description. The relationships amongst these approaches and the relative advantages and disadvantages are discussed. The reduction of numerical error, the ability to resolve multivalued solutions, and the ability to achieve resolution a scale smaller than droplet spacing lead to a preference of the Lagrangian method over the Eulerian method. However, when resolution is desired on a scale smaller than the average droplet spacing, the location of each droplet is known only in a statistical manner. The advantages of a probabilistic formulation in this case are evaluated.