James C.
Beck A. Paul
Watkins ABSTRACT Hitherto, all polydisperse spray models have been based on discretizing the liquid flow field into groups of equally sized droplets. The work assessed here involves the implementation of a spray model [1-3] that captures the full polydisperse nature of the spray flow without using droplet size classes. The parameters used to describe the distribution of droplet sizes are the first four moments of the droplet number distribution function. Transport equations are written for the two moments which represent, per unit volume, the liquid mass and surface area, and two more moments representing the sum of the droplet radii and droplet number are approximated via use of a presumed distribution function which is allowed to vary in space and time. The velocities to be used in the two transport equations are obtained by defining moment-average quantities and constructing further transport equations for the relevant moment-average velocities. An equation for the energy of the liquid phase and standard gas-phase equations, including a k-e turbulence model, are also solved. All the equations are solved in a Eulerian framework using the finite-volume approach, and the phases are coupled through source terms. Effects such as droplet breakup and droplet—droplet collisions are also included through the use of source terms, and all the source terms are expressed in terms of the four moments of the droplet size distribution in order to find the net effect on the whole spray flow field.
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