ILASS Americas 16th Annual Conference on Liquid Atomization and Spray Systems
May 2003, Monterey, California
A mathematical framework for modeling partly-resolved particles or droplets in a flowfield can be developed using methods borrowed from Large-Eddy Simulations (LES) of turbulence. We begin by constructing an equation set that is valid over the full physical domain, including the portions internal to the particles. The filtering process is then unaffected by the presence of particles, and can be applied over the full domain. For very small particles, the resulting equations reduce to the standard point-particle models, and illustrate how the particle drag forces should be interpolated onto a discrete grid. As the particle size increases, these equations provide a series of extensions to the point-particle models, allowing a range of models from small particles with simple wake effects to large particles where the flow is nearly resolved. We demonstrate the utility of this framework by calculating simple particle models for two cases of particle sizes, including one where the particle diameter is on the order of the computational grid spacing, and show that it provides sensible model parameters and produces appropriately accurate results.