| A numerical and analytical investigation is presented in this thesis in which the major characteristics of spray and single droplet impingement are modeled. First a stochastic model based on the sampling of velocity and size distributions of secondary droplets is used to simulate impingement breakup. The numerical predictions are compared to experimental results yielding acceptable agreement. The effect of surface roughness on the splashing threshold is incorporated into the study and is found to play a major role in dictating the average sizes of secondary droplets. The second part of this thesis presents an analytical model of single droplet splashing on a slightly wetted surface. The crown walls created by the impact are treated as a series of two surfaces of discontinuity from which the jump conditions are developed along with the governing equation for crown radius. Both viscid and inviscid situations are treated. The results are validated by comparing with experimental and computational results from the literature. The effects of target surface film height and wall friction on the crown radius evolution, mass absorbed into the crown, and momentum lost are investigated. Crown height calculations are performed and an overall energy analysis, which includes a statistical representation of secondary droplet quantities, is applied to the splashing event. It is found that the splashing characteristics are only sensitive to variations in film height and Weber number not Reynolds number. Lastly, the formation and evolution of a liquid film produced by impingement are modeled numerically. The governing equations for the film are derived and are subsequently solved using a particle method. It is shown that during the time where most of the film evolution takes place, the gravitational force and gas-induced shear stress are negligible. It is also shown that the thin film assumptions break down when a derived non-dimensional quantity becomes greater than or equal to O(1), fortunately this occurs late after impingement when no substantial film evolution takes place. Numerical predictions are compared to experimental data consisting of film edge displacement and film thickness measurements resulting in reasonable agreement. |
