Computability of spray flows is an important issue, from both fundamental and practical perspectives. Spray flows have important applications in fuel injection, agriculture, medical devices, and industrial processes such as spray cooling. For this reason, many efforts have been devoted to experimental, computational and some theoretical aspects of spray flows. In particular, primary atomization, the process of bulk liquid transitioning to small droplets, is a central and probably the most difficult aspect of spray flows. This thesis discusses developed methods, results, and needed improvements in the modeling of primary atomization using a predictive Sauter Mean Diameter (SMD) formula. Primary atomization for round injectors and simplex atomizers is modeled using a three-step procedure. For each spray geometry, a volume-of-fluid simulation is run to resolve the trajectory of the intact liquid core. Atomization criterion is applied to the volume-of-fluid velocity field to determine atomization sites. Local droplet size is predicted at the atomization sites using the quadratic formula for Sauter Mean Diameter. Droplets with the computed drop size are injected from the atomization sites and are tracked as point-particles. A User Defined Memory (UDM) code is employed to compute steady-state Sauter Mean Diameter statistics at locations corresponding to experimental interrogation locations. The resulting Sauter Mean Diameter, droplet trajectory, and droplet velocity are compared against experimental data to validate the computational protocol. This protocol can be implemented on coarse-grid, time-averaged simulations of spray flows, and produces convincing results when compared with experimental data for pressure-atomized sprays with and without swirl. This approach is general and can be adapted in any spray geometry for complete and efficient computations of spray flows.