The accuracy of spray simulations depends strongly on the initial and boundary conditions imposed on both the gaseous and the liquid phase. In many applications the droplet size distribution and droplet velocities close to the atomizer cannot be determined. In this study, a semi-empirical primary atomization model for Lagrangian particle tracking of the dispersed phase in Euler-Lagrange simulations is proposed. The examined atomization concept of a liquid jet in cross-flow subjected to a high velocity air stream is a configuration typical of industrial gas turbine applications. The model provides initial and boundary conditions not only via correlations for global parameters like characteristic diameters, it also delivers the sizes, starting positions and velocities of the droplets. This leads to an improved approximation of the droplet formation, droplet size distribution, and droplet propagation encountered in real sprays, which is here assessed by comparing simulation results with measurements.