For simulations of liquid jets in crossflows, the primary atomization can be treated with the quadratic formula, which has been derived from integral form of conservation equations of mass and energy in our previous work. This formula relates the drop size with the local kinetic energy state, so that local velocity data from the volume-of-fluid (VOF) simulation prior to the atomization can be used to determine the initial drop size. This initial drop size, along with appropriately sampled local gas velocities, is used as the initial conditions in the dispersed-phase simulation. This procedure has been performed on a coarse-grid platform, with good validation and comparison with available experimental data at realistic Reynolds and Weber numbers, representative of gas-turbine combustor flows. The computational procedure produces all the relevant spray characteristics: spatial distributions of drop size, velocities, and volume fluxes, along with global drop size distributions. The primary atomization module is based on the conservation principles and is generalizable and implementable to any combustor geometries for accurate and efficient computations of spray flows.