Primary atomization is the key element in spray flow simulations. We have, in our previous work, used and validated the integral form of the conservation equations, leading to the "quadratic formula" for determination of the drop size during spray atomization in various geometry. A computational protocol has been developed where this formulation is adapted to existing computational frameworks for continuous and dispersed (droplet) liquid phase, for simulations of pressure-atomized sprays with and without swirl. In principle, this protocol can be applied to any spray geometry, with appropriate modifications in the atomization criterion. The pre-atomization continuous liquid motion (e.g. liquid column or sheet) is computed using volume-of-fluid (VOF) or similar methods, then the velocity data from this computation is input to the quadratic formula for determination of the local drop size. This initial drop size, along with the local liquid velocities from VOF, is then used in a Lagrangian tracking algorithm for the post-atomization dispersed droplet calculations. 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 geometries for complete and efficient computations of spray flows.

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