Acoustics and ligament formation within a self-generating and self-sustaining pulsating three-stream injector are analyzed and discussed due to the importance of breakup and atomization of jets for agricultural, chemical, and energy-production industries. An extensive parametric study was carried out to evaluate the effects of simulation numerics and boundary conditions using various comparative metrics. Numerical considerations and boundary conditions made quite significant differences in some parameters, which stress the importance of using documented and consistent numerical discretization recipes when comparing various flow conditions and geometries. Validation exercises confirmed that correct droplet sizes could be produced computationally, the Sauter mean diameter (SMD) of droplets/ligaments could be quantified, and the trajectory of a droplet intersecting a shock wave could be accurately tracked. Swirl had a minor impact by slightly moving the ligaments away from the nozzle outlet and changing the spray to a hollow cone shape. Often, metrics were synchronized for a given simulation, indicating that a common driving mechanism was responsible for all the global instabilities, namely, liquid bridging and fountain production with shockletlike structures. Interestingly, both computational fluid dynamics (CFD) and the experimental non-Newtonian primary droplet size results, when normalized by distance from the injector, showed an inversely proportional relationship with injector distance. Another important outcome was the ability to apply the models developed to other nozzle geometries, liquid properties, and flow conditions or to other industrial applications.