The current study investigates the flow structures within an aerated-liquid (barbotage) injector, which is designed to facilitate the rapid breakup of a hydrocarbon fuel jet prior to its entering a scramjet combustor, and the spray structures in the corresponding crossflow. Simulations of the transient, three-dimensional, two-phase flow within the "out-in" injector operating at different gas-to-liquid (GLR) mass ratios and in the corresponding crossflow domain have been performed, and the results compared with experimental pressure measurements of the injector and shadowgraph images of the crossflow. The numerical method solves a "mixture" model of two-phase flow using a preconditioning strategy. High-order spatial accuracy and good interface-capturing properties are facilitated by the use of shock-capturing schemes combined with second order TVD methods. Also, an immersed boundary method is used to investigate the probe effects, and a droplet transport model is used in the crossflow simulations to get more details about effect of droplet size. The injector simulation results highlight the effects of mesh refinement and turbulence model on the predicted solutions. The pressure drop across the injector is predicted reasonably well by the computational methodology, and the trend of increasing injector pressure with increasing GLR is captured properly. Predictions of the absolute pressure level within the injector show some discrepancies in comparison with experimental data but agree well with theoretical estimates. The results of the injector simulations with plenum included are consistent with the results of the discharge tube cases. If the centerline pressure is close to the experimental data, the gas mass flow rate at outlet will approach a value below the experimental data. If the gas mass flow rate at outlet approaches the experimental data, then the centerline pressure will be higher than the experimental data, but agrees well with theoretical analyses. The intrusion of the probe has little effect on the flowfield if the probe is contained wholly within the liquid core, but does affect the flowfield if the probe tip is in the two-phase mixing region, instead of the liquid core. The results of crossflow show that the two-phase flow injects into the crossflow, bends towards the streamwise direction, disperses into a spray plume, and initiates a horse-shoe shape structure of the jet in the cross-sectional planes. The result based on the previous injector simulation at a higher inlet gas pressure shows best penetration height prediction among all freestream Mach 0.3 cases. Including the droplet transport model gives a similar spray structure in the X-Z centerplane as that of the mixture model, but gives a different spray structure in the cross-sectional planes. The horse-shoe shaped structure fades away with increases in the droplet diameter size, and the liquid mass accumulates to the X-Z centerplane.