Practical aero-engine fuel injection systems are highly complicated, combining complex fuel atomizer and air swirling elements to achieve good fuel-air mixing as well as long residence time in order to enhance both combustion efficiency and stability. While detailed understanding of the multiphase flow processes occurring in a realistic injector has been limited due to the complex geometries and the challenges in near-field measurements, high fidelity, first principles simulation offers, for the first time, the potential for a comprehensive physics-based understanding. In this work, such simulations have been performed to investigate the spray atomization and subsequent droplet transport in a swirling air stream generated by a complex multi-nozzle/swirler combination. A Coupled Level Set and Volume Of Fluid (CLSVOF) approach is used to directly capture the liquid-gas interface and an embedded boundary (EB) method is applied to flexibly handle the complex injector geometry. The ghost fluid (GF) method is also used to facilitate simulations at realistic fuel-air density ratio. Adaptive mesh refinement (AMR) and Lagrangian droplet models are used to efficiently resolve the multi-scale processes. To alleviate the global constraint on the time-step imposed by locally activated AMR near liquid jets, a separate AMR simulation focusing on jet atomization was performed for relatively short physical time and the resulting Lagrangian droplets are coupled into another simulation on a uniform grid at larger time-steps. The high cost simulations were performed at the U.S. Department of Defense high performance computing facilities using over 5000 processors. Experiments at the same flow conditions were conducted at UTRC. The simulation details of flow velocity and vorticity due to the interaction of the fuel jet and swirling air are presented. The velocity magnitude is compared with experimental measurement at two downstream planes. The two-phase spray spreading is compared with experimental images and the flow details are further analyzed to enhance understanding of the complex physics.