In the most application of nozzle with gas-liquid two-phase flow, the quality of mixture in exhaust of nozzle is the most important parameter as well as the flow velocity. On the other hand, in some industrial application, such as water injection in forced induction (turbocharged or supercharged) internal combustion engine the spray quality is the main goal of designing. In this case and for improving of injection performance the air-water two phase nozzle injection flow is more remarkable subject. There are two ways for this purpose, premixed or un-premixed air-water in entrance of the nozzle. In both cases, the nozzle not only has to accelerate gas and liquid to extra high velocity, but also it is supposed to have a high quality mixture in exhaust of nozzle. In this study, the turbulent gas-liquid two-phase premixed/un-premixed flow through the nozzle is simulated by the Eulerian-Lagrangian approach. The gas phase is treated as a continuum by solving the time-averaged Navier-Stokes equations, while the liquid as a dispersed phase is solved by tracking a large number of droplets through the calculated flow field. The pressure, velocity and Mach number profiles as well as air flow-rates and particle residence time inside the nozzle for various back pressure values have been computed. This work has been validated by comparison of pressure profiles and air flow-rates between simulated results and available experimental results for un-premixed nozzle flow.