To assist the industrial engine design process, 3-D computational fluid dynamics simulations are widely used, bringing a comprehension of the underlying physics unattainable from experiments. However, the multiphase flow description involving a liquid fuel jet injected into the chamber is still in its early stages of development. There is a pressing need for a spray model that is time efficient and accurately describes the cloud of fuel and droplet dynamics downstream of the injector. Eulerian descriptions of the spray are well adapted to this highly unsteady configuration. The challenge is then to capture accurately both the evaporating spray polydispersity and its two-way mass, momentum and energy interactions with the surrounding gas phase in this framework. The Eulerian Multi-Size Moment (EMSM) model, a high-order (in size) moment model has proved to be well adapted for the treatment of polydispersity. Moreover, it requires less computational effort relative to competing methods, with a single section for the size phase space. Academic test cases have demonstrated its great potential for industrial applications using one-way coupling. Recent modeling and numerical development efforts have resulted in an extension to two-way coupling with an unconditionally stable and accurate numerical scheme, while preserving the size moment space. All these developments have been successfully verified through injection simulations in the context of laminar flow. In the present contribution, in preparation for comparisons with experimental data, an extension to two-way coupling to account for the droplet-gas turbulence interactions is developed and validated for academic cases using physical data for realistic internal combustion engine conditions.