The study concerns the modeling and simulation of gas-droplet and droplet-droplet interactions on spray dynamics and droplet size distribution in turbulent spray flows where the spray is described in an Eulerian framework. The primary focus is to develop a suitable mathematical model that can describe the underlying physics including the polydispersion of the spray, evaporation, drag, coalescence, and interaction with the convective gas flow. This is achieved by applying the direct quadrature method of moments, which is extended to account for evaporation, drag force and coalescence by implementing well-established standard models available in literature. The model is developed and formulated in three-dimensional physical space, whereas the computations are carried out in a one-dimensional geometric configuration since the reference experimental setup is only one-dimensional. A water spray carried by nitrogen was injected through a hollow cone nozzle into a cylindrical spray chamber. The results reveal that evaporation and coalescence have a significant effect on the droplet size distribution whereas the droplet velocity is influenced by drag force as anticipated. Computational and experimental results agree very well when coalescence is considered.