The application of compressor water injection in aeroengines is of renewed interest in the civil aviation industry. Water due to its unprecedented heat capacity has the potential to cool the engine air through evaporation and thus reduce the NOx emissions formed in a combustion process. It is well known that the evaporative cooling increases thermodynamic cycle efficiency and thus improves the fuel economy. A relatively unexplored area, however, is the entropy generation due to water phase change as well as the balance between the corresponding entropy yield and the savings from the cooling of the core compressor flow. Hence, little consensus in the literature exists on the ultimate effect of water injection on compressor efficiency. In this study, a numerical analysis of water injection on an axial transonic rotor was carried out. The compressor model was tested at near-peak efficiency conditions with and without water injection. The flow was analysed using the Eulerian-Lagrangian approach with two-way coupling and the k-ω Shear Stress Transport turbulence model with Reattachment Modification. A universal, second thermodynamic law approach to quantify the entropy generation is proposed and used to evaluate the compressor flow. Results show that evaporation can facilitate the compression process and does not impair the compressor efficiency if applied at favourable conditions. The entropy generation in droplet-laden flow scales according to the gains from cooling effect and losses due to the evaporation and increased friction in the fluid. Some of the discrepancies in the public domain could be addressed, showing that the observed improvement in compressor efficiency is highly sensitive to the entropy flux measurement location. Most benefits from water injection were observed at the rotor tip proving the case for part-span injection from an entropy balance perspective.