This work presents a comprehensive numerical study on the hydrodynamic behaviour and power consumption of a cylindrical vessel stirred by a two-blade impeller, employing the simulation by the RRF method (Rotation Reference Frame). The study focuses on addressing the issue of power consumption in the context of blade orientation referring to different values equal to α=15°, α=30°, α=45°, α=90°, α=135°, and α=180°. The primary objective is to identify a novel design that promotes effective fluid circulation and exhibits lower energy consumption compared to standard geometries. By employing the commercial CFD code ANSYS CFX 14.0, the research delves into the impact of fluid rheology and blade curvature on mixing efficiency. The validation of the results, achieved by comparing them with data from existing literature, demonstrated a satisfactory agreement. According to our obtained results, it has been observed that the energy consumption decreases when the blade orientation exceeds 90°. This study contributes valuable insights into both blade orientation and Reynolds number effects (ranging from 1 to 100 for laminar flow), with the ultimate goal of proposing innovative designs that optimize fluid mixing efficiency while minimizing the consumed energy.