Efforts to increase the power output of wind turbines include Diffuser Augmented Wind Turbines (DAWT) or a shroud for the rotor of a wind turbine. The selected duct has three main components: a nozzle, a diffuser, and a flange. The combined effect of these components results in enriched upstream velocity for the rotor installed in the throat of the duct. To obtain the maximum velocity in the throat of the duct, the optimum angles of the three parts have been analyzed. A code was developed to allow all the numerical steps including changing the geometries, generating the meshes, and setting up the numerical solver simultaneously. Finally, the optimum geometry of the duct has been established that allows a doubling of the flow velocity. The flow characteristics inside the duct have also been analyzed in detail. An H-Darrieus Vertical Axis Wind Turbine (VAWT) has been simulated inside the optimized duct. The results show that the power coefficient of the DAWT can be enhanced up to 2.9 times. Deep dynamic stall phenomena are captured perfectly. The duct advances the leading-edge vortex generation and delays the vortex separation.