Maximal power per device area of a ducted turbine

Abstract

The aerodynamic design of a ducted wind turbine for maximum total power coefficient was studied numerically using the axisymmetric Reynolds-averaged Navier–Stokes equations and an actuator disc model. The total power coefficient characterizes the rotor power per total device area rather than the rotor area. This is a useful metric to compare the performance of a ducted wind turbine with an open rotor and can be an important design objective in certain applications. The design variables included the duct length, the rotor thrust coefficient, the angle of attack of the duct cross section, the rotor gap, and the axial location of the rotor. The results indicated that there exists an upper limit for the total power coefficient of ducted wind turbines. Using an Eppler E423 airfoil as the duct cross section, an optimal total power coefficient of 0.70 was achieved at a duct length of about 15 % of the rotor diameter. The optimal thrust coefficient was approximately 0.9, independent of the duct length and in agreement with the axial momentum analysis. Similarly independent of duct length, the optimal normal rotor gap was found to be approximately the duct boundary layer thickness at the rotor. The optimal axial position of the rotor was near the rear of the duct but moved upstream with increasing duct length, while the optimal angle of attack of the duct cross section decreased.