Performance analysis of open and ducted wind turbines

In this paper the analysis of the aerodynamic performance of ducted wind turbines is carried out by means of a nonlinear and semi-analytical actuator disk model. It returns the exact solution in an implicit formulation as superposition of ring vortices properly arranged along the duct surface and the wake region. In comparison with similar and previously developed models, the method can deal with ducts of general shape, wake rotation and rotors characterised by radially varying load distributions. Moreover, the nonlinear mutual interaction between the duct and the turbine, and the divergence of the slipstream, which is particularly relevant for heavily loaded rotors, are naturally accounted for. Present results clearly show that a properly ducted wind turbine can swallow a higher mass flow rate than an open turbine with the same rotor load. Consequently, the ducted turbine achieves a higher value of the extracted power. The paper also presents a detailed comparison between the aforementioned nonlinear and semi-analytical actuator disk method and the widely diffused CFD actuator disk method. The latter is based on the introduction of an actuator disk model in a CFD package describing the effects of the rotor through radial profiles of blade forces distributed over a disk surface. A set of reference numerical data, providing the inviscid axisymmetric velocity and pressure field distributions, are generated with controlled accuracy. Owing to an in-depth analysis of the error generated by the semi-analytical method and to the exactness of the solution in its implicit form, the collected data are well-suited for code-to-code validation of existing or newly developed computational methods.