Optimum design of contra-rotating wind turbines with adjacent rotors

A downstream installed contrarotating rotor can efficiently extract the residual kinetic energy of a wind turbine wake, thus increasing the overall power coefficient. A significant interaction between the two rotors exists so that, to completely exploit the device potential, it is not advisable to adopt a classical design procedure conceived for a single-rotor configuration, as commonly seen in the existing literature. In particular, current approaches also oversimplify the design of the back rotor by merely mirroring the front rotor geometry, rather than optimising it for its power extraction duties. To fill this knowledge gap, the paper presents an original design strategy expressly conceived for contra-rotating wind turbines. This new approach optimises the geometry of both rotors, fully accounting for the interaction between them and the wake rotation at the outlet of the front wheel. The procedure adopts a calculus of variations approach aimed at maximising the overall power coefficient. It relies on a classical actuator disk model and is it valid for two adjacent rotors with the same diameter. As a result, the optimal chord and pitch distributions of the two rotors are evaluated for any combination of the front and back tip speed ratios. The procedure can be applied to marine turbines, too.