Aerodynamic characterization of a rotor in free rotation

An airborne, tethered, multi-rotor wind turbine, effectively a rotorcraft kite, provides one platform for accessing the energy in high altitude winds. The kite is maintained at altitude by its rotors operating in autorotation, and its equilibrium attitude and dynamic performance are affected by the aerodynamic rotor forces, which in turn are affected by the orientation and motion of the craft. The aerodynamic forces produced by such rotors can vary significantly depending on orientation, influencing the dynamics and stability of the system. This paper reviews the aerodynamic performance of an autorotating rotor through a range of angles of attack, and develops an aerodynamic model suitable for use in analysis of the dynamics, stability and design of a rotorcraft kite. The analysis utilizes a blade element model coupled with momentum theory for torque-free autorotation. The model uses a rigid-rotor assumption and is nominally limited to cases of small induced inflow angle and constant induced velocity. The model allows for linear twist. In order to validate the model, several rotors – off-the-shelf model-aircraft propellers – were tested in a low speed wind tunnel. Custom-built mounts allowed rotor angles of attack from 0 to 105 degrees in the test section, providing data for thrust, horizontal force, and angular velocity. Experimental results showed increasing thrust and angular velocity with rising pitch angles, whereas the in-plane horizontal force peaked and dropped after a certain value. The straightforward analytical results showed disagreement with the experimental trends especially at high pitch angles. The discrepancy was attributed to the rotor operating in turbulent wake and vortex ring states at high pitch angles, where momentum theory has proven to be invalid. However, adding a term for resisting torque to the model gives analytical results that show trends similar to the experimental values.