Connecting thrust and torque with the wake tip vortex geometry - application to wind turbines and propellers

Wind turbines and propellers have historically been analysed using either blade element momentum theory or vortex methods. This Master of Science thesis deals with the latter type. In present free wake methods, the vortices trailing off the blades are assumed to be governed only by the Biot-Savart potential flow induction law, forming a helical surface sheet. In reality, partly due to viscosity, however, the vorticity is concentrated into tip vortices, one per blade tip, and into root vorticity of a more indistinct character. A look at some basic aspects of flow mechanics was seen as necessary to explain the discrepancy between present theory and reality. The result of this work is a method to calculate radius and pitch of the concentrated tip vortex spirals, from given values of the thrust and torque coefficients CT and CQ and a given strength of the maximum circulation around the blade(s). To achieve this, the inverse problem must be solved. I.e., from known tip vortex spiral parameters the corresponding CT and CQ were first calculated and saved in a database. This database is henceforth used together with an interpolation routine, which makes inversion possible. The computer code for the inversion is also part of the thesis.