Actuator Disc Methods Applied to Wind Turbines

This thesis concerns the axisymmetric actuator disc model and its extension to a three dimensional actuator line technique which, combined with the incompressible Navier-Stokes equations, are applied to describe the aerodynamics of wind turbine rotors. The developed methods are used to investigate the aerodynamic behaviour of coned rotors, rotors exposed to yawed inflow and tunnel blockage. Miscellaneous investigations are conducted in order
to analyze the consistence of some basic assumptions of the Blade Element Momentum (BEM) method, such as the influence of pressure on expanding streamtubes and the accuracy of tip correction theories. In the latter case an inverse formulation of the equations were applied.

Results for the coned rotor demonstrates that the Navier-Stokes methods, both the actuator disc and actuator line, captures the changed aerodynamic flow behaviour whereas a modified BEM method is incapable of handling flow through coned rotors. For rotors exposed to yawed inflow, the actuator disc method combined with appropriate sub models predicts structural loads with good accuracy. At high yaw angles the actuator line method capture observed effects from the root vortex, which axisymmetric methods is incapable of. Computations on rotors inserted into a tunnel show that the Navier-Stokes methods fully resolve the effects of tunnel blockage. A new solution to the inviscid axial momentum analysis on tunnel blockage by Glauert, is also presented. The new solution compares excellent with results presented for the equivalent free air speed obtained with the Navier-Stokes methods.

An analysis of pressure forces acting on expanding the streamtubes revealed that the influence of pressure forces is negligible for the velocities at the rotor disc. A new approach to solve the heavily loaded actuator disc is presented, using a new numerical technique based on solving the equations original formulated by Wu. The formulations is fast to run on computer, however, less accurate than Navier-Stokes computations. A new method for inverse determination of the tip-correction factor is believed to be correct, however, the obtained results reveal uncertainties which needs further investigations.