Steady and transient inflow dynamics with actuator disk vortex theory

Abstract

The actuator disk is a well-known and widely used theoretical tool in wind engineering. This work proposes a new theory based on an actuator surface, capable of treating time-varying vectorial load distributions and yaw/pitch misalignment. A simplified representation of vortex motion is used to arrive at a tractable problem. The theory is not restricted to disks; arbitrary coplanar (optionally disjoint) actuator surfaces may be modeled. Some of the theoretical novelties used in the modeling includes use of the fractional Laplacian and extensive use of the Fourier transform on R2. Promising experimental validation based on pitch-step experiments at the Tjæreborg turbine is furnished. Comparisons are also made to existing methodologies. Analysis and numerical work shows that the model encapsulates Coleman's vortex theory.