An unsteady actuator annulus relationship for simplified multi-kite systems

Abstract

For classical horizontal axis wind turbines, there are many available ’engineering models’ that describe therelationship between unsteady induction factors and the nondimensional parameters describing the turbine’s per-formance, such as thrust coefficient. There is, as of yet, no such simple unsteady actuator annulus relationshipsuitable for multiple-kite airborne wind energy systems (MAWES). This work approximates such a relationshipfrom the Biot-Savart integral of a frozen, periodic vortex tube representing the geometry of a simplified pumping-cycle MAWES. A comparison is made between the behavior of a MAWES as predicted with this new actuatorannulus relationship and with the classic Pitt-Peters model.