Engineering Wake Induction Model For Axisymmetric Multi-Kite Systems

Multi-kite airborne wind energy systems (MAWES) fly two or more kites in a high-altitude orbit that allows a main tether to unroll a generator. An engineering wake induction model could simplify the (axisymmetric) aerodynamics of such an unsteady actuator-annulus with variable thrust-coefficient, flight-radius, and downwind-direction apparent velocity, in comparison to high-fidelity wake models. To the authors' knowledge, existing engineering models do not predict the influence of variable flight radius. The goal of this paper is to synthesize a MAWES engineering model, a closed-form function approximating the axial induction factor ã, specifically at the kite mid-span, using linearized wake parameters, as available from a dynamics solver. A vortex tube model is used to construct a plausible approximation of the induction, which is then heavily simplified for computation tractability while retaining important flow physics.