Simulation of Tethered Underwater Kites: Three Dimensional Trajectories for Power Generation

Abstract

In this paper, a numerical simulation of three dimensional motion of tether undersea kites (TUSK) for power generation is studied. TUSK systems consist of a rigid-winged kite, or glider, moving in an ocean current. One proposed concept uses a tethered kite which is connected by a flexible tether to a support structure with a generator on the ocean surface. The numerical simulation models the flow field in a three-dimensional domain near the rigid undersea kite wing by solving the full Navier-Stokes equations. A two-step projection method along with Open Multi-Processing (OpenMP) is employed to solve the flow equations. In order to track the rigid kite, an immersed boundary method is used. A NACA 0021 airfoil is used for the cross section shape of the kite, and the tension forces in the elastic tethers are modeled by a simple Hooke’s law. A grid refinement study has been carried out to ensure the independence of the numerical results on the grid mesh resolution. Also, the Reynolds number independency has been studied. PID control methods are used to adjust the kite pitch, roll and yaw angles during power (tether reel-out) and retraction (reel-in) phases to obtain desired kite trajectories. During the reel-out phase the kite moves in successive cross-current motions in a figure-8 pattern, the tether length increases and power is generated. During reel-in the kite motion is along the tether, and kite hydrodynamic forces are reduced so that net positive power is produced. Kite trajectories, hydrodynamic forces on the kite, kite tether tension and output power are determined and analyzed for a baseline TUSK simulation.