Unsteady wake modelling for tidal current turbines

The authors present a numerical model for three-dimensional unsteady wake calculations for tidal turbines. Since wakes are characterised by the shedding of a vortex sheet from the rotor blades, the model is based on the vorticity transport equations. A vortex sheet may be considered a jump contact discontinuity in tangential velocity with, in inviscid hydrodynamic terms, certain kinematic and dynamic conditions across the sheet. The kinematic condition is that the sheet is a stream surface with zero normal fluid velocity; the dynamic condition is that the pressure is equal on either side of the sheet. The dynamic condition is explicitly satisfied at the trailing edge only, via an approximation of the Kutta condition. The shed vorticity is the span-wise derivative of bound circulation, and the trailed vorticity is the time derivative of bound circulation, and is convected downstream from the rotors using a finite-volume solution of vorticity transport equations thus satisfying the kinematic conditions. Owing to an absence in the literature of pressure data for marine turbines, results from the code are presented for the NREL-UAE Phase IV turbine. Axial flow cases show a close match in pressure coefficients at various spanwise stations; however, yawed flow cases demonstrate the shortcomings of a modelling strategy lacking viscosity.