Helicoidal vortex model for steady and unsteady flows

Abstract

A helicoidal vortex model is used to predict the flow past the blades of a wind turbine. As the tip speed ratio (TSR) varies, the environment in which the blades operate varies, and for low enough TSR, the local angle of attack α will be larger than ( α) Clmax, the incidence of maximum lift. The problem becomes highly nonlinear and it is shown that adding an artificial viscosity term to the equation allows the iterative algorithm to converge toward a smooth solution that is physically acceptable. The introduction of unsteady effects is useful to understand the cyclic forces and moments due to yaw or tower interaction, both for the design of blades to account for fatigue and for power output prediction. The 2-D impulsively plunging plate problem is solved with a semi-implicit scheme and the integral and numerical solutions compared and shown to be in excellent agreement. A 2-D test case to study the convection of a periodic shedding of vorticity downstream of a blade element is analyzed using the same semi-implicit algorithm and a stretched mesh similar to that used to model a turbine vortex sheet. The scheme captures accurately the vorticity distribution in the wake. Finally, the scheme is applied to the simulation of the NREL two-bladed rotor in yaw to assess the validity of the approach.