The induction zone/factor and sheared inflow: A linear connection?

Abstract

Sheared inflow causes significant periodic load variations in wind turbine blades, but has only limited impact on the mean wake deficit. Following these findings the wind speed reduction upstream of the turbine - referred to as the induction zone - might also show little difference to uniform inflow. Using the local free-stream velocity to normalise the upstream flow-field should then render uniform and sheared inflow induced velocity profiles indiscernible, hinting towards wind shear acting solely as a linear addition. This has great implications in BEM methods for determining the velocity at the blades and also for near-rotor lidar measurements. The latter being applied in for power/loads assessment and turbine control. LES simulations with an actuator line representation of the rotor confirm the linearity assumption for moderate wind shear. To estimate the normal velocities at the disc the annularly averaged thrust coefficient is best suited, when the induction is imposed on the inflow profile. A strictly local relationship breaks down in strongly sheared flow. A simple induction zone model devised for uniform inflow estimates the velocity upstream within ±0.5% even at extreme shear in the upper half of the rotor and at least three rotor radii away from the turbine.