Quantifying error of lidar and sodar Doppler beam swinging measurements of wind turbine wakes using computational fluid dynamics

摘要

Wind-profiling lidars are now regularly used in boundary-layer meteorologyand in applications such as wind energy and air quality. Lidar windprofilers exploit the Doppler shift of laser light backscattered fromparticulates carried by the wind to measure a line-of-sight (LOS) velocity.The Doppler beam swinging (DBS) technique, used by many commercial systems,considers measurements of this LOS velocity in multiple radial directions inorder to estimate horizontal and vertical winds. The method relies on theassumption of homogeneous flow across the region sampled by the beams. Usingsuch a system in inhomogeneous flow, such as wind turbine wakes or complexterrain, will result in errors.To quantify the errors expected from such violation of the assumption ofhorizontal homogeneity, we simulate inhomogeneous flow in the atmosphericboundary layer, notably stably stratified flow past a wind turbine, with a meanwind speed of 6.5 m s at the turbine hub-height of 80 m.This slightly stable case results in 15° of wind direction changeacross the turbine rotor disk. The resulting flow field is sampled in thesame fashion that a lidar samples the atmosphere with the DBS approach,including the lidar range weighting function, enabling quantification of theerror in the DBS observations. The observations from the instruments locatedupwind have small errors, which are ameliorated with time averaging.However, the downwind observations, particularly within the first two rotordiameters downwind from the wind turbine, suffer from errors due to theheterogeneity of the wind turbine wake. Errors in the stream-wise componentof the flow approach 30% of the hub-height inflow wind speed close to therotor disk. Errors in the cross-stream and vertical velocity components arealso significant: cross-stream component errors are on the order of 15%of the hub-height inflow wind speed (1.0 m s) and errors in thevertical velocity measurement exceed the actual vertical velocity.By three rotor diameters downwind, DBS-based assessments of wake wind speeddeficits based on the stream-wise velocity can be relied on even within thenear wake within 1.0 m s (or 15% of the hub-height inflow windspeed), and the cross-stream velocity error is reduced to 8% whilevertical velocity estimates are compromised. Measurements of inhomogeneousflow such as wind turbine wakes are susceptible to these errors, andinterpretations of field observations should account for this uncertainty.