Wake Width: Discussion of Several Methods How to Estimate It by Using Measured Experimental Data

Abstract

Several methods of defining and estimating the width of a turbulent wake are presented and tested on the experimental data obtained in the wake past an asymmetric prismatic airfoil NACA 64(3)-618, which is often used as tip profile of the wind turbines. Instantaneous velocities are measured by using the Particle Image Velocimetry (PIV) technique. All suggested methods of wake width estimation are based on the statistics of a stream-wise velocity component. First, the expansion of boundary layer (BL) thickness is tested, showing that both displacement BL thickness and momentum BL thickness do not represent the width of the wake. The equivalent of 99% BL thickness is used in the literature, but with different threshold value. It is shown that a lower threshold of 50% gives more stable results. The ensemble average velocity profile is fitted by Gauss function and its σ-parameter is used as another definition of wake width. The profiles of stream-wise velocity standard deviation display a two-peak shape; the distance of those peaks serves as wake width for Norberg, while another tested option is to include the widths of such peaks. Skewness (the third statistical moment) of stream-wise velocity displays a pair of sharp peaks in the wake boundary, but their position is heavily affected by the statistical quality of the data. Flatness (the fourth statistical moment) of the stream-wise velocity refers to the occurrence of rare events, and therefore the distance, where turbulent events ejected from the wake become rare and can be considered as another definition of wake width. The repeatability of the mentioned methods and their sensitivity to Reynolds’ number and model quality are discussed as well.