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.

Grid turbulence studied by Particle Image Velocimetry

“…Wakes are widening as described e.g. by [14] -note the double maxima of TKE at small distance (Fig. 3(a)), at later stage (Fig.…”

Effect of Manufacturing Inaccuracies on the Wake Past Asymmetric Airfoil by PIV

“…We see that the wake width increases with distance; however, at small Reynolds numbers, there is a minimum of the wake width. This minimum would be more apparent when taking into account the fluctuations, as shown in [35]. The observed growth of wake width is approximately linear, but, according to Eames [36], the transition to ∼ x 0.5 growth can be expected downstream.…”

“…At the highest Re, some noise appears in the bottom right corner. The wake width δ w can be calculated by using multiple approaches [35] depending on which physical property has to be explored [35]; this shows that for comparison purposes, the most suitable wake width is determined as twice the σ-parameter of a Gaussian function fitted to the ensemble-average stream-wise velocity profile:…”

Vorticity statistics in the near wake of asymmetric prismatic airfoil NACA 64-618 at negative angle of attack –10° at Reynolds numbers 1.6 ⋅ 104 and 1.6 ⋅ 105 in distance 0.0 – 0.4 × chord past trailing edge measured by Particle Image Velocimetry

“…Therefore, the wake is bounded by the sharp cliff of skewness in the most distant area, in which a vortex can be ejected. This property can be used as a wake boundary [9]. The flatness (or 4 th statistical moment or kurtosis, česky koeficient špičatosti) is…”