Wake characteristics of a utility-scale wind turbine under coherent inflow structures and different operating conditions

Understanding the wake characteristics of wind turbines under the influence of atmospheric turbulence is crucial for developing advanced turbine control algorithms, such as the coordinated turbine control for improving the performance of the entire wind farm as an integrated system. In this work, we systematically investigate the wake of a utility-scale wind turbine for different thrust coefficients, which is relevant to the coordinated axial induction control. Large-eddy simulation (LES) with novel actuator surface models for turbine blades and nacelle is employed to simulate turbine wakes. Different thrust coefficients are achieved by varying the tip-speed ratio, i.e., $\lambda =6.8,7.8,8.8,9.3$. The inflow is generated from a precursory simulation using a very large computational domain to include the large-scale flow structures in atmospheric turbulence. The computed results show that varying the tip-speed ratio gives rise to differences in wake statistics, such as the wake recovery rate and the turbulence intensity. However, the computed results also reveal similarities in wakes from different tip-speed ratios. It is found that the characteristic velocity defined by the thrust on the rotor scales the turbine-added turbulence kinetic energy computed based on different wake center locations. For all considered tip-speed ratios, two dominant frequencies of the large-scale motion of the wake are observed, one is the dominant low frequency of the large-scale flow structures in the inflow prevailing at almost all downwind locations, the other one is the frequency of Strouhal number about 0.15 prevailing at far wake locations ($>3\sim 4$ rotor diameters). The existence of the inflow frequency in the large-scale motion of wakes shows the effects of incoming large-scale flow structures on wake meandering. The Strouhal number of the second frequency, however, is typical for that of vortex shedding behind bluff bodies. This finding suggests the coexistence of the two mechanisms for wake meandering, i.e., inflow large-scale turbulent flow structures and the wake shear layer instability, with the corresponding motion termed inflow-driven wake meandering and shear-induced wake meandering, respectively. The effects of wake and turbine energy extraction on motion of different frequencies are examined for different tip-speed ratios. As approaching the turbine upwind, the energy of the low-frequency motion of the inflow is significantly attenuated, while the energy of the motion at frequencies higher than the inflow low frequency are observed to increase for most cases. In the near wake, decreases of energy are observed for all the frequencies in almost all the cases. At far wake locations, the energy of the motion at all frequencies is increased to a level higher than that of the inflow (at $2D$ turbine upwind) in almost all the cases. At last, the statistics of wake centers in the spanwise and vertical directions are examined. It is found that the probability density function (PDF) profiles of wake center fluctuations nearly collapse with each other for different tip-speed ratios. The Gaussian distribution is found to be an acceptable approximation for the PDF of wake center locations at near wake locations (e.g., $2D,4D$, and $6D$ turbine downwind), while it is a poor approximation at far wake locations (greater than $8D$ turbine downwind). Downwind variations of the mean values and the standard deviations of wake center fluctuations are also observed to nearly collapse with each other for different tip-speed ratios. The observed similarities of turbine wake statistics illuminate the possibility of developing advanced engineering models taking into account the unsteady features of turbine wakes for advanced turbine controls.

Figure 1

Power (a) and thrust (b) coefficients for different tip-speed ratios of the EOLOS wind turbine.

Figure 2

Statistics of the inflow. (a) and (b) contours of the time-averaged downwind velocity and TKE, respectively, on the $y-z$ plane from the inflow simulation, where the instantaneous flowfields are saved for the wind turbine simulation; (c) vertical profiles of the downwind velocity $\langle u\rangle$ (solid line) averaged in time and the spanwise direction and the logarithmic law $\frac{\langle u\rangle }{u^{*}}=\frac{1}{\kappa }ln\left(\frac{z}{z_0}\right)$ (dashed line), (d) the vertical profile of the TKE $k$ averaged in time and the spanwise direction, (e) the spanwise profile of the time-averaged downwind velocity at turbine hub hight ($z=z_h$), and (f) the spanwise profile of the TKE $k$ at turbine hub hight ($z=z_h$). The yellow boxes in (a) and (b) show the part employed in turbine simulations.

Figure 3

Contours of the instantaneous downwind velocity on the horizontal plane located at turbine hub height for (a) $\lambda =6.8$, (b) $\lambda =7.8$, (c) $\lambda =8.8,$ and (d) $\lambda =9.3$, respectively.

Figure 4

Variation of time and disk-averaged downwind velocity at different downwind locations. Red solid line, $\lambda =6.8$; green dashed line, $\lambda =7.8$; blue dash-dot line, $\lambda =8.8$; gray dash-dot-dot line, $\lambda =9.3$.

Figure 5

Downwind variation of (a) the disk-averaged turbulence intensity and (b) the maximum turbulence intensity within the disk for the three components of turbulence intensity, i.e., ${\sigma }_u, {\sigma }_v$, and ${\sigma }_w$ for the downwind, spanwise, and vertical components, respectively. Red solid line, $\lambda =6.8$; green dashed line, $\lambda =7.8$; blue dash-dot line, $\lambda =8.8$; gray dash-dot-dot line, $\lambda =9.3$. (a) ${\langle {\sigma }_{u,v,w}\rangle }_{\mathrm{disk}}$ and (b) ${\left({\sigma }_{u,v,w}\right)}_{\mathrm{disk},\max }$.

Figure 6

Spanwise profiles of velocity deficits $\langle \mathrm{\Delta }u\rangle$ for (a) averaged for all wake center locations, and (b)–(d) averaged when $-R\le y_c\le R, y_c<-R$, and $y_c>R$, respectively, at different downwind locations. Red solid line, $\lambda =6.8$; green dashed line, $\lambda =7.8$; blue dash-dot line, $\lambda =8.8$; cyan dotted line, $\lambda =9.3$.

Figure 7

Vertical profiles of velocity deficits $\langle \mathrm{\Delta }u\rangle$ for (a) averaged for all wake center locations, and (b)–(d) averaged when $-R\le (z_c-z_h)\le R, z_c-z_h<-R, z_c-z_h>R$, respectively, at different downwind locations. Red solid line, $\lambda =6.8$; green dashed line, $\lambda =7.8$; blue dash-dot line, $\lambda =8.8$; cyan dotted line, $\lambda =9.3$.

Figure 8

Spanwise profiles of turbine-added TKE $\mathrm{\Delta }k$ for (a) computed for all wake center locations, and (b)–(d) computed when $-R\le y_c\le R, y_c<-R$, and $y_c>R$, respectively, at different downwind locations. Red solid line, $\lambda =6.8$; green dashed line, $\lambda =7.8$; blue dash-dot line, $\lambda =8.8$; cyan dotted line, $\lambda =9.3$.

Figure 9

Vertical profiles of turbine-added TKE $\mathrm{\Delta }k$ for (a) computed for all wake center locations, and (b)–(d) computed when $-R\le (z_c-z_h)\le R, z_c-z_h<-R, z_c-z_h>R$, respectively, at different downwind locations. Red solid line, $\lambda =6.8$; green dashed line, $\lambda =7.8$; blue dash-dot line, $\lambda =8.8$; cyan dotted line, $\lambda =9.3$.

Figure 10

PSD profiles from cases of different tip-speed ratios at different downwind locations. The PSD is computed using the spanwise velocity fluctuations at different turbine downwind locations along the rotor centerline and normalized by the variance at $x=-2D$. Red solid line, $\lambda =6.8$; Green dashed line, $\lambda =7.8$; Blue dash-dot line, $\lambda =8.8$; Cyan dotted line, $\lambda =9.3$.

Figure 11

Downwind variations of the maximum PSD and the corresponding frequency in the four regions of different ranges of frequency for (a) $0.01\le fD/U_h<0.02$, (b) $0.02\le fD/U_h<0.14$, (c) $0.14\le fD/U_h<0.2,$ and (d) $0.2\le fD/U_h<0.32$, respectively. The PSD is computed using the spanwise velocity fluctuations at different downwind locations along the rotor centerline and normalized by the variance at $x=-2D$. Red solid line, $\lambda =6.8$; Green dashed line, $\lambda =7.8$; Blue dash-dot line, $\lambda =8.8$; Cyan dotted line, $\lambda =9.3$. It is noticed that the data are sampled every $0.5D$ and $1D$ in the turbine downwind and turbine upwind direction, respectively.

Figure 12

Scattered points showing instantaneous wake center locations at different downwind locations for the entire simulation time. Tip-speed ratio $\lambda =7.8$.

Figure 13

PDF of wake center locations in the spanwise direction at turbine hub height and different turbine downwind locations. Red solid lines, $\lambda =6.8$; green dashed lines, $\lambda =7.8$; blue dash-dot lines, $\lambda =8.8$; cyan dotted lines, $\lambda =9.3$. The thick black lines represent the fitted Gaussian distribution with the mean and standard deviation averaged from four cases.

Figure 14

PDF of wake center locations in the vertical direction along the rotor centerline at different turbine downwind locations. Red solid lines, $\lambda =6.8$; green dashed lines, $\lambda =7.8$; blue dash-dot lines, $\lambda =8.8$; cyan dotted lines, $\lambda =9.3$. The thick black lines represent the fitted Gaussian distribution with the mean and standard deviation averaged from four cases.

Figure 15

Skewness and kurtosis of wake center locations for (a) and (c) in the spanwise direction and (b) and (d) in the vertical direction, respectively, at different downwind locations. Red circles, $\lambda =6.8$; green squares, $\lambda =7.8$; blue triangles, $\lambda =8.8$; cyan diamonds, $\lambda =9.3$.

Figure 16

Mean and standard deviation of wake center locations for (a) and (c) in the spanwise direction and (b) and (d) in the vertical direction, respectively, at different downwind locations. Red solid lines, $\lambda =6.8$; green dashed lines, $\lambda =7.8$; blue dash-dot lines, $\lambda =8.8$; cyan dotted lines, $\lambda =9.3$. The thick black lines represent the Gaussian fitted mean and standard deviation averaged over the four cases. The black dashed lines show the best-fitted slopes of the thick black lines.

Figure 17

Effects of different window functions on the PSD profiles at different downwind locations for the $\lambda =7.8$ case. The PSD is computed using the spanwise velocity fluctuations at different turbine downwind locations along the rotor centerline and normalized by the variance at $x=-2D$. Red solid line, no window function; Green dashed line, $W_1$; Blue dash-dot line, $W_2$. The separation between two adjacent segments $S=20000$.

Figure 18

Effects of different values of separation $S$ on the PSD profiles at different downwind locations for the $\lambda =7.8$ case. The PSD is computed using the spanwise velocity fluctuations at different turbine downwind locations along the rotor centerline and normalized by the variance at $x=-2D$. Red solid line, $S=100000$; Green dashed line, $S=50000$; Blue dash-dot line, $S=20000$; Cyan dotted line, $S=10000$. We use $L=100000$ and the window function $W_2$ for tests with different values of $S$.