1 Introduction

With the fast growing number of wind farms being installed worldwide, it is necessary to obtain a deep understanding of wind turbine working principles and its energy conversion process. Today, wind turbines are often placed close together in small clusters or in large wind farms (Ivanell et al., 2009), which means that they operate in the wakes of the upstream wind turbines. Inflow conditions dominated by vortical structures created by upstream turbines may reduce the power performance for the downstream turbines. Thus, a good understanding and modeling of the wake behavior of wind turbines is of great significance to guide the operations of wind farms.

Wind turbine wakes can be distinctly divided into the near wake regions and the far wake regions. The near wake region is taken as the area just behind the rotor, approximately up to one rotor diameter downstream (Vermeer et al., 2003). The wind turbine near the wake region is characterized by a complex coupled vortex system, unsteadiness, and strong turbulence heterogeneity (Zhang et al., 2012). The investigation of wind turbine’s near wake flow characteristics has important significations. It constitutes the basis of wind turbine load calculation, aeroacoustic noise control, and blade design. As the numerical simulation model does not yet have sufficient accuracy, the experimental method to explore the mechanism of wind turbine wake flow is still of great significance. In the past few years, there have been many investigations on the wind turbine near wake which primarily focus on their global properties, such as power coefficient Cp (Jiang et al., 2007; Chu and Chiang, 2014), axial force coefficient CT, average velocities (Vermeer, 2001; Abdelsalam et al., 2014), and tip vortex properties (Whale and Anderson, 1993; Lignarolo et al., 2014). The investigation of the distribution of average velocity behind the horizontalaxis wind turbine rotor has revealed an expansion and a decay of the 3D wake (Hu and Du, 2009). Some experimental investigations into the properties of the vortex wake behind a wind turbine rotor have revealed the formation and evolution of the helical tip vortices (Whale et al., 2000; Yang et al., 2012). It can be found that the previous studies on the wake tend to either concern velocity distribution or tip vortex properties, and only a few studies have been done on turbulent kinetic energy and Reynolds stresses in the near wake. However, turbulent flow characteristics reflected by turbulent kinetic energy and Reynolds stresses have a significant impact on the energy output process of wind turbines (Breton et al., 2014). Therefore, in this paper, the wind turbine near wake flow parameters, including instantaneous vorticity, average velocities, turbulent kinetic energy, and Reynolds stresses, are studied, and their evolution rules in the near wake are summarized.

Phase-locked particle image velocimetry (PIV) is now widely employed to measure flow statistics such as velocity (Hirahara et al., 2005; Lee and Wu, 2013), turbulence intensity (Whale et al., 1996; Liu et al., 2010), shear stress (Angele and Muhammad-Klingmann, 2006; Stafford et al., 2012), and vorticity (Whale et al., 2000; Jin et al., 2014), and to subsequently identify large-scale coherent flow structures. Compared with traditional PIV, time resolved particle image velocimetry (TRPIV) has a higher sampling frequency and can grasp more detailed information of flow structures. TRPIV possesses obvious advantages in measuring the instantaneous flow field parameters, so it will play a more important role in the investigation of wind turbine wakes. In our present experiment, TRPIV is applied to measure wind turbine flow properties at different tip speed ratios (TSRs).

The present paper addresses the need for detailed measurements of wind turbine near wakes, to establish an experimental database to validate computational fluid dynamics models. Both instantaneous properties and average properties are presented, and the flow properties are compared among different TSRs. All the flow properties and the size are normalized, so the results can also serve as a reference to the experimental or simulated data of different operating conditions.

2 Experimental setup

The experimental setup is composed of a wind turbine model, closed wind tunnels, TRPIV testing system, and a tracer particle generator. Fig. 1 shows the overall layout of the experimental equipment. Fig. 2 shows the size of the wind tunnel, the wind tunnel cross-sectional area, which is a square whose size is 920 mm×920 mm, and a wind turbine main shaft with a center distance from the ground of 460 mm, and the radius of the wind turbine blade is 165 mm. The blockage ratio of the rotor swept area to the cross-sectional area of the wind tunnel in the present experiment is 10.1%. According to previous studies (Chen and Liou, 2011; Chu and Chiang, 2014), the blockage correction is less than 5% and not required when the blockage ratio is around 10% in the wind tunnel experiment. Therefore, the influence of the blockage ratio is limited and no blockage correction is performed in the present study. Fig. 3 shows the testing window for the TRPIV experiment. The wind turbine model used in the experiment is a miniature of a 100 W wind turbine, and the size ratio of the model to the wind turbine prototype is 1:4.2. The rated wind speed of the 100 W wind turbine is 8 m/s, the starting wind speed is 3.5 m/s, and the rated TSR is 5. The NACA4415 airfoil is adopted in the wind turbine model, and the detailed chord and twist distributions of the blade are shown in Table 1.

Fig. 1
figure 1

Experimental setup

Full size image
Fig. 2
figure 2

Diagram of the wind tunnel size

Full size image
Fig. 3
figure 3

TRPIV testing window

Full size image
Table 1
figure Tab1

Blade chord and twist distributions in the radial direction

Full size image

The experiments were conducted in the Key Laboratory of the Wind and Solar Power Energy Utilization Technology Ministry of Education and Inner Mongolia Construction, China. The wind turbine was arranged at B1/K2 closed test section in the wind tunnel. The wind speed can be adjusted in the range of 0–60 m/s, and the experiments are conducted at chord Reynolds numbers in the range of 5455–23 145. The TRPIV test system uses the Nd:YLF laser (German LaVision Company) with an operating frequency range of 1.10 kHz. The peak energy of the laser is 200 mJ, while the energy is 10 mJ when the frequency is 1 kHz, and the pulse duration is 150 ns. The maximum frame rate of high-speed 12 bit charge-coupled device (CCD) camera can be up to 5400 fps, and the frame rate in this experiment is set at 1000 fps, while the corresponding resolution is 1024×1024 pixels. Tracer particles in these experiments are using dioctyl sebacate (DEHS), and its particle diameter is about 1 μm.

The PIV data and the mode for the correlation can be selected by using the vector calculation. The cross-correlation algorithm is applied to calculate a vector field on two single-exposed images. The PIV evaluation is performed in a multi pass with decreasingly smaller window sizes, and the window sizes are between 32×32 pixels and 64×64 pixels with 75% and 50% overlaps, respectively. In addition, the high accuracy mode for the final passes is applied so that a more sophisticated reconstruction algorithm can be used for the image correction and reconstruction.

The wind turbine yaw angle is 0° in the present experiments, and the laser beam is vertical to the plane of the ground and goes through the rotation axis of the wind wheel. The acquisition camera is placed outside the wind tunnel and is vertical to the laser plane. Through the organic glass window, the filming area of the camera is about 230 mm×230 mm. One of the wind turbine blades is defined as the reference No. 1 blade and the plane where the reference No. 1 blade leading edge is rotated to the laser plane as the 0° plane. Using the phase locked position system, data collection begins when the No. 1 blade rotates to the 0° plane, and 1000 samples are collected every second as the sampling frequency is 1000 Hz. In the present experiments, the inflow wind velocity is 11 m/s, the turbulence intensity of inflow is 0.5%, and the TSRs are in the range of 3–5. The testing conditions are summarized in Table 2.

Table 2
figure Tab2

Testing conditions set

Full size image

3 Results and discussion

3.1 Evolution of instantaneous flow structures

With the help of TRPIV technology, instantaneous flow field data can be collected at a high frequency. To analyze the evolution rules of near wake instantaneous flow structures, the flow parameters are measured every 0.001 s in our present study. Fig. 4 shows the instantaneous vortex structures when the TSR is 4 and the No. 1 blade rotates to the 0° plane. The process of vortex generation and shedding in the near wake can be observed from Fig. 4. In addition, unsteady vortex structures shedding from the blade roots and turbine nacelle are also visualized clearly from the PIV measurement results.

Fig. 4
figure 4

Instantaneous vortex structures when tip speed ratio is four

Full size image

The formation and evolution rules of the wind turbine near the wake vortex structures are displayed in Fig. 5, which shows the near wake vortex from 0 s to 0.008 s as the time that the wind turbine rotates 1/3 circular is 0.00785 s when the TSR is 4. It was found that a blade tip vortex generated when No. 1 blade rotates to 0° plane at 0 s, and then the tip vortex sheds from the turbine blade and moves downstream. As shown in Fig. 4, the blade tip vortex induced by the No. 1 blade and the other two tip vortices induced by other blades form a moving tip vortex array in the 0° plane. The next blade tip vortex generation can be observed at 0.008 s (about 1/3 rotor rotation period).

Fig. 5
figure 5

Evolution of instantaneous vortex structures when the tip speed ratio is four

Full size image

3.2 Average velocities

Fig. 6 shows the contours of a normalized axial average velocity u/U when the inflow wind velocity U (U refers to the inflow velocity at the turbine hub height) is 11 m/s and the TSR is 4. This result displays part of the flow areas behind the wind turbine, and the position of the wind turbine can be seen in Fig. 6. The obvious velocity increased region and velocity deficit region can be observed, and the velocity deficit region corresponding to the region where the kinetic energy from the wind is transformed into the mechanical energy of the wind turbine rotors. Velocity backflow phenomenon can be observed in the wind turbine blade root region, which is due to the wind energy encountering a great loss of dynamic pressure in this region.

Fig. 6
figure 6

Contours of normalized axial average velocity u/U when tip speed ratio is four

Full size image

Detailed flow field information should be obtained, so that the experimental results can be employed to verify the numerical model. Fig. 7 shows the near wake axial average velocity quantitative characteristics of different TSRs at different downstream locations. From these results, it is found that the axial velocity deficit region primarily occurred at y/R less than 0.4, in the upper wake when y/R is larger than 0.9, the axial velocity may exceed the inflow wind velocity, and u/U may reach as large as 1.2 because of the blockage effect. In the middle, there exists a region where the velocity nearly remains at the inflow velocity, when y/R is between 0.5 and 0.9. A conclusion also can be made that the wake influence region in the axial direction is far more than one radius length as the fluid axial average velocity has not fully recovered to the inflow velocity when x/R=1.0. Generally speaking, the average velocity shares similar trends for cases with different TSRs, and when y/R is larger than 0.4, the axial velocity increases as the TSR increases. A phenomenon can be observed in Fig. 7 that the velocity curves at different TSRs converge at one point where y/R is about 0.9 and u/U is about 1.0, which means that the axial average velocity at different TSRs in the wake reach the inflow velocity almost at the same radial location. As the axial flow interference factor is defined as a=1-u/U, the distribution characteristics of the axial flow interference factor can also be acquired from the results, and it can be found that the axial interference factor decreases along the radial direction. The distribution characteristics of the axial interference factor obtained from the wind tunnel experiment can be applied to analyzing the validity of the assumptions of the blade-element momentum method.

Fig. 7
figure 7

Vertical profiles of the normalized axial average velocity u/U for three different tip peed ratios at six different downstream locations

Full size image

To acquire the evolution rules of the axial average velocity along the downstream direction, vertical profiles of the normalized axial average velocity u/U at x/R=0.2, 0.6, 1.0 when the TSR is 4 are presented in Fig. 8. This result suggests that the axial average velocity increases along the downstream direction when y/R is less than 0.25, which is due to the axial velocity in the blade root region suffering a greater loss in kinetic energy, then it would obtain from the kinetic energy in the upper fluid in the near wake region. The axial average velocity decreased when y/R is between 0.25 and 1.0, which can be explained by that fluid kinetic energy in this region, which is partly used to compensate the loss in static pressure, as the static pressure of fluid has suffered a great loss when the wind goes through the wind turbine blades. The decline in the axial velocity behind the wind turbine blades would lead to the fluid volume expansion in the near wake, so the axial average velocity in the region, with y/R larger than 1.0, would increase. Accordingly, a conclusion can be made from the analyses that in the 3D flow field of wind turbine near wake, wind in the region y/R is between 0.25 and 0.9 and would expand toward both the blade tip region and the blade root region. A conclusion can also be made from the distribution of the velocity that the turbulence intensity of the fluid in the near wake would be strengthened after the wind goes through the wind turbine blade.

Fig. 8
figure 8

Vertical profiles of the normalized axial average velocity u/U for three different downstream locations when the tip speed ratio is four

Full size image

Fig. 9 shows the contours of the normalized radial average velocity v/U when the inflow wind velocity U is 11 m/s and the TSR is 4. Fig. 10 shows the vertical profiles of the normalized radial average velocity v/U of different TSRs at different downstream locations. The results suggest that the radial velocity decreases along the flow direction. After the inflow wind flows through the wind turbine, the wind obtains the radial velocity by the reaction force from the blade. The radial velocity decreases gradually as the vortex strength decreases along the flow direction. The radial velocity is larger at y/R=0.4 in the region above the wind turbine nacelle, which is because this region is affected by the blade root vortex and blade circumferential vortex. At the same TSR, it can be found that the radial velocity has an increased tendency along the radial direction in the later half radial length wake region, and the radial average velocity decreases in the region above the blade tip. When x/R is 0.6, 0.8, and 1.0, the negative radial velocity can be observed, which signifies that the fluid flows back to the main axis center in these regions.

Fig. 9
figure 9

Contours of normalized radial average velocity v/U when the tip speed ratio is four

Full size image
Fig. 10
figure 10

Vertical profiles of the normalized radial average velocity v/U for three different tip speed ratios at six different downstream locations

Full size image

3.3 Turbulent kinetic energy

In a 2D condition, turbulent kinetic energy can be defined as

$${\rm{TKE}} = \frac{1}{2}\left( {\overline {u{\prime ^2}} + \overline {v{\prime ^2}} } \right)$$
((1))

where u′ denotes the axial velocity fluctuations, and v′ denotes the radial velocity fluctuations.

Fig. 11 shows the contour of the normalized turbulent kinetic energy when the inflow wind velocity U is 11 m/s and the TSR is 4. Fig. 12 shows the vertical profiles of normalized turbulent kinetic energy of different TSRs at different downstream locations. Generally, turbulent kinetic energy decreases along the flow direction. The turbulent kinetic energy would appear to have two peaks at approximately y/R=0.3 and y/R=0.9. The turbulent kinetic energy is larger when y/R=0.2–0.4, and it also encounters a larger fluctuation among different TSRs in this region. In the region of y/R=0.6, the turbulent kinetic energy is smaller than that in both y/R=0.4 and y/R=0.8, which is a minimum point because both the tip vortices and central vortices have a weaker effect in this region. The turbulent kinetic energy value in y/R=0.9 is larger than that in y/R=1.0, which can be explained by the influence of the tip vortex, which primarily focuses on the region y/R=0.9 instead of the region y/R=1.0.

Fig. 11
figure 11

Contours of normalized turbulent kinetic energy TKE/ U 2 when the tip speed ratio is four

Full size image
Fig. 12
figure 12

Vertical profiles of the normalized turbulent kinetic energy TKE/ U 2 for three different tip speed ratios at six different downstream locations

Full size image

3.4 Reynolds stress

Fig. 13 shows the contours of the normalized Reynolds stress \(\overline {u\prime u\prime } /{U^2}\) when the inflow wind velocity U is 11 m/s and the TSR is 4. Fig. 14 shows the vertical profiles of the normalized Reynolds stress \(\overline {u\prime u\prime } /{U^2}\) of different TSRs at different downstream locations. From the results, it can be found that the Reynolds stress decreases along the axial direction and it goes to zero in the end. The maximum Reynolds stress appears in the region y/R=0.3–0.4, which is also the maximum turbulent kinetic energy region. In the region of y/R=0.6 and y/R=1.0, the Reynolds stress meets its minimum point.

Fig. 13
figure 13

Contours of the normalized Reynolds stress \(\overline {u\prime u\prime } /{U^2}\) when the tip speed ratio is four

Full size image
Fig. 14
figure 14

Vertical profiles of the normalized Reynolds normal stress for three different tip speed ratios at six different downstream locations

Full size image

Fig. 15 presents the comparison among different normalized Reynolds normal stresses \(\overline {u\prime u\prime } /{U^2},{\rm{ }}\overline {v\prime v\prime } /{U^2}\) and Reynolds shear stress \(\overline {u\prime v\prime } /{U^2}\) when the TSR is 4. A conclusion can be made from the results that the Reynolds normal stresses and Reynolds shear stress share the same evolution rule, they increased at the blade root and the blade tip due to the effect of the blade root vortices and tip vortices. The Reynolds shear stress \(\overline {u\prime v\prime } /{U^2}\) is less than the Reynolds normal stresses \(\overline {u\prime u\prime } /{U^2}\) and \(\overline {v\prime v\prime } /{U^2}\) . In addition, \(\overline {u\prime u\prime } /{U^2}\) is larger than \(\overline {u\prime v\prime } /{U^2}\) and \(\overline {v\prime v\prime } /{U^2}\) in the blade root region, while \(\overline {v\prime v\prime } /{U^2}\) is larger than \(\overline {u\prime v\prime } /{U^2}\) and \(\overline {u\prime u\prime } /{U^2}\) in the blade tip region.

Fig. 15
figure 15

Comparisons among different Reynolds stresses at six different downstream locations when the tip speed ratio is four

Full size image

4 Conclusions

The investigation into the flow properties of wind turbine near the wake has been carried out. The results from the present TRPIV experiment enable us to obtain the near wake detailed data such as instantaneous vorticity, average velocities, turbulence kinetic energy, and Reynolds stresses. Qualitative and quantitative analyses of the flow field results shows that: (i) the wind turbine near the wake flow field can be divided into three regions in the radial direction: velocity increased region, velocity remain unchanged region, and velocity deficit region, and the axial average velocities at different TSRs in the wake reach the inflow velocity almost at the same radial location; (ii) the radial average velocity has an increased tendency along the radial direction in the later half radial length wake region, while it decreases above the blade tip region; (iii) the turbulent kinetic energy would appear to have two peaks at approximately the y/R=0.3 and y/R=0.9 regions, and turbulence kinetic energy would meet its minimum value in the half blade radius height region along the radial direction; (iv) Reynolds shear stress is less than the Reynolds normal stresses, \(\overline {u\prime u\prime } /{U^2}\) is larger than \(\overline {u\prime v\prime } /{U^2}\) and \(\overline {v\prime v\prime } /{U^2}\) in the blade root region, while \(\overline {v\prime v\prime } /{U^2}\) is larger than \(\overline {u\prime v\prime } /{U^2}\) and \(\overline {u\prime u\prime } /{U^2}\) in the blade tip region.