Experimental study on wake interference characteristics of horizontal-axis wind turbine

To investigate the flow field distribution under the interference of multiple wind turbine wakes, two different types of ground-based LiDARs were used to conduct wind measurement experiments in a wind farm. Taking the wake field distribution characteristics of two wind turbines as an example, combined with wind measurement data, the complex wake interference flow field is classified into three typical interference conditions: non-wake, partial wake and full wake. And the wake development characteristics under the above three wake conditions are quantitatively analyzed. The results show that under the condition of non-wake interference, the wakes are independent of each other, the wake recovery rate is basically the same. Under partial wake and full wake interference conditions, the wake center recovery rate of the downstream wind turbine decreases, and the wake recovery rate drops most obviously under the full wake interference condition.


Introduction
Wind turbine wake effect is a major factor affecting the distribution of the flow field inside a wind farm.The cause of its formation is that the upstream wind turbine absorbs energy from the incoming wind.According to energy conservation theory, the energy obtained by the downstream wind turbine is reduced, which leads to a decrease in power generation.Meanwhile, the increase in turbulence intensity caused by the wake effect would affect the fatigue load of the wind turbine.In some large wind farms, the typical value of power generation loss caused by wind turbine wake is 10%~20% [1][2], and when the downwind wind turbines are completely in the wake region, the loss can be as high as 30%~40 % [3].
With the big growth of LiDAR wind measurement technology of recent years, the problem of threedimensional flow field measurement in wind farms has been well resolved.Many scholars have used LiDAR to study the wake characteristics of wind turbines and achieved good results.The influence of turbulence intensity on the characteristics of wind turbine wake variations of a wind turbine based on LiDAR measurement data was studied in Literature [4].Literature [5] used two LiDARs to study the three-dimensional wake characteristics of a 1.5 MW wind turbine and verified the wake model.Literature [6] adopted two LiDARs to research the development trend of wake in mountainous terrain.
The LiDAR wind measurement experiments mentioned above were mostly used to study on the formation and distribution mechanism of wake flow in a wind turbine, which is the basis for exploring the characteristics of complex wake field.With the increase of the installed capacity of wind farms and the staggered arrangement of multiple wind turbines, the wake interfere with each other inevitably, and the flow field become complicated accordingly.Therefore, studying the wake field distribution in a wind farm and the state of the wake region where the wind turbine is located is of great significance for the coordinated control, layout optimization and power prediction of wind turbines.Based on this, two wind LiDARs were used to for the wind turbine wake interferometry experiments in a wind farm in Hebei Province, China.Combined with the measurement results, the wake interference conditions were classified and the wake development characteristics of the corresponding conditions were quantitatively analyzed.

LiDAR and wind turbine
The wind measurement experiment was conducted at a mountain wind farm in Hebei Province, China.The wind farm has fifty wind turbines, which are relatively densely distributed.Four wind turbines produced by United Power company were set as the wake measurement target, and the parameters are shown in Table 1.In order to accurately research the characteristics of wake interference in wind farms, two different Doppler LiDARs are used in this study, both of which are ground-based, one is vertical wind profile LiDAR, model WP350, using its Doppler-Beam-Swing measurement mode (DBS mode, four-beam scanning) to obtain the inflow information, including wind direction, wind speed, turbulence intensity, etc; the other is a three-dimensional scanning LiDAR, model W3D6000, which is used to measure the wake distribution.The experiment mainly uses its Plan-Position-Indicator measurement mode (PPI mode, fixed elevation angle by varying azimuth) to obtain wake speed distribution information of the wind turbine hub height plane.The schematic diagram of measurement modes is shown in Figure 1.

Wind measurement scheme
The measured wind turbine is located at the northern boundary of the wind farm, with less interference from other wind turbine wake downstream from the main wind, which helps WP350 obtain accurate incident wind speed information.By analyzing the wind data at the height of 65 m from the wind measurement tower in the past two years during the measurement period, it is judged that the main wind direction is north and northwest.Based on this, the experimental layout is shown in Figure 2 and the distance D represents the diameter of the wind turbine rotor (77 m).

Experimental results and analysis
Through a comprehensive analysis of the inflow and wake speed information measured by the LiDAR WP350 and W3D6000, it is show that the dominant wind direction during the measurement period is in the northwest direction.For comprehensive analyze the wind field distribution characteristics under wake interference conditions, the wake distribution of wind turbines 10-1 and 10-2 is focused in this study, and the wind turbine 10-2 is subjected to the wake interference of turbine 10-1.The quantification analysis of wake interference characteristics is carried out for three typical wake interference conditions of non-wake, partial wake and full wake.The inflow information of the corresponding wake conditions is shown in Table 2.For the evaluation index of the degree of wind pulsation in the incoming wind of the wind turbine, the following formula is used in this study to calculate the turbulence intensity [7].Among them, σ is the standard deviation of the 10-minute average wind speed;  is the 10-minute average measured wind speed: In the process of quantitative analysis of wake characteristics, the dimensionless wake recovery rate parameter u* is used to describe the recovery rate characteristics of the wake region, and the corresponding expression is shown in equation ( 2): Among them, u is the wake wind speed; u 0 is the inflow wind speed of the wind turbine.

Cloud chart of wake measurement results
Figure 3 is a cloud diagram of the wake speed distribution in the plane of the wind turbine hub height under three wake conditions obtained from the inverse calculation of the LiDAR W3D6000 measured wind data.Figure 3(a) corresponds to the wake condition without wake interference.Under this wake condition, the wakes of the four wind turbines are relatively independent, and no wake interference occurs.In addition, it can be seen from the Figure 3(a) that as the distance away from the wind turbine increases, the wake speeds of the four wind turbines all show a trend of gradual recovery, and the wake center has the lowest wind speed.Meanwhile, the wake distribution is approximately symmetrical.
When the incoming wind speed is 7.58 m/s and the wind direction is 291°, part of the wake interference occurs between wind turbines 10-1 and 10-2, as shown in Figure 3(b).Compared with the non-wake condition, due to the change of the wind direction, in the direction perpendicular to the wind direction, the two wind turbines form a staggered layout with a smaller interval.In the Figure 3(b), it can be clearly seen that the incoming wind condition of turbine 10-2 is partially affected by the wake of turbine 10-1.As the downwind distance increases, the wake boundaries of turbine 10-1 and 10-2 begin to interfere with each other and gradually blend into a wake trail.
Figure 3(c) is a cloud diagram of the wake speed distribution under the full wake interference condition.The corresponding inflow wind speed of the wind turbine 10-1 is 8.42 m/s and the wind direction is 286°.In this wind downward, the two wind turbines form a tandem arrangement.It can be seen from the Figure 3(c) that turbine 10-2 is full in the wake of turbine 10-1, and the wake speed of 10-2 is significantly lower than that of turbine 10-1.

Analysis of Wake Development Characteristics
In order to quantitatively analyze the wake development characteristics of the three wake conditions, the wind speed of the wake center at the same positions in the downwind direction of the wind turbines 10-1 and 10-2 were selected as a comparison.As shown in Figure 4(a), under the condition of non-wake interference, the wake center wind speed of wind turbines 10-1 and 10-2 show a trend of gradual recovery.At the position of 3.5D in the downwind direction of the wind turbines, the wind speed difference between the two turbines is the largest, which is 0.87 m/s.This phenomenon could be explained that due to the location is in the wake transition region, the wake speed fluctuation is large, so the wind speed difference between the two wind turbines would also fluctuate.As the wake continues to move forward, the wind speed difference begins to gradually decrease until it approaches zero.When reaching the 7D position, the wake center wind speeds of the two wind turbines both returned to the inflow wind speed.Under this wake condition, since there is no obvious wake interference between the wind turbines, the trend of the wake center wind speed recovery rate of the turbines 10-1 and 10-2 is basically the same.
Wake center wind speed recovery rate under the partial wake interference condition is shown in Figure 4(b).It can be also observed that the wake center wind speeds of the two wind turbines show a trend of gradual recovery, but the overall wake recovery rate under this wake condition is significantly lower than that of the non-wake condition, and the wake speed difference between the two wind turbines is also larger.Under no-wake conditions, the average difference between the wake center wind speeds of wind turbines 10-1 and 10-2 is 0.3353 m/s, and both recovery to the inflow wind speed at the location of 7D.However, for the partial wake condition, the difference in average wake center wind speed between the two wind turbines is as high as 0.9898 m/s, and it has not recovered to the inflow wind speed at the location of 7.7D.The above phenomenon shows that since the incoming wind and wake of the downwind wind turbine is affected by the wake of the upwind wind turbine, which in turn affects the inflow wind speed and wake recovery rate of the downwind turbines.At the same time, as the wakes of wind turbines interfere with each other, the wake recovery rate of upstream wind turbines is also affected.
The comparison of the recovery rate of the wake center wind speed under the full wake interference condition is shown in Figure 4(c).In the coordinate system established under this wake condition, the distance between wind turbines 10-1 and 10-2 is less than 4D, so only the wake center wind speeds at three typical positions in the downwind direction of turbine 10-1 are intercepted.At the same downwind position, the wake center wind speed of turbine 10-2 is significantly lower than the wake center wind speed of turbine 10-1, and the average wind speed difference is as high as 1.3828 m/s, which is significantly higher than the average wind speed difference between the non-wake condition and partial wake condition.Corresponding to Figure 3(c), it can be seen that the turbine 10-2 is completely in the wake of turbine 10-1, causing its incoming wind speed to be severely disturbed, so its wake speed is also reduced accordingly, which explains the reason for the above-mentioned large wind speed difference.
In addition, it could be observed from Table 2 that the turbulence intensity under the full wake condition is significantly higher than that under the non-wake and partial wake conditions.Owing to the reason known that turbulence intensity could accelerate the energy exchange between the wake and the ambient wind speed, thereby increasing the wake recovery rate.However, the results in Figure 4(c) show that the wake recovery rate has not improved significantly, and only recovered to 78% of the incoming wind speed at position 7.14D.In response to this phenomenon, related studies have shown that the turbulence intensity of the inflow wind and the axial thrust coefficient of the wind turbine comprehensively affect the wake recovery rate, and the weights of the two are close to the equal [8][9].Although turbulence could accelerate the wake recovery, the wind turbine in the state of full wake has greater influence on its wake recovery rate due to the unstable incoming wind speed it faces.

Conclusion
In this paper, two different LiDARs are used to investigate the wake interference characteristics of multiwind turbines.According to the experimental results, the wake interference phenomena is classified, and a comparative study on the development characteristics of wakes is conducted.The following conclusions could be drawn: 1) When the relative position of the wind turbines is determined, the change of the wind direction causes the wake of the upstream wind turbine and the downstream wind turbine to appear three wake conditions: non-wake interference, partial wake interference and full wake interference.Through the classification and quantitative analysis of the complex flow field under the interference of multi-wind turbine wakes, it could provide certain guiding significance for optimizing the layout of large-scale wind farms and the field-level cooperative control in operation.
2) Under the condition without wake interference, the wakes of the two wind turbines are relatively independent, and the wake recovery rate is basically the same.
3) Under partial wake interference condition, the recovery rate of the wake center of upstream wind turbines is faster than that of downstream wind turbines, and the average difference is 0.9898 m/s.Meanwhile, due to the mutual interference of the wakes, the wake recovery rate of the upstream wind turbine is also affected.
4) Under the full wake interference condition, the wind turbine in the downwind region is completely affected by the wake of the upwind turbine, and its wake recovery rate decreases most obviously under the three wake conditions, and the average wind speed difference is 1.3828 m/s.

Figure 2 .
Figure 2. Experimental layout of wake interference test project.

Figure 3 .
Figure 3. Cloud chart of wake distribution measured by PPI mode: (a) non-wake interference condition; (b) partial wake interference condition; (c) full wake interference condition.

Figure 4 .
Figure 4. Wake center recovery rate under three typical wake conditions: (a) non-wake interference condition; (b) partial wake interference condition; (c) full wake interference condition.

Table 1 .
Main parameters of wind turbine.