The computational fluid dynamics method was used to simulate the flow field around a wind turbine at the yaw angles of 0°, 15°, 30°, and 45°. The angle of attack and the relative velocity of the spanwise sections of the blade were extracted with the reference points method. By analyzing the pressure distribution and the flow characteristics of the blade surface, the flow mechanism of the blade surface in the yawed condition was discussed. The results showed that the variations of the angle of attack and the relative velocity were related to the azimuth angle and the radius in the yawed condition. The larger the yaw angle was, the larger the variation was. The pressure distribution in the spanwise sections was affected by both the angle of attack and the relative velocity. The angle of attack was more influential than the relative velocity. At the same yaw angle, when the angle of attack decreased, the
The yawed condition is one of the most important operation conditions of a wind turbine. A wind turbine is in the yawed condition when it is in a yaw error condition or it is deflected artificially to improve the total power of a wind farm [
The AOA is the main factor that determines the output and the aerodynamic load of wind turbines [
In addition to the AOA, the relative velocity also affects the flow characteristics of the blade surface. According to the literature review, we can find that there have been few in-depth studies on the flow characteristics of a wind turbine blade surface in the yawed condition from the perspective of the relationship among the AOA, relative velocity, and flow field. Thus, in this study, the small three-blade horizontal axis wind turbine was selected as the research object to analyze the pressure distribution on the blade surface and the flow characteristics around the blade at different yaw angles and to discuss the influence mechanism of the yawed condition on the unsteady flow characteristics of the blade surface. The results will provide a reference for the design and operation of wind turbines.
The wind turbine used in this study is shown in
As shown in
The velocity inlet and pressure outlet conditions were selected for the inlet and outlet of the stationary region. A no-slip condition was selected for the surfaces of the wind turbine and the ground. The symmetry boundary was applied for the top, left, and right sides of the stationary region. The dimensions of the computational region are shown in
The selection of the turbulence model was very important for the CFD simulation. The
Polyhedral mesh was used in this study. To capture the flow details on the blade surface well, a small mesh size was set for the blade surfaces, and the leading and trailing edges of the blades were encrypted. There were 20 boundary layers on the surfaces of the blades. The first grid height in the normal direction from the blade surfaces was about 0.01 mm, and the normal growth rate was 1.2. The dimensionless distance normal to wall
To verify the rationality of the calculation model, the output power of the wind turbine in the yawed condition was measured with a wind tunnel experiment. The experiment was performed in an open test section of the B1/K2 wind tunnel located at the Key Laboratory of Wind Energy and Solar Energy Technology of Ministry of Education of China. The wind tunnel with the inner diameter of 2 m for the open test section could supply 0–20 m/s of uniform airflow. The output power of the wind turbine was collected with a Norma5000 system that was part of the Fluke high-precision six-phase power detection and analysis system. The system error was within ±0.05% of the measured value and within ±0.05% of the measured range.
From the CFD simulated flow field data of the vertical axis wind turbines, Elsakka extracted the velocities of the well-selected reference points around the blades with which the AOA was calculated [
The leading-edge point of the S airfoil used in this study was set as the origin of the XOY coordinate system. Four groups of reference points were selected. The first, second, and third groups were all composed of double points, and the fourth group was composed of a single point. The coordinates of each point are shown in
The 2D computational region and the simulation method are available by Widad et al. [
Case 1 | Case 2 | Case 3 | Case 4 | ||||||
---|---|---|---|---|---|---|---|---|---|
AOA (°) | Velocity (m/s) | △ |
△ |
△ |
△ |
△ |
△ |
△ |
△ |
2 | 10 | 21.5 | 0.4 | 26.3 | −0.1 | 3.9 | 0.2 | 1.8 | −1.0 |
30 | 23.9 | 0.4 | 29.1 | 0.0 | 4.4 | 0.2 | 3.3 | −1.1 | |
50 | 24.7 | 0.4 | 29.9 | 0.0 | 4.6 | 0.2 | 3.7 | −1.2 | |
8 | 10 | 0.7 | 9.4 | 0.4 | 12.7 | 0.4 | 2.7 | −3.2 | 4.4 |
30 | 0.8 | 10.2 | 0.5 | 13.7 | 0.3 | 3.0 | −3.5 | 4.6 | |
50 | 0.8 | 10.5 | 0.5 | 14.0 | 0.3 | 3.1 | −3.6 | 4.7 | |
12 | 10 | 2.1 | 12.8 | 1.1 | 15.9 | 1.2 | 2.8 | −4.5 | 4.7 |
30 | 1.0 | 8.1 | 0.9 | 11.1 | 0.4 | 2.1 | −4.2 | 4.3 | |
50 | 1.0 | 8.1 | 0.9 | 11.2 | 0.4 | 2.1 | −4.3 | 4.3 | |
18 | 7 | 1.4 | 8.7 | 1.1 | 10.2 | 1.2 | 4.8 | −4.0 | 4.6 |
10 | 1.0 | 5.8 | 0.8 | 7.3 | 0.9 | 4.6 | −2.9 | 3.9 |
The deviations are shown in
Johansen et al. [
For the airfoil, the AOA and the Reynolds number (
To better observe the changing law of the AOA and the relative velocity with the radius and the azimuth, three sections were selected, which were the 25%, 65%, and 95%
Two yaw conditions of 15° and 45° were selected to analyze the influence of the yaw angle on the pressure distribution on the blade surface. As shown in
The flow characteristics at the 25%
In
According to this analysis, the changing law of the lift force at the different spanwise sections was consistent with the changing law of the AOA. The AOA, however, was not the only factor that affected the lift force. As shown in
Compared with other working conditions, the same phenomenon existed. At the 25%
Through the above analysis, it could be seen that even at the 45° yaw, the flow separation of the leading edge at the blade root region was only found at the 0°–60° azimuth. Large-scale and destructive flow separation did not occur. This might have been due to the following reasons:
The influence of the airfoil. The airfoil of the blades used in this study had smaller leading-edge radius, thickness, and camber, which were different from those of the National Renewable Energy Laboratory (NREL) Phase VI wind turbine (an S809 airfoil with a larger thickness was used) that often have been analyzed in the literature. The large-scale flow separation occurred at the airfoil trailing edge of the NREL Phase VI wind turbine at the rated condition. The separation of the laminar boundary layer near the leading edge with the action of a large adverse pressure gradient usually occurred in the airfoil in this study. When the adverse pressure gradient decreased, the flow became turbulent and then re-attached to the blade surface. The influence of the dynamic stall. The critical AOA in the yawed condition changed periodically, making the critical AOA for the dynamic stall much larger than the critical AOA of the 2D static stall. This effect gradually increased from the tip region to the root region of the blade. When the AOA at the root region reached its maximum value, the vortex did not propagate from the leading-edge area along the upper surface of the airfoil to the trailing edge and the airfoil did not enter a deep stall. The influence of The influence of the working condition. The rated working condition in this study was examined. Theoretically, when the velocity of the free stream increases, the separation increases as a result of the increase of the AOA.
In this study, the distributions of the AOA and the relative velocity, as well as the flow characteristics of the S-airfoil wind turbine for yaw cases, were analyzed according to the CFD method. The flow mechanism on the blade surface was discussed further. The conclusions were as follows:
In a rotation period, the AOA and the relative velocity of the spanwise sections changed with the increase of the azimuth angle according to the law of cosines and anti-cosines. The larger the yaw angle was, the larger the fluctuation amplitude was. From the root region to the tip region of the blade, the fluctuation amplitude decreased gradually. In the yawed condition, the AOA and the Reynolds number affected the pressure distribution of the blade surface and the power output characteristics more. The influence of the AOA on the pressure distribution was greater than that of the Reynolds number. At the same time, the reverse change between the Reynolds number and the AOA reduced the influence degree of the AOA. With an increase in the yaw angle, the large fluctuation amplitude of the AOA appeared at the blade root region, resulting in a vortex that appeared and disappeared continuously at the leading edge of the suction surface of the blade. Because of the influence of the airfoil shape, the Reynolds number, and the working conditions, the separation did not propagate along the chord to the trailing edge of the blade, but the flow state of the suction surface still showed obvious dynamic characteristics.
The research results described in this paper could provide theoretical guidance for the development of flow control methods on the blade surface of a wind turbine, especially on the surface of the blade root in the yawed condition, to reduce the influence on the power loss and the power fluctuation of a wind turbine.
In this research, only the rated condition was studied. In the follow-up work, the yawed condition for different wind speeds and tip speed ratios will be analyzed, to obtain more comprehensive and instructive conclusions.
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