The evolution laws of the large-eddy coherent structure of the wind turbine wake have been evaluated via wind tunnel experiments under uniform and turbulent inflow conditions. The spatial correlation coefficients, the turbulence integral scales and power spectrum are obtained at different tip speed ratios (TSRs) based on the time-resolved particle image velocity (TR-PIV) technique. The results indicate that the large-eddy coherent structures are more likely to dissipate with an increase in turbulence intensity and TSR. Furthermore, the spatial correlation of the longitudinal pulsation velocity is greater than its axial counterpart, resulting into a wake turbulence dominated by the longitudinal pulsation. With an increase of turbulence intensity, the integral scale of the axial turbulence increases, meanwhile, its longitudinal counterpart decreases. Owing to an increase in TSR, the integral scale of axial turbulence decreases, whereas, that of the longitudinal turbulence increases. By analyzing the wake power spectrum, it is found that the turbulent pulsation kinetic energy of the wake structure is mainly concentrated in the low-frequency vortex region. The dissipation rate of turbulent kinetic energy increases with an increase of turbulence intensity and the turbulence is transported and dissipated on a smaller scale vortex, thus promoting the recovery of wake.
When air flows through a rotating wind wheel, the momentum tends to decrease thereby forming a local viscous region wherein the wind speed decreases in the downstream of the wind wheel rotor. This region in the wind turbine is known as wake, which is a continuous large-scale turbulent coherent structure that comprises associated vortexes and ordered vortexes components in the space range [
In recent years, with the application of computational fluid dynamics technology [
The above mentioned results have contributed to the understanding of the structures of wind turbine wakes, while revealing the flow mechanism of the wind turbine wake to some extent. However, there is a need to visualize the influence of turbulence intensity on the motion trajectory of the blade tip vortex. Furthermore, the evolution laws for the large-vortex coherent structures still need to be determined [
The time-resolved PIV (TR-PIV) technology can not only display the physical form of the wake and provide quantitative information of the instantaneous flow field, but it can also break through the shortcomings of the single-point measurement methods, such as the hot-wire anemometer and the laser doppler velocity methods. Moreover, it can obtain the turbulence integral scale directly by the method of spatial correlation of pulsation velocity [
In the present study, the wake of a horizontal axis wind turbine was studied under uniform and turbulent inflow conditions using TR-PIV in the closed test section of a low-speed wind tunnel. Based on this, we obtained the wake turbulence characteristics, correlation coefficient, and turbulence integral scale of the wind turbine model. This is conducive to further understanding the essence of turbulence, which would reveal the unsteady evolution laws of a large-eddy coherent structure, and provide experimental data for performing numerical calculations of a wind turbine wake.
The wind tunnel is mainly composed of a dynamic section, a rectification section, a contraction section, a closed test section, a diffuser, and an open test section, with a length of 24.59 m. The maximum inflow wind speed can reach 60 m/s. All experiments are conducted in the closed test section that has a 2.5 m length, a half expansion angle of 0.46° and a square cross-sectional area increases from 920 mm × 920 to 1000 mm × 1000 mm.
The NACA4415 horizontal axis wind turbine model is installed at the closed test section of the B1/K2 wind tunnel.
Turbulence intensity (TI) is one of the important parameters to describe the characteristics of wake flow of wind turbines. The mathematical representation is as follows:
Typically, the turbulence intensity is less than 0.2% when the atmospheric boundary layer of the wind tunnel flows freely. According to the information provided by IEC61400-1 [
The two types of grids used in the experiment are: grid A, with 67% porosity and 16% turbulence intensity of inflow; and grid B, with 45% porosity and 12% turbulence intensity of inflow. The schematic diagrams of these grids are provided in
In this experiment, the TR-PIV test system uses the Nd:YLF DY300 high repetition rate laser (German LaVision Company, Germany) with the maximum output power of 150 W, pulse width of 100 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 are using glycol and glycerol, and its average particle diameter is 1–3 μm. Sampling frequency range is 1–10 kHz, that is, 103–104 samples can be collected per second, which is suitable for the study of turbulence characteristics.
By vector calculation, the TR-PIV data and the mode for the correlation can be obtained. The cross correlation algorithm is used to calculate the vector field of two single-exposure images. TR-PIV is evaluated using a multi-channel method with decreasingly smaller window sizes, and the window sizes are between 32 × 32 pixels and 64 × 64 pixels and overlapping rates of 75% and 50%, respectively. Furthermore, the high accuracy mode for the final passes is applied in order to a more sophisticated reconstruction algorithm can be used for the image correction and reconstruction.
The size of the experimental shooting window is 200 mm × 200 mm, as shown in the
During the test, the axial position of the mobile wind turbine model and the grid is adopted to replace the position of the moving CCD camera and the laser light source for shooting. This ensures that the phase position of the shooting surface, laser generator, and high-speed acquisition CCD camera can be fixed, which improves the testing accuracy and shortens the testing time.
Considering limitations of the experimental conditions in the closed test section, the wind turbine moves an axial position every 300 mm (i.e., 1
TSR ( |
Blade tip speed (m/s) | Wheel rotation speed (r/min) |
---|---|---|
4 | 40 | 2548 |
5 | 50 | 3185 |
6 | 60 | 3822 |
The turbulence intensity in the closed test section of the wind tunnel is 0.1% by conducting statistical analysis on the sample data of 1000 velocity vector graphs, which can meet the requirements of a stable incoming wind speed for the wind turbine. This ensures that the incoming flow field in the test area is uniform, stable, and horizontal.
The spatial correlation coefficient is used to quantitatively describe the spatial dependence of physical quantities. Through the spatial correlation coefficient, the correlation of the pulsation velocity between the study points and the target point in the wake region can be analyzed, and on this basis, the significant coherent structure characteristics in the flow can be obtained. The expression of spatial correlation coefficient is as follows
The point near the blade tip behind the wind rotor is more suitable for power spectrum analysis of fluctuating wind speed because that the tip vortex area is a typical large-eddy coherent structure. Therefore, the point (30 mm, 170 mm) near the blade tip behind the wind rotor at location 1# is selected as the target point. The symbol of “×” represents its location in
Based on the instantaneous velocity data measured by TR-PIV, the correlation between the research points at locations 2#–5# and the target point at location 1# were calculated by programming in PYTHON according to
Through the analysis of
By comparing
Under turbulent inflow, the axial and longitudinal coherent structures in the location 1# can also be identified, however, those in the locations 2# and 3# cannot be identified. By comparison, it is found that the large-eddy coherent structure of the longitudinal pulsation velocity is dominant to that of the axial one. This indicates that the behavior of longitudinal entrainment is stronger than the axial diffusion of coherent structures.
The number of identified coherent structures increases with an increase in tip speed ratio, it also shows that the tip vortex distance decreases, namely, the wake cycle of the coherent structure is reduced, coherent structures become closer, the enhanced interaction between tip vortexes makes the coherent structures more vulnerable to breakage.
The quantitative analysis of the coherent structures in
The number of peaks and peak value of the correlation coefficient of the axial and longitudinal space increases along with an increase in the tip speed ratio. This indicates an increasing of the number of identifiable coherent structure, however, the peak attenuation speed accelerates simultaneously. The longitudinal spatial correlation coefficient is significantly greater than that in the axial direction. This indicates that the longitudinal correlation structure is less likely to decay than the axial one. Moreover, the wake turbulence is characterized by longitudinal pulsation, which is consistent with the conclusions derived earlier in
From a physical view, the pulsation velocity correlation coefficient between two points can represent the influence range of the vortex strength. If
The turbulence integral scale is a concept based on the statistical average, which can approximately reflect the average scale of the overall vortex in the turbulence field, and is called the “large scale” of turbulence, i.e., the scale of the large vortex. By integrating the spatial correlation coefficient along the radial direction, the quantity with length dimension is obtained, which is called the turbulence integral length scale
The spatial correlation coefficient of the pulsation velocity were extracted, when
4 | 15.9 | 16.9 | 19.4 | 21.6 | 23.9 | 88.2 | 41.6 | 36.3 | 21.9 | 17.9 |
5 | 15.1 | 15.4 | 15.6 | 17.2 | 19.3 | 90.3 | 43.8 | 41.5 | 28.3 | 22.3 |
6 | 11.5 | 12.2 | 14.3 | 15.1 | 15.8 | 94.2 | 50.8 | 39.9 | 35.2 | 24.2 |
0.1% | 15.1 | 15.4 | 15.6 | 17.2 | 19.3 | 90.3 | 43.8 | 41.5 | 28.2 | 22.3 |
12% | 16.3 | 18.0 | 27.5 | 24.3 | 18.8 | 14.1 | ||||
16% | 18.2 | 21.4 | 31.7 | 21.2 | 16.2 | 11.1 |
By comparative analysis, it is found that the integral scale of axial turbulence gradually increases with the downstream development of wake, which indicates that the large-scale vortex gradually expands and diffuses along the mainstream direction. On the contrary, the integral scale of longitudinal turbulence gradually decreases, which indicates that the vortex structure is squeezed in the longitudinal direction. With an increase in the tip speed ratio, the integral scale of axial turbulence decreases, while that of longitudinal turbulence increases. With an increase in turbulence intensity, the integral scale of axial turbulence increases, meanwhile, that of its longitudinal counterpart decreases.
The Fourier transform of the signal is the frequency spectrum, which is another way of representing the signal. The power spectrum is the Fourier transform of the autocorrelation function of the signal, that is, the signal is calculated autocorrelation, and then the Fourier Transformation, which describes the relationship between the energy characteristics of a signal and the frequency, can be used to analyze the carrying of different frequency components [
According to the K41 theory, the energy spectrum curve of homogeneous isotropic turbulence with large Reynolds number has energy region, inertia sub-region and dissipative region. The transport process of turbulent kinetic energy in the inertia sub-region is as follows: turbulent pulsation transmits step by step from large-scale vortex (energy-containing region) to small-scale vortex (dissipative region), The turbulent vortex absorbs the energy of the large scale vortex and transfers it to the small scale turbulent vortex without dissipation. The slope of inertial sub-region distribution in the energy spectrum is −5/3. To better understand the multi-scale characteristics of wind turbine wakes we need to understand the influence of the scale range on wake structure to carry out pulsating velocity power spectrum analysis on wind turbine wakes, and to discuss the energy transfer characteristics between multi-scale vortex systems.
Under uniform inflow and turbulent inflow,
The turbulent power spectrum value in either direction decreases rapidly as an increase of the frequency, which indicates that the turbulent pulsation kinetic energy gradually attenuates. It can be seen that the turbulent pulsation kinetic energy is mainly provided by the vortex with low frequency. From the perspective of the turbulent power spectrum value, the power spectrum peak in the X direction is significantly smaller than in the Y direction with the wake moving downstream. This implies that the attenuation of the turbulent pulsation kinetic energy in the Y direction is weaker than that in the X direction. Furthermore, this confirms the conclusion that longitudinal correlation is greater than axial correlation.
If the pulsation components of various frequencies are considered as turbulent vortexs of different scales, these scales are a concept of uncertainty. There are several typical scales in wake turbulence [
According to the cascade process of turbulent kinetic energy proposed by Richardson, the dissipation rate of the turbulent kinetic energy (
1# | 2# | 3# | 4# | 5# | 1# | 2# | 3# | 1# | 2# | 3# | |
5.71 | 5.42 | 5.83 | 5.54 | 5.72 | 2.70 | 2.81 | 2.92 | 2.56 | 3.01 | 3.23 | |
0.18 | 0.24 | 0.27 | 0.29 | 0.32 | 0.10 | 0.12 | 0.13 | 0.85 | 0.10 | 0.11 | |
2.89 | 1.02 | 0.61 | 0.47 | 0.31 | 21.3 | 18.2 | 13.4 | 28.8 | 14.7 | 9.85 |
Using the instantaneous velocity field data measured by TR-PIV, the spatial correlation coefficients of the pulsating velocity were calculated, with and without the grid. Subsequently, we obtained the coherent structure, turbulence integral scale of the wind turbine wake and power spectrum under different working conditions and explored the evolution laws of the large vortex coherent structure in the wake of the wind turbine.
The large vortex coherent structures in the wake of a wind turbine are periodic in nature. With the wake developing downstream, the coherent structures gradually dissipate and spatial correlation of pulsation velocity the correlation becomes worsen. The spatial correlation of the longitudinal pulsation velocity is greater than that of the axial one, moreover, the wake turbulence pulsation is dominated by the longitudinal pulsation. Furthermore, as the wake developed downstream, the integral scale of axial turbulence gradually increases, whereas that of the longitudinal turbulence decreases simultaneously. This indicates that the large-scale vortex evolves and diffuses along the mainstream direction and that the vortex structure is squeezed in the longitudinal direction. With an increase of turbulent intensity, the coherent structures tend to dissipate. When Several isolated peaks in the power spectrum represent the existence of coherent structure. If the isolated peak cannot be identified in the power spectrum, it indicates the disappearance of coherent structure. At this time, the large vortex is broken into small vortex, indicating that the wake enters the far wake region. The isolated peak value could still be identified within 4.5 Through the wake power spectrum analysis, it is found that the turbulent pulsation kinetic energy of the wake structure is mainly concentrated in the low-frequency large-scale vortex region. The momentum transport in the inertial sub-region increases with the increase in turbulence intensity, and that the width of the inertial sub-region (gradient = −5/3) increases with the downstream wake development. Moreover, with an increase in turbulence intensity, the dissipation rate of the turbulent kinetic energy increase, and the Taylor and dissipation scales decrease. In other words, turbulence is transported and dissipated on a smaller scale vortex, which is more conducive to the energy transfer between multi-scale vortexes in the wake and promotes wake recovery.