*3.5. Wake Characteristic*

Figure 16 shows the velocity distribution of the plane which is perpendicular to the main flow direction and 45 mm behind the rotor plane. The first row represents the experiment result, the second row represent the result of standard kernel and the third row represents the result of anisotropic kernel. The data area is a ring with outer radius of 500 mm and inner radius of 140 mm. The standard deviation as shown in Equation (9) is used to evaluate the difference between simulation and experimental result. Here, n is the number of sample points, *vsim* is the simulation result and *vexp* is the experimental result.

$$E = \sqrt{\frac{\sum\_{i=1}^{n} \left(v\_{sim} - v\_{exp}\right)^2}{n\upsilon\_{inlet}^2}}\tag{9}$$

**Figure 16.** The velocity magnitude contour of the plane (45 mm behind the rotor) perpendicular to the main flow direction. The origin is the main shaft location and the data area is a ring with outer radius of 500 mm and inner radius of 140 mm. The first row represents the experiment result, the second row represent the result of standard kernel and the third row represents the result of anisotropic kernel.

As shown in Figure 17, the simulations show good agreement with the experimental result, the standard deviation between the simulation and experimental result is less than 6%. Furthermore, the standard deviation results illustrate that the value has little influence on the velocity distribution in the rotor plane.

Figure 18 shows the velocity distribution of the plane along with the main flow. The first row represents the experiment result, the second row represent the result of standard kernel and the third row represents the result of anisotropic kernel. The x coordinate represents the distance from the rotor plane and the y coordinate represents the radius position from the main shaft. The data area is from 45 mm to 615 mm behind the rotor and 140 mm to 500 mm away from the main shaft. The velocity distribution shows that the actuator line method can accurately simulate the pattern of the wake flow of a wind turbine. However, it also shows that the peak velocity of simulations is lower and the wake pattern is flatter compared with the experimental results. Figure 19 shows the standard deviation of velocity between simulations and experimental results. Although the improvement of velocity distribution is not significant, simulations with anisotropic regularization kernel show a more accurate result compared with simulations using the standard kernel.

**Figure 17.** Standard deviation of the velocity magnitude in the plane perpendicular to the main flow direction.

**Figure 18.** The velocity magnitude contour of the plane along with the main flow. The origin is the rotor center. The data area is from 45 mm to 615 mm behind the rotor and 140 mm to 500 mm away from the main shaft.

**Figure 19.** Standard deviation of the velocity magnitude in the plane along with the main flow.

Figure 20 shows the vorticity results. It is clear that the actuator line method gives a flatten prediction of the vorticity distribution because of the simplification of wind turbine blade. The peak vorticity of the experiment is much larger than the simulation result and the region of the high vorticity region is much smaller. However, the actuator line method gives a reliable prediction of the wake pattern. It is difficult to use standard deviation function to evaluate the vorticity results, because

both the position and the absolute value must be taken into consideration. Therefore, the correlation coefficient as defined in Equation (10) is used as the evaluation metric.

$$\mathbf{C} = \frac{\sum \left( \upsilon\_{sim} - \overline{\upsilon\_{sim}} \right) \left( \upsilon\_{exp} - \overline{\upsilon\_{exp}} \right)}{\sqrt{\sum \left( \upsilon\_{sim} - \overline{\upsilon\_{sim}} \right)^2 \sum \left( \upsilon\_{exp} - \overline{\upsilon\_{exp}} \right)^2}} \tag{10}$$

**Figure 20.** The vorticity magnitude contour of the plane along with the main flow. The origin is the rotor center. The data area is from 45 mm to 615 mm behind the rotor and 140 mm to 500 mm away from the main shaft.

The correlation coefficient neglects the average value difference between two distributions, but focuses on the pattern. In this study, the size of the high vorticity region and its position will significantly affect the correlation coefficient. Figure 21 shows the correlation coefficient between simulations and the experimental results. As the actuator line model predicts a flatter vorticity distribution, the correlation coefficient is not too good. However, simulations with a correlation coefficient higher than 0.5 give a reliable prediction of the position of high vorticity region, which means these simulations give a reliable prediction of the wake pattern. Furthermore, the correlation coefficient is significantly improved when using the anisotropic regularization kernel, especially when using the special mesh at the same time. As the main difference between the standard kernel and the anisotropic one is the thickness parameter, it can be concluded that the thickness parameter has a significant influence on the wake pattern prediction.

**Figure 21.** The comparison of the correlation coefficient.

It should be noticed that the number of elements of the special mesh is lower than the refined mesh, but the correlation coefficient of the simulations using the special mesh is much higher than the simulations using refined mesh. These simulations obviously take the advantages of the anisotropic regularization kernel and significantly improve the performance of the actuator line model. A special mesh with refinement in the main flow direction together with the anisotropic regularization kernel will give a more accurate and lower computational cost simulation of the wind turbine.
