## 3 Numerical Results
### Acoustical Analysis  
Effects of Wind Shear and Yaw on Sound Emission  
Figure 12 illustrates the polar plot of the sound pressure level in the function of azimuth angle of blade 1 for the four cases, which is called the amplitude modulation (AM) noise. AM noise is often a big issue because it gives more perception to the people living nearby. However, it should be noted that there are two different phenomena that make AM noise: one is caused by the blade noise directivity change during its operation [4] and another is caused by the non-uniform flow and operation, such as wind shear and yaw. In the present study, the latter is focused. The observer is located at 1.5 m height and a distance of 500 m downstream from the turbine (500 m away from the turbine is often a place where people are living although the sound propagation effects due to ground  
Figure 11: Power and thrust coefficients with a pitch adjustment: (**a**) \(C_{p}\) for Case 1; (**b**) \(C_{T}\) for Case 1; (**c**) \(C_{p}\) for Case 2; (**d**) \(C_{T}\) for Case 2; (**e**) \(C_{p}\) for Case 3; (**f**) \(C_{T}\) for Case 3; (**g**) \(C_{p}\) for Case 4; (**h**) \(C_{T}\) for Case 4.  
and atmospheric conditions are not considered here). The choice of the 500 m distance downstream location is to minimize the AM noise created by the blade noise directivity change. The speed of sound used in the calculations is 340 m/s. The turbulence level and turbulence length scale are set as 3% and 100 m, respectively. This choice was made in accordance with the 0.3 wind shear exponent defined in the scenarios. A more realistic choice can be made when the detailed flow information is measured. The 0\({}^{\circ}\) azimuth angle is defined when blade 1 is vertically down and coincides with the tower. All these four scenarios are performed with no control. As can be observed in Cases 1 and 3, the sound pressure level is slightly larger when the shear is included, while it significantly decreases with a 10\({}^{\circ}\) yaw, i.e., for both Cases 2 and 4. Normally, the SPL from one blade is highest when it is pointing upwards. The reason can be seen from the BPM sound prediction equations that the SPL is related to the fifth power of the oncoming velocity. For the case of three blades, at zero azimuth angle (blade 1 is pointing downwards), the other two blades are pointing at 120\({}^{\circ}\) and 240\({}^{\circ}\) when the noise is almost highest during its operation for Cases 3 and 4. Figure 13 illustrates the comparison of SPL regarding different control scenarios. It can be observed that compared with the non-controlled case, the controlled SPL results, i.e., with control techniques I and II, are similar for Case 1 and Case 2. For Case 1, the peaks for both control strategies are in step, whereas the magnitude of the no control results is slightly smaller. For Case 2, the fluctuations are also generally in step, and both the time and magnitude of the peaks are consistent. Therefore, the implementation of the control techniques may not lead to noise reductions for the no-shear scenarios. The main reason for the negligible difference in Cases 1 and 2 is that the modifications of the pitch and the corresponding AoA are relatively small where the fluctuations of noise level are mainly due to blade deflections. A larger difference is expected for a larger pitch. It should be noted that Case 2 corresponds to a slightly lower SPL as compared to Case 1, due to the yaw-caused lower axial wind speed. For Cases 3 and 4, a larger decrease of SPL, i.e., about 0.4 dB, can be observed by introducing either control strategy I or II, whereas the trend remains the same. No significant difference can be found between the results of the two control techniques. It can be concluded that by introducing the control techniques, the reduction of SPL can be realized for the shear scenarios. In comparison to the angle of attack plots in Figure 8 with those plots of SPL in Figure 13, a non-linear effect between these two quantities is seen due to the blade structural responses.