## 3 Results and Discussions
### Coupled Flow and Noise Simulations for a Wind Turbine Array
#### 3.4.4 Wind Turbine ANPropagation across Multi-Wake
The overall sound pressure variation for different cases is smaller as compared to the previous results shown in Figure 14. This is due to the mixing of three individually simulated propagation field. Among all the test cases, Case 3 can be regarded as the worst-case scenario. For example, around the distance of \(x\) = 1800 m, there is an obvious increase of SPL due the strong downward refraction at this region, which is also observed in Figure 16c at \(x\) = 1800 m.  
Figure 12:0 SPL of wind turbine #1 (Source: Lp) received at 1500 m distance (2 m height): with geometric attenuation and air absorption, Case 1 and Case 3 with all propagation effects. Figure 12:1 ANPropagation from all ANSources: (**a**) Case 1, homogeneous atmospheric condition, no wake effect; (**b**) Case 2, homogeneous atmospheric condition with multi-wakes; (**c**) Case 3, downward refraction and multi-wakes; (**d**) Case 4, upward refraction and multi-wakes. Figure 12:2 _Cont._  
Similar to the procedures previously mentioned for Figure 15, Figure 19a-c show the noise spectra from wind turbines #1, 2, and 3, respectively. The difference is that the three wind turbines are individually considered for its noise generation and propagation at the given frequencies (20 Hz  
Figure 12:3 RSPL simulated at \(f=1000\) Hz and \(b=-3\): (**a**) ANPropagation by wind turbine #1 downstream of the wakes of wind turbines #1, 2, 3; (**b**) ANPropagation by wind turbine #2 downstream of the wakes of wind turbines #2, 3; (**c**) ANPropagation by wind turbine #3 downstream of the wakes of wind turbine #3; (**d**) superimposed RSPL from all wind turbines #1, 2, 3. Figure 12:4 The RSPL at 2 m height extracted from four cases of Figure 12:5  
5000 Hz). Due to the presence of velocity deficit in the wake, the inflow conditions of the two downstream wind turbines are slightly different, and thus the ANSources of the three wind turbines are slightly different from each wind turbine. In each figure, the original ANSource is shown on top of the other noise spectra. Similar to the situations in Figure 15, geometrical attenuation plays an primary role in the large noise reduction for ANPropagation at \(f<1000\) Hz, and the noise absorption by air has a strong effect at \(f>1000\) Hz. As expected, Case 3 shows more distinct characteristics for the frequencies. In Figure 19, the receiver is fixed at \(x=2500\) m, \(z=2\) m, therefore the sound pressure is largely attenuated for wind turbine #1 due to the longest propagation distance. A similar behavior is seen for wind turbines #2 and #3, where the noise level is the highest for wind turbine #3 due to the shortest relative distance from source to receiver. Figure 19a-c also show that at different relative propagation distances 2500 m (#1), 1940 m (#2) and 1380 m (#3), the distribution of SPL maintains some similarity. The differences of these sound spectra come from the combined effect of wake flow and the propagation distance. Finally, the total noise received from the three wind turbines can be got through logarithmically adding the sound spectra from individual wind turbines. In Figure 19d, the sources Lp1, Lp2, and Lp3 represent the ANSource level of the three wind turbines. The major difference is seen at the middle frequency range, which is due to the different input velocity data obtained from flow simulation. Case 1 and Case 3 all show that the most significant influence comes from wind turbine #3, which is not a surprise. To highlight more detailed difference in the noise spectra, a few typical values are compared in Figure 12:6 At \(f=20\) Hz, the summated SPL from three turbines (Case 3) is 37.92 dB which is 3 dB higher than that from wind turbine #3 (Case 3). This difference becomes smaller when frequency increases. This implies that the low frequency noise generated from the far upstream wind turbines still plays an important role. On the other hand, if a simple sound propagation algorithm is applied, such as shown in the last column of Table 1, a large error is observed in a frequency range below 1000 Hz.