# Effects of Turbulence Modeling on the Simulation of Wind Flow over Typical Complex Terrains
## 4 Results and Discussions
### Case 2: Askervein Hill Field Experiment (TU-03B)  
Figure 9 shows numerical results in comparison with the experimental data and the LES results [46]. From Figure 9, it can be seen that the numerical wind speeds of the four RANS turbulence models are generally consistent with the initial values given by the inlet, while the LES results are obviously large above 10 m in height. Regarding the simulation of the TKE, there are obvious differences in the numerical results of the four turbulence models, where the TKE error simulated by the Mod RSM model (\(e_{\text{TKE}}=8\%\); \(z=10\) m) and the Mod SST \(k\)-\(\omega\) (\(e_{\text{TKE}}=7.8\%\); \(z=10\) m) are smaller than that of the standard models (\(e_{\text{TKE,Std SST k-\omega}}=32\%\); \(e_{\text{TKE,Std RSM}}=25\%\); z = 10 m) below the height of 100 m at the RS point. Figure 10a also shows that, near the ground, there is a decay phenomenon of the TKE simulated with the Std RSM model and the Std SST \(k\)-\(\omega\) model from the inlet to the front of the simulated object, while the TKE simulated with the Mod SST \(k\)-\(\omega\) and Mod RSM models is better maintained. This decay of the TKE (the TKE in front of the simulated object is not consistent with the initial value given at the inlet) also affects the simulation of wind flow over the hill, as can be seen in Figure 10b, where the TKE values of the four models differ significantly on the windward and leeward slopes of the hill. Then, as can be seen in Figure 11, the results of the four turbulence models are almost the same at the windward slope, with more obvious differences at the hilltop and leeward slopes, and similar conclusions can be found in the literature [8]. In the current simulation, the Std SST \(k\)-\(\omega\) model underestimates the wind speed at the top and leeward slope (\(e_{\text{u,A-hilltop}}=5.6\%\); \(e_{\text{u,mean(A)}}=14.92\%\); \(e_{\text{u,max(A)}}=78.96\%\)), and the Std RSM model also underestimates the wind speed at the leeward slope (\(e_{\text{u,A-hilltop}}=1.97\%\); \(e_{\text{u,mean(A)}}=12.3\%\); \(e_{\text{u,max(A)}}=61.3\%\)). The Mod RSM model performs well from the windward slope to the leeward slope (\(e_{\text{u,A-hilltop}}=0.79\%\); \(e_{\text{u,mean(A)}}=6.3\%\); \(e_{\text{u,max(A)}}=10.4\%\)), while the Mod SST \(k\)-\(\omega\) model overestimates the wind speed at the leeward slope (\(e_{\text{u,A-hilltop}}=3.39\%\); \(e_{\text{u,mean(A)}}=13.6\%\); \(e_{\text{u,max(A)}}=42.7\%\)). The results of line AA and line B also show that the Std SST \(k\)-\(\omega\) and Mod SST \(k\)-\(\omega\) models have insufficient wind acceleration near the hilltop, and the Std RSM model underestimates the wind speed at the leeward slope. Figure 9: Numerical results at the RS location in the Askervein experiment case. ‘Cup’, ‘Sonic’, ‘Tilted Gill UVW’, ‘Vertical Gill UVW’, and ‘BRE tala kite’ stand for the different types of experimental data and fitting the Sonic data with the log-law wind speed profile. (**a**) Vertical distribution of the wind speed; (**b**) TKE profile. From Figure 11, all of the four RANS models underestimate the TKE on the leeward slope, while the TKE in the LES model is larger than the experimental value because the incoming TKE in the LES model is also larger (as seen in Figure 9). However, the large TKE of the LES model on the leeward slope also indicates that the experimental data here may have been underestimated, and that the RANS model has a limited predictive capability of the inverse pressure gradient, resulting in insufficient TKE generation. On the leeward slope, the result of the Mod RSM model (\(\varepsilon_{\text{TKE,max(A-leeward)}}=28.46\%\)) and Mod SST \(k\)-\(\omega\) model (\(\varepsilon_{\text{TKE,max(A-leeward)}}=29.89\%\)) are relatively better, while the Std SST \(k\)-\(\omega\) model (\(\varepsilon_{\text{TKE,max(A-leeward)}}=51.33\%\)) seriously underestimates the TKE.