## 5 3D BEM-DMST Code Experimental Validation
### DeepWind Demonstrator  
The 3D BEM code is finally validated against the experiments performed on the DeepWind Demonstrator, which features a Troposkein rotor shape and the DU06W200 airfoil designed on purpose for VAWT applications. The demonstrator turbine is a downscaled model of a VAWT conceived for future floating offshore applications; its installation in the actual floating foundation foresees a backward tower tilt \(\beta\) equal to \(15^{\circ}\) in standard operation. The DeepWind demonstrator was tested in the GVPM, both in upright and tilted configurations, and it is here compared to 3D BEM predictions. In the calculation, the rotor tilt is modelled considering the rotor in upright configuration subjected to a wind skew equal to the rotor axis tilt angle. Moreover, the assumption that the velocity component is normal to the rotor axis is made. Effective wind speed approaching the blade is therefore obtained by Equation (19). \[V_{\infty eff}=V_{\infty}\cos\beta \tag{19}\]  
The spanwise component of the free stream velocity is neglected, which appears reasonable considering the limited skew angles as imposed for 3D BEM simulations conducted in this study. Comparisons between 3D BEM and experiments are presented for DeepWind rotational speeds of 200 rpm and 300 rpm in Figure 8a,b respectively, both in upright and tilted operating conditions. First considering the power coefficient at 200 rpm, the 3D BEM captures the trend of experiments and the peak \(C_{P}\) values, with a light underestimate of the TSR of peak \(C_{P}\), for both upright and tilted rotor. It has to be noted that power coefficient estimates remain  
Figure 8: DeepWind performance. within the uncertainty bands for TSRs higher than those of the peak power. Results lose in accordance for low TSRs, where C\({}_{P}\) predictions appear very close to the experimental data but larger discrepancies appear in dimensional terms (with maximum differences between 3D BEM of about 10% at \(V_{0}=11\)m/s for both upright and tilted rotor). The reason for that may be ascribed to the different aerodynamic behaviour of blade sections. Experimental data seem to be affected by a local severe stall, which leads to a local drop in the power plot for a wind speed of 11 m/s, after that the effect disappears and the power rises again as wind speed increases. Conversely the 3D BEM power curves decrease monotonically after the peak at \(V_{0}=9\) m/s. Polars of the 3D BEM have been smoothed and abrupt drops of lift and drag coefficients are avoided to ensure good convergence ability of the algorithm. As already discussed, dynamic stall predictions still remain affected by uncertainty at very low TSRs because of the inherent approximation of the implemented models. Both these features might explain the discrepancy between experiments and predictions at high wind speed. Comparing Troposkein 450 W and DeepWind Demonstrator results, one may notice that 3D BEM predictions are in better agreement for the latter case although the architecture of the two machines and geometry are quite similar and the models applied are the same. Above all, the attention must be drawn on the fact that largest discrepancies are observed at high wind speeds (low TSRs) in the case of Troposkein 450 W and DeepWind Demonstrator 200 rpm in Figures 6b and 8b. Good accordance is found at low wind speeds up to the power peak, whereas discrepancies become higher above 10 m/s. When Reynolds number increases, a better agreement is found for DeepWind Demonstrator at 300 rpm. Therefore it is assumed that uncertainty related to low Reynolds numbers is evident in the comparison with experimental data. The effect of rotor tilt is also of interest: at high wind speeds, upright and tilted rotor show minimal differences for both experimental and 3D BEM data.