## 5 3D BEM-DMST Code Experimental Validation
### Microgeneration Troposkein 450 W  
The predicted performance of the Troposkein VAWT with a rated power of 450 W is compared to experiments in Figure 6, where \(\lambda\) is referred as equatorial TSR. The matching between the experiments and the prediction is not excellent as the one found for the H-shaped turbine, though remaining satisfactory especially in the peak \(C_{P}\) region. The predicted peak \(C_{P}\) value is in close agreement with the experimental datum and occurs, both in the experiment and in the prediction, in a relatively wide 'flat' region of the \(C_{P}\) curve comprised between TSR vales of 3.1 and 3.5. As already observed for H-shaped VAWT, the non-dimensional analysis shows the highest gap of \(C_{P}\) at high TSRs (wind speeds lower than 10 m/s); conversely the agreement once again looks better when considering dimensional quantities. For wind velocities exceeding the peak one, both shows a constant power production (Figure 6b), while experiments evidence a power decrease up to 15 m/s where a plateau is finally reached. The thrust coefficient (Figure 6c) shows a very good agreement up to the optimal TSR value; for higher TSRs, experiments show a very slight \(C_{X}\) reduction, while 3D BEM conversely predicts a slight increase followed by a plateau at \(\lambda=4\). Overall, the 3D BEM code appears capable of quantitatively predicting Troposkein performance, despite the quality of the prediction reduces for high wind speed regimes. At first glance, one might have expected a level of agreement similar to the one obtained for H-shaped VAWT, since the two VAWTs share the size and airfoil shape, but the radical difference between the rotor architectures must be taken into account. Due to complex shape of Troposkein rotor, featuring bent blades towards the basement and the top of the  
Figure 6: Comparison of experimental and 3D BEM results for the Troposkein-shaped 450 W case. pole, huge angles of attack are expected at very low peripheral speeds at blade tips also for relatively high vales of TSR at the equatorial section. This implies to include, for any point along the performance curve, local predictions at the blade tip suffering severe limitations of the models implemented and possibly available in the literature. Blade sections close to the pole behave more like struts and fluid structure interaction is poorly captured by 3D BEM model. This is a crucial feature of any VAWT not featuring a 3D rotor shape, and deserves a proper analysis. Assuming to cut the rotor with planes normal to the turbine rotational axis, the blade sections coincide exactly with the design airfoil shape (NACA0021) only at the equatorial plane. Otherwise, the intersections with the blade originate thicker 'virtual' airfoils approaching the tips. As a consequence, the assumption underlying the 3D BEM approach is to consider, at each blade section, the design airfoil shape and correspondent streamtube wind velocity equal to the normal component to the airfoil stacking line. The neglected effect of the span-wise velocity component in Troposkein rotors is unavoidable unless new aerodynamic coefficients are obtained for each 'virtual' airfoil shape. For the sake of simplicity and model conciseness the'standard' approximation is considered in order to have affordable run times of the 3D BEM code. A detailed spanwise/axial analysis of the rotor aerodynamics is reported in Figure 7a, where the incremental contribution of rotor slices to the \(C_{P}\) and power are shown to highlight the impact of each section of the Troposkein rotor shape. Troposkein semi-span is ideally split according to vertical discretization, resulting in several plain slices for each rotor hemisphere, with a decreasing slice width towards the blade tip. The incremental \(C_{P}-\lambda\) trend (Figure 7a) is determined by adding the contribution of each pair of symmetric slices incrementally, so that at \(z/H=1\) the power coefficient curve results the one of the entire rotor.