**5. Synthesis of the E**ff**ects into the BEM Modeling**

Finally, to prove that the two investigated key phenomena, i.e., the increased energy content and the improved airfoil performance at low *Re* in the turbulent wind, are indeed responsible for the increase of the power coefficient under turbulent conditions, they have been combined into an engineering Blade Element Momentum (BEM) model. It is well known that this theory is, on the one hand, able to deliver sufficiently reliable results in terms of overall performance, while providing, on the other hand, scarce definition of the torque profile during the revolution and of the flow field past the turbine [39]. In the perspective of the present study, however, the use of a simple BEM model (although making use of the most advanced features presently available for this theory) was thought to be of particular interest to test the impact of the discussed phenomena. More specifically, the claimed result is that a proper combination of corrections for the energy content in the flow and for the airfoil polars can accurately predict the turbine performance variation in turbulent flows even with a very simple theory.

#### *5.1. Setup*

The VARDAR code of the Università degli Studi di Firenze (Italy) [39] has been used for the analysis. The prediction capabilities of this research code have been validated over the last ten years on a variety of small H-Darrieus turbines, proving its high accuracy in comparison to other existing codes. The BEM formulation inside the VARDAR code is based on an improved version of a *Double Multiple Streamtubes Approach with Variable Interference Factors* originally proposed by Prof. Paraschivoiu in [9]. With respect to the "standard" formulation, the Glauert's correction for high-induction cases based on recent experimental data has been implemented. To increase the accuracy in predicting VAWT aerodynamics, several sub-models have been embedded within the code, including the corrections to account for the finite aspect ratio of the blades using the Lanchester–Prandtl model, the parasitic torque of the struts, and the streamtube expansion model presented in [9], although the impact of this on the simulation of small turbines like the one investigated in this work is negligible, as discussed in [34]. Furthermore, based on recent findings about the aerodynamics of airfoils in cycloidal motion, specific corrections are included to correct airfoil polars in order to account for flow curvature effects, i.e., the *virtual camber* effect [36] and the *virtual incidence* [40]. Another important additional feature recently included in the code is the polar smoothing procedure discussed in [41]. Finally, several dynamic stall models are included, i.e., those proposed by Gormont, Berg, Strickland, and Paraschivoiu [9]; in the present study, Berg's one with a calibration factor of 30 has been used.

According to the discussed hypotheses, the CFD-based airfoil polars presented in Section 4 (obtained for a turbulence intensity of 9.5%) have been used in the present study, along with an average wind speed corrected by Equation (1) in comparison to experiments, equal to 9.2 m/s.
