*1.1. Background*

The interest in cheap and environment friendly electrical energy generation, lately driven also by the need for meeting stricter standards of clean energy production, has resulted in a wide range of scientific research on the subject of renewable energy sources. One of the leading technologies is wind energy, which is reaching a cost of energy competitive (in the case of large rotors) with other conventional sources. Although the majority of installed wind energy power today comes from wind farms made of several large horizontal axis wind turbines (HAWTs), the disclosing of new diffusion frontiers like deep-water offshore applications or installations in densely inhabited environments

are putting new focus on different turbine architectures, like Darrieus vertical axis wind turbines (VAWTs) [1]. This technology has some undisputed advantages (e.g., the insensitivity to wind direction, the possibility of putting the generation system on the ground, the lower susceptibility to highly turbulent flows [2,3]), but their efficiency is lower compared to that of HAWTs. This is not only due to intrinsically more complex aerodynamics with a continuous variation of the angle of attack (AoA), often leading to dynamic stall [4], but also due to the lack of systematic scientific research from their conception in the 1920s up to the 1990s [2]. If this efficiency gap is somehow filled, many scientists forecast a significantly more important role of VAWTs in the near future [5].

Among different approaches to reach this scope, lately increasing attention is given to the possibility of applying passive flow control devices to Darrieus blades [6], in order to delay the onset of stalls and improve the lift-to-drag ratio, especially at medium-low Reynolds numbers. Gurney flaps (GFs) are one of the technologies in the spotlight. In the early 1970s, the American racing driver Dan Gurney came out with an idea to fix a short metal bar at the trailing edge on his racing car rear wing. After conducting few tests, he found out that this simple modification allowed approaching turns with higher velocity and also increasing the car speed on straight lines. The simple construction of this device has encouraged researchers to investigate its application in different areas [7–10], and especially in wind turbines, where they do represent one of the most interesting solutions [11,12]. It has been found that the effect of the lift coefficient enhancement of the GF is connected with the change of the flow structure at the trailing edge, as it is shown in Figure 1, which reports the vorticity contours near the trailing edge of the airfoil. The two large separation bubbles around the sharp trailing edge are replaced by two thinner vortices inducing a lower drag. The Gurney flap also delays the flow separation to a higher angle of attack. The gain on the lift coefficient is burdened with increments of the drag coefficient. Thus, it is a particularly good solution in case of applications where the drag force is of minor importance, like in the case of Darrieus VAWTs.

**Figure 1.** (**A**) Flow field around smooth airfoil; (**B**) flow field around an airfoil with a Gurney flap (field data of vorticity from numerical calculation of the authors).

#### *1.2. Objectives*

The aim of the present study is to assess the possible benefits provided by GFs if used on airfoils subject to continuous variations of the angle of attack, as in the blades of Darrieus wind turbines. More specifically, focus is given to the symmetric NACA 4-digits airfoils, which have been shown to be particularly effective in VAWTs [13]. The airfoil thickness represents the first investigated parameter; values of 12% chord (NACA0012), 15% chord (NACA0015), 18% chord (NACA0018), and 21% chord (NACA0021) are considered. Then, the impact of different heights and shapes of the GFs on the performance of these airfoils is evaluated in static conditions, but also in dynamic pitching movements. It is often erroneously thought that the variation of the angle of attack in the Darrieus-type cycloidal motion can be modeled as a pure pitching motion. However, different energy extractions take place upwind and downwind, which in turn impose a notable variation of the AoA in those zones [2]. Moreover, the change of sign of the AoA in proximity of the azimuthal positions of 0◦ and 180◦ leads to very sudden variation rates, which are also responsible for the onset of dynamic stall [14].

To meet the objectives described above, the use of computational fluid dynamics (CFD) is mandatory. Due to the complex flow structures taking place behind the GF, the continuous variation of the AoA, and the existence of large separated regions when the stall appears, the simpler modeling methods (e.g., a panel method) are insufficient for this scope [6,15]. In order to limit the computational cost, the unsteady Reynolds-averaged formulation of the Navier–Stokes equations (URANS approach) is used for the presented analyses as the best compromise. Due to the wide range of spatial and temporal scales that need to be captured in the flow features in the presented problem, more accurate methods addressing the turbulent flows such as direct numerical simulation (DNS) or large eddy simulation (LES) would be in fact unusable. In addition, recent examples in the literature showed that the proposed approach is able to properly capture all the effects connected to the use of GFs [6]. A key original model developed for the study presented in this paper is represented by the definition of AoA variations that match exactly the functioning conditions in a broad range of Darrieus VAWTs. These were defined upon combination of detailed full-CFD simulations carried out by the authors and computation of airfoil in pitching motion. Finally, the obtained results were extended using radial basis functions (RBFs) interpolation to provide a comprehensive overview of the effects of GFs installation on the performance of selected airfoils.

## *1.3. Organization of the Study*

The study is organized as follows. Section 2 presents the study cases that have been used both for the calibration and validation of the numerical approach and for the sensitivity analyses. Section 3 presents the methods that were used for the analysis. A description of the CFD settings, including their validation, is first presented; then, the development of the AoA variation trends that mimic the Darrieus functioning is discussed. Section 4 is the main body of the study, including results obtained for static airfoils as well as results obtained for dynamic airfoils in Darrieus-like motion. In this section the multivariate sensitivity analysis based on the radial basis functions (RBFs) interpolation is presented. Section 5 summarizes the main outcomes of the study.
