**2. Study Cases**

#### *2.1. Experimental Validation Benchmark*

In order to assess the effectiveness of the numerical techniques prior to proceed with the extended sensitivity analysis on the GF effects on the airfoil in Darrieus-like motion, an experimental benchmark was identified. In particular, the test case presented by researchers from the Technical University (TU) of Berlin in [16] was used. Dedicated experimental studies were conducted inside the laminar wind tunnel of the Hermann Föttinger Institute. The tested airfoil was NACA0021 with the Gurney flap on the pressure side. As discussed, this airfoil was also used in one of the study cases of the sensitivity analysis; therefore the experimental case was then fully representative for the scope of this study.

In [17] the authors presented a variety of tests with different Reynold numbers (Re = 140 k and Re = 180 k) and GF size and mounting configuration. For the sake of brevity, the CFD validation was here reported only for the configuration with the GF conventionally mounted on the pressure side, depicted in Figure 2, which shows a sketch of the Gurney flap geometry used in the experiments. Table 1 reports the chosen test conditions for the validation and the Gurney flap height is given by a percentage value of chord length. For any additional details on experimental measurements (which are not the original content of the present work), please refer to [17].

**Figure 2.** Experimental Gurney flap (GF) geometry.

**Table 1.** Details of the experimental setup.


## *2.2. Gurney Flaps*

Two different types of Gurney flap mounting were investigated (represented in Figure 3). In further detail, the conventional one-side mounting (A) is the most common method, generally including the GF mounted towards the pressure side of the airfoil. In case of functioning onboard a Darrieus turbine, however, each side of the airfoil acts alternatively as the pressure or suction side depending on the fact that the blade is moving in the upwind or downwind half of the trajectory [18]. On this basis, both the configuration with the GF facing out and the one facing in with respect to the revolution centre were tested. In addition to these configurations, the one presented in Figure 3B, called "fish tail" in the following, was also tested. This configuration was thought to somehow reply to the contrasting requests discussed before, i.e., it is able to provide the power augmentation both for positive and negative incidence angles, partially limiting the additional drag coming from the half working in the suction side by inclining it with respect to the chord. In this sense, it can be considered as an evolution of the "both-side" configuration tested in [6].

**Figure 3.** GF configurations: (**A**) one-side GF; (**B**) fish tail GF.

For the scopes of the present work, the two configurations were tested with GFs having a length varying in the range of 0% to 5% of the chord length.

#### *2.3. Test Plan*

As discussed, the scope of the study was to evaluate the effectiveness of GFs as power augmentation devices when operating on board Darrieus turbine. To this end, three configurations of an airfoil in cycloidal motion were considered. The idea was to reproduce realistic functioning conditions in terms of Reynolds number, AoA variation trend, and inflow. On this basis, relevant study cases were selected from the literature, with particular attention to those already tested by some of the authors and for which a relevant body of data was available. The configurations are summarized in Table 2. Upon examination of the table, one can notice that one important parameter that has been taken into account is the equivalent turbine solidity, calculated as in Equation (1).

$$
\sigma = \frac{Nc}{D} \tag{1}
$$


**Table 2.** Summary of the operational conditions considered for the study cases.

The solidity of the rotor is in fact an index of how much the turbine is "permeable" to the flow, thus of how much the energy extraction is unbalanced between the upwind and the downwind portion of the revolution. In more detail, the higher the solidity, the more kinetic energy from the wind is harvested by the upwind part and the less energy can be harvested by the downwind part. The velocity used to calculate the blade Reynolds number, presented in Table 2, is an average value of the relative wind velocity during the revolution. The turbine tip-speed ratio (TSR) is conventionally defined as the ratio between the peripheral speed of the airfoil and the undisturbed wind velocity.

The study cases presented in Table 2 were used in particular to extract realistic trends of variation of the angle of attack and the relative air speed on the airfoils. These curves, presented in Figure 4, were obtained with the procedure described in [19] and slightly smoothed to purge them by unphysical discontinuities arising during the calculation of the induced velocity in areas of macro-vorticity, as discussed in the reference. The trends of Figure 4 were then used as an input for the sensitivity analysis on the GF effects. To this end, they were applied to four different uncambered airfoils of different thickness-to-chord ratios, namely the NACA0012, NACA0015, NACA0018, and NACA0021 (shown in Figure 5).

**Figure 4.** Variation trends for the angle of attack and the relative wind velocity for the selected study cases.

**Figure 5.** Investigated NACA airfoils.
