**2. Energy Content of Turbulent Wind: Evidence from Recent CFD Simulations**

An important effort has been devoted in recent years to increase the accuracy of CFD simulations for the prediction of the performance of Darrieus wind turbines. To this end, a variety of approaches have been proposed, ranging from detailed unsteady Reynolds-averaged Navier–Stokes (U-RANS) approaches (e.g., [28–31]) to more advanced Detached Eddy Simulation (DES) [32] or Large Eddy Simulation (LES) approaches [33]. These latter approaches however, often require enormous calculation costs, which are often prohibitive, leading the researchers to compromises that often do not ensure fully reliable results. A recent study on the effects of turbulence on Darrieus VAWTs is reported in [7]. In this work, a new method to reproduce with a U-RANS approach the turbulence conditions typically found in wind energy applications (in terms of realistic scales of turbulence intensity and length scale) was developed. An innovative user-defined function was developed to assign a randomly variable velocity inlet boundary conditions able to create flow structures having a prescribed length scale; additionally, numerical settings have been tuned so as to allow the correct inflow turbulence level, controlling the numerical dissipation due to the U-RANS approach.

The authors then applied the method to the case study of [23] (see Figure 1), which also represents the one used in the present work, showing that an increase of the turbine performance was indeed achieved. In particular, the impact of the flow macrostructures on the turbine was analyzed as well as the contraction effect on the wake apparent in Figure 1.

Upon examination of the simulation data, the turbine performance increase was connected to two main phenomena:


**Figure 1.** Computed contours for the dimensionless streamwise velocity: (**A**) turbine simulation with turbulence, and (**B**) turbine simulation without turbulence.

The first phenomenon was not addressed in [7], and it will represent the key element of the present study. The second one was instead somehow quantified, and it is briefly reported here since it is pivotal for the correct understanding of the present approach. In particular, if a turbulent velocity profile can be reasonably characterized as a randomly fluctuating one around the mean flow speed (see Figure 2), its energy content has to be scaled with the cube of the speed itself, thus leading in general to higher energy levels in turbulent wind with respect to a uniform one. In detail, an *equivalent velocity* to be considered to reflect the energy potential can be defined as in Equation (1), where *E* is the wind specific energy content of the turbulent flow, ρ is the air density:

**Figure 2.** Comparison between a uniform wind speed, a real fluctuating one and its equivalent speed as in Equation (1).

The same authors, however, also pointed out that the flow macrostructures corresponding to the turbulence length scale typical of wind energy applications generate a non-periodic fluctuation of the relative speed oncoming on the airfoils in cycloidal motion onboard a Darrieus turbine. This, in turn, generates a variation of the local tip-speed ratio (TSR), which is defined as in Equation (2):

$$TSR = \frac{a\mathcal{R}}{\mathcal{U}}\tag{2}$$

It has to be stressed that these fluctuations happen in very short times, which are generally much lower than those required by the regulation system to act. The turbine revolution speed ω can then reasonably be considered as constant. The effect of the above is that it is indeed true that energy content is increased, but it is also true that it is extracted with a lower efficiency, as the optimal TSR is never maintained, as illustrated in Figure 3.

**Figure 3.** Schematic representation of the variation of turbine power coefficient due to a local variation of the incoming wind velocity at a fixed revolution speed.

As a result, in [7] a performance increase lower than that theoretically predictable based on Equation (1) was found. In any case, both targets were much lower than the experimental evidence on [23]. This was connected to the possible increase of low Reynolds airfoils' aerodynamics in turbulent wind, which are addressed instead in the following of the present study.

#### **3. Experimental Tests**

In the framework of the present work, two types of experimental tests were carried out. The most important ones were focused on reproducing correctly the turbulence levels of interest inside a wind tunnel [33] and on assessing the impact of turbulence on a two-blade small Darrieus VAWT [23]. These tests have been already presented in relevant technical papers: they will be then only briefly recalled here to give the reader a complete overview on the broad results of the entire research program. In addition, however, detailed measurements of isolated airfoils in turbulent conditions were repeated recently. The scope of these additional tests was to quantify the effect of turbulence on stall delay and maximum lift-to-drag ratio enhancement, in order to obtain a new set of aerodynamic polars for use in engineering simulation models.
