*5.2. Wind Tunnel Simulation*

The wind flow around the structure will be simulated using the software turbulent flow. This module aims to solve the Navier–Stokes equations presented in (5) by modeling the fluid domain around the airflow as a mesh of discrete elements. The set of Equations (5) counts with the fluid density *ρ*, the fluid velocity **u**, the fluid pressure *p* and the fluid dynamic viscosity *μ*. The finer the mesh, the more precise the results are. However, it is always a trade off, as thinner mesh elements imply more computation time. Due to this, the smallest geometry details were removed using the "Cleanup" tool. The equations will be evaluated using a computational assessment technique. Up-to-date, there are three different techniques: Direct Numerical Simulation (DNS), which solves all the eddies, from the largest to the smallest, Large Eddy Simulation (LES), where only the large-scale eddies are resolved and Reynolds-Averaged Navier–Stokes (RANS), a completely different time-averaged method that does not resolve eddies explicitly, choosing to instead model its effect using the concept of turbulent viscosity. RANS is not an explicit method and, therefore, is less computationally expensive, with that being the primary reason for its use in this work [13].

The Navier–Stokes are moment0conservation equations, relating the inertial force *ρ ∂***u** *<sup>∂</sup><sup>t</sup>* + **u** · ∇**u** , with the pressure force −∇*p*, the viscous forces ∇ · *μ* ∇**<sup>u</sup>** + (∇**u**)*T*− 2 <sup>3</sup> (∇ · **u**)**I** as well as with an external force **F**.

$$\begin{cases} \rho \left( \frac{\partial \mathbf{u}}{\partial t} + \mathbf{u} \cdot \nabla \mathbf{u} \right) = -\nabla p + \nabla \cdot \left[ \mu \left( \nabla \mathbf{u} + (\nabla \mathbf{u})^T - \frac{2}{3} (\nabla \cdot \mathbf{u}) \mathbf{I} \right) \right] + \mathbf{F} \\ \frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \mathbf{u}) = 0 \\ \rho = \rho(p, T) \end{cases} \tag{5}$$

After choosing the assessment technique or turbulence model type, a turbulence model needs to be chosen accordingly. For the RANS, the software makes nine different turbulence models available (which can be consulted at the software library). However, for the case study, the *k*- turbulence model, where k refers to turbulent kinetic energy and the rate of dissipation on turbulent kinetic energy, is selected. Of the reasons behind its election, its good performance for complex geometries, its stability and the possibility to use wall functions stood out. Wall functions are adopted to resolve the thin boundary layer near the wall, preventing the use of a very fine mesh. Essentially, they provide an offset so that the mesh does not need to go near the wall; moreover, being the straightforward solution, a relationship is used to characterize the flow [13].

An incompressible flow approximation is used, assuming the fluid's density as constant, implying that the divergence of the fluid velocity is zero, as suggested in Expression (6). The wind tunnel dimensions are 295 m in height, 200 m in width and 100 m in depth. The above-mentioned structure is placed inside the tunnel. Only the parts of the structure that are inside this wind tunnel are subject to the wind, as illustrated on Figure 4.

$$
\nabla \cdot \mathbf{u} = 0 \Rightarrow -\frac{2}{3} (\nabla \cdot \mathbf{u}) = 0. \tag{6}
$$

The main goal of the following simulation is to calculate the power generated by the wind turbine by Betz's law and through the equation described above.

As altitude increases, atmospheric pressure decreases. As altitude increases, the amount of gas molecules in the air decreases, and the air becomes less dense than air nearer to sea level. One can calculate the atmospheric pressure at a given altitude. Temperature and humidity also affect the atmospheric pressure. Pressure is proportional to temperature and

inversely proportional to humidity. However, at the height of 190 m, this variation in air pressure is not significant. Therefore, the reference air pressure and temperature were considered, as they are values that do not significantly affect the results. Regarding the wind speed, three different simulations were performed, considering the minimum, average and maximum speed, as in Figure 5. This is the input inserted at the open boundary.

**Figure 5.** Betz Law.

In Figure 6, the resulting wind flow is illustrated, being characterized by velocity magnitude, orientation and direction. The velocity magnitude's values are differentiated by colors whose legend can be seen at the right border. This figure is for an input speed of 8.28 m/s, but several simulations were performed for different wind speeds.

**Figure 6.** Wind speed using the software.

As we have seen before, the main goal is to take *v*2. The values taken from the performed simulations are shown in Table 6.

**Table 6.** Values of wind speed before and after the rotor.

