*3.3. Domain Meshing*

The accuracy of the model results was sensitive to the size and distributions of the mesh. For this three-dimensional simulation study, two diverse zones—the rotating and stationary zones—were drawn. A vertical cylinder around the turbine was considered to be the rotating zone, and the whole wind tunnel test section excluding this cylinder was the stationary zone, as shown in Figure 10.

**Figure 10.** Two different zones of the IceWind turbine's domain: rotating and stationary zones.

A mesh independency study was carried out. Figure 11 shows the relation between static torque and the number of elements at an air velocity of 15.8 m/s for the IceWind turbine at θ = 90◦. For element numbers of 4.5 <sup>×</sup> 106 and 7.8 <sup>×</sup> 106, the value of static torque (N·m) was almost the same. To give a high level of accuracy, 7.8 <sup>×</sup> <sup>10</sup><sup>6</sup> elements were used.

**Figure 11.** Relation between static torque and the number of elements at an air velocity of 15.8 m/s for the IceWind turbine at θ = 90◦.

Figures 12 and 13 show that computational mesh consists of tetrahedral cells. It is very fine around the blades and shaft (maximum y<sup>+</sup> below 2). A close-to-equilateral coarse mesh is generated in the stationary zone. The contact between these two zones is considered to be the interface boundary condition, and this guarantees that continuity in the flow field is acquired while minimizing numerical errors. Second order discretization was used for all solution variables [9].

**Figure 12.** Mesh of the IceWind turbine domain (section): (**a**) elevation and (**b**) side view.

**Figure 13.** Mesh of the IceWind turbine domain (zoomed in): (**a**) elevation, (**b**) plan, and (**c**) plan (zoomed in).

#### *3.4. Turbulence Modeling Approach*

The regime of the system was laminar. Previous studies showed that the *k*-ε and Spallart-Allmaras models cannot catch and predict the flow progress, especially in the laminar separation bubble [10,11]. Therefore, the SST *k*-ω model [12,13] can be utilized as a low Reynolds turbulence model with no additional damping functions. Shear Stress Transport (SST) formulation is created by combining the *k*-ω and *k*-ε models. This structure supports the use of the SST method to switch to the *k*-ε model to

revoke the problems of *k*-ω in inlet free-stream turbulence properties and utilize the *k*-ω formulation in the internal parts of the boundary layer. The *k*-ω SST model is a commonly used turbulent model in VAWT simulations [14–20]. Furthermore, it is a good predictor of turbulence in adverse pressure gradients and separating flow.

Two mathematical formulas, *k* and ω equations, are proposed for use in SST methods below [9]:

$$\frac{\partial(\rho k)}{\partial t} + \frac{\partial(\rho \, k \, u\_i)}{\partial \mathbf{x}\_i} = \frac{\partial}{\partial \mathbf{x}\_j} \Big(\Gamma\_k \frac{\partial k}{\partial \mathbf{x}\_j}\Big) + \mathbf{G}\_k - \mathbf{Y}\_k + \mathbf{s}\_k \tag{1}$$

$$\frac{\partial(\rho\omega)}{\partial t} + \frac{\partial(\rho\omega \,\, u\_i)}{\partial \mathbf{x}\_i} = \frac{\partial}{\partial \mathbf{x}\_j} \Big(\Gamma\_\omega \frac{\partial \omega}{\partial \mathbf{x}\_j}\Big) + \mathbf{G}\_\omega - \mathbf{Y}\_\omega + \mathbf{s}\_\omega \tag{2}$$

where Γ*<sup>k</sup>* and Γ<sup>ω</sup> express the active diffusivity of *k* and ω. *sk* and *s*<sup>ω</sup> are user-defined source terms. *Gk* and *G*<sup>ω</sup> show the turbulent kinetic energy generation due to the mean velocity gradients. *Yk* and *Y*<sup>ω</sup> mean the dissipation of *k* and ω due to turbulence.

The chosen fluid model for computation comprises air at 25 ◦C, pressure equal to one atmosphere, isothermal heat transfer, and a turbulent flow model.

For laminar steady flow, the simulations were run to reach steady state conditions, and the residuals reached a value of less than 6 <sup>×</sup> <sup>10</sup><sup>−</sup>5, as shown in Figure 14.

**Figure 14.** Relation between residuals and the number of iterations at an air velocity of 15.8 m/s for the IceWind turbine at θ = 90◦.
