*1.2. Basic Mathematical Formulations*

In this article, the dimensionless analysis of wind turbines is employed [19]. The non-dimensional rotational speed (Tip-Speed Ratio, *TSR*) is defined as:

$$TSR = \frac{aR}{V} \,\prime \tag{1}$$

with ω—wind turbine rotational speed, *R—*rotor radius, and *V*—the reference wind speed. In order to present the wind turbine efficiency, the power coefficient *Cp* is introduced, as follows:

$$Cp = \frac{P}{\frac{\rho \times \pi R^2 \times V^3}{2}}\tag{2}$$

with *P*—wind turbine power and ρ—fluid density. Lastly, pressure coefficient *cpress* relates static pressure *p* to the dynamic pressure, as:

$$c\_{\text{press}} = \frac{p}{\frac{\rho V^2}{2}}.\tag{3}$$

#### **2. Object of the Study**

The rotor is a three-bladed GUST HAWT. This small wind turbine has a nominal power 350 W at a wind velocity of 8.4 m/s [20]. The blades are of variable chord and twist angle (Figure 1) and are constructed upon NREL S826 and S834 airfoils [21]. The examined rotor radius *R* is equal to 0.8 m, which is the same as that used in experimental investigation used as a reference. For wind speed *V* = 8.4 m/s, at optimum *TSR* = 5, the local Reynolds number (at each blade station, thus taking chord length as a characteristic dimension) is of an order of magnitude of 1.2 <sup>×</sup> <sup>10</sup>5.

**Figure 1.** Blade geometry (left): (**a**) general view; (**b**) top view; (**c**) leading edge and suction side; and (**d**) wind turbine prototype during wind tunnel testing (own materials).

The material which was used to produce the prototype blades was Polyamide PA66 MO as an optimal choice between stiffness, allowable stresses, manufacturability, and price. The material was bought in sheets with dimensions 90 × 610 × 2000 mm and blades were milled on CNC machine. The material properties of this material, necessary for structural analysis, are grouped in Table 1. Since

the blade was machined from a uniform piece of material, in the structural simulation, an isotropic material model is assumed.
