*2.5. Modifications to Ideal Design*

The ideal blade design seen so far did not account for various practical aspects that have to be considered in a real design [43]. The ideal blade first needs to be tapered at the tip. In this area, tip losses, which are not considered during preliminary design, would greatly decrease the energy extracted at blade tip [19,38]. In the present study, the tip region was tapered from 95% blade span outwards empirically. Since BEM methods were used in the present preliminary design study, although Prandtl's tip and hub-loss corrections were included in this work, accurate tip-loss evaluation was not possible and the influence of different tapering strategies was hard to assess. In fact, despite the fact that BEM methods are able to capture the primary effects of blade tapering by resolving blade– chord variations, the chord variations at the blade tip also influence tip-vortex strength and, as a consequence, blade loading. While some tip-loss correction models are somewhat sensible for tip chord distribution [44], Prandtl's model is not [24]. Moreover, while these corrections may be more sophisticated, they remain unlinked to the underlying physics; therefore, to properly study the effects of this phenomena, more sophisticated aerodynamic models are required. Decreasing the chord at the tip region also decreases aerodynamic loading, which is beneficial from a load standpoint and has little aerodynamic penalty due to the presence of the aforementioned tip-losses.

The blade also needs to be tapered at the blade root, where it is connected to the rotor hub. In this area, the local tip–speed ratio is very low, the local radius is short, and the produced torque is thus very low. On this basis, it is common practice to taper a blade empirically.

The lift and drag coefficients used throughout the blade must also be corrected to account for 3D flow effects. 3D effects were first noted by Himmelskamp [45] and tend to greatly increase the high-angle of attack lift of the inboard sections of a rotating blade [46]. These effects are present in rotating blades and although the underlying physics are not fully understood to this day, they seem to be caused by complex flow interactions in the boundary layer. In practical terms, radial pressure nonuniformities along the rotor blade crease radial flow patterns, which have the main effect of delaying the stall. A brief explanation of the phenomena, as well as additional references, can be found in Chapter 3 of [10]. In the present study, the model proposed by Bak [47] was adopted and suggested. This model corrects both the lift and drag coefficients, and it can be relatively easily applied as an empirical correction step before the aerodynamic simulations are performed. The inclusion of 3D-effects was found to have a notable impact on turbine performance, especially for the stall-regulated turbine, as shown in Figure 3. Power was found to vary quite noticeably. At 12 m/s, the blades with a fixed −6.5◦ pitch angle produced 49.4 kW (3D) and 48.4 kW (2D), while the blades with a −5◦ pitch angle produced 50.4 kW (2D) and 59.8 kW (3D).

**Figure 3.** Generator power as a function of wind speed for the stall-regulated ideal blade design with 2D lift and drag coefficients, the ideal design with 3D effects, and the final design with 3D effects.

For this reason, the fixed blade pitch of the stall-regulated turbine was further tuned, and the twist of the inboard sections of the blade, which are most affected by stall delay, were modified to ensure the desired regulation characteristics, as shown in Figure 4. Reducing the twist angle increases the angle of attack, therefore pushing this part of the blade towards the stall. In fact, the angle of attack can be found from the flow angle *ϕ*, twist angle *δ*, and pitch angle *θ* as:

$$
\mathfrak{a} = \mathfrak{p} - \delta - \theta \tag{7}
$$

**Figure 4.** Changes to the optimal twist distribution to ensure good stall regulation.

Therefore, reducing the twist angle increases angle of attack, although it should be noted that changing blade twins influences axial and tangential induction, therefore changing the induced velocities and affecting the flow angle in Equation (7). The overall trend, however, remains valid, although some trial and error might be necessary. In other words, changing the twist angle can be seen as partial compensation for the stall delay effect, which, in contrast and as the name suggests, tends to delay the point of the stall, thus negatively affecting the blade's regulation capacity.
