*7.2. Power Coe*ffi*cient Comparison for Di*ff*erent (DR*/*DT)*

Figure 7 shows the power curves of the AHDT for the two-bladed rotors corresponding to the solidity of σ = 0.5. Each subplot in Figure 7 shows the power curve (*Cp* vs. λ) for their respective diameter ratio (DR/DT). The power curves are calculated for a range of Re <sup>=</sup> 1.2 <sup>×</sup> <sup>10</sup><sup>5</sup> to Re <sup>=</sup> 2.7 <sup>×</sup> 105. Figure 5b shows the comparison of the maximum power coefficient (*Cp*max) with the investigated Re and DR/DT ratio. As mentioned before, the DR/DT = 20 corresponds to the conventional Darrieus rotor. Figure <sup>8</sup> shows the *Cp* curve at different Re ranging from Re <sup>=</sup> 1.2 <sup>×</sup> 105 to Re <sup>=</sup> 2.7 <sup>×</sup> 105. It can be seen from Figure <sup>8</sup> that for the low Re of 1.2, 1.5 and 1.8 <sup>×</sup> 105, the optimal TSR is 3.2.

**Figure 7.** *Cp* vs Tip Speed Ratio (TSR) for different DR/DT.

**Figure 8.** *Cp* vs TSR for different Re.

However, for a higher Re of 2.1, 2.4 and 2.7 <sup>×</sup> 105, the optimal TSR shifts to 3.4. The maximum power coefficient increases by 11.7% at Re = 1.5 <sup>×</sup> 105 when compared to Re = 1.2 <sup>×</sup> 105. At Re = 1.8, 2.1 and 2.4 <sup>×</sup> 105, the percentage increase in *Cp*max is 18.4%, 24.6% and 30% higher than the *Cp*max at Re <sup>=</sup> 1.2 <sup>×</sup> <sup>10</sup>5. At Re <sup>=</sup> 2.7 <sup>×</sup> <sup>10</sup>5, the *Cp*max value is 0.533 which is 33.6% higher than the *Cp*max obtained at the low Re of 1.2 <sup>×</sup> 105. For the diameter ratio up to DR/DT = 2.5, the *Cp* curves show a dip before

reaching the maximum *Cp*, except for the DR/DT = 20. By poring over the data, it is evident that the power loss occurs at TSR ~2. The loss in power reflecting as the dip is attributed to the vortices from the cylinder interacting with the Darrieus blades. The frequency of the vortices can be deduced from Strouhal number (*St*) as given by Equation (10),

$$S\_l = f\_l D / V \tag{10}$$

where *fs* is the vortex-shedding frequency, *D* is the across-wind dimension of the body, and *V* is the mean velocity of the uniform flow. The frequency of the vortices and the blade passing frequency are correlated at TSR 2, resulting in power loss. The *Cp* curve of the larger diameter cylinder does not exhibit this kind of power loss, as the cylinder acts as a bluff body generating a large wake, where the wake width occupies most of the downstream path. For DR/DT = 1.5, the maximum *Cp* achieved for the Re = 2.7 <sup>×</sup> 105 is 0.27, whereas for the same Re, DR/DT = 20, the peak *Cp* is 0.53 (Table 1). It is evident that the diametrical ratio of 1.5 and 2 significantly reduce the power coefficient by more than half. Hence, these diameters are not suitable for AHDT. Another interesting finding is that the maximum *Cp* is a sharp curve for the lower diameter ratio, and as the cylinder diameter increases, the maximum *Cp* although it is low, is maintained over a wider TSR, making the curve flat rather than sharp. The advantage is that a higher power can be extracted from the turbine for a wide wind speed range.


**Table 1.** Difference in *Cp* at various Re.

The difference in the *Cp* values for a low Re of 1.2 <sup>×</sup> 105 is comparatively lower than the difference in *Cp* for the higher Re of 2.7 <sup>×</sup> 105 for different diameter ratios. At lower Re, the Darrieus rotor by itself has a lower *Cp* value and the impact of turbulent flow from the cylinder is comparatively low. The peak *Cp* value for Re 1.2 <sup>×</sup> 105 stays at 0.3 for all the investigated diameters. As the diametrical ratio increases to 1.5, the *Cp* curve stays at 0.1 for all the TSR. It can be concluded from the *Cp* curves comparison for various DR/DT that the DR/DT = 2.5, 2 and 1.5 reduces the *Cp* by more than half, hence these diameters are not suitable for AHDT further optimization.
