*7.3. E*ff*ect of Re on Cp for Di*ff*erent DR*/*DT*

Re is a critical factor in determining the power production capability and starting behaviour of a Darrieus rotor. For a conventional Darrieus rotor, the starting torque entirely rests on the lift generated at low Re, but for AHDT, the starting torque is generated by drag rather than lift. Hence, the study on the influence of Re aims to shed light on the power performance of AHDT and flow over cylinder rather than the starting behaviour of AHDT at low Re. By comparing different diametrical ratios for the given Re, i.e. wind speed, a suitable cylinder diameter or in other words, the diameter of the Savonius buckets, can be determined.

It is not always pertinent to choose a smaller diameter cylinder to maximize the Cp of Darrieus rotor, as the vortices of the cylinder at a given Re can deteriorate the torque of Darrieus blades more than larger diameter cylinder. Hence, it is imperative to perform the simulation iteratively for DR/DT = 20 to DR/DT =1.5. The results are critical from the structural perspective, as a loss in Cp will indicate a vortex shedding and further instigate to optimize the aspect ratio of the cylinder. Based on the Re regime, the flow over the cylinder may differ at large. The pressure gradient on the cylinder and the boundary layer may give rise to vortices of different diameters. The boundary layer upstream of the cylinder must overcome a strong pressure gradient set up by the cylinder. This leads to separation of the flow, and in the separated region, a vortex system is developed which is stretched around the cylinder like a horseshoe. Hence, AHDT behaviour at higher Re = 2.1 <sup>×</sup> 10<sup>5</sup> is of particular interest. The Cp curves for the investigated Re are shown in Figure 8. For all the diametrical ratios, except DR/DT = 1.5, the Cp curves are almost similar. The Cp values increase steadily as the Re increases. For 2.4 <sup>×</sup> 105, the peak Cp achieved is 0.3 for all the diametrical ratios except 1.5, for which the Cp is 0.2, due to wake expansion as seen from Figure 9. Vorticity contours corresponding to the DR/DT = 1.5 reveal that the Darrieus blades are operating in the large wake generated by the cylinder as shown in Figure 10.

**Figure 9.** Pressure contours (Pa) for AHDT at β = 0◦.

**Figure 10.** Vorticity contours (S<sup>−</sup>1) for AHDT at β = 0◦.

#### *7.4. Discussion of Pressure and Vorticity Contours*

The pressure contours for different diametrical ratios are compared in Figures 11 and 12 for azimuthal position 0◦ and 30◦ respectively. The azimuthal angle is of particular interest to analyze in detail, as the wake from the Darrieus blades and the Savonius buckets in closed conditions (cylinder) will be maximum, resulting in a higher power loss. For the rest of the azimuthal angles, the wake from the Darrieus blades are dispersed before it reaches the Savonius buckets. For the ratio DR/DT = 20, the flow pattern in the rotor is similar to a conventional Darrieus rotor, as the cylinder resembles the center shaft of the conventional turbine. For some of the cantilevered tower designs, the centre shaft diameters will be even higher than the diametrical ratio of 20. The wake pattern observed is similar to the Darrieus rotor, with low pressure behind the Darrieus blades with a peak power coefficient

of 0.35. For DR/DT = 3.5, the cylinder wake starts to appear with a low-pressure zone downstream. The corresponding vorticity for the azimuthal angle β = 0◦ indicates that the flow on the cylinder starts to separate with alternate vortices on both sides. The vortices are small and smoothly travel downstream, eventually regaining the freestream velocity. At β = 30◦, a similar pressure drop occurs without any noticeable difference between two angles. For the ratio DR/DT = 3, the cylinder diameter is comparatively larger, and the pressure drops around the cylinder is noticeable.

**Figure 11.** Pressure contours (Pa) for AHDT at β = 30◦.

**Figure 12.** Vorticity contours (S<sup>−</sup>1) for AHDT at β = 30◦.

The wake arising due to the pressure difference from the Darrieus blades progressively extends to the center cylinder, forming a large low-pressure zone. Though the intensity is not high, the low-pressure zone influences the power loss, decreasing the peak power coefficient as evident from Figure 7. For the ratio DR/DT = 2.5, the cylinder influence on the power coefficient of the Darrieus rotor is well pronounced. From the pressure contours on Figure 11d, the low-pressure zone extends from the upstream Darrieus blades through the cylinder to the downstream blades. The significant loss in power can be attributed to the size of the vortices compared to the blade chord and the downstream path where it encounters the blades. TSR plays a crucial role in generating asymmetric alternating wake. Von Karman vortices are formed due to flow separation from the cylinder. Up to this diametrical ratio, the wake can be clearly distinguished between the Darrieus blades and the cylinder wake. As the cylinder diameter increases further to the ratio of DR/DT = 2, the whole rotor is in the wake, which is evident from the pressure contour as shown in Figure 11e,f. An interesting finding is that the flow starts to deflect before it reaches the cylinder, disturbing the flow upstream on the Darrieus rotor. Due to the low speed and high energy turbulent flow, the Darrieus blades also leave a large wake behind. As evident from the corresponding *Cp* graph, the power loss is significantly low as power generation happens only at limited azimuthal angles and the energy has to be expended for the majority of the downstream travel path. The same flow pattern repeats for other azimuthal positions. The von Karman vortices are unstable and break down due to Strouhal instability.

#### **8. Conclusions**

2D steady-state simulations are performed on the proposed AHDT in an effort to determine the optimum Savonius diameter that can be integrated with the Darrieus rotor to maximize its performance for the complete operating range. Turbulence is modelled with the *k-*ω SST equation. As the flow pattern over the cylinder will be sub critical or critical based on the Re, the study systematically investigates their performance on Darrieus rotor with a fixed diameter. The power loss of the Darrieus rotor is more than half for the cylinder diameter ratio (DR/DT) of 2 and 1.5, as power has to be expended for the blades when it passes through downstream. A smaller (DR/DT) leads to a smaller Savonius bucket diameter which reduces the turbine performance in the low wind speeds. Hence, it can be concluded that DR/DT should lie around 3 to maximize the Darrieus turbine performance for the whole of the wind speed spectrum. The optimum diameter can be concluded after evaluating the performance of the high solidity three-bladed turbine and the starting capability when the Savonius rotor is in open condition. The starting performance of AHDT with open Savonius will be investigated in part 2, extending the current study. The investigation of the performance of AHDT with various airfoil profiles, solidity, and aspect ratios can be intriguing for future research.

**Author Contributions:** Funding acquisition, S.R. and H.W.; Project administration, H.W.; Supervision, T.-C.L.; Writing—original draft, P.M.K. and M.R.S.; Writing—review & editing, K.S.

**Funding:** This research was funded by 2016 ASTAR AME IRG Grant.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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