*3.2. Post-Processing and Analysis of the Results*

A thorough post-processing analysis of the flow-field in terms of velocity, turbulence production, and vorticity was carried out for two specific azimuthal rotor positions evidenced in Figure 7. In blue, the instantaneous position named as "position 0◦" in which the blades are located at θ = 0◦, 90◦, 180◦, and 270◦. In red, the instantaneous position named as "position 45◦" in which the blades are located at θ = 45◦, 135◦, 225◦, and 315◦. In this way the analysis is quite representative of the rotor behavior within a revolution. Only the λmax condition results are presented as the other operating conditions lead to very similar considerations. The images showed hereinafter explain both the reasons for the poor accuracy of the RANS turbulence models and the low efficiency of these rotors.

In Figure 8, the contours of velocity magnitude for the three turbulence models demonstrate the strong differences in the flow-field prediction. The DDES results (Figure 8a) demonstrate the capability to accurately capture structures which are smaller and more defined than those obtained from the RANS simulations. Indeed, the RANS models seem to diffuse the swirling structures more than the DDES model. This result was expectable since the LES modeling inside the DDES was inherently more accurate. Furthermore, the flow separation dynamic of the blades at azimuthal positions θ = 90◦ and 270◦ appears to be different, also between the transition and the SST k-ω models. In this condition, indeed, the transition model predicted larger scale vortices compared to the SST k-ω

model. The above suggests that the RANS models overestimate the dimensions of the flow structures and their diffusion within the grid. Therefore, the negative effects of unsteady phenomena like dynamic stall and blade-vortex interaction, in the down-wind sector, would be probably overestimated as well. For example, the blade at θ = 0◦ shows a recirculation area near the trailing edge in Figure 8b,c, which is larger than that in Figure 8a. This seems to denote that the RANS models in this case of micro rotor, tend to predict an earlier flow separation, which in turn results in higher turbulence production and finally lower torque. Considering the fact that both the RANS models predicted negative torque at λmax, while the DDES showed excellent accuracy, it can be supposed that the RANS models led to unphysical flow-field predictions. A possible explanation may be related to the fact that the small dimensions of the rotor generate flow structures that the RANS averaging is not able to capture despite the very high spatial and temporal discretization. Thus, the more advanced physical solution provided by the DDES model appears to be more suitable in the case of such micro rotors.

**Figure 7.** Azimuthal rotor position reference for the post-processing analysis.

The contours of turbulent intensity for the three turbulence models in Figure 9 further confirm this assumption. The RANS models predict a massive and smoothed turbulence production. The DDES model instead predicts much less turbulence production in smaller and more defined structures. The massive turbulence production of the RANS models results in high rotor energy dissipation, which is not realistic. Moreover, the large turbulence structures in Figure 9b,c produce much more influences on the downwind blades than those in the DDES model. This further confirms that the physics beyond the RANS models does not seem to be suitable for the simulation of the highly unstable conditions related to such small rotors.

The vorticity field presented in Figure 10 shows very different results between the three turbulence models. Again, the DDES (Figure 10a) demonstrate the capability to predict more defined and less smoothed structures but with much higher vorticity within the cores of the shed vortices, compared to the RANS model results. In light of the widely known capability of the LES to accurately predict the eddies behavior, and thanks to the excellent numerical-experimental agreement evidenced in Figure 6, the DDES model appears to be more physically realistic. In cases like that in the present work, in which the operating conditions are massively dominated by unstable shedding of vortices, the RANS modeling clearly leads to wrong physical predictions. This issue is reduced on larger rotors

in which more stable flow-field conditions lead to less shedding of vortices, and therefore to a better physical agreement of the RANS models.

(**a**) (**b**)

**Figure 8.** Contours of velocity magnitude for DDES (**a**), RANS Transition (**b**) and RANS SST k-ω (**c**) at 0◦ azimuthal position at λmax = 0.29.

(**a**) (**b**)

**Figure 9.** Contours of turbulent intensity for DDES (**a**), RANS Transition (**b**) and RANS SST k-ω (**c**) at 0◦ azimuthal position at λmax = 0.29.

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**Figure 10.** Contours of vorticity for DDES (**a**), RANS Transition (**b**) and RANS SST k-ω (**c**) at 0◦ azimuthal position at λmax = 0.29.

Similar considerations can be made for the position 45◦. In Figures 11–13 the contours of velocity magnitude, the contours of turbulence intensity, and the contours of vorticity are shown, respectively. In this case, all the blades are subjected to angles of attack such that the flow is fully separated. The differences between the DDES and the RANS results are even more evident. The velocity field appears smoother in the RANS compared to the DDES. In Figure 12, the massive unrealistic turbulence production, predicted by the RANS models, is even higher than in Figure 9, with respect to the DDES results. The contours of Figure 13 confirm the complexity of the vorticity field predicted by

the DDES simulation, compared to the smoothed and less complex structures obtained thorough the RANS simulations.

(**a**) (**b**)

(**c**)

**Figure 11.** Contours of velocity magnitude for DDES (**a**), RANS Transition (**b**) and RANS SST k-ω (**c**) at 45◦ azimuthal position at λmax = 0.29.

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**Figure 12.** *Cont.*

**Figure 12.** Contours of turbulent intensity for DDES (**a**), RANS Transition (**b**) and RANS SST k-ω (**c**) at 45◦ azimuthal position at λmax = 0.29.

(**c**)

**Figure 13.** Contours of vorticity for DDES (**a**), RANS Transition (**b**) and RANS SST k-ω (**c**) at 45◦ azimuthal position at λmax = 0.29.

The accuracy demonstrated by the DDES results allows for an insight into the poor efficiency that characterizes such micro rotors. Figures 8, 9 and 10a show that the blade at the azimuthal position θ = 0◦ is just affected by an incipient boundary layer instability even though the local AoA is approximately 0◦. A shedding of vortices is already clearly evident in the airfoil wake.

In this regard, the details reported in Figure 14a,b clarify this assumption. The velocity vectors show boundary layer instabilities, which generate a consistent turbulent kinetic energy production. This is probably due to the low Reynolds number and the related strong sensitivity of the laminar boundary layer to the adverse pressure gradients. This earlier instability leads also to earlier flow

separation, which can emphasize the negative effects of the dynamic stall as the blade moves towards higher azimuthal positions. Since the instability limits the attached flow condition phase, the blade azimuthal angle phases in which high lift to drag ratios are achievable are very limited as well. This means that the rotor operates under stall conditions for almost the entire blade rotation. As the blades are subjected to separation for most of the rotation, the dynamic stall, which inherently affects VAWTs, develops more than in large rotors, thus causing higher cyclic losses. The chart in Figure 15 reports the trend of the local blade AoA as a function of the azimuthal blade position, calculated by means of Qblade code at different tip speed ratios. Despite the fact that Qblade results are not as accurate, they provide a fast estimation of the local blade AoA during a complete rotor revolution. The rapid increase of the local AoA is related to the low peripheral speed, which in turn is due to the low torque produced, caused by the aforementioned instability.

(**a**) (**b**)

**Figure 14.** Velocity vectors (**a**) and contours of turbulence kinetic energy (**b**) for a blade at θ = 0◦ and λmax = 0.29.

**Figure 15.** Qblade calculated local AoA as a function of the azimuthal blade position for different tip speed ratios.

Figure 16 further confirms the above considerations. The velocity vectors (a), the contours of turbulent kinetic energy (b) and the pressure coefficient (c) for a blade at azimuthal position θ = 15◦ are shown. In this specific condition, at λmax = 0.29, the local blade AoA is approximately 8◦. Despite the low AoA, the velocity vectors demonstrate an extensive area of instability, in the form of a kind of laminar bubble, near the trailing edge of the suction side of the blade. This instability produces high turbulent kinetic energy (Figure 16b), which increases the energy dissipation. The pressure coefficient in Figure 16c, calculated with respect to the flow velocity at inlet, shows the effects of these bubbles on the pressure distribution over the suction side of the blade. This in turn impacts negatively on the lift generated by the blade. As the blade moves toward higher azimuthal positions, the instability rapidly moves toward the leading edge, thus influencing the entire suction side of the blade with large flow separation and massive production of swirling structures. The subsequent onset of the dynamic stall further worsens the aerodynamic performance of the blade.

(**a**) (**b**)

**Figure 16.** Velocity vectors (**a**), contours of turbulence kinetic energy (**b**) and pressure coefficient (**c**) for a blade at azimuthal position θ = 15◦ and λmax = 0.29.

Thus, summarizing, the most important macroscopic evidence for the poor performance of micro H-Darrieus rotors is the fact that the turbine cannot accelerate sufficiently even at high flow speed. The cause of this is essentially due to the precocity with which boundary layer instability and separation occur in terms of AoAs. The very low Reynolds numbers, due to the small dimensions, seem to be the main responsible factor for this early instability, which manifests itself through massive production of vortices and turbulence. Furthermore, the early separation affects the development of the dynamic stall, since the range of AoAs in which it can be triggered is certainly wider. All these effects strongly limit the lift generation as they represent a source of cyclic losses. Moreover, the small dimensions of

the radius do not allow for the generation of sufficient torque so that the rotor is not able accelerate at tangential speeds such to overcome the instabilities.
