**4. Summary and Conclusions**

Although one may think micro wind turbines are of little scientific and industrial interest, the literature analysis in the present paper demonstrates that micro rotors represent an attractive solution for small size energy harvesters in many industrial applications. However, at such small scales, the advantages of the vertical axis solution are reduced by the poor rotor efficiency due to the onset of highly unstable boundary layer conditions as the rotor size decreases. The possibility to thoroughly analyze the fluid dynamic causes of the poor efficiency certainly represents a key step for the improvement of these micro rotors. Furthermore, in general, the simulation of the unstable conditions of VAWTs, which arise at low tip speed ratio, is still a very complex problem.

For these reasons, in this work, the authors present the implementation of a 2D CFD model for the simulation of a micro VAWT designed, constructed and tested in the subsonic wind tunnel of the University of Catania. For this purpose, three different turbulence models were evaluated: the SST Transition and SST k-ω RANS models and the hybrid RANS/LES Delayed DES. The thorough temporal and spatial discretization sensitivity study demonstrated that a very fine spatial and temporal discretization was necessary in order to capture the high vorticity gradients related to the unstable conditions, and thus to obtain independent results. While the RANS SST Transition model and SST k-ω model both led to unphysical torque predictions, the Delayed Detached Eddie Simulation, coupled to a transition formulation for the RANS region, was able to accurately reproduce the measured power coefficient.

The thorough post-processing comparison between the RANS and the DDES model results allowed for the identification of the reasons of the poor accuracy of the RANS models. In the highly unstable conditions related to micro rotors, both the RANS models predicted a massive turbulence production which was smoothed in large structures according to the inherent characteristics of the Reynolds averaging. The DDES model instead predicted a higher vorticity but in smaller and more defined swirling structures, leading to much lower turbulence production, and hence lower energy dissipation. In light of the excellent agreement between the DDES and the experimental results, it could be concluded that, in general, for a reliable simulation of the unstable condition of VAWTs the advanced DDES model appear to be the most suitable. However, a fine spatial and temporal discretization is needed to resolve the high vorticity gradients near the blades.

However, the most important result of this work was that the DDES, with transitional treatment for the RANS region, allowed for a thorough insight into the causes of the poor performance of micro H-Darrieus rotors. The small radius of these rotors together with the low cord Reynolds numbers of the blades involved the onset of early separation and boundary layer instabilities. These phenomena constantly affected the micro rotor operating conditions also because of a wider development of the dynamic stall for large part of the azimuthal blade position. All this involved a significant limitation of the torque generated since the rotor operated under high cyclic losses. The negative impact of the reduction of the geometrical scale was evidently much more significant in Darrieus VAWT than in HAWT.

The results of the present work provide some guidelines for the improvement of the efficiency of micro VAWTs as well. First of all, the use of specific low Reynolds number airfoils could reduce the onset of the instabilities, therefore allowing for higher torque generation and, therefore, higher rotational speeds. Different blade pitch angles may be more efficient in these small rotors than in the larger rotors. Simple variable blade pitch systems could be easily and cheaply applied to these rotors thanks to 3D printers. All this will be investigated in detail in future works.

**Author Contributions:** Conceptualization, S.M., S.B., R.L., M.M.; methodology, S.M. and S.B.; software, S.M.; validation, S.M. and S.B.; formal analysis, S.M., S.B., R.L., M.M.; investigation, S.M., S.B., M.M.; resources, R.L.; data curation, S.M. and S.B.; writing—original draft preparation, S.M.; writing—review and editing, S.M.; visualization, S.M.; supervision, R.L. and M.M.; project administration, R.L. and M.M. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Acknowledgments:** This research is supported by "Programma ricerca di Ateneo UNICT 2020-22 linea 2" of the University of Catania.

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