**1. Introduction**

The interest for micro wind power generation is growing, since micro wind turbines appear to be very suitable for powering low-power devices such as wireless sensors, actuators, controllers, and small lightning systems. Usually, these devices are powered by means of chemical batteries, which however must be periodically replaced, therefore representing a challenge for a reliable power supply. For this reason, small-size energy harvesters are increasingly used in order to realize reliable self-powered systems. Small-scale wind turbines represent an attractive solution for the electricity generation in such small-size energy harvesters.

Previous studies about miniature wind turbines mainly focused on Horizontal Axis Wind Turbine (HAWT) due to the fact they had acceptable efficiency despite the small scale. Xu et al. [1] developed an experimental test and a numerical predictive model on a miniature HAWT with a diameter of

15 cm. They obtained a maximum efficiency of approximately 27%. Kishore et al. [2,3] designed and characterized a small-scale portable wind turbine of approximately 40 cm that showed very low cut-in velocity and a maximum efficiency of 30% with a rated power of 1.4 W. Zakaria et al. [4] performed an experimental investigation of a centimeter-scale wind turbine, thus showing the strong effect of the very low Reynolds number on the rotor performance as they obtained an efficiency of only 3–4%. An interesting application of miniature HAWT was proposed again by Xu et al. [5]. They developed a physical-based model for the prediction of the optimal load resistance and the experimental characterization of the micro turbine. The efficiency was found to be lower than 10%. Ionescu et al. [6] studied the possibility to optimize small VAWTs through the use of different techniques such as specific low Re airfoils, blade shapes, and passive and active flow control. A special design optimization of a cost-effective micro turbine was implemented by Leung et al. [7]. The multi-bladed rotor, with a radius of approximately 12 cm, reached a maximum power coefficient (Cp) of 12%. Howey et al. [8] designed a miniature shrouded multi-bladed wind turbine by means of the BEM theory. The experimental study result demonstrated a maximum efficiency just over 10%. Park et al. [9] made a feasibility study about the use of micro wind turbines to power wireless sensors on a bridge. They were able to demonstrate how a micro turbine, with a diameter of 14 cm, can generate sufficient energy for this specific application.

Micro wind turbines are often used for wind tunnel experiments as well. As the wind tunnel dimensions are usually limited, only small size rotors can be tested. In this regard, Bastankhah et al. [10] designed and analyzed a miniature wind turbine with a rotor diameter of 15 cm. They demonstrated that an accurate fluid dynamic design for specific low Reynolds number was of utmost importance for reaching high efficiency. In this case they obtained a maximum Cp of approximately 40%. The authors of the present paper presented a numerical and experimental study regarding a three bladed micro HAWT for wind tunnel applications [11]. An efficiency of about 30% was found.

The studies presented above demonstrate the scientific interest toward micro wind rotors and highlight the fact that small rotors need a very accurate fluid dynamic design in order to obtain high efficiency. This is mainly due to two factors. Very low Reynolds numbers drastically reduce the airfoil performances and the small dimensions emphasize the unsteadiness and the instabilities, as will be demonstrated hereinafter. It is no coincidence that VAWTs have not been taken into consideration in the aforementioned studies. Indeed, in these rotors, the unsteady phenomena affect the performance much more than in HAWTs and the scale reduction drastically augments negative effects such as dynamic stall, blade-wake interaction as well as low Reynolds number influence. However, the advantages of VAWTs, such as constructive simplicity, omnidirectionality with respect to the flow, and positioning of the generation unit on the ground, make these turbines deserve further investigation in the aforementioned small-scale applications. For instance, Mutlu et al. [12] evaluated the performance of in-pipe VAWT for turbo solenoid valve system, finding interesting results.

In light of the above, in the present work the authors developed a 2D CFD model of a H-Darrieus VAWT with a diameter of 20 cm. The CFD model was validated by means of wind tunnel experiments carried out in the subsonic wind tunnel at the University of Catania. This micro rotor operated at very low tip speed ratios and very low Re, which caused strong and sudden boundary layer instability (separation and unsteady vortex shedding) leading to early dynamic stall development and large lift losses on the blade. This involved that most of the CFD procedures, proposed in the literature for largest rotors, may not be suitable in this case.

The experimental H-Darrieus rotor had 4 NACA 0012 blades and it was designed and constructed with a 3D printer. Further details about the experimental set up are presented in the next section. In order to develop an accurate and reliable CFD model of such micro rotor, a thorough sensitivity study was carried out. The study analyzed the spatial and temporal discretization sensitivity and the influences of three different turbulence models. The turbulence models evaluated were the widely used RANS fully turbulent SST k-ω model, the transition SST model by Menter, and the hybrid RANS/LES Delayed Detached Eddy Simulation model (DDES) coupled to the transition SST model

by Menter for the RANS region. Furthermore, the results were compared to those obtained through the use of a double multiple stream-tube 1D model (DMSTM) using the commercial software Qblade with the suitable aerodynamic polar for an average rotor Reynolds number of approximately 40,000. The global comparison with the experimental data demonstrated that the DDES turbulence model with a very fine spatial and temporal discretization was the one able to provide accurate predictions of the rotor performance in terms of average power coefficient (Cp). The other turbulence models highly underestimated the average Cp despite the very fine spatial and temporal discretization. On the other hand, Qblade DMSTM results demonstrated a surprising proximity to the Cp experimental data, at least in a portion of the curve.

The results obtained through the post-processing of the CFD 2D model allowed the authors to gain an important insight into to the fluid dynamics of micro Darrieus rotors and to clarify the physical reasons for the very poor performance of these turbines when the geometrical scale is reduced. The boundary layer instability, accurately detected through the use of DDES, seemed to be the most important reason for the poor performance of such small rotors. Furthermore, this instability was strongly related to the reduced geometrical scale, which led to very low operating Reynolds numbers. At these very low Re, the boundary layer is mostly laminar and, as is widely known, a laminar boundary layer is more sensitive to adverse pressure gradients that trigger laminar bubbles, separation, and sudden transition.
