# Optimizing Bladeless Wind Turbines: Morphological Analysis and Lock-In Range Variations
## 1 Introduction  
Currently, the energy sector is undergoing significant changes, shifting from centralized fossil fuel-based systems to decentralized models that rely on renewable energies [1]. In this context, the lower intensity of renewable energy resources and the possible network saturation underscore the importance of situating energy generation closer to consumption points [2]. Consequently, governmental initiatives have emerged to promote self-consumption facilities, that help in this energy transition [3]. In recent years, there has been notable progress in the development of innovative wind energy harvesting designs [4]. These innovations involve triboelectric nanogenerator (TENG) technology [5], as well as wind-induced vibrations. Notably, vortex-induced vibration (VIV) energy harvesters boast versatility [6], offering promise in establishing wind energy within distributed energy production framework [7], as seen in bladeless models developed by Vortex Bladeless [8; 9; 10]. The integration of BWTs through the interaction with multiple energy system technologies introduces new challenges as well as opportunities within future energy systems [11]. These BWT energy harvesters address several drawbacks associated with traditional turbines [12; 13; 14]. They mitigate negative impacts on bird wildlife [15] by minimizing collision risks [16] and environmental impact [17], minimize electromagnetic interference with communication frequencies, and have negligible visual and acoustic impacts. Their installation in residential settings, owing to the absence of gears and low maintenance needs, opens possibilities for hybridizing this technology with solar photovoltaics for self-consumption, optimizing energy availability even during low-solar-radiation periods or at night [18]. Maintaining stationary alignment irrespective of wind direction is crucial for these turbines, similar to the principles outlined in [19] utilizing cylindrical shapes. Furthermore, modifying parameters like taper ratio [20] and surface roughness [21] allows for optimizing vibration characteristics at different wind speeds, thereby maximizing energy generation, as evidenced by studies such as [22; 23]. Despite their advantages, these energy harvesters have limitations, notably a narrow operational wind speed range called \"Lock-In range\" [24]. Efforts to address this include analysing monostable softening behaviour in the broadband VIV energy harvesting. The novelty of this work lies in the exploration of VIV dynamics in bluff bodies supported by a cantilever rod, exhibiting circular oscillation rather than linear. Thus, both from an aerodynamic and functional point of view, these devices are akin to single-blade horizontal-axis wind turbines, differing significantly in their rotation angles, as shown in Figure 1.  
The choice of geometries studied here is consistent with their rotational nature, wherein the diameter of the mast section correlates with the distance to the rotation axis. Specifically, the investigation focuses on scaled models akin to Vortex Bladeless prototypes [26], spanning from the Vortex Nano models (0.85 m height, 0.07 m diameter, and 1.70 Kg weight) to the Vortex Atlantis models (9 m height, 0.72 m diameter, and 1300 Kg weight), as shown in Figure 2.  
To achieve this, a series of controlled experiments were conducted in a wind tunnel, covering a range of Reynolds numbers from 2 K to 6 K. This study considered different surface conditions (smooth and rough) as well as various cylindrical mast geometries (convergent, straight, and divergent). This comprehensive analysis aims at elucidating the impact of surface characteristics and geometric parameters on the overall efficiency and energy generation potential of BWT energy harvesters. The paper is organized as follows.