Solidity effects on the performance of vertical-axis wind turbines

Abstract

The variety of configurations for vertical-axis wind turbines (VAWTs) make the development of universal scaling relationships for even basic performance parameters difficult. Rotor geometry changes can be characterized using the concept of solidity, defined as the ratio of solid rotor area to the swept area. However, few studies have explored the effect of this parameter at full-scale conditions due to the challenge of matching both the non-dimensional rotational rate (or tip speed ratio) and scale (or Reynolds number) in conventional wind tunnels. In this study, experiments were conducted on a VAWT model using a specialized compressed-air wind tunnel where the density can be increased to over 200 times atmospheric air. The number of blades on the model was altered to explore how solidity affects performance while keeping other geometric parameters, such as the ratio of blade chord to rotor radius, the same. These data were collected at conditions relevant to the field-scale VAWT but in the controlled environment of the lab. For the three highest solidity rotors (using the most blades), performance was found to depend similarly on the Reynolds number, despite changes in rotational effects. This result has direct implications for the modelling and design of high-solidity field-scale VAWTs.

An analytical blockage correction model for high-solidity turbines

“…High fidelity laboratory and numerical experiments with porous plates and wind turbines indicated that the proposed correction performs equally as well as conventional ones in low-solidity regimes, but becomes more accurate as the solidity/induction factor increases. The applicability of the current model might be somewhat limited in conventional horizontal axis wind turbines, as they tend to operate in low-solidity regimes, but might become especially relevant when considering blockage effects in high-solidity configurations such as many-bladed vertical axis wind turbines, tidal turbines, and more generally bluff bodies of arbitrary porosity, including the fully solid limit in which splitter plates are used to suppress vortex shedding, and where no blockage correction model is currently available (see, for instance, Apelt & West 1975;Chapman et al 2013;Miller et al 2021). effect of the vena contracta is negligible.…”

“…The above prediction is identical to the one obtained using the Rankine-Froude theory (Hansen 2015), which constitutes the basis of most blockage correction models for porous plates and wind turbines. Figure 1 shows the well-known failure of the Rankine-Froude-Taylor theory when porosity becomes small, which limits the applicability of blockage correction models to high-porosity regimes (Apelt & West 1975;Ross & Polagye 2020a;Miller et al 2021). Appendix A presents a relation that connects u * with β = A p /A (where A p and A are the porous and gross areas of the plate, respectively), proposed by Taylor & Davies (1944).…”

“…Figure 1 shows the well-known failure of the Rankine–Froude–Taylor theory when porosity becomes small, which limits the applicability of blockage correction models to high-porosity regimes (Apelt & West 1975; Ross & Polagye 2020 a ; Miller et al. 2021). Appendix A presents a relation that connects with (where and are the porous and gross areas of the plate, respectively), proposed by Taylor & Davies (1944).…”

“…While these models are reliable in conventional wind turbine operation regimes, their use is deemed questionable when the effective solidity of the turbine increases beyond a certain limit (Whelan et al 2009;Kinsey & Dumas 2017;Ross & Polagye 2020a) due to the well-known failure of the Rankine-Froude theory in high-solidity regimes (Hansen 2015;Ayati et al 2019;Bempedelis & Steiros 2022). Blockage correction is customarily not applied in such cases (Apelt & West 1975;Ayati et al 2019;Steiros et al 2020;Miller, Duvvuri & Hultmark 2021), an exception being the fully solid body case with vortex shedding, where the semi-empirical model of Maskell (1963) is used. Moreover, low-porosity corrections to the Rankine-Froude theory, like the well-known Glauert's correction (Hansen 2015), rely on data fitting, and do not yield the necessary information to develop a blockage correction model.…”

“…2019; Steiros et al. 2020; Miller, Duvvuri & Hultmark 2021), an exception being the fully solid body case with vortex shedding, where the semi-empirical model of Maskell (1963) is used. Moreover, low-porosity corrections to the Rankine–Froude theory, like the well-known Glauert's correction (Hansen 2015), rely on data fitting, and do not yield the necessary information to develop a blockage correction model.…”