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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. 

Abstract. We introduce an improved formulation of the double-multiple streamtube (DMST) model for the prediction of the flow quantities of vertical axis wind turbines (VAWT). The improvement of the new formulation lies in that it renders the DMST valid for any induction factor, i.e., for any combination of rotor solidity and tip speed ratio. This is done by replacing the Rankine–Froude momentum theory of the DMST, which is invalid for moderate and high induction factors, with a new momentum theory recently proposed, which provides sensible results for any induction factor. The predictions of the two DMST formulations are compared with VAWT power measurements obtained at Princeton's High Reynolds number Test Facility, over a range of tip speed ratios, rotor solidities, and Reynolds numbers, including those experienced by full-scale turbines. The results show that the new DMST formulation demonstrates a better overall performance, compared to the conventional one, when the rotor loading is moderate or high. 

Laboratory experiments were performed on a geometrically scaled vertical-axis wind turbine model over an unprecedented range of Reynolds numbers, including and exceeding those of the full-scale turbine. The study was performed in the high-pressure environment of the Princeton High Reynolds number Test Facility (HRTF). Utilizing highly compressed air as the working fluid enabled extremely high Reynolds numbers while still maintaining dynamic similarity by matching the tip speed ratio (defined as the ratio of tip velocity to free stream, $\unicode[STIX]{x1D706}=\unicode[STIX]{x1D714}R/U$ ) and Mach number (defined at the turbine tip, $Ma=\unicode[STIX]{x1D714}R/a$ ). Preliminary comparisons are made with measurements from the full-scale field turbine. Peak power for both the field data and experiments resides around $\unicode[STIX]{x1D706}=1$ . In addition, a systematic investigation of trends with Reynolds number was performed in the laboratory, which revealed details about the asymptotic behaviour. It was shown that the parameter that characterizes invariance in the power coefficient was the Reynolds number based on blade chord conditions ( $Re_{c}$ ). The power coefficient reaches its asymptotic value when $Re_{c}>1.5\times 10^{6}$ , which is higher than what the field turbine experiences. The asymptotic power curve is found, which is invariant to further increases in Reynolds number.