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Vortical impulse theory is used to investigate the relationship between turbine thrust and the near-wake velocity and vorticity fields. Three different hypotheses regarding the near-wake structure allow the derivation of novel expressions for the thrust on a steadily rotating wind turbine, and these are tested using stereoscopic particle-image velocimetry (PIV) data acquired just behind a rotor in a water channel. When one assumes that vortex lines and streamlines are aligned in a rotor-fixed frame of reference, one obtains a PIV-based thrust estimate that fails even to capture the trend of the directly measured thrust, and this failure is attributed to an implicit assumption that most of the generated thrust does useful work. When one neglects the axial gradients of radial velocity, the PIV-based thrust estimate captures the measured thrust trend, but underpredicts its magnitude by approximately $33\,\%$ . The third and most promising physical proposition treats the trailing vortices as purely ‘rolling’ structures that exhibit zero-strain rate in their cores, with the corresponding thrust estimates in close agreement with direct thrust measurements. This best-performing expression appears as a correction to the classical thrust expression from momentum theory, possessing additional squared-velocity terms that can account for the high-thrust regime of turbine operation that is typically addressed empirically. 

The transient pressure field around a moderately thick airfoil is studied as it undergoes ramp-type pitching motions at high Reynolds numbers and low Mach numbers. A unique set of laboratory experiments were performed in a high-pressure wind tunnel to investigate dynamic stall at chord Reynolds numbers in the range of $0.5\times 10^6\leq Re _c\leq 5.5\times 10^6$ in the absence of compressibility effects. In addition to variations of mean angle and amplitude, pitching manoeuvres at reduced frequencies in the range of $0.01\leq k\leq 0.40$ were studied by means of surface-pressure measurements. Independently of the parameter variations, all test cases exhibit a nearly identical stall behaviour characterized by a gradual trailing-edge stall, in which the dynamic stall vortex forms approximately at mid-chord. The location of the pitching window with respect to the Reynolds-number-dependent static stall angle is found to define the temporal development of the stall process. The time until stall onset is characterized by a power law, where a small excess of the static stall angle results in a drastically prolonged stall delay. The reduced frequency exhibits a decrease in impact on the stall development in the case of angle-limited pitching manoeuvres. Beyond a critical reduced frequency, both load magnitudes and vortex evolution become reduced frequency independent and instead depend on the geometry of the motion and the convective time scale, respectively. Overall, the characteristics of vortex evolution induced by dynamic stall show remarkable similarities to the framework of optimal vortex formation reported in Gharib et al. ( J. Fluid Mech. , vol. 360, 1998, pp. 121–140). The data from this study are publicly available at https://doi.org/10.34770/b3vq-sw14 . 

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.