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While confinement is understood to increase the power and thrust coefficients of cross-flow turbines, how the optimal rotor geometry changes with the blockage ratio -- defined as the ratio between the array projected area and the channel cross-sectional area -- has not been systematically explored. Here, the interplay between rotor geometry and the blockage ratio on turbine performance is investigated experimentally with an array of two identical cross-flow turbines at blockage ratios from 35% to 55%. Three geometric parameters are varied -- the number of blades, the chord-to-radius ratio, and the preset pitch angle -- resulting in 180 unique combinations of rotor geometry and blockage ratio. While the optimal chord-to-radius ratio and preset pitch angle do not depend on the blockage ratio, the optimal blade count increases with the blockage ratio -- an inversion of the relationship between efficiency and blade count typically observed at lower blockage. To explore the combined effects of rotor geometry, rotation rate, and the blockage ratio on array performance, we utilize two bluff-body models: dynamic solidity (which relates thrust to the rotor geometry and kinematics) and Maskell-inspired linear momentum theory (which describes the array-channel interaction as a function of the blockage ratio and thrust). By combining these models, we demonstrate that the array time-average thrust coefficient increases with dynamic solidity in a manner that is self-similar across blockage ratios. Overall, these results highlight key design principles for cross-flow turbines in confined flow and provide insights into the similarities between the dynamics of cross-flow turbines and bluff bodies at high blockage., Comment: SUBMITTED to the Journal of Renewable and Sustainable Energy. To access the supporting dataset prior to publication, please contact Aidan Hunt

The performance and near-wake characteristics of a turbine in a confined flow depend on the blockage ratio, defined as the ratio of the turbine projected area to the channel cross-sectional area. While blockage is understood to increase the power coefficient for turbine "fences" spanning a channel, most investigations at the upper range of practically-achievable blockage ratios have been theoretical or numerical in nature. Furthermore, while linear momentum actuator disk theory is frequently used to model turbines in confined flows, as confinement increases, the ability of this idealized model to describe performance and flow fields has not been established. In this work, the performance and near-wake flow field of a pair of cross-flow turbines are experimentally evaluated at blockage ratios from 30% to 55%. The fluid velocity measured in the bypass region is found to be well-predicted by the open-channel linear momentum model developed by Houlsby et al. (2008), while the wake velocity is not. Additionally, self-similar power and thrust coefficients are identified across this range of blockage ratios when array performance is scaled by the modeled bypass velocity following Whelan et al.'s (2009) adaptation of the bluff-body theory of Maskell (1963). This result demonstrates that, despite multiple non-idealities, relatively simple models can quantitatively describe highly confined turbines. From this, an analytical method for predicting array performance as a function of blockage is presented. Overall, this work illustrates turbine performance at relatively high confinement and demonstrates the suitability of analytical models to predict and interpret their hydrodynamics., Comment: SUBMITTED to Journal of Fluid Mechanics. Data supporting this manuscript will soon be available at https://doi.org/10.5061/dryad.dfn2z35b5

Cross-flow turbine blades encounter a relatively undisturbed inflow for the first half of each rotational cycle ("upstream sweep") and then pass through their own wake for the latter half ("downstream sweep"). While most research on cross-flow turbine optimization focuses on the power-generating upstream sweep, we use singled-bladed turbine experiments to show that the downstream sweep strongly affects time-averaged performance. We find that power generation from the upstream sweep continues to increase beyond the optimal tip-speed ratio. In contrast, the power consumption from the downstream sweep begins to increase approximately linearly beyond the optimal tip-speed ratio due in part to an increasingly unfavorable orientation of lift and drag relative to the rotation direction as well as high tangential blade velocities. Downstream power degradation increases faster than upstream power generation, indicating the downstream sweep strongly influences the optimal tip-speed ratio. In addition, particle image velocimetry data is obtained inside the turbine swept area at three tip-speed ratios. This illuminates the mechanisms underpinning the observed performance degradation in the downstream sweep and motivates an analytical model for a limited case with high induction. Performance results are shown to be consistent across 55 unique combinations of chord-to-radius ratio, preset pitch angle, and Reynolds number, underscoring the general relevance of the downstream sweep.

Cross-flow turbines harness kinetic energy in wind or moving water. Due to their unsteady fluid dynamics, it can be difficult to predict the interplay between aspects of rotor geometry and turbine performance. This study considers the effects of three geometric parameters: the number of blades, the preset pitch angle, and the chord-to-radius ratio. The relevant fluid dynamics of cross-flow turbines are reviewed, as are prior experimental studies that have investigated these parameters in a more limited manner. Here, 223 unique experiments are conducted across an order of magnitude of diameter-based Reynolds numbers ($\approx 8\!\times\!10^4 - 8\!\times\!10^5$) in which the performance implications of these three geometric parameters are evaluated. In agreement with prior work, maximum performance is generally observed to increase with Reynolds number and decrease with blade count. The broader experimental space clarifies parametric interdependencies; for example, the optimal preset pitch angle is increasingly negative as the chord-to-radius ratio increases. As these experiments vary both the chord-to-radius ratio and blade count, the performance of different rotor geometries with the same solidity (the ratio of total blade chord to rotor circumference) can also be evaluated. Results demonstrate that while solidity can be a poor predictor of maximum performance, across all scales and tested geometries it is an excellent predictor of the tip-speed ratio corresponding to maximum performance. Overall, these results present a uniquely holistic view of relevant geometric considerations for cross-flow turbine rotor design and provide a rich dataset for validation of numerical simulations and reduced-order models., Comment: This article appeared in Hunt et al., Renewable and Sustainable Energy Reviews 206, 114848 (2024), and may be found at https://doi.org/10.1016/j.rser.2024.114848. Data supporting this manuscript may be found in the Dryad digital repository at https://doi.org/10.5061/dryad.mpg4f4r8p

In confined flows, such as river or tidal channels, arrays of turbines can convert both the kinetic and potential energy of the flow into renewable power. The power conversion and loading characteristics of an array in a confined flow is a function of the blockage ratio, defined as the ratio of the array's projected area to the channel cross-sectional area. In this work, we explore experimental methods for studying the effects of the blockage ratio on turbine performance while holding other variables constant. Two distinct methods are considered: one in which the array area is held constant and the channel area is varied, and another in which the array area is varied and the channel area is held constant. Using both approaches, the performance of a laboratory cross-flow turbine array in a water tunnel is evaluated at blockage ratios ranging from 30% to 60%. As the blockage ratio is increased, the coefficient of performance increases, eventually exceeding the Betz limit and unity. While similar trends are observed with both experimental approaches, at high blockage and high tip-speed ratios, the values of the performance and force coefficients are found to depend on the experimental approach. The advantages and disadvantages of each approach are discussed. Ultimately, we recommend investigating blockage effects using a fixed array area and variable channel area, as this approach does not convolve blockage effects with interactions between the turbine blades and support structures., Comment: This is a preprint that was accepted for the Proceedings of the 15th European Wave and Tidal Energy Conference, held in Bilbao, Spain in September 2023. The version that appeared in the proceedings can be found at https://doi.org/10.36688/ewtec-2023-203

Cross-flow turbine performance and flow fields exhibit cycle-to-cycle variations, though this is often implicitly neglected through time- and phase-averaging. This variability could potentially arise from a variety of mechanisms -- inflow fluctuations, the stochastic nature of dynamic stall, and cycle-to-cycle hysteresis -- each of which have different implications for our understanding of cross-flow turbine dynamics. In this work, the extent and sources of cycle-to-cycle variability for both the flow fields and performance are explored experimentally under two, contrasting operational conditions. Flow fields, obtained through two-dimensional planar particle image velocimetry inside the turbine swept area, are examined in concert with simultaneously measured performance. Correlations between flow-field and performance variability are established by an unsupervised hierarchical flow-field clustering pipeline. This features a principal component analysis (PCA) pre-processor that allows for clustering based on all the dynamics present in the high-dimensional flow-field data in an interpretable, low-dimensional subspace that is weighted by contribution to overall velocity variance. We find that the flow-field clusters and their associated performance are correlated primarily with inflow fluctuations, despite relatively low turbulence intensity, that drive variations in the timing of the dynamic stall process. Further, we find no evidence of substantial cycle-to-cycle hysteresis. Clustering reveals persistent correlations between performance and flow-field variability during the upstream portion of the turbine rotation. The approach employed here provides a more comprehensive picture of cross-flow turbine flow fields and performance than aggregate, statistical representations., Comment: PUBLISHED at Experiments in Fluids https://doi.org/10.1007/s00348-023-03725-5

Cross-flow turbines convert kinetic power in wind or water currents to mechanical power. Unlike axial-flow turbines, the influence of geometric parameters on turbine performance is not well-understood, in part because there are neither generalized analytical formulations nor inexpensive, accurate numerical models that describe their fluid dynamics. Here, we experimentally investigate the effect of aspect ratio - the ratio of the blade span to rotor diameter - on the performance of a straight-bladed cross-flow turbine in a water channel. To isolate the effect of aspect ratio, all other non-dimensional parameters are held constant, including the relative confinement, Froude number, and Reynolds number. The coefficient of performance is found to be invariant for the range of aspect ratios tested (0.95 - 1.63), which we ascribe to minimal blade-support interactions for this turbine design. Finally, a subset of experiments is repeated without controlling for the Froude number and the coefficient of performance is found to increase, a consequence of Froude number variation that could mistakenly be ascribed to aspect ratio. This highlights the importance of rigorous experimental design when exploring the effect of geometric parameters on cross-flow turbine performance., Comment: This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Hunt et al, J. Renewable Sustainable Energy 12, 054501 (2020) and may be found at https://doi.org/10.1063/5.0016753. Supplementary material can be found in the UW ResearchWorks archive at http://hdl.handle.net/1773/45618

Straight-bladed cross-flow turbines are computationally explored for harvesting energy in wind and water currents. One challenge for cross-flow turbines is the transient occurrence of high apparent angles of attack on the blades that reduces efficiency due to flow separation. This paper explores kinematic manipulation of the apparent angle of attack through intracycle control of the angular velocity. Using an unsteady Reynolds-averaged Navier-Stokes (URANS) model at moderate Reynolds numbers, the kinematics and associated flow physics are explored for confined and unconfined configurations. The computations demonstrate an increase in turbine efficiency up to 54%, very closely matching the benefits shown by previous intracycle control experiments. Simulations display the time-evolution of angle of attack and flow velocity relative to the blade, which are modified with sinusoidal angular velocity such that the peak torque generation aligns with the peak angular velocity. With optimal kinematics in a confined flow there is minimal flow separation during peak power generation, however there is a large trailing edge vortex (TEV) shed as the torque decreases. The unconfined configuration has more prominent flow separation and is more susceptible to Reynolds number, resulting in a 41% increase in power generation under the same kinematic conditions as the confined flow., Comment: 21 pages, 13 figures, submitted to: AIAA Journal

Cross-flow turbines, also known as vertical-axis turbines, convert the kinetic energy in moving fluid to mechanical energy using blades that rotate about an axis perpendicular to the incoming flow. In this work, the performance of a two-turbine array in a recirculating water channel was experimentally optimized across sixty-four unique array configurations. For each configuration, turbine performance was optimized using tip-speed ratio control, where the rotation rate for each turbine is optimized individually, and using coordinated control, where the turbines are optimized to operate at synchronous rotation rates, but with a phase difference. For each configuration and control strategy, the consequences of co- and counter-rotation were also evaluated. We hypothesize how array configurations and control cases influence interactions between turbines and impact array performance.

The near-wake of a vertical-axis cross-flow turbine (CFT) was modeled numerically via blade-resolved $k$-$\omega$ SST and Spalart-Allmaras RANS models in two and three dimensions. Results for each case are compared with experimental measurements of the turbine shaft power, overall drag, mean velocity, turbulence kinetic energy, and momentum transport terms in the near-wake at one diameter downstream. It was shown that 2-D simulations overpredict turbine loading and do not resolve mean vertical momentum transport, which plays an important role in the near-wake's momentum balance. The 3-D simulations fared better at predicting performance, with the Spalart-Allmaras model predictions being closest to the experiments. The SST model more accurately predicted the turbulence kinetic energy while the Spalart-Allmaras model more closely matched the momentum transport terms in the near-wake. These results show the potential of blade-resolved RANS as a design tool and a way to "extrapolate" experimental flow field measurements., Comment: 22 pages, 12 figures