Experimental Investigations into the Fluid Dynamics and Forcing Underlying Cross-flow Turbine Operation

Abstract

Within the wind and marine energy sectors, axial-flow (i.e., horizontal axis) turbines are a well-established and well-understood approach to converting the kinetic energy in a moving fluid to electricity. Recent cross-flow (i.e., vertical axis) turbine research has yielded substantial performance gains through the exploitation of unsteady fluid dynamics for individual turbines and mutually beneficial interactions between closely-spaced turbines in arrays. However, an understanding of the dynamics underlying cross-flow turbine operation remains incomplete due to the presence of fluid phenomena that are difficult to model, including dynamic stall, flow curvature effects, and the influence of the turbine on the surrounding flow, called induction. This thesis considers the intricate relationship between the flow physics and performance of cross-flow turbines and augments understanding of their fundamental operation. First, 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 (PIV) inside the turbine swept area, are correlated simultaneously with measured performance using an unsupervised hierarchical clustering pipeline. A principal component analysis (PCA) pre-processor is employed 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. These inflow fluctuations drive variations in the timing of the dynamic stall process, while hysteresis between cycles is found to be negligible. Clustering reveals persistent ties 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. Second, 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 single-bladed turbine experiments to show that the downstream sweep strongly affects time-averaged performance. Specifically, 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. Downstream power degradation increases faster than upstream power generation, indicating the downstream sweep strongly influences the optimal tip-speed ratio. In addition, PIV 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 limiting case with high induction or an infinite tip-speed ratio. 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 significance of the downstream sweep to cross-flow turbine performance. Third, while investigating trends in terms of turbine-level forces and torques is important, it does not tell the full story of cross-flow turbine operation. Identification of blade-level forces and torques allows for specific investigations into how effectively fluid forcing on the blade drives rotation and can aid in blade structural design. Further, the determination of blade-level forces allows more robust comparison to computational fluid dynamic simulations. Here, we present a methodology for extracting blade-level forces and moments from experimental measurements at the axis of rotation for a single-bladed turbine. The method is based on knowledge of the flow physics and its validity is assessed via comparison with equivalent blade-only large-eddy simulations. By applying this method, we identify the fluid force components contributing to cross-flow turbine power production and forcing, illuminating the significance of the commonly ignored pitching moment. Failing to consider this term leads to an over-prediction of cross-flow turbine performance. Overall, these three works contribute new methods, fundamental knowledge, and data to the field of cross-flow turbine research and together they constitute a set of well-characterized benchmark cases useful for informing future works that consider different turbine geometries, kinematics, or non-ideal inflows. Further these works provide useful insight applicable to improving reduced-order models and turbine structural design.