In a confined flow, the performance of a turbine and its near-wake fluid dynamics 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 for predicting and interpreting their hydrodynamics.
The performance and economics of turbines in a tidal array are largely dependent on the power per turbine, and so approaches that can increase this power are crucial for the development of tidal energy. In this paper, we combine a two-scale partial array model and a one-dimensional channel model to investigate the effects of blockage, turbine arrangement, and channel dynamics on tidal turbines. The power per turbine is obtained as the product of two parameters: a power coefficient measuring the power acquired from the instantaneous flow and an environment coefficient showing the response of th…
Turbine wake and farm blockage effects may significantly impact the power produced by large wind farms. In this study, we perform Large-Eddy Simulations (LES) of 50 infinitely large offshore wind farms with different turbine layouts and wind directions. The LES results are combined with the two-scale momentum theory (Nishino & Dunstan 2020, J. Fluid Mech. 894, A2) to investigate the aerodynamic performance of large but finite-sized farms as well. The power of infinitely large farms is found to be a strong function of the array density, whereas the power of large finite-sized farms depends on b…
The efficiency of tidal-stream turbines in a large array depends on the balance between negative effects of turbine-wake interactions and positive effects of bypass-flow acceleration due to local blockage, both of which are functions of the layout of turbines. Here we investigate the hydrodynamics of turbines in an infinitely large array with aligned or staggered layouts for a range of streamwise and lateral turbine spacing. First, we present a theoretical analysis based on an extension of the Linear Momentum Actuator Disc Theory (LMADT) for perfectly aligned and staggered layouts, employing a…
Under the term global blockage, the cumulative induction of wind turbines in a wind farm has been recently suspected to be responsible for observed overestimations of the energy yield in large-size wind farms. In this paper, the practice of modeling this effect after linear superposition of single turbine inductions, calculated with three of the most recent analytic models, is compared to Large-Eddy-Simulations of wind farms. We compare the models across two different farms, composed of 9 and 49 turbines, with two different heights of the atmospheric boundary layer, 300 and 500 m. The results …
Turbine wake and local blockage effects are known to alter wind farm power production in two different ways: (1) by changing the wind speed locally in front of each turbine; and (2) by changing the overall flow resistance in the farm and thus the so-called farm blockage effect. To better predict these effects with low computational costs, we develop data-driven emulators of the `local' or `internal' turbine thrust coefficient $C_T^*$ as a function of turbine layout. We train the model using a multi-fidelity Gaussian Process (GP) regression with a combination of low (engineering wake model) and…
High-order large-eddy simulations are performed to study the performance and flow field of a ducted wind turbine operating at different tip speed ratios. To evaluate the effects of the duct, simulations with the same tip speed ratios are also performed on the corresponding open-rotor turbine. It is found that the ducted turbine consistently obtains higher power outputs than the open-rotor counterpart, and the duct itself enhances flow turbulence and blade trailing-edge vortices but weakens tip and hub vortices. Flow bifurcation is observed at the largest tip speed ratio and is identified to be…
The near wake of a small-scale wind turbine is investigated using Particle Image Velocimetry (PIV) experiments at different tip speed ratios ($λ$). The wind turbine model had a nacelle and a tower mimicking real scale wind turbines. The near wake is found to be dominated by multiple coherent structures including the tip vortices, distinct vortex sheddings from the nacelle and tower, and wake meandering. The merging of the tip vortices is found to be strongly dependent on $λ$. A convective length scale ($L_c$) related to the pitch of the helical vortices is defined which is shown to be a better…
Encouraged by recent studies on the performance of tidal turbine arrays, we extend the classical momentum actuator disc theory to include the free surface effects and allow the vertical arrangement of turbines. Most existing literatures concern one dimensional arrays with single turbine in the vertical direction, while the arrays in this work are two dimensional (with turbines in both the vertical and lateral directions) and also partially block the channel which width is far larger than height. The vertical mixing of array scale flow is assumed to take place much faster than lateral one. This…
Cross-flow, or vertical-axis, turbines are a promising technology for capturing kinetic energy in wind or flowing water and their inherently unsteady fluid mechanics present unique opportunities for control optimization of individual rotors or arrays. To explore the potential for beneficial interactions between turbines in an array, coherent structures in the wake of a single two-bladed cross-flow turbine are examined using planar stereo particle image velocimetry in a water channel. First, the mean wake structure of this high chord-to-radius ratio rotor is described, compared to previous stud…
