Experimental validation of a linear momentum and bluff-body model for high-blockage cross-flow turbine arrays

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's 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.

Methods
This data was collected in the Alice C. Tyler flume at the University of Washington using a laboratory-scale two-turbine array. Further details of the physical system and data acquisition for performance and PIV may be found in our manuscript.