DOI: 10.5061/dryad.dfn2z35b5
title: Data from: Experimental validation of a linear momentum and bluff-body model for high-blockage cross-flow turbine arrays

description: 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.
description: 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.
description: # Data from: Experimental validation of a linear momentum and bluff-body
 model for high-blockage cross-flow turbine arrays Dataset:
 [https://doi.org/10.5061/dryad.dfn2z35b5](https://doi.org/10.5061/dryad.dfn2z35b5) Supporting Article (*Physical Review Fluids*): [https://doi.org/10.1103/tpzz-df14](https://doi.org/10.1103/tpzz-df14) Supporting Article (Open-Access on arXiv): [https://doi.org/10.48550/arXiv.2408.16705](https://doi.org/10.48550/arXiv.2408.16705) This dataset provides performance data and near-wake flow field data for a cross-flow turbine array tested at high blockage at the University of Washington. The array's hydrodynamic performance (e.g., power and thrust coefficients) was collected at blockage ratios between 30% and 55% using a custom laboratory-scale turbine test rig in the Alice C. Tyler flume at the University of Washington, and the near-wake flow field for a subset of conditions was characterized using particle image velocimetry (PIV). The experimental methods and results are discussed in detail in our paper ["Experimental validation of a linear momentum and bluff-body model for high-blockage cross-flow turbine arrays"](https://doi.org/10.1103/tpzz-df14). The data are provided as three files. A brief summary is provided below, and the variables within each file are subsequently described in detail. * `performanceData.mat`: Performance data (e.g., power and thrust coefficients) as a function of tip-speed ratio (TSR) for the turbine array at blockage ratios between 30% and 55%. This structure also includes the analytical velocities and blockage corrected performance quantities obtained by applying the confinement models of Houlsby *et al.* (2008) and Steiros* et al.* (2022) to the experimental data, as described in the supporting manuscript. * `nearWakePIV_0.6Downstream.mat`: Near-wake PIV flow fields 0.6 turbine diameters downstream of the array at 36.7%, 45.0%, and 55.0% blockage and various tip-speed ratios. * `nearWakePIV_1.5Downstream.mat`: Near-wake PIV flow fields 1.5 turbine diameters downstream of the array at 36.7%, 45.0%, and 55.0% blockage and various tip-speed ratios. ## File: `performanceData.mat` `performanceData.mat` contains all array performance measurements. This file contains three variables: `baseline`, `submergence`, and `comments`. ### `baseline` The `baseline` variable contains aggregated core experimental performance results of the paper. `baseline` is a structure of performance data (e.g., power and thrust coefficients) for the turbine array at 30%, 33.4%, 36.7%, 40.1%, 45.0%, 50.0%, and 55.0% blockage. Each row of the structure corresponds to a different blockage ratio that was tested. Key performance metrics are provided in time-averaged and phase-median forms at each tip-speed ratio. Includes non-PIV flow field data (e.g., freestream velocity, depth measurements), as well as analytical velocities and blockage corrected performance quantities obtained by applying the confinement models of Houlsby *et al.* (2008) and Steiros *et al.* (2022) to the experimental data. The fields of `data` are categorized and described below: ###### Experiment Specification * `label`: A short string identifier of the blockage condition that was tested (e.g., "B30" for 30% blockage). * `beta_nom`: Nominal blockage ratio [fraction] corresponding to the experiment. ###### Time-Average Performance * `TSR`: Time-average tip-speed ratio. * `CP`: Time-average array-average coefficient of performance as a function of TSR. * `CP_IQR`: Inter-quartile range of the cycle-averaged array-average coefficient of performance. Rows represent each TSR, whereas the columns represent the 25th and 75th percentiles, respectively. * `CP_blade`: CP with losses due to the blade support structures subtracted. * `CT`: Time-average array-average coefficient of thrust as a function of TSR. * `CT_IQR`: Inter-quartile range of the cycle-averaged array-average coefficient of thrust. Rows represent each TSR, whereas the columns represent the 25th and 75th percentiles, respectively. * `CL`: Time-average rotor-average coefficient of lateral force as a function of TSR. * `CL_IQR`: Inter-quartile range of the cycle-averaged rotor-average coefficient of lateral force. Rows represent each TSR, whereas the columns represent the 25th and 75th percentiles, respectively. * `CF`: Time-average array-average coefficient of resultant horizontal force (i.e., the vector sum of CT and CL) as a function of TSR. * `CF_IQR`: Inter-quartile range of the cycle-averaged array-average coefficient of resultant horizontal force. Rows represent each TSR, whereas the columns represent the 25th and 75th percentiles, respectively. * `CQ`: Time-average rotor-average coefficient of torque as a function of TSR. * `CQ_IQR`: Inter-quartile range of the cycle-averaged rotor-average coefficient of torque. Rows represent each TSR, whereas the columns represent the 25th and 75th percentiles, respectively. ###### Phase-Median Performance * `CP_phase`: Phase-median array-average coefficient of performance as a function of TSR and theta. Rows correpsond to each TSR, whereas columns correspond to each theta. * `CT_phase`: Phase-median array-average coefficient of thrust as a function of TSR and theta. Rows correpsond to each TSR, whereas columns correspond to each theta. * `CL_phase`: Phase-median rotor-average coefficient of lateral force as a function of TSR and theta. Rows correpsond to each TSR, whereas columns correspond to each theta. * `CF_phase`: Phase-median array-average coefficient of resultant horizontal force as a function of TSR and theta. Rows correpsond to each TSR, whereas columns correspond to each theta. * `CQ-phase`: Phase-median rotor-average coefficient of torque as a function of TSR and theta. Rows correpsond to each TSR, whereas columns correspond to each theta. ###### Flow Parameters * `Uinf`: Freestream velocity [m/s] as a function of TSR. * `h`: Far upstream dynamic depth [m] as a function of TSR. * `hx`: Dynamic depth [m] at various streamwise locations in line with Turbine B as a function of TSR. Rows correspond to each TSR, whereas columns correspond to each streamwise location. * `xFST`: Streamwise position corresponding to each column of hx, normalized by the turbine outermost diameter. * `temp`: Water temperature [C] measured during the experiment. * `TI`: Turbulence intensity [%] measured during the experiment. * `beta`: Channel blockage ratio [fraction] as a function of TSR as measured during the experiment. * `Fr_h`: Depth-based Froude number as a function of TSR as measured during the experiment. * `Re_D`: Diameter-based Reynolds number as a function of TSR as measured during the experiment. * `subNorm`: Normalized submergence depth (s/h) as a function of TSR as measured during the experiment. ###### Confinement Models * `houlsby`: A structure of flow field quantities and re-scaled performance obtained by applying the model of Houlsby *et al.* (2008) to the experimental data. - `steiros`: A structure of flow field quantities and re-scaled performance obtained by applying the model of Steiros *et al.* (2022) to the experimental data. The `houlsby` and `steiros` sub-structures have some or all of the following fields: * `ub`: Bypass velocity [m/s] predicted from the confinement model. * `uw`: Wake velocity [m/s] predicted from the confinement model. * `ut`: Velocity through the turbine [m/s] predicted from the confinement model. * `Uinf_prime`: Unconfined freestream velocity [m/s] predicted from a Glauert-derived blockage correction based on the confinement model. * `h2`: Water depth [m] just upstream of the actuator disk predicted from open-channel linear momentum theory (`houlsby` only). * `h3`: Water depth [m] just downstream of the actuator disk predicted from open-channel linear momentum theory (`houlsby` only). * `h4`: Water depth [m] at the location downstream of the actuator disk where the static pressure is equal in the core and bypass flows predicted from open-channel linear momentum theory (`houlsby` only). * `h5`: Water depth [m] far downstream of the actuator disk predicted from open-channel linear momentum theory (`houlsby` only). * `CP_bluff`: CP scaled by the corresponding bypass velocity, `ub`. * `CT_bluff`: CT scaled by the corresponding bypass velocity, `ub`. * `TSR_bluff`: TSR scaled by the corresponding bypass velocity, `ub`. * `CP_prime`: CP scaled by the corresponding unconfined freestream velocity, `Uinf_prime`. * `CT_prime`: CT scaled by the corresponding unconfined freestream velocity, `Uinf_prime`. * `TSR_prime`: TSR scaled by the corresponding unconfined freestream velocity, `Uinf_prime`. Further details regarding these fields can be found in the supporting paper. ### `submergence` The `submergence` variable contains aggregated performance data for the array at different submergence depths at 36.7%, 45.0%, and 55.0% blockage (see Appendix A in the supporting paper). `submergence` is a structure that organizes the results by blockage and by submergence depth. Each row of `submergence` represents a different blockage ratio and has the following fields. * `label`: A short string identifier of the blockage condition that was tested (e.g., "B36" for 36.7% blockage). * `betaNom`: Nominal blockage ratio [fraction] corresponding to the experiment. * `data`: Data for all submergence depths tested at a particular blockage. Each row of `submergence.data` represents a different submergence depth, indicated by the `label` field (e.g., "B36_S05" for 36.7% blockage and s/h = 0.05). The fields of `submergence.data` are the same as those for `baseline` (see documentation above) with the exception of fields related to linear momentum and bluff-body scaling, which are not included in `submergence.data`. ### `comments` The `comments` variable contains a structure that describes the meaning and format of each field in the `baseline` and `submergence` structures as provided above. Each field of `comments` contains a description for the corresponding field in `baseline`, `baseline.houlsby`, `baseline.steiros`, `submergence`, and/or `submergence.data`. ## File: `nearWakePIV_0.6Downstream.mat` `nearWakePIV_0.6Downstream.mat` contains PIV flow fields located 0.6 turbine diameters downstream of the array at 36.7%, 45.0%, and 55.0% blockage and various tip-speed ratios. This file contains two variables: `pivData` and `pivComments`. ### `pivData` `pivData` is a structure of aggregated PIV flow fields organized by blockage and tip-speed ratio. Like the `baseline` and `submergence` structures, the `label` and `beta_nom` fields of `pivData` indicate which blockage ratio the associated flow fields correspond to. The flow field data for each blockage is provided in the `data` field, which is itself a structure that has the following fields: * `label`: A short text description of the conditions the data corresponds to (e.g., "B36_TSR16" for 36.7% blockage and TSR = 1.6) * `TSR`: Time-average tip-speed ratio at which this flow field was collected. * `Y`: A matrix of y-coordinates (cross-stream) normalized by the turbine diameter (D=31.5cm). The origin "0" is defined at the center of Turbine B. The center of Turbine A is at +1.2D * `Z`: A matrix of z-coordinates (vertical) normalized by the turbine blade span (H=21.5cm). The origin "0" is defined at the midspan of the turbines, such that +/- H/2 correspond to the top and bottom of the turbine's projected area. * `UxUinf`: The time-averaged streamwise velocity, Ux, at each Y-Z coordinate, normalized by the freestream velocity, Uinf, measured by the ADV. * `UxUb`: The time-averaged streamwise velocity, Ux, at each Y-Z coordinate, normalized by the bypass velocity predicted from linear momentum theory, ub. * `UxUw`: The time-averaged streamwise velocity, Ux, at each Y-Z coordinate, normalized by the wake velocity predicted from linear momentum theory, uw. * `TKE`: Mean turbulent kinetic energy across all phases of data, normalized by the freestream velocity squared. TKE is calculated for each phase (i.e., azimuthal position) of PIV data acquisition, then averaged across all phases to yield the provided values. * `Vort`: Time-averaged streamwise vorticity, averaged across all phases and normalized by Uinf/c, where c is the blade chord length and Uinf is the freestream velocity. , ...The values provided are obtained by calculating the phase-average vorticity for each phase (i.e., azimuthal position) of PIV data acquisition, and then averaging across all phases. * `STD`: Standard deviation of the streamwise velocity field, normalized by the freestream velocity. The provided values are calculated as the standard deviation of the phase-average velocity fields across all phases of PIV data acquisition. Note that the `TKE`, `Vort`, and `STD` fields are only provided for the optimal tip-speed ratio at each blockage ratio (TSR = 2.6 at 36.7% blockage, TSR = 2.9 at 45.0% blockage, and TSR = 3.6 at 55.0% blockage). An example of how to plot the PIV flow fields in MATLAB is provided in `pivPlotExample.m`. Further details regarding these fields can be found in the supporting paper. ### `pivComments` `pivComments` is a structure that includes a description of each of the fields of `pivData.data`, including data format and units, as described above. Each field of `pivComments` corresponds to a field of `pivData.data`. ## File: `nearWakePIV_1.5Downstream.mat` `nearWakePIV_1.5Downstream.mat` contains PIV flow fields located 1.5 turbine diameters downstream of the array at 36.7%, 45.0%, and 55.0% blockage and various tip-speed ratios. This file contains two variables, `pivData` and `pivComments`, which are formatted identically to those in `nearWakePIV_0.6Downstream.mat` (see above). It is noted that the `TKE`, `Vort`, and `STD` fields are not provided for these flow fields. ## Code/software It is recommended that MATLAB/Octave be used to view this data. An example MATLAB script that demonstrates how to plot the PIV data, `pivPlotExample.m`, is provided. The code used to apply the confinement models of Houlsby *et al.* and Steiros *et al.* to the data, as described in the manuscript, is [openly available on GitHub](https://github.com/aidan-hunt/turbine-confinement-models).