Dataset: https://doi.org/10.5061/dryad.dfn2z35b5

Supporting Article (Physical Review Fluids): https://doi.org/10.1103/tpzz-df14
Supporting Article (Open-Access on arXiv): 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".

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:

• 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.

• 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.

• 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.

• 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.

• 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.