# Flow Field Measurement of Laboratory-Scaled Cross-Flow Hydrokinetic Turbines: Part I—The Near-Wake of a Single Turbine

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Apparatus and Methodology

#### 2.1. Turbine Towers and Mechanical Design

#### 2.2. Electronics

#### 2.3. Particle Image Velocimetry

## 3. Results and Discussion

#### 3.1. Fast Fourier Analysis

#### 3.2. Data Convergence

#### 3.3. Mean Flow

#### 3.4. Kinetic Energy

#### 3.5. Quantitative Evaluation

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

MHK | Marine hydrokinetic turbine |

EDM | Electrical discharge machining |

VAWT | Vertical axis wind turbine |

LDV | Laser Doppler velocimetry |

## References

- Bahar, H. Renewables 2020—Analysis and Forecast to 2025; Report; International Energy Angency: Paris, France, 2020; Available online: https://www.iea.org/reports/renewables-2020 (accessed on 28 March 2021).
- Narune, A.; Prasad, E. Renewable Energy Market by Type (Hydroelectric Power, Wind Power, Bioenergy, Solar Energy, and Geothermal Energy), and End Use (Residential, Commercial, Industrial, and Others): Global Opportunity Analysis and Industry Forecast, 2018–2025; Report EN 17140; Allied Market Research: Portland, OR, USA, 2019. [Google Scholar]
- Wu, J.; Huang, J.; Han, X.; Xie, Z.; Gao, X. Ecology: Three-Gorges dam experiment in habitat fragmentation? Science
**2003**, 300, 1239–1240. [Google Scholar] [CrossRef] - Jackson, S.; Sleigh, A. Resettlement for China’s Three Gorges Dam: Socio-economic impact and institutional tensions. Communist Post Commun. Stud.
**2000**, 33, 223–241. [Google Scholar] [CrossRef] - Tilt, B.; Braun, Y.; He, D. Social impacts of large dam projects: A comparison of international case studies and implications for best practice. J. Environ. Manag.
**2009**, 90, S249–S257. [Google Scholar] [CrossRef] - Dabiri, J. Potential order-of-magnitude enhancement of wind farm power density via counter-rotating vertical-axis wind turbine arrays. J. Renew. Sustain. Energy
**2011**, 3, 043104. [Google Scholar] [CrossRef][Green Version] - Brownstein, I.D.; Wei, N.J.; Dabiri, J.O. Aerodynamically Interacting Vertical-Axis Wind Turbines: Performance Enhancement and Three-Dimensional Flow. Energies
**2019**, 12, 2724. [Google Scholar] [CrossRef][Green Version] - Jiang, Y.; Zhao, P.; Stoesser, T.; Wang, K.; Zhou, L. Experimental and numerical investigation of twin vertical axis wind turbines with a deflector. Energy Convers. Manag.
**2020**, 209, 112588. [Google Scholar] [CrossRef] - Li, Y.; Calisal, S. Modeling of twin-turbine systems with vertical axis tidal current turbines: Part 1—Power Output. Ocean. Eng.
**2010**, 37, 627–637. [Google Scholar] [CrossRef] - Li, Y.; Calisal, S. Modeling of twin-turbine systems with vertical axis tidal current turbine: Part 2—Torque Fluctuation. Ocean. Eng.
**2011**, 38, 550–558. [Google Scholar] [CrossRef] - Bachant, P.; Wosnik, M. Performance measurements of cylindrical- and spherical-helical cross-flow marine hydrokinetic turbines, with estimates of exergy efficiency. Renew. Energy
**2014**, 74, 318–325. [Google Scholar] [CrossRef] - Bachant, P.; Wosnik, M.; Gunawan, B.; Neary, V. Experimental study of a reference model vertical-axis cross-flow turbine. PLoS ONE
**2016**, 11, e0163799. [Google Scholar] [CrossRef][Green Version] - Bachant, P.; Wosnik, M. Effects of Reynolds number on the energy conversion and near-wake dynamics of a high solidity vertical-axis cross-flow turbine. Energies
**2016**, 9, 73. [Google Scholar] [CrossRef][Green Version] - Strom, B.; Brunton, S.; Polagye, B. Intracycle angular velocity control of cross-flow turbines. Nat. Energy
**2017**, 2, 17103. [Google Scholar] [CrossRef] - Bachant, P.; Wosnik, M. Modeling the near-wake of a vertical-axis cross-flow turbine with 2-D and 3-D RANS. J. Renew. Sustain. Energy
**2016**, 8, 053311. [Google Scholar] [CrossRef][Green Version] - Mannion, B.; Leen, S.; Nash, S. A two and three-dimensional CFD investigation into performance prediction and wake characterisation of a vertical axis turbine. J. Renew. Sustain. Energy
**2018**, 10, 034503. [Google Scholar] [CrossRef] - Mannion, B.; McCormack, V.; Leen, S.; Nash, S. A CFD investigation of a variable-pitch vertical axis hydrokinetic turbine with incorporated flow acceleration. J. Ocean. Eng. Mar. Energy
**2019**, 5, 21–39. [Google Scholar] [CrossRef][Green Version] - Mannion, B.; McCormack, V.; Kennedy, C.; Leen, S.; Nash, S. An experimental study of a flow-accelerating hydrokinetic device. Proc. Inst. Mech. Eng. Part J. Power Energy
**2018**, 1, 148–162. [Google Scholar] [CrossRef][Green Version] - Ross, H.; Polagye, B. An experimental assessment of analytical blockage corrections for turbines. Renew. Energy
**2020**, 152, 1328–1341. [Google Scholar] [CrossRef][Green Version] - Araya, D.; Colonius, T.; Dabiri, J. Transition to Bluff-Body Dynamics in the Wake of Vertical-Axis Wind Turbines. J. Fluid Mech.
**2017**, 813, 346–381. [Google Scholar] [CrossRef][Green Version] - Doan, M.N.; Alayeto, I.H.; Padricelli, C.; Obi, S.; Totsuka, Y. Experimental and computational fluid dynamic analysis of laboratory-scaled counter-rotating cross-flow turbines in marine environment. In Proceedings of the ASME 2018 5th Joint US-European Fluids Engineering Division Summer, Montreal, QC, Canada, 15–20 July 2018; American Society of Mechanical Engineer: New York, NY, USA, 2018; Volume 2, p. V002T14A003. [Google Scholar]
- Doan, M.N.; Alayeto, I.H.; Kumazawa, K.; Obi, S. Computational fluid dynamic analysis of a marine hydrokinetic crossflow turbine in low Reynolds number flow. In Proceedings of the ASME-JSME-KSME 2019 8th Joint Fluids Engineering, San Francisco, CA, USA, 28 July–1 August 2019; American Society of Mechanical Engineer: New York, NY, USA, 2019; Volume 2, p. V002T02A067. [Google Scholar]
- Alayeto, I.H.; Doan, M.N.; Kumazawa, K.; Obi, S. Wake characteristics comparison between isolated and pair configurations of marine hydrokinetic crossflow turbines at low Reynolds numbers. In Proceedings of the ASME-JSME-KSME 2019 8th Joint Fluids Engineering, San Francisco, CA, USA, 28 July–1 August 2019; American Society of Mechanical Engineer: New York, NY, USA, 2019; Volume 1, p. V001T01A037. [Google Scholar]
- Markovic, U.V. Characterizing the Wake and the Performance of a Marine Hydrokinetic Turbine in a Tandem Array Configuration. Master’s Thesis, Bucknell University, Lewisburg, PA, USA, 2016. [Google Scholar]
- Doan, M.; Kai, Y.; Obi, S. Twin Marine Hydrokinetic Cross-Flow Turbines in Counter Rotating Configurations: A Laboratory-Scaled Apparatus for Power Measurement. J. Mar. Sci. Eng.
**2021**, 8, 918. [Google Scholar] [CrossRef] - Lust, E.; Flack, K.; Luznik, L. Survey of the near wake of an axial-flow hydrokinetic turbine in quiescent conditions. Renew. Energy
**2018**, 129, 92–101. [Google Scholar] [CrossRef] - Araya, D.; Dabiri, O. A comparison of wake measurements in motor-driven and flow-driven turbine experiments. Exp. Fluids
**2015**, 56, 150. [Google Scholar] [CrossRef] - Suryadi, A.; Ishii, T.; Obi, S. Stereo PIV measurement of a finite, flapping rigid plate in hovering condition. Exp. Fluids
**2010**, 49, 447–460. [Google Scholar] [CrossRef] - Suryadi, A. The Phase-Avreaged Velocity Measurement and the Estimation of Pressure Force of a Periodically Moving Body. Ph.D. Thesis, Keio University, Yokohama, Japan, 2011. [Google Scholar]
- MathWroks. Fast Fourier Transform. Available online: https://www.mathworks.com/help/matlab/ref/fft.html (accessed on 28 March 2021).
- Antonia, R.; Bisset, D.; Browne, L. Effect of Reynolds number on the topology of the organized motion in a turbulent boundary layer. J. Fluid Mech.
**1990**, 213, 267–286. [Google Scholar] [CrossRef] - Kim, H.; Kline, S.; Reynolds, W. The production of turbulence near a smooth wall in a turbulent boundary layer. J. Fluid Mech.
**1971**, 15, 133–160. [Google Scholar] [CrossRef]

**Figure 1.**A 3D illustration (

**a**) and side-view (

**b**) of the flume facility with its main components. The red arrow on the left picture indicates the water flow direction.

**Figure 2.**Pictures of the apparatus in action: a single turbine inside the water channel (

**a**), a laser sheet illuminates seeding particles behind the turbine (

**b**), and a raw PIV picture (

**c**).

**Figure 3.**A rendered picture of the turbine apparatus (

**a**) and its critical mechanical and electronic components (

**b**).

**Figure 5.**An illustration of the turbine configurations studied in this article: Turbine T1 (

**a**) and Turbine T2 (

**b**). The regions of interest are enclosed inside the red dashed lines, and the arbitrary points for time-series data extraction are highlighted with the 4 red circles inside the dashed lines.

**Figure 6.**The power curve of each turbine with the flow measurement points highlighted. In the power measurement experiment, turbine T2 stalled at $\lambda =0.75$ [25]. This figure displays a linear extrapolation of T2 ${C}_{P}$ at $\lambda =0.75$.

**Figure 7.**The FFT analyses of the time series streamwise and transverse velocities at the 4 points, highlighted in Figure 5, in the near-wake of the T1 turbine configuration at $\lambda =0.75$.

**Figure 8.**The FFT analyses of the time series streamwise and transverse velocities at the 4 points, highlighted in Figure 5, in the near-wake of the T2 turbine configuration at $\lambda =1.05$.

**Figure 9.**An example of the flow converged over more than 100 phases of the T1 configuration at $\lambda =0.85$ and at $\mathsf{\Phi}={71}^{\circ}$. The vertical axes are the streamwise and transverse velocities, at the 4 points highlighted in Figure 5, averaged over time.

**Figure 10.**An example of the flow converged over more than 100 phases of the T2 configuration at $\lambda =0.85$ and at $\mathsf{\Phi}=13.{6}^{\circ}$. The vertical axes are the streamwise and transverse velocities, at the 4 points highlighted in Figure 5, averaged over time.

**Figure 11.**The time-averaged non-dimensionalized velocity and vorticity of the T1 configuration at $\lambda =0.75$ (

**a**), $\lambda =0.85$ (

**b**), and $\lambda =1.05$ (

**c**) with the associated power coefficients. The red circle displays turbine T1 rotation center.

**Figure 12.**The time-averaged non-dimensionalized velocity and vorticity of the T2 configuration at $\lambda =0.75$ (

**a**), $\lambda =0.85$ (

**b**), and $\lambda =1.05$ (

**c**) with the associated power coefficients. The blue circle displays turbine T2 rotation center.

**Figure 13.**The streamwsie velocity component of turbine T1 (

**a**) and T2 (

**b**) at the 3 tip–speed ratios and 4 streamwise locations.

**Figure 14.**The time -averaged kinetic energy of the flow behind turbine T1 (

**a**) and turbine T2 (

**b**). The red circle displays turbine T1 rotation center, while the blue circle displays turbine T2 rotation center.

**Figure 15.**The fluctuating component of the phase-averaged kinetic energy of the flow behind turbine T1 at various phase angles and tip–speed ratios. The red circle displays turbine T1 rotation center.

**Figure 16.**The fluctuating component of the phase-averaged kinetic energy of the flow behind turbine T2 at various phase angles and tip–speed ratios. The blue circle displays turbine T2 rotation center.

**Figure 17.**The random component of the phase-averaged kinetic energy of the flow behind turbine T1 at various phase angles and tip–speed ratios. The red circle displays turbine T1 rotation center.

**Figure 18.**The random component of the phase-averaged kinetic energy of the flow behind turbine T2 at various phase angles and tip–speed ratios. The blue circle displays turbine T2 rotation center.

**Figure 19.**Summary of the kinetic energy components of turbine T1 (red) and T2 (blue) at $x/{D}_{t}=1.0$ averaged over space and time.

**Table 1.**Comparison of each configuration temporally and spatially averaged divergence at $x/{D}_{t}=1.0$.

$\mathit{\lambda}$ | $\overline{\mathit{D}}(\mathit{x}=1)$ T1 | $\overline{\mathit{D}}(\mathit{x}=1)$ T2 |
---|---|---|

0.75 | 0.285 | 0.312 |

0.85 | 0.232 | 0.247 |

1.05 | 0.318 | 0.328 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Doan, M.N.; Kai, Y.; Kawata, T.; Obi, S.
Flow Field Measurement of Laboratory-Scaled Cross-Flow Hydrokinetic Turbines: Part I—The Near-Wake of a Single Turbine. *J. Mar. Sci. Eng.* **2021**, *9*, 489.
https://doi.org/10.3390/jmse9050489

**AMA Style**

Doan MN, Kai Y, Kawata T, Obi S.
Flow Field Measurement of Laboratory-Scaled Cross-Flow Hydrokinetic Turbines: Part I—The Near-Wake of a Single Turbine. *Journal of Marine Science and Engineering*. 2021; 9(5):489.
https://doi.org/10.3390/jmse9050489

**Chicago/Turabian Style**

Doan, Minh N., Yuriko Kai, Takuya Kawata, and Shinnosuke Obi.
2021. "Flow Field Measurement of Laboratory-Scaled Cross-Flow Hydrokinetic Turbines: Part I—The Near-Wake of a Single Turbine" *Journal of Marine Science and Engineering* 9, no. 5: 489.
https://doi.org/10.3390/jmse9050489