# Flow Field Measurement of Laboratory-Scaled Cross-Flow Hydrokinetic Turbines: Part II—The Near-Wake of Twin Turbines in Counter-Rotating Configurations

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methodology

## 3. Results and Discussion

#### 3.1. Effect of Phase Difference

#### 3.2. Effect of Separation Distance

#### 3.3. Note on Effect of Relative Incoming Flow Angle

#### 3.4. Quantitative Assessment

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

MHK | Marine hydrokinetic turbine |

VAWT | Vertical axis wind turbine |

PIV | Particle image velocimetry |

## References

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**Figure 1.**An illustration of the twin turbine apparatus variations: (

**a**) counter-rotating and (

**b**) overlapping turbines with the separation distance of $1.25{D}_{t}$ and $1.00{D}_{t}$. The figure was adapted from [10].

**Figure 2.**An overview of the monoscopic particle image velocimetry setup. The figure was adapted from [11].

**Figure 4.**Different turbine configurations used in the near-wake measurement experiments: (

**a**) forward counter-rotating at $\mathsf{\Delta}\Phi ={0}^{\xb0}$, (

**b**) forward counter-rotating at $\mathsf{\Delta}\Phi ={60}^{\xb0}$, (

**c**) forward overlapping at $\mathsf{\Delta}\Phi ={60}^{\xb0}$, (

**d**) backward counter-rotating at $\mathsf{\Delta}\Phi ={0}^{\xb0}$, (

**e**) backward counter-rotating at $\mathsf{\Delta}\Phi ={60}^{\xb0}$, and (

**f**) backward overlapping at $\mathsf{\Delta}\Phi ={60}^{\xb0}$. The red and blue circles illustrate the turbine T1 and T2 rotational center correspondingly. The flow measurement areas are enclosed inside the black dashed lines.

**Figure 5.**The power curves of counter-rotating configurations, which was adapted from [10], with the flow measurement points highlighted.

**Figure 6.**The phase-averaged flow fields behind the forward counter-rotating configurations at $\lambda =1.05$. The power coefficients of these configurations are 0.116 and 0.103 for $\mathsf{\Delta}\Phi ={0}^{\xb0}$ (

**a**–

**d**) and $\mathsf{\Delta}\Phi ={60}^{\xb0}$ (

**e**–

**h**) correspondingly. The displayed phase angles $\Phi $ belong to turbine T1 in red color. The color shows the non-dimensionalized phase-averaged velocity magnitude.

**Figure 7.**A zoomed in picture of Figure 6a. The re-circulation zones behind the turbines are enclosed in the purple solid lines.

**Figure 8.**A zoomed in picture of Figure 6h. The re-circulation zone behind turbine T1 is enclosed in the purple solid lines.

**Figure 9.**The phase-averaged flow fields behind the backward counter-rotating configurations at $\lambda =0.90$. The power coefficients of these configurations are 0.108 and 0.103 for $\mathsf{\Delta}\Phi ={0}^{\xb0}$ (

**a**–

**d**) and $\mathsf{\Delta}\Phi ={60}^{\xb0}$ (

**e**–

**h**) correspondingly. The displayed phase angles $\Phi $ belong to turbine T1 in red color. The color shows the non-dimensionalized phase-averaged velocity magnitude.

**Figure 10.**A zoomed in picture of Figure 9e. The re-circulation zone behind turbine T2 is enclosed in the purple solid lines.

**Figure 11.**The power curves of counter-rotating and overlapping configurations at $\mathsf{\Delta}\Phi ={60}^{\xb0}$, which was adapted from [10], with the flow measurement points highlighted.

**Figure 12.**The phase-averaged flow fields behind the forward counter-rotating (

**a**–

**d**) and overlapping (

**e**–

**h**) configurations at $\mathsf{\Delta}\Phi ={60}^{\xb0}$ and $\lambda =0.95$. The power coefficients of these configurations are 0.120 and 0.128 for forward counter-rotating ($\mathsf{\Delta}\Phi ={60}^{\xb0}$) and overlapping configuration correspondingly. The displayed phase angles $\Phi $ belong to turbine T1 in red color. The color shows the non-dimensionalized phase-averaged velocity magnitude.

**Figure 13.**The phase-averaged flow fields behind the backward counter-rotating (

**a**–

**d**) and overlapping (

**e**–

**h**) configurations at $\mathsf{\Delta}\Phi ={60}^{\xb0}$ and $\lambda =0.75$. The power coefficients of these configurations are 0.097 and 0.092 for forward counter-rotating ($\mathsf{\Delta}\Phi ={60}^{\xb0}$) and overlapping configuration correspondingly. The displayed phase angles $\Phi $ belong to turbine T1 in red color. The color shows the non-dimensionalized phase-averaged velocity magnitude.

**Table 1.**Comparison of each configuration’s temporally and spatially averaged kinetic energy at $x/{D}_{t}=1.0$ and the associated power coefficient.

Forward/Backward | $\lambda $ | $\mathsf{\Delta}\Phi $ | Separation Distance | ${C}_{P}$ | ${P}_{\overline{K}}(x=1)$ |
---|---|---|---|---|---|

Forward | 1.05 | 0 | 1.25 | 0.116 | 0.263 |

Forward | 1.05 | ${60}^{\xb0}$ | 1.25 | 0.103 | 0.268 |

Backward | 0.90 | 0 | 1.25 | 0.108 | 0.259 |

Backward | 0.90 | ${60}^{\xb0}$ | 1.25 | 0.103 | 0.264 |

Forward | 0.95 | ${60}^{\xb0}$ | 1.25 | 0.120 | 0.277 |

Forward | 0.95 | ${60}^{\xb0}$ | 1.00 | 0.128 | 0.227 |

Backward | 0.75 | ${60}^{\xb0}$ | 1.25 | 0.097 | 0.269 |

Backward | 0.75 | ${60}^{\xb0}$ | 1.00 | 0.092 | 0.357 |

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**MDPI and ACS Style**

Doan, M.N.; Kawata, T.; Obi, S.
Flow Field Measurement of Laboratory-Scaled Cross-Flow Hydrokinetic Turbines: Part II—The Near-Wake of Twin Turbines in Counter-Rotating Configurations. *J. Mar. Sci. Eng.* **2021**, *9*, 777.
https://doi.org/10.3390/jmse9070777

**AMA Style**

Doan MN, Kawata T, Obi S.
Flow Field Measurement of Laboratory-Scaled Cross-Flow Hydrokinetic Turbines: Part II—The Near-Wake of Twin Turbines in Counter-Rotating Configurations. *Journal of Marine Science and Engineering*. 2021; 9(7):777.
https://doi.org/10.3390/jmse9070777

**Chicago/Turabian Style**

Doan, Minh N., Takuya Kawata, and Shinnosuke Obi.
2021. "Flow Field Measurement of Laboratory-Scaled Cross-Flow Hydrokinetic Turbines: Part II—The Near-Wake of Twin Turbines in Counter-Rotating Configurations" *Journal of Marine Science and Engineering* 9, no. 7: 777.
https://doi.org/10.3390/jmse9070777