# Effects of Reynolds Number on the Energy Conversion and Near-Wake Dynamics of a High Solidity Vertical-Axis Cross-Flow Turbine

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## Abstract

**:**

## 1. Introduction

#### Modes of Reynolds Number Dependence

## 2. Experimental Setup

**Figure 1.**University of New Hampshire Reference Vertical Axis Turbine (UNH-RVAT) turbine model. Turbine blades and struts made from NACA 0020 profiles with 0.14 m chord. Note that the upper and lower mounting flanges have been excluded, as these were included in the tare drag measurements.

**Figure 2.**Experimental setup photo (

**a**) and drawing (

**b**): turbine test bed installed in the UNH tow tank.

#### 2.1. Test Plan

**Table 1.**Turbine diameter and approximate blade chord Reynolds numbers for the tow speeds used in the experiment.

Tow Speed (m/s) | ${\mathit{Re}}_{\mathit{D}}$ | ${\mathit{Re}}_{\mathit{c},\mathbf{ave}}$ ($\mathit{\lambda}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{9}$) |
---|---|---|

0.3 | $0.3\times {10}^{6}$ | $0.8\times {10}^{5}$ |

0.4 | $0.4\times {10}^{6}$ | $1.1\times {10}^{5}$ |

0.5 | $0.5\times {10}^{6}$ | $1.3\times {10}^{5}$ |

0.6 | $0.6\times {10}^{6}$ | $1.6\times {10}^{5}$ |

0.7 | $0.7\times {10}^{6}$ | $1.9\times {10}^{5}$ |

0.8 | $0.8\times {10}^{6}$ | $2.1\times {10}^{5}$ |

0.9 | $0.9\times {10}^{6}$ | $2.4\times {10}^{5}$ |

1.0 | $1.0\times {10}^{6}$ | $2.7\times {10}^{5}$ |

1.1 | $1.1\times {10}^{6}$ | $2.9\times {10}^{5}$ |

1.2 | $1.2\times {10}^{6}$ | $3.2\times {10}^{5}$ |

1.3 | $1.3\times {10}^{6}$ | $3.4\times {10}^{5}$ |

#### 2.2. Data Processing

#### 2.3. Uncertainty Analysis

**Table 2.**Average expanded uncertainty estimates (with 95% confidence) for mean velocity measurements at each tow speed.

${\mathit{U}}_{\mathbf{\infty}}$ (m/s) | U (m/s) | V (m/s) | W (m/s) |
---|---|---|---|

$0.4$ | $1\times {10}^{-2}$ | $7\times {10}^{-3}$ | $6\times {10}^{-3}$ |

$0.6$ | $1\times {10}^{-2}$ | $8\times {10}^{-3}$ | $8\times {10}^{-3}$ |

$0.8$ | $2\times {10}^{-2}$ | $1\times {10}^{-2}$ | $1\times {10}^{-2}$ |

$1.0$ | $2\times {10}^{-2}$ | $1\times {10}^{-2}$ | $1\times {10}^{-2}$ |

$1.2$ | $2\times {10}^{-2}$ | $1\times {10}^{-2}$ | $1\times {10}^{-2}$ |

## 3. Results and Discussion

#### 3.1. Performance

**Figure 6.**UNH-RVAT measured mean power (

**a**) and drag (

**b**) coefficients at $\lambda =1.9$ plotted versus the Reynolds number. Error bars indicate expanded uncertainty estimates for 95% confidence, which for ${C}_{P}$ is dominated by systematic error estimates from the torque transducer operating at the lower end of its measurement range.

#### Relation to Static Foil Characteristics

`NCrit = 9`(default ${\mathrm{e}}^{n}$ transition criteria parameter for an average wind tunnel) and no forced boundary layer transition. Characteristics were computed for the approximate average blade chord Reynolds numbers encountered in the tow tank experiments.

**Figure 7.**Normalized maximum lift coefficient (

**a**), drag coefficient (

**b**), and lift-to-drag ratio (

**c**) computed by XFOIL at various $R{e}_{c}$ for each profile.

**Figure 8.**Geometric angle of attack (

**a**), relative velocity (

**b**), and torque coefficient (

**c**) calculated with a NACA 0020 foil operating at $\lambda =1.9$.

**Figure 9.**Reynolds number dependence of the normalized peak torque coefficient calculated from static foil coefficients and blade kinematics, compared to experimental data from a cross-flow turbine. Note that the experimental data represents the mean torque coefficient, not the maximum.

#### 3.2. Wake Characteristics

**Figure 12.**Mean streamwise velocity (

**a**) and turbulence kinetic energy (

**b**) profiles at $z/H=0.0$. Turbine diameter Reynolds number $R{e}_{D}$ is indicated by the legend.

#### 3.2.1. Dominant Timescales and Turbulence Spectra

**Figure 13.**Cross-stream velocity (normalized by ${U}_{\infty}$) spectra at $z/H=0.25$, $y/R=-1.0$ ($-0.5$ m in Figure 3) (

**a**) and $y/R=1.5$ ($+0.75$ m in Figure 3) (

**b**). Dashed vertical lines indicate $[1,3,6,9]$ times the turbine rotational frequency. Shaded regions indicate 95% confidence intervals assuming a ${\chi}^{2}$ distribution.

#### 3.2.2. Transport of Mean Momentum and Kinetic Energy

**Figure 14.**Normalized streamwise momentum transport quantities computed as weighted averages from Equation (8).

**Figure 15.**Normalized mean kinetic energy transport quantities computed as weighted averages based on Equation (9), omitting the non-measured streamwise derivatives. Note that directions of the turbulent transport terms refer to the directions of their partial derivatives.

## 4. Conclusions

- Acquire static lift and drag coefficient data for the desired blade profile.
- For azimuthal angles of 0 to 180 degrees and a given tip speed ratio, calculate the geometric angle of attack and relative velocity magnitude from the blade and undisturbed free stream velocity (taken as unity) vectors.
- Extract the maximum value of ${C}_{T}$, and repeat this process for static foil data at multiple $Re$.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

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.
https://doi.org/10.3390/en9020073

**AMA Style**

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(2):73.
https://doi.org/10.3390/en9020073

**Chicago/Turabian Style**

Bachant, Peter, and Martin Wosnik.
2016. "Effects of Reynolds Number on the Energy Conversion and Near-Wake Dynamics of a High Solidity Vertical-Axis Cross-Flow Turbine" *Energies* 9, no. 2: 73.
https://doi.org/10.3390/en9020073