# The Design of High Efficiency Crossflow Hydro Turbines: A Review and Extension

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Studies

## 3. Computational Studies

#### 3.1. The Flow in Crossflow Turbines

#### 3.2. Design Improvement of the 0.53 kW Turbine

#### 3.3. Design Improvement of 7 kW Turbine

## 4. Design Principle for High Efficiency Turbines

- Runner radius ratio: ${R}_{2}/{R}_{1}=0.68$ [5,19]. Table 1 shows little variation in this parameter in experiments and simulations. It is reasonable, however, to assume ${R}_{2}/{R}_{1}$ must be sufficiently large to allow the water flow to turn in the air-space before entering the second stage where signifciant power may be extracted. Thus, it is unlikely that ${R}_{2}/{R}_{1}$ could be much lower than $0.68$.
- Outer and inner blade angles (${\beta}_{1b}$ and ${\beta}_{2b}$, respectively): To minimize flow separation on the blades, ${\beta}_{1b}$ should be equal to ${\beta}_{1}$, which can be computed from Equation (1). For example, ${\beta}_{1b}\approx {39}^{\circ}$ would be in the maximum efficiency range as obtained by [19] and numerically validated by [5]. Similarly, ${\beta}_{2b}$ can be chosen as 90${}^{\circ}$ [5,19]. Since ${\beta}_{2b}$ = 55${}^{\circ}$ and 90${}^{\circ}$ gave similar efficiencies (about 90% efficiency) in the experiment of [20], this parameter may not be a critical to turbine efficiency.
- Entry arc angle, ${\theta}_{s}$, interacts with the runner geometry, Q, and H. ${\theta}_{s}$ = 80${}^{\circ}$ to 90${}^{\circ}$ gives the maximum efficiency in the cases considered.
- Nozzle aspect ratio: $W/{h}_{0}$ = 1.14 can be a good choice, and was the value for the highest efficiency turbines considered here. In general, $W/{h}_{0}$ probably depends on ${\theta}_{s}$ and ${R}_{1}$, [5,19]. This parameter determines the width of the runner and nozzle and the overall physical dimensions and weight of the runner.

## 5. Areas for Research and Development

- further experimental and numerical studies of turbines with ${\eta}_{max}\ge 90\%$. Characterization of internal flow features, particularly of the nozzle and assessment of power extracted from the two stages. Measurements of the flow through the blades would be difficult but valuable to check—for example, computational predictions of separation.
- experimental and numerical studies on selection of optimum number of blades. The ratio ${\theta}_{s}/{R}_{1}$ may be a relevant design parameter when compared to the selection of number of buckets in Pelton runners.
- experimental and numerical studies of dual-nozzle crossflow turbines. The general finding in the simulations that the first and second stages occupy less that ${180}^{\circ}$ suggests this possibility for reducing the size of the runner, improving the power density and runner loading, and reducing vibration.
- experimental and numerical studies on cavitation and its impact on the performance of efficient designs over a wide range of operating conditions. The only investigation to date of cavitation in crossflow turbines was for a low efficiency design.

## 6. Conclusions

- The design principle for achieving high efficiency is converting the head at the nozzle inlet into kinetic energy at the runner entry and matching the entry flow with the runner design. A two-dimensional analytical model developed by Adhikari and Wood [2] gives a simple analytic equation for the nozzle rear-wall shape, the condition for converting the head into kinetic energy, and the entry flow angle and the optimum operating speed for the runner design. The usefulness of these results was demonstrated by detailed computational simulations. The simulated runner speed for maximum efficiency was around $6\%$ higher than that from Equation (2) for the highest efficiency designs.
- Detailed investigation of the power extracted by each blade showed that the relative importance of the first or entry stage could vary significantly without a major impact on turbine performance. The second or exit stage could produce up to 38% of the power. This unique feature of crossflow turbines gives some flexibility in the runner design. For most runners that were studied, the total azimuthal extent of the two stages was less than ${180}^{\circ}$ suggesting that a double nozzle design could further increase the power density and cost effectiveness of crossflow turbines.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

CFD | Computational Fluid Dynamics |

RANS | Reynolds-Averaged Navier–Stokes Simulation |

3D | Three-dimensional |

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**Figure 1.**Schematic illustration of key geometrical parameters of crossflow turbine [2].

**Figure 2.**Comparison of CFD and experimental results for the power output of the 7 kW turbine at different flow rates and heads.

**Figure 3.**Water velocity vectors illustrating the flow separation on the blades at the first stage of the 7 kW turbine at ${\eta}_{max}=69\%$. Note that there is no flow separation on the second stage [5].

**Figure 6.**Contour plot of the magnitude of mean water velocity for the 0.53 kW turbine at maximum efficiency (H = 1.337 m, Q = 46 lps and N = 199.1 RPM). (

**a**) the original nozzle with a circular profile; and (

**b**) the new nozzle shape given by Equation (3).

**Figure 7.**Azimuthal variation of power extraction per blade in the 7 kW turbine at ${\eta}_{max}$ and ${\omega}_{max}\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}450$ RPM (Q = 105 lps and H = 10 m) [5].

**Figure 8.**Azimuthal variation of power extraction per blade in the 0.53 kW turbine at ${\eta}_{max}$ and ${\omega}_{max}=199.1$ RPM (Q = 46 lps and H = 1.337 m) [5].

**Figure 10.**Water velocity vectors illustrating the reduction in flow separation in the runner of the 7 kW turbine with the new nozzle and improved runner design at ${\eta}_{max}$ = 91%. $Q=105$ lps, $H=10$ m, and $N=500$ RPM. Note that there is a significant reduction in flow separation on the blades [5].

**Figure 11.**Comparison of torque production in the runner between the improved and the original runner with the new nozzle for the 7 kW turbine at ${\eta}_{max}$. Note that the original runner has ${N}_{b}$ = 20 and ${\beta}_{1b}={30}^{\circ}$, whereas the new runner has ${N}_{b}$ = 35 and ${\beta}_{1b}={39}^{\circ}$. For the purpose of comparison, the data are computed at each blade position and normalized with the torque for 35 blades. The first stage contributions for the original nozzle, the new nozzle with the original runner, and the new nozzle with improved runner are respectively 62%, 69%, and 73% [5].

**Table 1.**Summary of the design parameters used in the experimental studies. * indicates a value for maximum efficiency. Symbols are defined in Figure 1.

Source | $\mathit{\delta}$ | ${\mathit{\beta}}_{1\mathit{b}}$ | ${\mathit{\beta}}_{2\mathit{b}}$ | ${\mathit{R}}_{2}/{\mathit{R}}_{1}$ | ${\mathit{N}}_{\mathit{b}}$ | ${\mathit{\theta}}_{\mathit{s}}$ | $\mathit{\eta}$ |
---|---|---|---|---|---|---|---|

(deg) | (deg) | (deg) | (-) | (-) | (deg) | (%) | |

Macmore and Merryfield [7] | 16 | 30 | 90 | 0.66 | 20 | - | 68 |

Varga [8] | 16 | 39 | - | 0.66 | 30 | - | 77 |

Durali [9] | 16 | 30 | 90 | 0.68 | 24 | - | 76 |

Dakers and Martin [10] | 22 | 30 | 90 | 0.67 | 20 | 69 | 69 |

Johnson and White [11] | 16 | 39 | - | 0.68 | 18 | 60 | 80 |

Nakase et al. [12] | 15 | 39 | - | 0.68 | 26 | 90 | 82 |

Durgin and Fay [13] | 16 | 39 | - | 0.68 | 20 | 63 | 66 |

Khosrowpanah [14,15] | 16 | 39 | 90 | 0.68 | 15 | 58, 78, 90 * | 80 |

Horthsall [16] | 16 | - | - | 0.66 | 21 | - | 75 |

Ott and Chappell [17] | 16 | - | - | 0.68 | 20 | - | 79 |

Fiuzat and Akerker [18] | 20–24 * | 39 | 90 | 0.68 | 20 | 90 | 89 |

Desai [19] | 22 *–32 | 39 | 90 | 0.60–0.68 *–0.75 | 30 | 90 | 88 |

Totapally and Aziz [20] | 22 *–24 | 39 | 55 *–90 | 0.68 | 35 | 90 | 90 |

Design Parameter | 7 kW Turbine | 0.53 kW Turbine | Improved 7 kW Turbine | Improved 0.53 kW Turbine |
---|---|---|---|---|

Outer radius (${R}_{1}$), (mm) | 158 | 152.4 | 158 | 152.4 |

Inner radius (${R}_{2}$), (mm) | 105.86 | 103.63 | 105.86 | 103.63 |

Outer blade angle (${\beta}_{1b}$), (${}^{\circ}$) | 30 | 39 | 39 | 39 |

Inner blade angle (${\beta}_{2b}$), (${}^{\circ}$) | 90 | 90 | 90 | 90 |

Blade thickness (t), (mm) | 3 | 3.2 | 3 | 3.2 |

Number of blades (${N}_{b}$) | 20 | 30 | 35 | 35 |

Runner and nozzle width (W), (mm) | 150 | 101.6 | 94.34 | 101.6 |

Nozzle throat (${h}_{0}$), (mm) | 65 | 89 | 83 | 89 |

Nozzle entry arc (${\theta}_{s}$), (${}^{\circ}$) | 69 | 90 | 80 | 90 |

${\eta}_{max}$, (%) | 69 | 88 | 91 | 90 |

${\omega}_{max}$, (RPM) (Exp, CFD) | 450 | 199.1 | 500 | 199.1 |

${\omega}_{max}$ from Equation (2), (RPM) | 363 | 183 | 461 | 183 |

${\beta}_{1}$ from Equation (1), (${}^{\circ}$) | 37.7 | 41 | 41 | 41 |

${h}_{0}/\left({R}_{1}{\theta}_{s}\right)$ | 0.34 | 0.37 | 0.37 | 0.37 |

${\mathit{N}}_{\mathit{b}}$ | ${\mathit{\eta}}_{\mathit{max}}$ (%) |
---|---|

20 | 85.87 |

30 | 88.45 |

35 | 89.87 |

40 | 88.23 |

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**MDPI and ACS Style**

Adhikari, R.; Wood, D.
The Design of High Efficiency Crossflow Hydro Turbines: A Review and Extension. *Energies* **2018**, *11*, 267.
https://doi.org/10.3390/en11020267

**AMA Style**

Adhikari R, Wood D.
The Design of High Efficiency Crossflow Hydro Turbines: A Review and Extension. *Energies*. 2018; 11(2):267.
https://doi.org/10.3390/en11020267

**Chicago/Turabian Style**

Adhikari, Ram, and David Wood.
2018. "The Design of High Efficiency Crossflow Hydro Turbines: A Review and Extension" *Energies* 11, no. 2: 267.
https://doi.org/10.3390/en11020267