# Performance Investigation of the Immersed Depth Effects on a Water Wheel Using Experimental and Numerical Analyses

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Numerical Simulation Method

#### 2.1. Simulation Model

#### 2.2. Grid Division and Sensitivity Analysis

#### 2.3. Equation Discretization and Boundary Conditions

## 3. Reliability Verification

## 4. Results and Discussion

#### 4.1. Evaluation of Water Wheel Performance

#### 4.2. Analysis of the Flow Fields and Velocity Triangles

## 5. Conclusion and Future Work

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

λ | Tip-speed ratio |

${C}_{p}$ | Ratio of the energy extraction by water wheel to energy available in the water |

$\u2206d$ | Values between the upstream and downstream water depths |

${T}_{p}$ | Fluctuation amplitude ratio of water level |

$\rho $ | Water density |

$V{F}_{S}$ | Water volume fractions |

$\phi $ | The angle of a point at the top of the outside diameter of wheel in direction of rotation |

Vu | Tangential components of the absolute velocity |

Vr | Radial components of the absolute velocity |

## References

- Jones, Z. Domestic Electricity Generation Using Waterwheels on Moored Barge. Master’s Thesis, School of theBuilt Ennvironment, Heriot-Watt University, Edinburgh, UK, 2005. [Google Scholar]
- Choi, Y.; Yoon, H.; Inagaki, M.; Ooike, S.; Kim, Y.J.; Lee, Y.H. Performance improvement of a cross-flow hydro turbine by air layer effect. In IOP Conference Series: Earth and Environmental Science; IOP Publishing: Bristol, UK, 2010; p. 012030. [Google Scholar]
- Choi, Y.-D.; Lim, J.-I.; Kim, Y.-T.; Lee, Y.H. Performance and internal flow characteristics of a cross-flow hydro turbine by the shapes of nozzle and runner blade. J. Fluid Sci. Technol.
**2008**, 3, 398–409. [Google Scholar] [CrossRef] [Green Version] - Bartle, A. Hydropower potential and development activities. Energy Policy
**2002**, 30, 1231–1239. [Google Scholar] [CrossRef] - Zapata, S.; Castaneda, M.; Aristizabal, A.J.; Cherni, J.; Dyner, I. Assessing renewable energy policy integration cost, emissions and affordability the Argentine case. In Proceedings of the Decarbonization, Efficiency and Affordability: New Energy Markets in Latin America, 7th ELAEE/IAEE Latin American Conference, Buenos Aires, Argentina, 10–12 March 2019. [Google Scholar]
- Senior, J.; Wiemann, P.; Muller, G. The rotary hydraulic pressure machine for very low head hydropower sites. In Proceedings of the Hidroenergia Conference, Wroclaw, Poland, 23–26 May 2008; pp. 1–8. [Google Scholar]
- Murdock, H.E.; Gibb, D.; André, T.; Appavou, F.; Brown, A.; Epp, B.; Kondev, B.; McCrone, A.; Musolino, E.; Ranalder, L.; et al. Renewables 2019 Global Status Report. 2019. Available online: https://wedocs.unep.org/handle/20.500.11822/28496 (accessed on 22 December 2019).
- Pujol, T.; Montoro, L. High hydraulic performance in horizontal waterwheels. Renew. Energy
**2010**, 35, 2543–2551. [Google Scholar] [CrossRef] - Müller, G.; Kauppert, K. Performance characteristics of water wheels. J. Hydraul. Res.
**2004**, 42, 451–460. [Google Scholar] [CrossRef] - Turnock, S.R.; Muller, G.; Nicholls-Lee, R.F.; Denchfield, S.; Hindley, S.; Shelmerdine, R.; Stevens, S. Development of a floating tidal energy system suitable for use in shallow water. 2007. Available online: https://eprints.soton.ac.uk/48752/1/1055.pdf (accessed on 19 January 2020).
- Quaranta, E. Investigation and Optimization of the Performance of Gravity Water Wheels. Ph.D. Thesis, Politecnico di Torino, Torino, Italy, 2017. under review. [Google Scholar]
- Quaranta, E.; Revelli, R. Optimization of breastshot water wheels performance using different inflow configurations. Renew. Energy
**2016**, 97, 243–251. [Google Scholar] [CrossRef] - Quaranta, E.; Revelli, R. Output power and power losses estimation for an overshot water wheel. Renew. Energy
**2015**, 83, 979–987. [Google Scholar] [CrossRef] - Quaranta, E.; Revelli, R. Performance characteristics, power losses and mechanical power estimation for a breastshot water wheel. Energy
**2015**, 87, 315–325. [Google Scholar] [CrossRef] - Quaranta, E.; Müller, G. Sagebien and Zuppinger water wheels for very low head hydropower applications. J. Hydraul. Res.
**2018**, 56, 526–536. [Google Scholar] [CrossRef] [Green Version] - Quaranta, E.; Revelli, R. CFD simulations to optimize the blade design of water wheels. Drink. Water Eng. Sci.
**2017**, 10, 27–32. [Google Scholar] [CrossRef] [Green Version] - Quaranta, E.; Revelli, R. Hydraulic behavior and performance of breastshot water wheels for different numbers of blades. J. Hydraul. Eng. ASCE
**2016**, 143, 04016072. [Google Scholar] [CrossRef] - Jasa, L.; Priyadi, A.; Purnomo, M.H. Experimental Investigation of Micro-Hydro Waterwheel Models to Determine Optimal Efficiency. Appl. Mech. Mater.
**2015**, 776, 413–418. [Google Scholar] [CrossRef] - Nishi, Y.; Inagaki, T.; Li, Y.; Omiya, R.; Fukutomi, J. Study on an undershot cross-flow water turbine. J. Therm. Sci.
**2014**, 23, 239–245. [Google Scholar] [CrossRef] - Nguyen, M.H.; Jeong, H.; Jhang, S.S.; Kim, B.G.; Yang, C. A parametric study about blade shapes and blade numbers of water wheel type tidal turbine by numerical method. J. Korean Soc. Mar. Environ. Saf.
**2016**, 22, 296–303. [Google Scholar] [CrossRef] - Nguyen, M.H.; Jeong, H.; Yang, C. A study on flow fields and performance of water wheel turbine using experimental and numerical analyses. Sci. China Technol. Sci.
**2018**, 61, 464–474. [Google Scholar] [CrossRef] - Adanta, D.; Arifianto, S.A.; Nasution, S.B. Effect of Blades Number on Undershot Waterwheel Performance with Variable Inlet Velocity. In Proceedings of the 2018 4th International Conference on Science and Technology (ICST), Yogyakarta, Indonesia, 7–8 August 2018; pp. 1–6. [Google Scholar]
- Nishi, Y.; Inagaki, T.; Li, Y.; Omiya, R.; Hatano, K. Research on the flow field of undershot cross-flow water turbines using experiments and numerical analysis. In Proceedings of the IOP Conference Series: Earth and Environmental Science, Jakarta, Indonesia, 23–24 January 2014; p. 062006. [Google Scholar]
- Tevata, A.; Inprasit, C. The effect of paddle number and immersed radius ratio on water wheel performance. Energy Procedia
**2011**, 9, 359–365. [Google Scholar] [CrossRef] [Green Version] - Castro-García, M.; Rojas-Sola, J.I. Technical and functional analysis of Albolafia waterwheel (Cordoba, Spain): 3D modeling, computational-fluid dynamics simulation and finite-element analysis. Energy Conv. Manag.
**2015**, 92, 207–214. [Google Scholar] [CrossRef] - Vidali, C.; Fontan, S.; Quaranta, E.; Cavagnero, P.; Revelli, R. Experimental and dimensional analysis of a breastshot water wheel. J. Hydraul. Res.
**2016**, 54, 473–479. [Google Scholar] [CrossRef] - Nguyen, M.H.; Kim, J.H.; Kim, B.K.; Yang, C. A Comparison of Performance of Six and Twelve-Blade Vane Tidal Turbines between Single and Double Blade-row Types. Korean Soc. Fluid Mech.
**2015**, 18, 51–58. [Google Scholar] - Muller, G. The effect of using upper shroud on the performance of a breashoot water wheel. J. Phys. Conf. Ser.
**2019**, 012269. [Google Scholar] - Masud, I.; Yusuke, S.; Suwa, Y. Performance prediction of zero head turbine at different water levels. In Proceedings of the IOP Conference Series: Earth and Environmental Science, Bogor, Indonesia, 10–11 September 2019; p. 012048. [Google Scholar]
- Paudel, S.; Linton, N.; Zanke, U.C.; Saenger, N. Experimental investigation on the effect of channel width on flexible rubber blade water wheel performance. Renew. Energy
**2013**, 52, 1–7. [Google Scholar] [CrossRef] - Butera, I.; Fontan, S.; Poggi, D.; Quaranta, E.; Revelli, R. Experimental Analysis of Effect of Canal Geometry and Water Levels on Rotary Hydrostatic Pressure Machine. J. Hydraul. Eng. ASCE
**2020**, 146, 04019071. [Google Scholar] [CrossRef] - Cleynen, O.; Kerikous, E.; Hoerner, S.; Thévenin, D. Characterization of the performance of a free-stream water wheel using computational fluid dynamics. Energy
**2018**, 165, 1392–1400. [Google Scholar] [CrossRef] - Batten, W.M.J.; Weichbrodt, F.; Muller, G.U.; Hadler, J.; Semlow, C.; Hochbaum, M.; Dimke, S.; Frohle, P. Design and stability of a floating free stream energy converter. In Proceedings of the 34th World Congress of the International Association for Hydro-Environment Research and Engineering: 33rd Hydrology and Water Resources Symposium and 10th Conference on Hydraulics in Water Engineering, Brisbane, Australia, 26 June–1 July 2011; p. 2372. [Google Scholar]
- Wulandari, R.; Mizar, M.A.; Andoko. Optimization design of Goose-Leg waterwheel next-G to extract energy of free water flow. AIP Conf. Proc.
**2016**, 030068. [Google Scholar] - Müller, G.; Jenkins, R.; Batten, W. Potential, performance limits and environmental effects of floating water mills. River Flow
**2010**, 2010, 707–712. [Google Scholar] - Muller, G.; Denchfield, S.; Marth, R.; Shelmerdine, B. Stream wheels for applications in shallow and deep water. In Proceedings of the Congress-International Association for Hydraulic Research, Venice, Italy, 1–6 July 2007; p. 707. [Google Scholar]
- Quaranta, E. Stream water wheels as renewable energy supply in flowing water: Theoretical considerations, performance assessment and design recommendations. Energy Sustain. Dev.
**2018**, 45, 96–109. [Google Scholar] [CrossRef] - Kumar, A.; Saini, R. Performance analysis of a Savonius hydrokinetic turbine having twisted blades. Renew. Energy
**2017**, 108, 502–522. [Google Scholar] - Nakajima, M.; Iio, S.; Ikeda, T. Performance of Savonius rotor for environmentally friendly hydraulic turbine. J. Fluid Sci. Technol.
**2008**, 3, 420–429. [Google Scholar] [CrossRef] [Green Version] - Sule, L.; Rompas, P. Performance of Savonius Blade Waterwheel with Variation of Blade Number. In Proceedings of the IOP Conference Series: Materials Science and Engineering, Nanjing, China, 17–19 August 2018; p. 012073. [Google Scholar]
- Yaakob, O.; Ismail, M.A.; Ahmed, Y.M. Parametric Study for Savonius Vertical Axis Marine Current Turbine using CFD Simulation. In Proceedings of the 7th International Conference on Renewable Energy Sources (RES’13), Kuala Lumpur, Malaysia, 2–4 April 2013; pp. 200–205. [Google Scholar]
- Golecha, K.; Eldho, T.; Prabhu, S. Influence of the deflector plate on the performance of modified Savonius water turbine. Appl. Energy
**2011**, 88, 3207–3217. [Google Scholar] [CrossRef] - Hassanzadeh, A.R.; Ahmed, Y.M.; Ismail1c, M.A. Numerical simulation for unsteady flow over marine current turbine rotors. Wind Struct.
**2016**, 23, 301–311. [Google Scholar] [CrossRef] - Adanta, D.; Budiarso, W.; Siswantara, A.I. Assessment of turbulence modelling for numerical simulations into pico hydro turbine. J. Adv. Res. Fluid Mech. Therm. Sci.
**2018**, 46, 21–31. [Google Scholar] - Kodirov, D.; Tursunov, O. Calculation of Water Wheel Design Parameters for Micro Hydroelectric Power Station. E3S Web Conf.
**2019**, 97, 05042. [Google Scholar] [CrossRef] - Akinyemi, O.S.; Liu, Y. CFD modeling and simulation of a hydropower system in generating clean electricity from water flow. Int. J. Energy Environ. Eng.
**2015**, 6, 357–366. [Google Scholar] [CrossRef] [Green Version] - Zaman, A.; Khan, T. Design of a water wheel for a low head micro hydropower system. J. Basic Sci. Technol.
**2012**, 1, 1–6. [Google Scholar] - Akinyemi, O.S.; Chambers, T.L.; Liu, Y. Evaluation of the power generation capacity of hydrokinetic generator device using computational analysis and hydrodynamic similitude. J. Power Energy Eng.
**2015**, 3, 71. [Google Scholar] [CrossRef] [Green Version] - Senior, J.A. Hydrostatic Pressure Converters for the Exploitation of Very Low Head Hydropower Potential. Ph.D. Thesis, University of Southampton, Southampton, UK, 2009. [Google Scholar]
- Denny, M. The efficiency of overshot and undershot waterwheels. Eur. J. Phys.
**2003**, 25, 193. [Google Scholar] [CrossRef] [Green Version] - Al Sam, A. Water Wheel CFD Simulations. 2010. Available online: http://lup.lub.lu.se/student-papers/record/1698088 (accessed on 22 December 2019).
- Nasir Mehmood, Z.L.; Khan, J. Diffuser augmented horizontal axis tidal current turbines. Res. J. Appl. Sci. Eng. Technol.
**2012**, 4, 3522–3532. [Google Scholar] - Acharya, N.; Kim, C.G.; Thapa, B.; Lee, Y.H. Numerical analysis and performance enhancement of a cross-flow hydro turbine. Renew. Energy
**2015**, 80, 819–826. [Google Scholar] [CrossRef] - Zhang, Y.; Li, C.; Xu, Y.; Tang, Q.; Zheng, Y.; Liu, H.; Fernandez-Rodriguez, E. Study on Propellers Distribution and Flow Field in the Oxidation Ditch Based on Two-Phase CFD Model. Water
**2019**, 11, 2506. [Google Scholar] [CrossRef] [Green Version] - Zhang, Y.; Xu, Y.; Zheng, Y.; Fernandez-Rodriguez, E.; Sun, A.; Yang, C.; Wang, J. Multiobjective Optimization Design and Experimental Investigation on the Axial Flow Pump with Orthogonal Test Approach. Complexity
**2019**, 2019. [Google Scholar] [CrossRef] [Green Version]

**Figure 12.**Velocity vectors at circumferential angle $\phi =135\xb0$. (

**a**) The immersed depth of 0.6 m; (

**b**) the immersed depth of 0.8 m; (

**c**) the immersed depth of 1.0 m; (

**d**) the immersed depth of 1.2 m.

**Figure 13.**Velocity vectors at circumferential angle $\phi =201\xb0$. (

**a**) The immersed depth of 0.6 m; (

**b**) the immersed depth of 0.8 m; (

**c**) the immersed depth of 1.0 m; (

**d**) the immersed depth of 1.2 m.

Inlet Velocity (m/s) | Numbers of Blade | Rotational Speeds (r/min) | Output in Experiments (kW) | Output in Numerical Simulation (kW) | Error (%) |
---|---|---|---|---|---|

3.0 | 8 | 2 | 10.90 | 11.34 | 4.1 |

3 | 14.09 | 14.61 | 3.7 | ||

3.92 (Optimal speeds) | 14.52 | 15.07 | 3.6 | ||

5 | 9.66 | 10.12 | 4.7 | ||

6 | 5.43 | 5.62 | 3.4 |

Immersed Depth (m) | Immersed Radius Ratio | Blockage Ratio | X |
---|---|---|---|

0.6 | $41.37\%$ | $26.32\%$ | $<1$ |

0.8 | $55.17\%$ | $35.09\%$ | $<1$ |

1.0 | $68.96\%$ | $43.86\%$ | $\approx 1$ |

1.2 | $82.76\%$ | $52.63\%$ | $>1$ |

© 2020 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 (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Zhao, M.; Zheng, Y.; Yang, C.; Zhang, Y.; Tang, Q.
Performance Investigation of the Immersed Depth Effects on a Water Wheel Using Experimental and Numerical Analyses. *Water* **2020**, *12*, 982.
https://doi.org/10.3390/w12040982

**AMA Style**

Zhao M, Zheng Y, Yang C, Zhang Y, Tang Q.
Performance Investigation of the Immersed Depth Effects on a Water Wheel Using Experimental and Numerical Analyses. *Water*. 2020; 12(4):982.
https://doi.org/10.3390/w12040982

**Chicago/Turabian Style**

Zhao, Mengshang, Yuan Zheng, Chunxia Yang, Yuquan Zhang, and Qinghong Tang.
2020. "Performance Investigation of the Immersed Depth Effects on a Water Wheel Using Experimental and Numerical Analyses" *Water* 12, no. 4: 982.
https://doi.org/10.3390/w12040982