# Design and Parametric Optimization of the High-Speed Pico Waterwheel for Rural Electrification of Pakistan

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## Abstract

**:**

## 1. Introduction

## 2. Design Characteristics of the Waterwheel

## 3. Methodology

#### 3.1. Experimental Method

#### 3.1.1. Design Parameters

_{d}is the drag coefficient for the blade geometry, ρ is the density of water, A

_{w}is the swept area of the blade (the area that is immersed in the water) and V

_{r}is the relative velocity of the blade to the flowing water. This equation is valid when the Reynolds number is greater than 3000 for the flow i.e., (R

_{e}> 3000). The drag coefficients for the three chosen blade shapes, which were calculated from the numerical results and validated with the available literature of immersed bodies as described by Pritchard et al. [29], are given in Table 2.

_{y}is the yield strength and n is the factor of safety.

_{w}is the swept area of the blade (projected area of the blade immersed in water sheet) and V is the velocity of the flowing water.

#### 3.1.2. Analytical Model

^{8}N/m

^{2}was conducted before fabrication of the turbine. The data for the static analysis was obtained from the analytical model. The waterwheel was fabricated with mild-steel material and the design parameters are presented in Table 2. The data is dependent on the irrigation channel dimensions and the available flow in that channel, which is considered in this research to utilize the maximum inflow of hydropower. The blade width is considered equal to the width of the water channel by maintaining a side clearance that allows for smooth rotation of the waterwheel. An analytical model was created using the equations provided in Section 4.2 including these parameters. The other parameters were obtained by instruments including a tachometer, a non-contacting velocity sensor and the dimensions of the irrigation channel. The fabricated model of waterwheel installed at the site is shown in Figure 3a.

#### 3.1.3. Test Facility

^{3}/s, respectively. The flowrate through the turbine swept area was recorded as 0.26 m

^{3}/s. The waterwheel was installed in such a way that the blades were fully submerged in water (submerged by 4 inches). An ONOSOKKI MP-981 sensor was used to measure the angular velocity of the rotor. The digital indicator used to record the RPM value was a SENSTECH DI-130 indicator. An eddy current dynamometer with precision range of less than ±0.001% was used to measure the torque of the waterwheel when it reached full speed condition. The schematic diagram of the system is given in Figure 4.

#### 3.1.4. Test Procedure

#### 3.2. Computational Fluid Dynamics (CFD) Method

#### 3.2.1. Numerical Design Model

#### 3.2.2. Blade Profiles

#### 3.2.3. Mesh Setup and Boundary Conditions

#### 3.2.4. Simulation Setup

^{2}. The volume of fluid model (VOF) is applied with an open channel flow as an explicit formulation for the straight channel case studies. The courant number adopted by default was 0.25, whereas for the inclined channel case studies, the volume of fluid model was applied with an open channel flow as an implicit formulation and implicit body force. The number of Eulerian phases were selected as two for both the straight channel and inclined channel cases. Two materials were selected for the two phases (the first phase was taken as the primary phase with air as the fluid, while the second phase was taken as a secondary phase with liquid-water at 25 °C as the fluid). The rotating domain was given an angular velocity according to the desired case under cell zone conditions. The solution method adopted was the Pressure-Velocity Coupling PISO scheme with a spatial discretization PRESTO scheme. Two different types of schemes were used for the discretization of the convective term in the equation for transport of the volume fraction. For the straight channel case studies, Compressive Interface Capturing Scheme for Arbitrary Meshes (CICSAM) was applied, whereas for the inclined channel case studies, the Modified High-Resolution Interface Capturing Scheme (Modified-HRIC) was applied. The turbulent intensity was taken as 5%, and the turbulent viscosity ratio was set to 10. The time step was chosen as 2 × 10

^{−5}s for the straight channel explicit scheme, whereas time step was set to 2 × 10

^{−3}s for the inclined channel implicit schemes. The maximum iterations per time step was set at 20, and a step function was used to identify volume fractions of water and air in the computational domain. The step function was defined as VFs = Step (d

_{w}− y), where dw is the water depth and y is the height parameter for the computational domain. According to this expression, when y ≤ d

_{w}, the volume fraction is water but when y > d

_{w}, the volume fraction is air in the domain. The results obtained for the numerical method were compared with the results of experimental method.

## 4. Results and Discussions

#### 4.1. Preliminary Static Analysis

^{8}N/m

^{2}, which is substantially higher than the highest von Mises stresses. Therefore, it is concluded that the material of the turbine is safe and can be used for further experimental and numerical analysis.

#### 4.2. Mesh Criterion

^{6}elements shows that the average torque of the turbine remains constant above this number of mesh elements. Therefore, 3.7 × 10

^{6}elements was chosen for all the turbines to perform testing in this research study. Moreover, the results show that the turbine attains a stable state at 4.6 s when it completes 11 revolutions. The flow and all monitoring parameters become stable when the waterwheel completes 11 revolutions; hence, all the parameters were exported above the stable state. The outer domain and 3-D refined meshing of the rotating domain are shown in Figure 9a,b, respectively. The mesh is refined by increasing the number of nodes near the target locations in the body to achieve high accuracy output results. However, this process increases the required computational power; therefore, to perform a mesh independent case study is a feasible solution to save time and computational power. The mesh is refined near the geometry of the blades in the outer domain meshing of the turbine, and similarly, the same is the case for the area near the turbine in the 3-D rotating fluid domain; the purpose of this is to achieve high accuracy in results at the target locations.

#### 4.3. Immersed Depth Variations

#### 4.4. Variations in Water Conduit Angle (Changing Angle of Attack)

#### 4.5. Test at Different Tip Speed Ratios (TSR)

_{p}) was calculated by varying the angular velocity; the variations of C

_{p}against TSR are shown in Figure 12. The results show that C

_{p}increases with increasing TSR values reaching its highest value at the optimum point and then starts decreasing again. The same trend was observed for all the three blade profiles. The highest values of C

_{p}are 0.88, 0.76 and 0.39 for the C-shape, V-shape and straight blade profiles, respectively. The results obtained from the simulations show that torque increases as angular velocity decreases, but the product of both, i.e., power output, is the highest for the C-shape profile compared with the V-shape and straight blade profiles. Once again, on the basis of the TSR analysis against performance parameters, it is concluded that the C-shape blade profile is the most suitable blade profile for the design of waterwheels.

#### 4.6. Results Verification and Validation

#### 4.7. Visualization of Contours

#### 4.8. Maximum Power Output on an Inclined Channel

#### 4.9. Overall Efficiency of the System

_{out}is the power output of the generator and can be calculated by using Equation (13), v

_{g}is the output voltage generator, and i

_{g}is the output current of the generator under full load condition.

## 5. Conclusions

- The experimental and numerical analysis results are closely related with each other, with small errors where the maximum error is recorded as 5%. In some simulations the result shows small deviations up to 2% from the experimental values, whereas in other, cases it shows deviation up to 5%.
- The waterwheel can be used as a high-speed wheel without losing the power generation capacity if it is efficiently design with a good blade profile geometry.
- The mass of the waterwheel plays an important role in its design; the critical mass for the wheel can be identified.
- The C-shape blade profile is the best geometry profile compared with the V-shape blade and straight blade. Turbines with the straight blade had the lowest performance in all the case studies.
- The downstream fluid exerts a backward force on the blades that affects the overall performance of the wheel. When the water wheel is installed on inclined channels, the performance characteristics of the waterwheel increase because the fluid on the downstream side falls down with the force of gravity and it has no effect on the blade. Therefore, the net force on the blade increases.
- The critical angle for the C-Shape blade turbine on the inclined channel is identified as θ = 45°. At an inclination angle of θ = 45°, when the C-shape blade becomes immersed in the water, it becomes parallel to the flowing water and thus produces less turbulence and smaller impact losses.
- Pico-scale high-speed waterwheels are the best solution for rural electrification because they have low fabrication, maintenance and per unit energy production costs. The payback period of such systems is also small.
- In the experimental setup the velocity of the stream was maintained at 4.1 m/s. When the velocity of the water was variated to the turbine, poor performance was noted below 3 m/s, and performance was increased by increasing velocity above 3 m/s. It is concluded that high-speed waterwheels operate most efficiently on streams that have a high flow velocity (greater than 3 m/s).
- The performance of the waterwheel increases when the water stream is directed as a jet towards the wheel.
- Increasing head improves the performance of the waterwheel, and it operates more efficiently on inclined channels compared with straight channels due to the datum head which increases on inclined channels.
- The waterwheel shows excellent performance characteristics when the blades are fully submerged in the stream, with a design aspect ratio of the wheel of 0.372.
- The overall efficiency of the turbine with the C-shape blade profile was calculated as 66.42%, which is reasonable for the generation of electricity in remote and rural areas.

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Quaranta, E.; Revelli, R. Output power and power losses estimation for an overshot water wheel. Renew. Energy
**2015**, 83, 979–987. [Google Scholar] [CrossRef] - Ahmad, S.; Abdullah, M.; Kanwal, A.; Tahir, Z.U.R.; Bin Saeed, U.; Manzoor, F.; Atif, M.; Abbas, S. Offshore wind resource assessment using reanalysis data. Wind Eng.
**2022**. [Google Scholar] [CrossRef] - Kanwal, A.; Tahir, Z.U.R.; Asim, M.; Hayat, N.; Farooq, M.; Abdullah, M.; Azhar, M. Evaluation of Reanalysis and Analysis Datasets against Measured Wind Data for Wind Resource Assessment. Energy Environ.
**2022**. [Google Scholar] [CrossRef] - Tahir, Z.U.R.; Asim, M.; Azhar, M.; Moeenuddin, G.; Farooq, M. Correcting solar radiation from reanalysis and analysis datasets with systematic and seasonal variations. Case Stud. Therm. Eng.
**2021**, 25, 100933. [Google Scholar] [CrossRef] - Yelguntwar, P.; Bhange, P.; Lilhare, Y.; Bahadure, A. Design fabrication & testing of a waterwheel for power generation in an open channel flow. Int. J. Res. Eng. Adv. Technol.
**2014**, 1, 47–51. [Google Scholar] - Reynolds, T.S. Stronger Than a Hundred Men: A History of the Vertical Water Wheel; JHU Press: Baltimore, MD, USA, 1983. [Google Scholar]
- Williamson, S.; Stark, B.; Booker, J. Low head pico hydro turbine selection using a multi-criteria analysis. Renew. Energy
**2014**, 61, 43–50. [Google Scholar] [CrossRef] - Ahmed, S.; Mahmood, A.; Hasan, A.; Sidhu, G.A.S.; Butt, M.F.U. A comparative review of China, India and Pakistan renewable energy sectors and sharing opportunities. enew. Sustain. Energy Rev.
**2016**, 57, 216–225. [Google Scholar] [CrossRef] - Cook, P. Infrastructure, rural electrification and development. Energy Sustain. Dev.
**2011**, 15, 304–313. [Google Scholar] [CrossRef] - Yah, N.F.; Oumer, A.N.; Idris, M.S. Small scale hydro-power as a source of renewable energy in Malaysia: A review. Renew. Sustain. Energy Rev.
**2017**, 72, 228–239. [Google Scholar] [CrossRef] [Green Version] - Powell, D.; Ebrahimi, A.; Nourbakhsh, S.; Meshkahaldini, M.; Bilton, A. Design of pico-hydro turbine generator systems for self-powered electrochemical water disinfection devices. Renew. Energy
**2018**, 123, 590–602. [Google Scholar] [CrossRef] - Khan, F.U.; Ahmed, A.; Jadoon, U.K.; Haider, F. Modeling, simulation and fabrication of an undershot floating waterwheel. J. Eng. Appl. Sci.
**2015**, 34, 55–69. [Google Scholar] - Hwang, I.S.; Lee, Y.H.; Kim, S.J. Optimization of cycloidal water turbine and the performance improvement by individual blade control. Appl. Energy
**2009**, 86, 1532–1540. [Google Scholar] [CrossRef] - Muller, G.; Wolter, C. The breastshot waterwheel: Design and model tests. ICE Proc.-Eng. Sustain.
**2004**, 157, 203–211. [Google Scholar] [CrossRef] - Jones, Z. Domestic Electricity Generation Using Waterwheels on Moored Barge. Mater’s Thesis, School of the Built Ennvironment, Heriot-Watt University, Edinburgh, Scotland, 2005. [Google Scholar]
- Denny, M. The efficiency of overshot and undershot waterwheels. Eur. J. Phys.
**2003**, 25, 193. [Google Scholar] [CrossRef] [Green Version] - Muller, G.; Denchfield, S.; Marth, R.; Shelmerdine, B. Stream wheels for applications in shallow and deep water. Proc. Congr.-Int. Assoc. Hydraul. Res.
**2007**, 32, 707. [Google Scholar] - Yassi, Y. Experimental study of a high speed micro waterwheel. Iran. J. Mech. Eng.
**2013**, 14, 34. [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] - Paudel, S.; Saenger, N. Effect of channel geometry on the performance of the Dethridge water wheel. Renew. Energy
**2018**, 115, 175–182. [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] - Nigussie, T.; Engeda, A.; Dribssa, E. Design, Modeling, and CFD Analysis of a Micro Hydro Pelton Turbine Runner: For the Case of Selected Site in Ethiopia. Int. J. Rotating Mach.
**2017**, 2017, 3030217. [Google Scholar] [CrossRef] [Green Version] - 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] - Quaranta, E.; Revelli, R. Gravity water wheels as a micro hydropower energy source: A review based on historic data, design methods, efficiencies and modern optimizations. Renew. Sustain. Energy Rev.
**2018**, 97, 414–427. [Google Scholar] [CrossRef] - Pujol, T.; Vashisht, A.; Ricart, J.; Culubret, D.; Velayos, J. Hydraulic efficiency of horizontal waterwheels: Laboratory data and CFD study for upgrading a western Himalayan watermill. Renew. Energy
**2015**, 83, 576–586. [Google Scholar] [CrossRef] - Ahmad, M.; Ghani, U.; Anjum, N.; Pasha, G.A.; Ullah, M.K.; Ahmed, A. Investigating the flow hydrodynamics in a compound channel with layered vegetated floodplains. Civ. Eng. J.
**2020**, 6, 860–876. [Google Scholar] [CrossRef] - Cornelis, S. Parametric Study of the Performance of an Impulse-Type Turbine with CFD. 2016. Available online: http://hdl.handle.net/10256/13242 (accessed on 25 April 2022).
- Shannon, R. Water Wheel Engineering. In Proceedings of the Sixth International Permaculture Conference, Perth, Australia, 28 September–1 October 1996. [Google Scholar]
- Pritchard, P.J.; Mitchell, J.W. Fox and McDonald’s Introduction to Fluid Mechanics; Wiley: Hoboken, NJ, USA, 2016. [Google Scholar]
- Hamed, H.F.A.; Kassem, A.M.; Ali, M.E.M. Design and modeling of hydro matrix power wheels contain nine wheels by using Matlab simulink. In Proceedings of the 2017 Nineteenth International Middle East Power Systems Conference (MEPCON), Cairo, Egypt, 19–21 December 2017; IEEE: Piscataway, NJ, USA, 2017. [Google Scholar]
- Yah, N.F.; Idris, M.S.; Oumer, A.N. Numerical investigation on effect of immersed blade depth on the performance of undershot water turbines. MATEC Web Conf. EDP Sci.
**2016**, 74, 00035. [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] - Budynas, R.G.; Shigley, J.E. Shigley’s Mechanical Engineering Design; McGraw-Hill: New York, NY, USA, 2011. [Google Scholar]
- Nasir Mehmood, Z.L.; Khan, J. Diffuser augmented horizontal axis tidal current turbines. Res. J. Appl. Sci. Eng. Technol.
**2021**, 4, 3522–3532. [Google Scholar] - 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] - Yamini, O.A.; Mousavi, S.H.; Kavianpour, M.R.; Ghaleh, R.S. Hydrodynamic performance and cavitation analysis in bottom outlets of dam using CFD modelling. Adv. Civ. Eng.
**2021**, 2021, 5529792. [Google Scholar] [CrossRef]

**Figure 5.**Three different shapes of blades: (

**a**) V-Shape profile, (

**b**) Straight blade profile, and (

**c**) C-Shape profile.

**Figure 10.**Variations with three blade profiles of immersed depth against (

**a**) average force acting on three blade profiles, (

**b**) average torque, (

**c**) power output, and (

**d**) efficiency of the turbine.

**Figure 11.**Variations of angle of water conduit against (

**a**) average torque and power output for C-shape blade, and (

**b**) efficiency of the C-Shape blade turbine on inclined channels.

**Figure 13.**Verification and validation results of CFD and experimental methods for (

**a**) average force acting on the C-shape blade profile, (

**b**) average torque, (

**c**) power output, and (

**d**) efficiency of the turbine.

**Figure 14.**(

**a**) Velocity contours of the C-shape blade profile on a straight channel. (

**b**) Pressure contours of the C-shape blade profile on a straight channel. (

**c**) Volume fraction contours of the C-shape blade profile on a straight channel.

**Figure 15.**(

**a**) Velocity contours of the C-shape blade profile on a θ = 45° inclined channel. (

**b**) Pressure contours of the C-shape blade profile on a θ = 45° inclined channel. (

**c**) Volume fraction contours of the C-shape blade profile on a θ = 45° inclined channel.

**Figure 16.**(

**a**) Blade entering the water on an inclined channel of θ = 45°. (

**b**) Demonstration of the blade tip making an angle φ with the flowing water.

Parameter | Value |
---|---|

Irrigation channel width (mm) | 915 |

Side clearance of irrigation channel (mm) | 152.5 |

Bottom clearance with the channel bed (mm) | 101.6 |

Thickness of the water sheet in the channel (mm) | 203.2 |

Volume flow rate of the channel (m^{3}/s) Volume flow rate through the waterwheel (m ^{3}/s) | 0.77 0.26 |

Dynamic viscosity of water µ (N s/m^{2}) Reynolds number for flow R _{e} | 1.79 × 10^{−5}470 × 10 ^{5} |

Parameters | Value |
---|---|

Rotor diameter (mm) | 546 |

Rotor width (mm) | 611.5 |

Blade dimensions (mm) (length × width × thickness) | 600 × 101.6 × 10 |

Number of blades immersed in water | 4 |

Number of blades installed on the rim | 15 |

Upstream velocity of water V1 (m/s) Downstream velocity of water V2 (m/s) | 4.1 3.5 |

Shaft diameter (mm) RPM of the Rotor Yield strength Sy (N/m ^{2)} Bending moment along Y-Axis M _{y} (N-m) Bending moment along Z-Axis M _{z} (N-m) Factor of safety (n) Drive gear number of teeth Driven gear number of teeth | 25 144 3.51 × 10 ^{8} 116.32 66.386 3 55 13 |

Blade shape used for CFD simulations | C-shape, V Shape, Straight Blade |

Blade shapes used for experimental analysis | C-shape |

Drag coefficients, C-shape blade | 2.3 |

V-shape blade | 2.2 |

Straight blade C-shape blade exposed on | 1.2 1.3 |

Back side of the flow |

Type | Head (m) | Max. Flow Rate (m^{3}/s) | Max. Efficiency (%) | Cost (€/kW) | Payback Time (Years) |
---|---|---|---|---|---|

Overshot wheels | 3−6 | 0.2 | 80−85 | 3900–4300 | 7.5–8.5 |

Breastshot wheels | 1−4 | 0.6−1 | 70−85 | 4000–7000 | 8–12 |

Undershot wheels | ≤1.5 | 1 | 70−85 | 6900–8700 | 12–17 |

Archimedes screw | 1−6 | 8 | 80−85 | 7400–7800 | 14.4–15.4 |

Proposed Model | 1–1.5 | 0.7–1.5 | 79.227 | 1000–1100 | 2.5–3 |

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## Share and Cite

**MDPI and ACS Style**

Asim, M.; Muhammad, S.; Amjad, M.; Abdullah, M.; Mujtaba, M.A.; Kalam, M.A.; Mousa, M.; Soudagar, M.E.M.
Design and Parametric Optimization of the High-Speed Pico Waterwheel for Rural Electrification of Pakistan. *Sustainability* **2022**, *14*, 6930.
https://doi.org/10.3390/su14116930

**AMA Style**

Asim M, Muhammad S, Amjad M, Abdullah M, Mujtaba MA, Kalam MA, Mousa M, Soudagar MEM.
Design and Parametric Optimization of the High-Speed Pico Waterwheel for Rural Electrification of Pakistan. *Sustainability*. 2022; 14(11):6930.
https://doi.org/10.3390/su14116930

**Chicago/Turabian Style**

Asim, Muhammad, Shoaib Muhammad, Muhammad Amjad, Muhammad Abdullah, M. A. Mujtaba, M. A. Kalam, Mohamed Mousa, and Manzoore Elahi M. Soudagar.
2022. "Design and Parametric Optimization of the High-Speed Pico Waterwheel for Rural Electrification of Pakistan" *Sustainability* 14, no. 11: 6930.
https://doi.org/10.3390/su14116930