Experimental and Numerical Analysis of the Clearance Effects between Blades and Hub in a Water Wheel Used for Power Generation
2. Mathematical Model and Entropy Production Theory
2.1. Governing Equation
2.2. The VOF Method
2.3. Standard k-ε Turbulence Model
2.4. Entropy Production Theory
3. Simulation Setup and Experimental Validation
3.1. Computation Domain and Boundary Conditions
- Inlet boundary: the water inlet boundary is set as the velocity inlet. The single variable method is adopted in that the inlet of water flow was set at 4 m/s to simulate the ultra-low head site condition. The direction of the inlet velocity is perpendicular to the inlet, and the turbulence intensity is set to a medium value of 5%. Considering that the water and air interface should be separated, the free surface level is set to the same height as the axis of rotation.
- Outlet boundary: the outlet of water flow is set as the pressure outlet, which value is the same as atmospheric pressure.
- Wall boundary: a no-slip wall is imposed on all other walls except the top of the area, which is set for symmetry .
- During the calculation process, the influence of gravity is considered. The unsteady calculation method is used to simulate the gas–liquid two-phase, in which the sliding grid is used in the rotation field to ensure that the wheel rotates at 4 rpm.
3.2. Numerical Method
3.3. Grid Verification and Validation of Results
4. Performance and Flow Characteristics of Water Wheels
4.1. Water Wheels Performance and Power Fluctuation
4.2. Analysis of Flow Fields
4.3. Energy Dissipation Analysis and Coupling Mechanism of Vorticity-Pressure
5. Characteristics and Distribution of Entropy Production
5.1. Distributions of EPR of Water Wheels
5.2. Distributions of EPWS of Water Wheels
- The numerical simulation and experimental results represent a relatively good agreement, with a maximum error of 3.5%.
- The torque of the water wheel has periodic transformation within a cycle of rotation, the maximum torque is reached at approximately 70.5° per period. Under the same working conditions, the performance of water wheels can be elevated by 8.7% by setting appropriate clearance.
- It was found that the average difference in water level is the highest in the water wheel with the 86 mm clearance configuration, and its fluctuation amplitude is the gentlest. The water wheels with 20 mm clearance and 120 mm clearance have a slight difference in the average difference in water level but the efficiency of maximum clearance (120 mm) is greater than that of minimum clearance (20 mm). The water wheel with optimal clearance can reduce air intruding into the water and attenuate the complexity of the water flow, potentially enhancing the performance of water wheels.
- It proved that the setting of water wheel clearance can attenuate outcomes of the blocking effect of the river channel and reduce the potential energy loss and kinetic energy dissipation while maintaining high efficiency. By comparing the most efficient two configurations of the vortex evolution and pressure distribution, it is illustrated that the optimal clearance can target eliminating vortical flow and improving flow adaptability, avoiding unnecessary energy losses, and decreasing the uneven pressure.
- As a new method, the irreversible energy loss characteristics can be intuitively diagnosed by using the entropy production method in water wheels under different clearance effects. The coupling mechanism of vorticity–pressure which will induce irreversible energy loss of the water wheel under different clearance effects is investigated. Hence, this research can provide a reference for the optimization of clearance between the hub and blade of water wheel performance.
Data Availability Statement
Conflicts of Interest
|Ui, V||velocity [m/s]|
|μ||dynamic viscosity [N·s/m2]|
|g||Gravitational acceleration [m/s2]|
|q||heat flux [W/m2]|
|s||specific entropy [J/kg·K]|
|ω||angular velocity [rev/s]|
|A||submerged water area [m2]|
|Δd||water depths [m]|
|θ||circumferential angle [deg]|
|ɛ||turbulent dissipation rate [m2/s3]|
|entropy production by direct dissipation [W/K]|
|entropy production by turbulent dissipation [W/K]|
|entropy production by wall shear stress [W/K]|
|EPDD||entropy production rate by direct dissipation [W/(m3·K)]|
|EPTD||entropy production rate by turbulent dissipation [W/(m3·K)]|
|EPWS||entropy production rate by wall shear stress [W/(m2·K)]|
|i, j||direction of Cartesian coordinates|
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|Elements (×106)||Averaged Torque (×105 N·m)|
|Material||Number of Blades||Flow Velocity (m/s)||Rotational Speed|
|Output in Experiments|
|Output in Numerical Result|
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Feng, W.; Zheng, Y.; Yu, A.; Tang, Q. Experimental and Numerical Analysis of the Clearance Effects between Blades and Hub in a Water Wheel Used for Power Generation. Water 2022, 14, 3640. https://doi.org/10.3390/w14223640
Feng W, Zheng Y, Yu A, Tang Q. Experimental and Numerical Analysis of the Clearance Effects between Blades and Hub in a Water Wheel Used for Power Generation. Water. 2022; 14(22):3640. https://doi.org/10.3390/w14223640Chicago/Turabian Style
Feng, Wenjin, Yuan Zheng, An Yu, and Qinghong Tang. 2022. "Experimental and Numerical Analysis of the Clearance Effects between Blades and Hub in a Water Wheel Used for Power Generation" Water 14, no. 22: 3640. https://doi.org/10.3390/w14223640