This study focuses on a DN50 pipeline-type Savonius hydraulic turbine. The torque variation of the turbine in a rotation cycle is analyzed theoretically in the framework of the plane potential flow theory. Related numerical simulations show that the change in turbine torque is consistent with the theoretical analysis, with the main power zone and the secondary power zone exhibiting a positive torque. In contrast, the primary resistance zone and the secondary resistance zone are characterized by a negative torque. Analytical relationships between the turbine’s internal flow angle θ, the deflector’s inclination angle α_{0}, and the coverage angle α of the power zone are introduced, and a method for calculating the optimal number of blades is proposed to maximize the power zone. Results are presented about performance tests conducted on five groups of hydraulic turbines with the blade number ranging from 3 to 7. Such results indicate that both the turbine’s recovery power and efficiency attain the highest values when the blade number is 4, which is in agreement with the number of blades calculated by the proposed method. Additionally, the study examines the effects of the flow rate on turbine parameters and the projected energy generation and cost savings for a specific pipeline configuration.

The total length of the water supply pipe network in the China’s Lanzhou New Area is more than 810 km, most of which is laid underground. The water supply suffers some freshwater losses due to leakages caused by the aging of some pipes in the network [

There are lots of energy recovery devices that can make good use of renewable resources to provide stable power for monitoring devices, such as solar panels and wind turbines [

Several researchers have focused their attention on how to optimize the Savonius turbine structure and its matching with the deflector to reduce the negative torque area of the turbine, thereby improving its recovery power. Basumatary et al. [^{3}/s. Zhou et al. [

Some researchers have also found that increasing the deflector can effectively avoid the vortex formed by the collision between cycle fluid and inflow and can significantly improve the turbine recovery efficiency. Golecha et al. [

The aforementioned research findings have significant theoretical relevance and engineering applications towards the enhancement of hydraulic performance for Savonius hydraulic turbines. Nonetheless, several unresolved issues remain, namely internal energy conversion mechanisms, incomplete design theories and methodologies, and unstable operations. These issues pose significant hindrances to the pursuit of theoretical research and practical implementation of Savonius hydraulic turbines.

In the present study, a method for calculating the optimal number of turbine blades was proposed based on the plane potential flow theory. A numerical simulation and experiments were carried out to verify the established analytical relationship. Further, we took the Chinese Lanzhou New Area as an example to analyze the energy saving effect and the economic benefits of the device under different working conditions. The study provides a valuable reference for the research on Savonius hydraulic turbines’ design optimization, performance prediction, and practical engineering application.

The structure of the Savonius hydraulic turbine is shown in _{0}, hub diameter _{h}, height _{b}, blade number _{i} and radius of _{i} given by

The deflector was installed upstream of the turbine to verify the recovery efficiency of the turbine [

Geometric parameter | Sign | Value |
---|---|---|

Pipe diameter (mm) | 50 | |

Turbine diameter (mm) | _{0} |
46 |

Hub diameter (mm) | _{h} |
6 |

Turbine height (mm) | 32.2 | |

Gap (mm) | 2 | |

Circular arc radius (mm) | _{i} |
– |

Blade thickness (mm) | _{b} |
1.5 |

Deflector length (mm) | 208 | |

Inclination angle (°) | 80 | |

Cavity radius (mm) | 25 |

To analyze the change of torque during the rotating process of the turbine, the incoming flow was assumed to be uniformly distributed and the inner flow velocity in the axial direction of the turbine to be zero (this assumption is validated in the subsequent text). Based on the plane potential flow theory, the three-dimensional turbine flow is approximately expressed by the two-dimensional flow on the vertical surface of the central axis, and the incoming flow working on the blade changes constantly. During a rotation cycle, the change of torque along a single blade can be divided into 4 zones, namely the main resistance power zone, the main power zone, the secondary resistance zone, and the secondary power zone.

The torque distribution diagram of different blade positions was as shown in

The preceding theoretical analysis was based on a single blade of the turbine, from which it was easily deduced that the interval of the change of torque was closely related to the structure of the turbine and deflector. To improve the working capacity, the turbine and deflector should be reasonably designed, as much as possible to increase the power zone BOD. However, it should be noted that the Savonius turbine usually has multiple blades, and that the number of blades is related to the power coverage angle. If the number of turbine blades is large, multiple blades appear in the power range, the rear sequence blades will block the flow in the front sequence blades and reduce the effective blade acting area; if the number of turbine blade is small, there is no rear sequence blade entering the power area, thus it is useless flow during this intermittent period. Therefore, on the basis of reasonable design of the maximum power area of a single blade of the turbine, the number of blades should be correctly selected so that the clip angle between adjacent blades is equal to the coverage angle of a single blade power area, with the maximum work produced by impacting the blade.

To calculate the coverage angle of the power zone, the theoretical model shown in

_{1}_{1},

The diameter of the turbine is

Under the assumption of uniform inflow, the gravity of fluid, the separation of flow, and the secondary flow were ignored in the turbine. The relationship between the fluid on the pressure and suction surface of the blade and its acting area is given by

The power torque and resistance torque of the blade are given by

where,

If the resistance and power torque of the blade are equal at position B, i.e.,

Then the relationship between the coverage angle

Thus, the coverage angle

When the turbine internal flow angle

As earlier mentioned, to improve the efficiency of energy utilization of the Savonius turbine, the angle of adjacent blades should be exactly equal to the angle covered by the power zone, and the optimal blade number is given by

Taking the turbine in this study as an example, it was found that Z ≈ 3.7 Therefore, the optimal number of blades of the turbine was selected as 4 in practical research.

Basically, the internal flow field in turbomachinery is considered be complex and turbulent due to operating conditions, since it is important to choose a proper model for turbulence modeling and evaluating Navier-Stokes equations. The two-equation model [

The Navier-Stokes equations [

where

The RNG

where _{T} is turbulent viscosity, coefficient of experience _{μ} = 0.09,

The turbulent kinetic energy

The dissipation rate of turbulent kinetic energy

where _{1} = 1.42, _{2} = 1.68, _{3} = 1.39, _{k} = _{ε} = 0.7179, _{eff} = _{t} and _{ε} are terms to adapt to the rapid flow with variable rate and streamline curvature, and its expression is:

where _{µ} = 0.0845, _{0} = 4.38, and

The whole computation domain is shown in

The software ANSYS CFX18.0 was employed for the unsteady calculation, with the RNG

The grid independence verification was carried out for the numerical simulation of the Savonius hydraulic turbine with four blades. Here, the water head was selected as the variation of grid independence verification. As is shown in

To verify the reliability of the numerical model, the head loss comparison between the three-dimensional simulation and experiments of the Savonius hydraulic turbine were carried out under different flow rates, as shown in ^{3}/h, and the error was less than 5% (4.9% and 4.6%). Thus, the adopted CFD numerical simulation method is reasonable for the study in this paper.

Considering that the theoretical analysis was based on the independence assumption that the inner flow velocity in the axial direction of the turbine was zero, the two-dimensional flow on the vertical plane of the central axis of the turbine was used to demonstrate the three-dimensional inner flow. To verify this assumption, the pressure contours and streamline diagrams on three slices at different vertical positions (X1, X2, X3) of the turbine are exhibited in ^{3}/h and the inlet pressure was 200 kPa. The pressure distribution at different heights were very similar, so were the streamline structures. Therefore, it was feasible to replace the three-dimensional flow field of the turbine with that of the middle section, as the flow field along the axis direction of the turbine does not change much.

To further verify the influence of blade number on the torque of the turbine blade, the torques of blades for five groups of different blade numbers were calculated for a flow rate of 5 m^{3}/h and an inlet pressure of 200 kPa. As shown in

As shown in

where

The rotating speed/water head–flow rate curve is shown in ^{3}/h, the water head exhibited a big difference between different blade numbers.

The electric power-flow rate curves are shown in ^{3}/h, the output power of the 4-blade turbine was lower than that of other blades number of turbines. Under such conditions, the turbine slipped on the shaft, the voltage of the generator was unstable, and the rotating speed electrical power decreased.

The efficiency-flow rate curves are shown in

The device which is the research object in this study has already been successfully applied in the process of energy recovery. Taking Chinese Lanzhou New Area as an example, the local area pipeline network layout is shown in

The schematic of the proposed system is shown in

Case | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|

Flow rate (m^{3}/h) |
3 | 4 | 5 | 6 | 7 |

Water head (m) | 0.41 | 0.71 | 1.62 | 1.63 | 2.24 |

Electric power (W) | 0.495 | 1.48 | 2.51 | 4.05 | 5.76 |

Efficiency (%) | 14.86 | 19.05 | 18.07 | 15.19 | 13.47 |

As is known, the efficiency and water head of a Savonius hydraulic turbine are basic parameters to measure its hydraulic performance. It was found that the water head linearly increased with increasing flow rate, as shown in

where

where

The seasonal proportion of water supply and its monthly flow rate in the Lanzhou New Area in 2020 are shown in

As is shown in

Parameters | Low-Peak | Mid-peak | High-peak | |
---|---|---|---|---|

May 12 | Flow rate (m^{3}/h) |
4.2 | 8.2 | 9.4 |

Water head (m) | 0.76 | 2.426 | 3.458 | |

Electric Power (W) | 1.6 | 10.42 | 31.5 | |

Efficiency (%) | 19.67 | 19.19 | 35.6 | |

December 10 | Flow rate (m^{3}/h) |
3.6 | 7.6 | 8.6 |

Water head (m) | 0.448 | 2.168 | 2.598 | |

Electric Power (W) | 0.82 | 7.1 | 14 | |

Efficiency (%) | 18.58 | 15.79 | 23.06 |

Equipment name | Remote manometers | Remote flowmeters | Remote control equipment |
---|---|---|---|

Actuator specification | DC6V-10mA | DC24V-20mA | AC220V-1.2A |

Power (W) | 0.06 | 0.48 | 15 |

Single day working hours (h) | 24 | 24 | 1 |

Single day power consumption (kW·h) | 0.0144 | 0.01152 | 0.015 |

From

Equipment name | Savonius hydraulic turbine | Remote monitoring equipment | Remote control equipment power supply |
---|---|---|---|

Input cost ($) | 392 | 138 | 157 |

Average use life (days) | 1825 | 324 | 1095 |

Annual failure rate (%) | 0.3 | 4.2 | 0.2 |

Annual maintenance expense ($) | 30 | 220 | 43 |

As presented in _{2}. Thus, the Savonius hydraulic turbine, as a clean energy recovery device could generate 86.4 kW·h, which could result in a reduction of about 111.8 kg CO_{2} emissions every year.

In this paper, a Savonius turbine which was used for micro power generation in a water pipeline system was studied theoretically, experimentally, and numerically. The turbine with a deflector was directly installed in the water pipeline system to supply data monitoring system. Experiments were carried out to verify the numerical simulation, and the effect of blade number on the torque and efficiency of turbine were investigated by numerical simulation. Moreover, based on the external characteristic parameters of the optimal number of blades turbine, the application of the devices was analyzed to predict its energy saving efficiency and economic benefits. The main results are as follows:

The variation of torque of the Savonius turbine in a rotation period could be divided into 4 zones: main resistance zone, main power zone, secondary power zone and secondary resistance zone. The main power zone and the secondary power zone were the zones of positive torque, and the main resistance zone and the secondary resistance zone were the zones of negative torque.

The analytical relationship between the coverage angle _{0} were established based on the maximum power zone. A calculation method for the optimal number of blades was proposed. Based on this method, the calculated optimal number of blades in this study was four. The power experiments on five groups of turbines with 3-, 4-, 5-, 6-, and 7-blades showed that both the recovery power and efficiency of the turbine were the highest (5.76 W and 19.05%, respectively) when the blade number was 4, which showed that the calculation method of the number of optimal blades proposed in this paper is valid.

With increasing flow rate, both the rotating speed and pressure difference of the Savonius turbine increased linearly, and the power increased slowly at first and then rapidly dropped. The increase of blade number was related to the decrease of the torque variation.

Taking the DN50 pipeline system in a certain area as an example, it was found that the use of the Savonius turbine can generate electricity energy of 28.17 kW·h in summer and 15.03 kW·h in winter. This would save about $593 in a year for a single node, and total savings in this area (for 15 nodes) of about $8408. Meanwhile, application of the device can reduce about 111.8 kg CO_{2} of emissions each year, and can reduce about 200 lithium batteries for a single node. Thus, the purpose of energy saving and emission reduction is realizable using this system.

None.

This research was funded by Gansu Outstanding Youth Fund (20JR10RA203), Gansu Province Youth Doctor Fund (2023QB-033), National Natural Science Foundation of China (52169019) and the Gansu Industry-University Support Fund (2020C-20).

The authors confirm contribution to the paper as follows: study conception and design: Xiaohui Wang, Kai Zhang; data collection: Kai Zhang, Zanxiu Wu; analysis and interpretation of results: Xiaohui Wang, Kai Zhang, Xiaobang Bai, Senchun Miao; draft manuscript preparation: Kai Zhang, Xiaohui Wang, Zanxiu Wu, Jicheng Li. All authors reviewed the results and approved the final version of the manuscript.

Not applicable.

The authors declare that they have no conflicts of interest to report regarding the present study.