# Study on the Hydraulic Response of an Open-Channel Water Transmission Project after Flow Switching

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Research Methods

#### 2.1. Governing Equations and Solutions

^{3}/s; g is the acceleration of gravity, m/s

^{2}; x is the space coordinate of the section, m; t is the time coordinate, s; q is the side inflow, m

^{3}/s; α is the momentum correction coefficient; A is the water passage area, m

^{2}; and S

_{f}is the friction ratio drop, which can be expressed by the following equation:

_{c}is the Manning roughness coefficient of the water conveyance channel and R is the hydraulic radius, m.

#### 2.2. Model Internal Boundary Conditions’ Generalization

_{k}and Q

_{k+}

_{1}represent the inlet and outlet flow of the pump (m

^{3}/s), respectively.

_{k+}

_{1}is the water level of the outlet pool (m); H

_{k}is the water level of the inlet pool (m); and a

_{k}, b

_{k}, and c

_{k}are the relevant parameters of the unit characteristic curve.

#### 2.3. Safety Regulation Time Frame

#### 2.4. Sobol Global Sensitivity Analysis

_{1}, x

_{2},..., x

_{n}), X = (x

_{1}, x

_{2},..., x

_{n}) is the parameter vector, and n is the number of parameters; the variance decomposition equation is expressed as:

_{i}represents the variance for the effect of the i-th parameter; V

_{i,j}represent the variance of the i-th and j-th parameters acting together; V

_{1,2,…,n}represents the variance of all parameters acting together; and S

_{T}represents the full sensitivity coefficient

#### 2.5. Overview of the Region

^{3}/s.

^{3}/s and operates in 8 use modes and 1 standby mode, and the designed water level below the station is 4.1 m. The specific information is shown in Table 1 and Figure 4.

#### 2.6. Hydrodynamic and Parameter Verification

## 3. Project Case

#### 3.1. Operation Setting

#### 3.2. Feasible Domain of Safety Regulation Time

#### 3.3. Parametric Sensitivity Analysis

#### 3.3.1. Sobol Global Sensitivity Analysis Method

#### 3.3.2. Analysis of the Results of the Sobol Method

#### 3.4. Fast Computational Equation Fitting

^{3}/s and a downstream water level of 7.6 m.

^{3}/s. The downstream water level of 7.6 m was chosen for the conditions to fit using Matlab’s toolbox. The results of the fitting are shown in Table 3.

_{t}is the latest time for regulation, h, and x is the flow change, m

^{3}/s.

#### 3.5. Test of the Fitting Equation

## 4. Conclusions

- (1)
- The latest regulation time at the Paihekou pumping station upstream and downstream was calculated in this study to determine the effects of the flow change, downstream water level, and upstream initial flow. It was found that, for the same initial flow and downstream water level, the regulation time decreased with the increase in the flow variation volume; for the same initial flow and flow variation volume, the latest regulation time decreased with the increase in the water level. The latest regulation time with the starting flow increased initially and subsequently reduced in a trending format for the same flow variation and downstream water level conditions.
- (2)
- The overall sensitivity index of the flow variation was found to be at the maximum when using the Sobol global sensitivity analysis method at the latest regulation time, which is connected to the starting upstream flow, the flow variation, and the downstream water level. At the same time, it was suggested for the method of the fitting equation to be used for the calculation of the most-recent regulation time in order to calculate it rapidly. The hydrodynamic model was used for testing, and the amount of flow change was chosen as a one variate to suit the computation of the most-recent regulation time. The results showed that the effect of the fit was better with the computed NSE = 0.98, and the fitting equation can be a perfect replacement.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Zhang, Z.; Tian, Y.; Lei, X.H. Study and application of general unsteady flow simulation model for complex open channel water transfer Project. In Proceedings of the 2018 CHES Annual Conference, Amsterdam, The Netherlands, 9–12 September 2018. [Google Scholar]
- Litrico, X.; Fromion, V. Simplified Modeling of Irrigation Canals for Controller Design. J. Irrig. Drain. Eng.
**2004**, 130, 373–383. [Google Scholar] [CrossRef] - Qi, J.S.; Cui, Y.R.; Wang, S.Y. Analysis of Hydraulic Response in Emergency Gate Control of the Water Supply Project in North Xinjiang. J. Water Resour. Archit. Eng.
**2021**, 19, 250–256. [Google Scholar] - Li, K.B.; Shen, B.; Li, Z.L. Open channel hydraulic response characteristics in irrigation area based on unsteady flow simula-tion analysis. Trans. Chin. Soc. Agric. Eng.
**2015**, 31, 107–114. [Google Scholar] - Schuurmans, J.; Clemmens, A.J.; Dijkstra, S.; Hof, A.; Brouwer, R. Modeling of Irrigation and Drainage Canals for Controller Design. J. Irrig. Drain. Eng.
**1999**, 125, 338–344. [Google Scholar] [CrossRef] - Bautista, E.; Clemmens, A.J. Volume Compensation Method for Routing Irrigation Canal Demand Changes. J. Irrig. Drain. Eng.
**2005**, 131, 494–503. [Google Scholar] [CrossRef] - Parrish, J. A Methodology for Automated Control of Sloping Canals; University of Iowa: Lowa City, IA, USA, 1997. [Google Scholar]
- Zheng, H.Z.; Tian, Y.; Wang, C. Study on the Predictive Control Method of Cascade Pumping Stations in Water Transfer System. Yellow River
**2018**, 40, 140–143. [Google Scholar] - Wahlin, B.T.; Clemmens, A.J. Automatic downstream water-level feedback control of branching canal networks: Simula-tion results. J. Irrig. Drain. Eng.
**2006**, 132, 208–219. [Google Scholar] [CrossRef] - Lu, L.B.; Lei, X.H.; Tian, Y. Research on the Characteristic of Hydraulic Response in Open Channel of the Cascade Pumping Station Project in an Emergent State. J. Basic Sci. Eng.
**2018**, 26, 263–275. [Google Scholar] - Li, M.X.; Tian, Y.; Lei, X.H. Analysis onemergency response time for accidental pump—Stop at multi—Stage pumping station of Water Diversion Project from Yangtze River to Huaihe River. Yangtze River
**2021**, 52, 212–217. [Google Scholar] - Liu, Z.Y.; Liu, M.Q. Analysis and Control of Pump-stopping Hydraulic Transient in Cascade Water Supply Pumping Station. China Rural Water Hydropower
**2006**, 7, 32–34. [Google Scholar] - Zhang, Z.; Lei, X.; Tian, Y.; Wang, L.; Wang, H.; Su, K. Optimized Scheduling of Cascade Pumping Stations in Open-Channel Water Transfer Systems Based on Station Skipping. J. Water Resour. Plan. Manag.
**2019**, 145, 05019011. [Google Scholar] [CrossRef] - Yan, P.; Zhang, Z.; Lei, X.; Zheng, Y.; Zhu, J.; Wang, H.; Tan, Q. A Simple Method for the Control Time of a Pumping Station to Ensure a Stable Water Level Immediately Upstream of the Pumping Station under a Change of the Discharge in an Open Channel. Water
**2021**, 13, 355. [Google Scholar] [CrossRef] - Zhu, J.; Zhang, Z.; Lei, X.; Yue, X.; Xiang, X.; Wang, H.; Ye, M. Optimal Regulation of the Cascade Gates Group Water Diversion Project in a Flow Adjustment Period. Water
**2021**, 13, 2825. [Google Scholar] [CrossRef] - Belaud, G.; Litrico, X.; Clemmens, A.J. Response Time of a Canal Pool for Scheduled Water Delivery. J. Irrig. Drain. Eng.
**2013**, 139, 300–308. [Google Scholar] [CrossRef] - Burt, C.M.; Feist, K.E.; Piao, X.S. Accelerated Irrigation Canal Flow Change Routing. J. Irrig. Drain. Eng.
**2018**, 144, 6. [Google Scholar] [CrossRef] - Liao, W.; Guan, G.; Tian, X. Exploring Explicit Delay Time for Volume Compensation in Feedforward Control of Canal Systems. Water
**2019**, 11, 1080. [Google Scholar] [CrossRef] - Kong, L.; Li, Y.; Tang, H.; Yuan, S.; Yang, Q.; Ji, Q.; Li, Z.; Chen, R. Predictive control for the operation of cascade pumping stations in water supply canal systems considering energy consumption and costs. Appl. Energy
**2023**, 341, 121103. [Google Scholar] [CrossRef] - Khatavkar, P.; Mays, L.W. Real-Time Operation of Water-Supply Canal Systems under Limited Electrical Power and/or Water Availability. J. Water Resour. Plan. Manag.
**2020**, 146, 04020012. [Google Scholar] [CrossRef] - Kucuk, H.; Turan, M.; Yarali, K.; Al-Sanabani, H.; Iskefiyeli, M. A new algorithm for load shifting operation of water pumping stations. J. Fac. Eng. Archit. Gaz.
**2021**, 36, 2087–2093. [Google Scholar] - Shahdany, S.M.H.; Maestre, J.M.; van Overloop, P.J. Equitable Water Distribution in Main Irrigation Canals with Constrained Water Supply. Water Resour. Manag.
**2015**, 29, 3315–3328. [Google Scholar] [CrossRef] - Wang, J.P.; Lv, W.B.; Fan, Q.F. New Empirical Equations of Equilibrium Flow Scour Depth of Open Channel Outlet. Water Resour. Power
**2013**, 31, 139–140. [Google Scholar] - Xia, W.Y.; Zhao, X.D.; Zhang, X.Z. Application of Empirical Equation of Sediment Transport Capacity in Forecast of Riv-erbed Erosion and Deposition of Jiaojiang River Estuary. Water Resour. Power
**2017**, 35, 101–103. [Google Scholar] - Li, G.H.; Zhang, Z.; Kong, L.Z. Research on the Hydraulic Control Method of Shaping II Hydropower Station. China Rural Water Hydropower
**2022**, 1, 196–199. [Google Scholar] - Malaterre, P.-O.; Rogers, D.C.; Schuurmans, J. Classification of Canal Control Algorithms. J. Irrig. Drain. Eng.
**1998**, 124, 3–10. [Google Scholar] [CrossRef] - Mu, J.-B.; Zhang, X.-F. Real-Time Flood Forecasting Method With 1-D Unsteady Flow Model. J. Hydrodyn.
**2007**, 19, 150–154. [Google Scholar] [CrossRef] - Wang, C.H.; Li, G.Z.; Xiang, X.H. Practical River Network Flow Calculation; Hohai University Press: Nanjing, China, 2015. [Google Scholar]
- Litrico, X.; Fromion, V.; Baume, J.-P.; Arranja, C.; Rijo, M. Experimental validation of a methodology to control irrigation canals based on Saint-Venant equations. Control Eng. Pract.
**2005**, 13, 1425–1437. [Google Scholar] [CrossRef] - Mehmed, Y. Steady Non-Uniform Flow in Open Channel; Water Resources and Electric Power Press: Beijing, China, 1987. [Google Scholar]
- Wang, C.; Yang, J.; Nilsson, H. Simulation of Water Level Fluctuations in a Hydraulic System Using a Coupled Liquid-Gas Model. Water
**2015**, 7, 4446–4476. [Google Scholar] [CrossRef] - Yan, P.; Zhang, Z.; Lei, X.; Hou, Q.; Wang, H. A multi-objective optimal control model of cascade pumping stations considering both cost and safety. J. Clean. Prod.
**2022**, 345, 131171. [Google Scholar] [CrossRef] - Zhang, Z. Research on Perception and Regulation Model of Water Delivery Process in Open Channel Water Transfer Project. Ph.D. Thesis, Hohai University, Nanjing, China, 2020. [Google Scholar]
- Olszewski, P. Genetic optimization and experimental verification of complex parallel pumping station with centrifugal pumps. Appl. Energy
**2016**, 178, 527–539. [Google Scholar] [CrossRef]

**Figure 6.**The result chart of the latest regulation time. (

**a**) Initial flow of 0–113.07 m

^{3}/s. (

**b**) Initial flow of 145.5–258.13 m

^{3}/s. (

**c**) Relationship between downstream water level, initial flow, and latest regulation time for the same amount of flow change.

**Table 1.**Engineering foundation information of Paihekou pumping station and Shushan pumping station.

The Pump Station | Type | Design Flow (m ^{3}/s) | Number | Design Flow (m ^{3}/s) | Water Level in Front of Station | ||
---|---|---|---|---|---|---|---|

Design (m) | Max (m) | Min (m) | |||||

Paihekou | Axial flow | 37.69 | 9 | 301.5 | 4.10 | 5.80 | 3.60 |

Shushan | Axial flow | 36.25 | 8 | 290 | 7.60 | 10.70 | 5.80 |

Initial Upstream Flow (m ^{3}/s) | 0 | 37.69 | 75.38 | 113.07 | 150.76 | 188.45 | 226.14 | 263.83 |
---|---|---|---|---|---|---|---|---|

Flow change (m ^{3}/s) | 37.69 | − | − | − | − | − | − | − |

75.38 | 75.38 | − | − | − | − | − | − | |

113.07 | 113.07 | 113.07 | − | − | − | − | − | |

150.76 | 150.76 | 150.76 | 150.76 | − | − | − | − | |

188.45 | 188.45 | 188.45 | 188.45 | 188.45 | − | − | − | |

226.14 | 226.14 | 226.14 | 226.14 | 226.14 | 226.14 | − | − | |

263.83 | 263.83 | 263.83 | 263.83 | 263.83 | 263.83 | 263.83 | − | |

301.5 | 301.5 | 301.5 | 301.5 | 301.5 | 301.5 | 301.5 | 301.5 |

Number | Variable | Fitting Equation Form | R^{2} |
---|---|---|---|

1 | Flow change | Linear function fitting | 0.77 |

2 | Exponential function fitting | 0.92 | |

3 | Logarithmic function fitting | 0.90 | |

4 | Power function fitting | 0.99 |

Number | Flow Change (m^{3}/s) | Number | Flow Change (m^{3}/s) |
---|---|---|---|

1 | 10 | 6 | 60 |

2 | 20 | 7 | 70 |

3 | 30 | 8 | 80 |

4 | 40 | 9 | 90 |

5 | 50 | 10 | 100 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 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 (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Zhang, N.; Ren, H.; Lin, F.
Study on the Hydraulic Response of an Open-Channel Water Transmission Project after Flow Switching. *Water* **2023**, *15*, 3201.
https://doi.org/10.3390/w15183201

**AMA Style**

Zhang N, Ren H, Lin F.
Study on the Hydraulic Response of an Open-Channel Water Transmission Project after Flow Switching. *Water*. 2023; 15(18):3201.
https://doi.org/10.3390/w15183201

**Chicago/Turabian Style**

Zhang, Naifeng, Honglei Ren, and Fei Lin.
2023. "Study on the Hydraulic Response of an Open-Channel Water Transmission Project after Flow Switching" *Water* 15, no. 18: 3201.
https://doi.org/10.3390/w15183201