# Research on Hydraulic Characteristics in Diversion Pipelines under a Load Rejection Process of a PSH Station

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## Abstract

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## 1. Introduction

## 2. Numerical Method of Computational Model

#### 2.1. Governing Equations

_{i}and x

_{j}are the coordinate components in different directions, x,j = 1,2,3; u

_{i}and u

_{j}are the velocity components in different directions, x,j = 1,2,3; p is the pressure; and μ and μ

_{t}represent the kinetic viscosity and turbulent viscosity, respectively. ${\mu}_{t}=\rho {C}_{\mu}\frac{{k}^{2}}{\epsilon}$, where ${C}_{\mu}$ is a constant.

#### 2.2. Turbulence Model

_{k}is the production of turbulence kinetic energy; μ

_{t}is turbulent viscosity; and the empirical constant values of the above formula are ${C}_{1\epsilon}=1.44$, ${C}_{2\epsilon}=1.92$, ${C}_{\mu}=0.09$,${\sigma}_{k}=1.0$, and ${\sigma}_{\epsilon}=1.3$.

#### 2.3. Mesh Independence Analysis

#### 2.4. Equations Discretization and Boundary Conditions

## 3. Case Model

## 4. Results Analysis

#### 4.1. Water Level Fluctuation in Surge Chamber

#### 4.2. The Pressure Fluctuation at the End of Pipeline

#### 4.3. Flow Velocity Distribution at Different Cross Sections in the Pipeline

#### 4.4. Flow Regime Analysis in the Bifurcated Pipeline

## 5. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## Nomenclature

${G}_{k}$ | Production of the turbulence kinetic energy | m^{2}/s^{2} |

$i$ | The phase | - |

$k$ | Turbulence kinetic energy | m^{2}/s^{2} |

$n$ | Number of phases | - |

N | Number of grid cells | - |

$p$ | Pressure | Pa |

${u}_{a}$ | Axial velocity | m/s |

${u}_{c}$ | Circumferential velocity | m/s |

${u}_{i}$,${u}_{j}$ | Velocity component | m/s |

${x}_{i}$,${x}_{j}$ | Coordinate component | m |

$t$ | Time | s |

$\rho $ | Fluid density | kg/m^{3} |

$\epsilon $ | Turbulent dissipation rate | m^{2}/s^{3} |

$\mu $ | Kinetic viscosity | Pa·s |

${\mu}_{t}$ | Turbulent viscosity | Pa·s |

${\alpha}_{w}$ | The volume fraction of water phase | - |

${\alpha}_{a}$ | The volume fraction of air phase | - |

$\Delta t$ | Time step size | s |

## Abbreviations

1D | One dimensional |

2D | Two dimensional |

3D | Three dimensional |

CFD | Computational fluid dynamics |

MOC | Method of characteristics |

MOI | Method of implicit |

RANS | Reynolds average Navier-Stokes |

PAT | Pump as turbine |

PISO | Pressure implicit with splitting of operators |

PRESTO | PREssure STaggering Option |

PSH | Pumped storage hydropower |

SIMPLEC | Semi-implicit method for pressure linked equations-consistent |

UDF | User defined function |

VOF | Volume of fluids |

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**Figure 2.**The schematic diagram of the diversion system of a pumped storage hydropower (PSH) station.

**Figure 4.**The curve of static pressure at the end of pipeline. CFD—computational fluid dynamics; MOC—method of characteristics.

**Figure 5.**Flow velocity distribution of each section at different times: (

**a**) the axial velocity of different sections when t = 50 s, (

**b**) the circumferential velocity of different sections when t = 50 s, (

**c**) the axial velocity of different sections when t = 90 s, (

**d**) the circumferential velocity of different sections when t = 90 s, (

**e**) the axial velocity of different sections when t = 130 s, (

**f**) the circumferential velocity of different sections when t = 130 s.

**Figure 8.**Local spiral flow in the pipeline at different times: (

**a**) t = 70 s, (

**b**) t = 90 s, (

**c**) t = 110 s, (

**d**) t = 130 s, (

**e**) t = 150 s, and (

**f**) t = 170 s.

Passages | Surge tank | Bifurcated pipe | Diversion pipe | Other region | Total |
---|---|---|---|---|---|

Mesh type | Tet | Hex/Tet | Hex | Hex/Tet | |

N/10^{4} | 90 | 20 | 100 | 10 | 220 |

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**MDPI and ACS Style**

Zhou, D.; Chen, H.; Chen, S.
Research on Hydraulic Characteristics in Diversion Pipelines under a Load Rejection Process of a PSH Station. *Water* **2019**, *11*, 44.
https://doi.org/10.3390/w11010044

**AMA Style**

Zhou D, Chen H, Chen S.
Research on Hydraulic Characteristics in Diversion Pipelines under a Load Rejection Process of a PSH Station. *Water*. 2019; 11(1):44.
https://doi.org/10.3390/w11010044

**Chicago/Turabian Style**

Zhou, Daqing, Huixiang Chen, and Shifan Chen.
2019. "Research on Hydraulic Characteristics in Diversion Pipelines under a Load Rejection Process of a PSH Station" *Water* 11, no. 1: 44.
https://doi.org/10.3390/w11010044