# Effects of Orifice Sizes for Uncontrolled Filling Processes in Water Pipelines

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## Abstract

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## 1. Introduction

## 2. Experimental Model

## 3. Numerical CFD Model

#### 3.1. Governing Equations

#### 3.2. Turbulence Model

#### 3.3. Assumptions, Boundary Conditions and Mesh Properties

- The air phase is simulated considering an ideal gas law.
- Fluids are considered compressible, non-isothermal, and immiscible.

## 4. Results and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

$DI$ | inner diameter |

${F}_{1}$ | blending function (-) |

$\mathbf{g}$ | gravitational acceleration vector (m/s^{2}) |

k | turbulence kinetic energy (m^{2}/m^{2}) |

p | pressure (N/m^{2}) |

${p}_{max}$ | maximum pressure (N/m^{2}) |

${P}_{i}/{\gamma}_{w}$ | inlet pressure head (m.wc) |

${P}_{k}$ | shear stress in CFD model (N/m^{2}) |

t | time (s) |

u | velocity component (m/s) |

$\mathbf{u}$ | velocity vector (m/s) |

${X}_{0}$ | initial air pocket length (m) |

$\gamma $ | air–water volume fraction (-) |

$\nu $ | mixture kinematic viscosity (m^{2}/s) |

$\mu $ | mixture dynamic viscosity (kg/ms) |

$\rho $ | mixture density (kg/m^{3}) |

$\omega $ | dissipation frequency (m^{2}/s^{3}) |

Subscripts | |

a | refers to air phase (e.g., air density) |

w | refers to water phase (e.g., water dynamic viscosity) |

t | refers to turbulence conditions (turbulent kinematic viscosity) |

Constants of the k-ω SST model | |

${\alpha}_{1}$ | 0.555 |

${\beta}^{*}$ | 0.09 |

${\beta}_{1}$ | 0.075 |

${\sigma}_{k1}$ | 0.85 |

${\sigma}_{\omega 1}$ | 0.50 |

${\alpha}_{2}$ | 0.44 |

${\beta}_{2}$ | 0.0828 |

${\sigma}_{k2}$ | 1.0 |

${\sigma}_{\omega 2}$ | 0.856 |

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**Figure 7.**Comparison of air pocket pressure patterns using the S050 air valve (diameter of 3.175 mm) and the 7.0 mm discharge orifice.

**Figure 8.**Comparison of water column velocity patterns using the S050 air valve (diameter of 3.175 mm) and the 7.0 mm discharge orifice.

Test | 1 | 2 | 3 |
---|---|---|---|

${P}_{i}/{\gamma}_{w}$ (m.wc) | 5.10 | 5.10 | 7.65 |

${X}_{0}$ (m) | 0.96 | 1.36 | 0.96 |

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**MDPI and ACS Style**

Aguirre-Mendoza, A.M.; Paternina-Verona, D.A.; Oyuela, S.; Coronado-Hernández, O.E.; Besharat, M.; Fuertes-Miquel, V.S.; Iglesias-Rey, P.L.; Ramos, H.M.
Effects of Orifice Sizes for Uncontrolled Filling Processes in Water Pipelines. *Water* **2022**, *14*, 888.
https://doi.org/10.3390/w14060888

**AMA Style**

Aguirre-Mendoza AM, Paternina-Verona DA, Oyuela S, Coronado-Hernández OE, Besharat M, Fuertes-Miquel VS, Iglesias-Rey PL, Ramos HM.
Effects of Orifice Sizes for Uncontrolled Filling Processes in Water Pipelines. *Water*. 2022; 14(6):888.
https://doi.org/10.3390/w14060888

**Chicago/Turabian Style**

Aguirre-Mendoza, Andres M., Duban A. Paternina-Verona, Sebastian Oyuela, Oscar E. Coronado-Hernández, Mohsen Besharat, Vicente S. Fuertes-Miquel, Pedro L. Iglesias-Rey, and Helena M. Ramos.
2022. "Effects of Orifice Sizes for Uncontrolled Filling Processes in Water Pipelines" *Water* 14, no. 6: 888.
https://doi.org/10.3390/w14060888