# Transient Phenomena Generated in Emptying Operations in Large-Scale Hydraulic Pipelines

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^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Study Development

_{v}) of 3300 s

^{2}/m

^{5}. This value refers to a valve opening degree of 55%, data obtained in previous analyses by the collaborating company. This valve is located at the point with the lowest topographical elevation (point P2), for the purpose of completely discharging the water during the emptying manoeuvre.

#### 2.1. Mathematical Model

- Equation of the rigid model that characterizes the movement of the emptying column:$$\frac{dv}{dt}=\frac{{p}_{1}^{*}-{p}_{atm}^{*}}{{\rho}_{w}{L}_{e}}+g\left(\frac{\u2206z}{{L}_{e}}\right)-f\frac{v\mid v\mid}{2D}-\frac{{R}_{v}g{A}^{2}v\mid v\mid}{{L}_{e}}$$
- Emptying column position:$$\frac{d{L}_{e}}{dt}=-vor{L}_{e}={L}_{0}-{{\displaystyle \int}}_{0}^{t}vdt$$

- Evolution of the air pocket:$$\frac{d{p}_{1}^{*}}{dt}=\frac{{p}_{1}^{*}k}{\left({L}_{T}-{L}_{e}\right)}\left(\frac{{\rho}_{aCN}{v}_{aCN}{A}_{adm}}{A{\rho}_{a}}-v\right)$$
- Continuity equation for the air pocket:$$\frac{d{\rho}_{a}}{dt}=\frac{{\rho}_{aCN\text{}}{v}_{aCN\text{}}\text{}{A}_{adm}-v\text{}A\text{}{\rho}_{a}\text{}}{\left({L}_{T}-{L}_{e}\right)\text{}A}$$
- Characteristic equation for the air valve during the emptying process:$${v}_{aCN}={C}_{adm}\sqrt{7\text{}{p}_{atm}^{*}\text{}{\rho}_{atm}\left[{\left(\frac{{p}_{1}^{*}}{{p}_{atm}^{*}\text{}}\right)}^{1.4286}-{\left(\frac{{p}_{1}^{*}}{{p}_{atm}^{*}\text{}}\right)}^{1.714}\right]}\phantom{\rule{0ex}{0ex}}or{Q}_{a}={v}_{aCN}\text{}{A}_{adm}$$

#### 2.2. Flow Rate Curves of the Air Valves

_{adm}).

_{adm}) of 0.75 is obtained in the inflow phase for the DN50 air valve.

#### 2.3. Initial and Boundary Conditions

^{3}; ${v}_{aCN}\left(0\right)$= 0; ${Q}_{a}\left(0\right)$= 0.

## 3. Application of the Mathematical Model to a Large-Scale Installation

#### 3.1. Water Flow Evolution

#### 3.2. Air Pocket Pressure Evolution

#### 3.3. Length and Velocity Evolution of the Water Column

#### 3.4. Evolution of the Air Flow that Enters the Air Valves

## 4. Discussion on the Comparison between Mathematical Model and Experimental Measures

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

$A$ | Cross-sectional area of the pipe (m^{2}) |

${A}_{adm}$ | Cross-sectional area of the air valve (m^{2}) |

${C}_{adm}$ | Discharge coefficient of the air valve (-) |

$D$ | Internal pipe diameter (m) |

${D}_{vent}$ | Internal diameter of the air valve (m) |

$f$ | Friction factor (-) |

$g$ | Gravity acceleration (m/s^{2}) |

${L}_{e}$ | Length of the emptying column (m) |

${L}_{T}$ | Total length of the pipe (m) |

${L}_{i}$ | Length of section i (m) |

$k$ | Polytropic coefficient (-) |

${p}_{1}^{*}$ | Absolute pressure of the air pocket (Pa) |

${p}_{atm}^{*}$ | Atmospheric pressure (Pa) |

${Q}_{a}$ | Air flow (m^{3}/s) |

${Q}_{w}$ | Water flow (m^{3}/s) |

${R}_{v}$ | Discharge coefficient of the valve (s^{2}/m^{5}) |

$t$ | Time (s) |

$v$ | Water velocity (m/s) |

${v}_{aCN}$ | Air velocity (m/s) |

$z$ | Elevation (m) |

$\u2206z$ | Elevation difference (m) |

${\rho}_{w}$ | Water density (kg/m^{3}) |

${\rho}_{a}$ | Air density (kg/m^{3}) |

${\theta}_{i}$ | Longitudinal slope (%) |

Superscript | |

$\ast $ | Absolute values |

Subscript | |

$a$ | Refers to air |

$i$ | Refers to the pipe section |

$nc$ | Refers to normal conditions |

$w$ | Refers to water |

$0$ | Refers to initial conditions |

## References

- Laanearu, J.; Annus, I.; Koppel, T.; Bergant, A.; Vučkovič, S.; Hou, Q.; van’t Westende, J.M.C. Emptying of large-scale pipeline by pressurized air. J. Hydraul. Eng.
**2012**, 138, 1090–1100. [Google Scholar] [CrossRef][Green Version] - Fuertes-Miquel, V.S.; Coronado-Hernández, O.E.; Iglesias-Rey, P.L.; Mora-Meliá, D. Transient phenomena during the emptying process of a single pipe with water-air interaction. J. Hydraul. Res.
**2019**, 57, 318–326. [Google Scholar] [CrossRef] - Coronado-Hernández, O.E. Transient Phenomena during the Emptying Process of Water in Pressurized Pipelines. Ph.D. Thesis, Polytechnic University of Valencia, Valencia, Spain, 2019. [Google Scholar]
- Fuertes-Miquel, V.S.; Coronado-Hernández, O.E.; Mora-Meliá, D.; Iglesias-Rey, P.L. Hydraulic modeling during filling and emptying processes in pressurized pipelines: A literature review. Urban Water J.
**2019**, 16, 299–311. [Google Scholar] [CrossRef] - Vasconcelos, J.G.; Wright, S.J. Rapid flow startup in filled horizontal pipelines. J. Hydraul. Eng.
**2008**, 134, 984–992. [Google Scholar] [CrossRef][Green Version] - Li, L.; Zhu, D.Z.; Huang, B. Analysis of pressure transient following rapid filling of a vented horizontal pipe. Water
**2018**, 10, 1698. [Google Scholar] [CrossRef][Green Version] - Bashiri-Atrabi, H.; Hosoda, T. The motion of entrapped air cavities in inclined ducts. J. Hydraul. Res.
**2015**, 53, 814–819. [Google Scholar] [CrossRef] - Zhou, L.; Liu, D.; Karney, B. Phenomenon of white mist in pipelines rapidly filling with water with entrapped air pocket. J. Hydraul. Eng.
**2013**, 139, 1041–1051. [Google Scholar] [CrossRef] - Ramezani, L.; Karney, B.; Malekpour, A. The challenge of air valves: A selective critical literature review. J. Water Resour. Plan. Manag.
**2015**, 141. [Google Scholar] [CrossRef] - Ramezani, L.; Karney, B.; Malekpour, A. Encouraging effective air management in water pipelines: A critical review. J. Water Resour. Plan. Manag.
**2016**, 142, 04016055. [Google Scholar] [CrossRef][Green Version] - American Water Works Association (AWWA). Manual of Water Supply Practices—M51: Air-Release, Air-Vacuum, and Combination Air Valves; American Water Works Association: Denver, CO, USA, 2016. [Google Scholar]
- Coronado-Hernández, O.E.; Fuertes-Miquel, V.S.; Besharat, M.; Ramos, H.M. Experimental and numerical analysis of a water emptying pipeline using different air valves. Water
**2017**, 9, 98. [Google Scholar] [CrossRef] - Liou, C.; Hunt, W.A. Filling of pipelines with undulating elevation profiles. J. Hydraul. Eng.
**1996**, 122, 534–539. [Google Scholar] [CrossRef] - Zhou, L.; Liu, D. Experimental investigation of entrapped air pocket in a partially full water pipe. J. Hydraul. Res.
**2013**, 51, 469–474. [Google Scholar] [CrossRef] - Izquierdo, J.; Fuertes, V.S.; Cabrera, E.; Iglesias, P.; García-Serra, J. Pipeline start-up with entrapped air. J. Hydraul. Res.
**1999**, 37, 579–590. [Google Scholar] [CrossRef] - Fuertes-Miquel, V.S.; López-Jiménez, P.A.; Martínez-Solano, F.J.; López-Patiño, G. Numerical modelling of pipelines with air pockets and air valves. Can. J. Civ. Eng.
**2016**, 43, 1052–1061. [Google Scholar] [CrossRef][Green Version] - León, A.; Ghidaoui, M.; Schmidt, A.; Garcia, M. A robust two-equation model for transient-mixed flows. J. Hydraul. Res.
**2010**, 48, 44–56. [Google Scholar] [CrossRef][Green Version] - Chaudhry, M.H. Applied Hydraulic Transients, 3rd ed.; Springer: New York, NY, USA, 2014. [Google Scholar]
- Wylie, E.; Streeter, V. Fluid Transients in Systems; Prentice Hall: Englewood Cliffs, NJ, USA, 1993. [Google Scholar]
- Martins, S.C.; Ramos, H.M.; Almeida, A.B. Conceptual analogy for modelling entrapped air action in hydraulic systems. J. Hydraul. Res.
**2015**, 53, 678–686. [Google Scholar] [CrossRef] - Tijsseling, A.; Hou, Q.; Bozkus, Z.; Laanearu, J. Improved one-dimensional models for rapid emptying and filling of pipelines. J. Press. Vessel Technol.
**2016**, 138, 031301. [Google Scholar] [CrossRef][Green Version] - Balacco, G.; Apollonio, C.; Piccinni, A.F. Experimental analysis of air valve behaviour during hydraulic transients. J. Appl. Water Eng. Res.
**2015**, 3, 3–11. [Google Scholar] [CrossRef] - Abreu, J.; Cabrera, E.; Izquierdo, J.; García-Serra, J. Flow modeling in pressurized systems revisited. J. Hydraul. Eng.
**1999**, 125, 1154–1169. [Google Scholar] [CrossRef] - De Marchis, M.; Freni, G.; Milici, B. Experimental analysis of pressure-discharge relationship in a private water supply tank. J. Hydroinform.
**2018**, 20, 608–621. [Google Scholar] [CrossRef][Green Version] - Mohan, S.; Abhijith, G.R. Hydraulic analysis of intermittent water-distribution networks considering partial-flow regimes. J. Water Res. Plann. Manag.
**2020**, 146, 04020071. [Google Scholar] [CrossRef] - Collins, R.P.; Boxall, J.B.; Karney, B.W.; Brunone, B.; Meniconi, S. How severe can transients be after a sudden depressurization? J. Am. Water Work. Assoc.
**2012**, 104, E243–E251. [Google Scholar] [CrossRef][Green Version] - Alexander, J.M.; Lee, P.J.; Davidson, M.; Duan, H.F.; Li, Z.; Murch, R.; Meniconi, S.; Brunone, B. Experimental validation of existing numerical models for the interaction of fluid transients with in-line air pockets. J. Fluids Eng.
**2019**, 141, 121101. [Google Scholar] [CrossRef] - Besharat, M.; Tarinejad, R.; Aalami, M.T.; Ramos, H.M. Study of a compressed air vessel for controlling the pressure surge in water networks: CFD and experimental analysis. Water Resour. Manag.
**2016**, 30, 2687–2702. [Google Scholar] [CrossRef] - Covas, D.; Stoianov, I.; Ramos, H.M.; Graham, N.; Maksimovic, C.; Butler, D. Water hammer in pressurized polyethylene pipes: Conceptual model and experimental analysis. Urban Water J.
**2010**, 1, 177–197. [Google Scholar] [CrossRef] - Alexander, J.M.; Lee, P.J.; Davidson, M.; Li, Z.; Murch, R.; Duan, H.F.; Meniconi, S.; Brunone, B. Experimental investigation of the interaction of fluid transients with an in-line air pocket. J. Hydraul. Eng.
**2020**, 146, 04019067. [Google Scholar] [CrossRef]

**Figure 4.**Evolution over time of water flow during the emptying process in section P2–P4. Comparison between the mathematical model and the experimental measurements.

**Figure 5.**Evolution over time of the pressure inside the pipe during the emptying process in section P2–P4.

**Figure 6.**Evolution over time of the position and velocity of the water column during the emptying process in section P2–P4.

**Figure 7.**Evolution over time of the airflow entering the two air valves during the emptying process in section P2–P4.

Section No. | Abscissa | Pipeline Shaft Height (m.a.s.l.) | Length (m) | Longitudinal Slope (%) | ||
---|---|---|---|---|---|---|

From | To | From | To | |||

1 | K0 + 563.329 (P2) | K0 + 646.017 | 104.23 | 105.8 | 82.688 | 1.898 |

2 | K0 + 646.017 | K0 + 667.767 | 105.8 | 107.12 | 21.75 | 6.065 |

3 | K0 + 667.767 | K1 + 052.458 (P3) | 107.12 | 107.44 | 384.691 | 0.083 |

4 | K1 + 052.458 (P3) | K1 + 301.062 | 107.44 | 108.94 | 248.604 | 0.603 |

5 | K1 + 301.062 | K1 + 434.515 | 108.94 | 111.05 | 133.453 | 1.58 |

6 | K1 + 434.515 | K1 + 583.373 (P4) | 111.05 | 111.82 | 148.858 | 0.517 |

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**MDPI and ACS Style**

Romero, G.; Fuertes-Miquel, V.S.; Coronado-Hernández, Ó.E.; Ponz-Carcelén, R.; Biel-Sanchis, F. Transient Phenomena Generated in Emptying Operations in Large-Scale Hydraulic Pipelines. *Water* **2020**, *12*, 2313.
https://doi.org/10.3390/w12082313

**AMA Style**

Romero G, Fuertes-Miquel VS, Coronado-Hernández ÓE, Ponz-Carcelén R, Biel-Sanchis F. Transient Phenomena Generated in Emptying Operations in Large-Scale Hydraulic Pipelines. *Water*. 2020; 12(8):2313.
https://doi.org/10.3390/w12082313

**Chicago/Turabian Style**

Romero, Guillermo, Vicente S. Fuertes-Miquel, Óscar E. Coronado-Hernández, Román Ponz-Carcelén, and Francisco Biel-Sanchis. 2020. "Transient Phenomena Generated in Emptying Operations in Large-Scale Hydraulic Pipelines" *Water* 12, no. 8: 2313.
https://doi.org/10.3390/w12082313