# Numerical and Experimental Study on the Process of Filling Water in Pressurized Water Pipeline

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## Abstract

**:**

## 1. Introduction

## 2. Numerical Simulation of the Water Filling Process of Pressurized Pipeline

#### 2.1. Model Development

^{5}pa. In the process of pipeline filling water, the inlet of air is not considered; we thus assume that the boundary of the air inlet is same as the side wall. The standard wall function method is adopted to calculate the side wall of the pipe and no slip boundary conditions are adopted. The pipe system is insulated and has no heat exchange with the fluid. At the beginning of water filling process, the water volume fraction in the calculation area is set to 0, the relative humidity of air is 50%. The volume fraction at the boundary of the inlet is set to 1, indicating that the fluid at the inlet is the physical parameters of the water and air phases under the temperature of 20 °C. The standard atmospheric pressure is shown in Table 1.

#### 2.2. Mathmatical Details of the Numerical Simulation

- 1.
- Continuity equation

- 2.
- Momentum equation

- 3.
- Energy equation

^{3}; t is time, s; μ is the dynamic viscosity coefficient; g is the gravitational acceleration, m/s

^{2}; F is the volumetric force, N; p is the pressure, Pa; T is the temperature, $\mathbb{C}$; S

_{T}is the source term.

- 4.
- Turbulence equation

_{k}represents the generation term of turbulent kinetic energy k caused by the average velocity gradient; G

_{b}represents the generation term of turbulent kinetic energy k caused by buoyancy; Y

_{m}represents the effect of compressible turbulent pulsation expansion on the total dissipation rate; g is the gravitational acceleration, m/s

^{2}; S

_{k}is the source term.

#### 2.3. Results of the Numerical Simulation

## 3. Physical Model Experiments

#### 3.1. Experimental Method

#### 3.2. Experimental Results

#### 3.3. Comparison of Experimental Results and Numerical Simulation Results

## 4. Conclusions

- (1)
- Under low flow rate conditions, there is more local trapped gas at the top of the pipeline, causing negative pressure at local high points in the pipeline. Under high velocity conditions, there is no gas stagnation at local high points in the pipeline, with a large number of bubbles collapsing at the top of the pipeline, causing large fluctuations in pipeline pressure. Therefore, in practical engineering, air valves should be installed at local high points in water pipelines to not only discharge trapped gas but also allow gas to enter when there is negative pressure in the pipeline.
- (2)
- The main flow patterns during the water filling process of right-angle elbow pipelines include stratified flow, slug flow, bubble flow, plug flow, and wavy flow. The larger the water filling velocity, the more frequent the conversion of water–air two-phase flow patterns in the pipeline. Pipeline pressure changes violently due to slug flow.
- (3)
- The pipeline water filling process can be divided into two stages. In the first stage, flow patterns and pressure in the pipeline change dramatically, while in the second stage, flow patterns and pressure in the pipeline gradually stabilize. Based on this principle, a phased water filling method can be adopted in practical engineering to effectively reduce pressure peaks and shorten water filling time.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 5.**Time variation of the water–air interaction under the working condition of case 1 obtained from numerical simulation.

**Figure 6.**Time variation of the water–air interaction under the working condition of case 2 obtained from numerical simulation.

**Figure 10.**Local velocity vector diagram and streamline diagram. (

**a**) a horizontal section at the left side, (

**b**) a vertical upward section, (

**c**) an upper horizontal section, (

**d**) a vertical downward section, (

**e**) a horizontal section at the right side.

**Figure 12.**Experimental facilities: (

**a**) pipeline, (

**b**) the reassure measurement system, (

**c**) the water flow measurement system, (

**d**) the air flow measurement system, (

**e**) high speed camera.

**Figure 15.**Time evolution of the pressure at the four indicated monitoring points: (

**a**) P1 monitoring point, (

**b**) P2 monitoring point, (

**c**) P3 monitoring point, (

**d**) P4 monitoring point.

Fluid | Density (kg/m ^{3}) | Dynamic Viscosity (pa∙s) | Surface Tension (N/m) |
---|---|---|---|

Water | 998.2 | 1.003 × 10^{−3} | 0.072 |

Air | 1.2 | 1.79 × 10^{−5} | 0.072 |

Condition | Inlet Velocity (m/s) | Calculated Pressure (kPa) | Measured Pressure (kPa) | Error (%) |
---|---|---|---|---|

Water filling | Velocity 0.6 m/s | 8.60 | 8.48 | 1.39 |

Water filling | Velocity 1.5 m/s | 15.37 | 14.86 | 3.32 |

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## Share and Cite

**MDPI and ACS Style**

Hu, J.; Wang, Q.; Zhang, Y.; Meng, Z.; Zhang, J.; Fan, J.
Numerical and Experimental Study on the Process of Filling Water in Pressurized Water Pipeline. *Water* **2023**, *15*, 2508.
https://doi.org/10.3390/w15142508

**AMA Style**

Hu J, Wang Q, Zhang Y, Meng Z, Zhang J, Fan J.
Numerical and Experimental Study on the Process of Filling Water in Pressurized Water Pipeline. *Water*. 2023; 15(14):2508.
https://doi.org/10.3390/w15142508

**Chicago/Turabian Style**

Hu, Jianyong, Qingbo Wang, Yuzhou Zhang, Zhenzhu Meng, Jinxin Zhang, and Jiarui Fan.
2023. "Numerical and Experimental Study on the Process of Filling Water in Pressurized Water Pipeline" *Water* 15, no. 14: 2508.
https://doi.org/10.3390/w15142508