# Gas Release and Solution as Possible Mechanism of Oscillation Damping in Water Hammer Flow

## Abstract

**:**

## 1. Introduction

## 2. Mathematical Models

#### 2.1. Continuity Equation

#### 2.2. Gas Release and Solution Equation

#### 2.3. Momentum Equations

#### 2.4. Boundary Conditions

#### 2.5. Method of Characteristics

#### 2.6. Numerical Scheme

#### 2.7. Micro-GA

^{10}= 1024 possible values) of the parameters ${m}_{0}$ and ${\theta}_{m}$, ranging, respectively, between 0 and 100 mg/m

^{3}, and between 10 and 1000 s, was used. A population size ${N}_{P}$ = 5 was used for the calibration of gas mass in the models with constant gass mass, where ${N}_{P}$ = 9 was used for the calibration of initial gas mass and relaxation time in the models with variable gas mass [22].

## 3. Experimental Installation

^{11}N/m

^{2}, roughness 0.1 mm, length 144.3 m) and it is fed by a centrifugal pump. A pressure tank is located at the downstream end of the pipe. The line pressure was measured with strain gauge pressure transducers, having a range of 0 to 10 bar, with maximum error of $\pm $0.5% of full-scale pressure. Discharge measurements were carried out with an electromagnetic flowmeter with adjustable full-scale velocity, with maximum errors of $\pm $0.1% of full scale. Each experimental test started from steady-state conditions by manually closing the ball valve at the upstream end of the pipe. The valve closure was estimated to take 0.04 s. Temperature as measured in all the experimental tests was 24 °C. Each physical property of water and air was indirectly evaluated as a function of the measured temperature. In Table 1, for each experimental test, values of initial discharge ${Q}_{0}$ and static head ${H}_{s}$ referred to the laboratory floor are shown.

## 4. Analysis of Results

## 5. Conclusions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 5.**Comparison of head oscillations computed with the 1D or 2D model without free gas with the experimental results for Test L3: (

**a**) 1D model, $t$ = 0 − 15 s; (

**b**) 2D model, $t$ = 0 − 15 s; (

**c**) 1D model, $t$ = 15 − 30 s; (

**d**) 2D model, $t$ = 15 − 30 s.

**Figure 6.**Comparison of head oscillations computed with the 2D model with constant or variable mass of free gas with the experimental results for Test L3: (

**a**) 2D model with constant mass of free gas, $t$ = 0 − 15 s; (

**b**) 2D model with variable mass of free gas, $t$ = 0 − 15 s; (

**c**) 2D model with constant mass of free gas, $t$ = 15 − 30 s; (

**d**) 2D model with variable mass of free gas, $t$ = 15 − 30 s.

**Figure 7.**Comparison of head oscillations computed with the 2D present model or with the Lam and Bremhorst [23] model without free gas with the experimental results for Test L3: (

**a**) 2D present model, $t$ = 0 − 15 s; (

**b**) 2D Lam and Bremhorst model, $t$ = 0 − 15 s; (

**c**) 2D present model, $t$ = 15 − 30 s; (

**d**) 2D Lam and Bremhorst model, $t$ = 15 − 30 s.

Test | ${\mathbf{Q}}_{0}$ (L/s) | ${\mathbf{V}}_{0}$ (m/s) | ${\mathbf{H}}_{\mathbf{s}}$ (m) | ${\mathbf{R}\mathbf{e}}_{0}$ |
---|---|---|---|---|

L1 | 0.207 | 0.091 | 68.12 | 5300 |

L2 | 0.409 | 0.179 | 66.87 | 10,500 |

L3 | 0.598 | 0.262 | 60.08 | 15,400 |

Test | 2D—Constant Mass | 2D—Variable Mass | |
---|---|---|---|

${\mathit{m}}_{0}$ (mg/m^{3})
| ${\mathit{m}}_{0}$ (mg/m^{3})
| ${\mathit{\theta}}_{\mathit{m}}$ (s) | |

L1 | 1.96 | 0.00 | 753.2 |

L2 | 17.30 | 6.16 | 754.2 |

L3 | 28.64 | 14.96 | 815.2 |

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**MDPI and ACS Style**

Pezzinga, G.
Gas Release and Solution as Possible Mechanism of Oscillation Damping in Water Hammer Flow. *Water* **2023**, *15*, 1942.
https://doi.org/10.3390/w15101942

**AMA Style**

Pezzinga G.
Gas Release and Solution as Possible Mechanism of Oscillation Damping in Water Hammer Flow. *Water*. 2023; 15(10):1942.
https://doi.org/10.3390/w15101942

**Chicago/Turabian Style**

Pezzinga, Giuseppe.
2023. "Gas Release and Solution as Possible Mechanism of Oscillation Damping in Water Hammer Flow" *Water* 15, no. 10: 1942.
https://doi.org/10.3390/w15101942