# Pressure Drop and Cavitation Analysis on Sleeve Regulating Valve

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Numerical Method

#### 2.1. Mathematical Model

^{7}. In the cavitation simulations, phase change occurs between the liquid phase and vapor phase. The simulations are conducted in steady state. The governing equations for the cavitation model used in this paper are based on a single-fluid approach, which regarded the mixture as one fluid. Thus, the mixture continuity and momentum equations are shown as

_{m}and μ

_{m}are defined as follows:

_{m}, ρ

_{v}, and ρ

_{l}represent the mixture, vapor, and liquid densities, respectively;

**v**is the mass average velocity vector; μ

_{m}, μ

_{v}and μ

_{l}represent the mixture, vapor, and liquid dynamic viscosities, respectively, and μ

_{t}is the turbulence viscosity; p is the pressure; α represents the vapor volume fraction.

_{l}is assumed as a constant and so are μ

_{l}, ρ

_{v}, and μ

_{v}. Meanwhile, it is assumed that the bubbles remain spherical and there is no thermal conductivity with tube linked with the valves. The liquid–vapor mass transfer is governed by the vapor transport equation:

_{e}and R

_{c}are defined as follows:

_{e}represents the mass rates of growth of vapor bubbles and R

_{c}represents the mass rates of breaking of vapor bubbles;

**v**

_{v}is the vapor phase velocity, p

_{v}is the saturation pressure of water, R

_{b}is the bubble radius and is defined as follows:

^{13}.

#### 2.2. Geometrical Model

#### 2.3. Mesh and Boundary Conditoms

_{l}and ρ

_{v}are set as 862.8 kg/m³ and 7.865 kg/m³, and μ

_{l}and μ

_{v}are set as 1.357 × 10

^{−4}Pa·s and 1.565 × 10

^{−5}Pa·s, respectively. The vaporization pressure of the liquid phase is set as 1.5 MPa which equals to the saturation vapor pressure of the water at 200 °C. Above operations are all carried out in Fluent 17.2.

## 3. Results and Discussion

#### 3.1. Comparsion between Full Opening State and Half Opening State

#### 3.2. Flow Field Analysis for Different Pressure Difference

#### 3.3. Cavitation Distribution Analysis for Difference Pressure Differences

_{v}is calculated and denoted as

_{u}is the inlet pressure, p

_{d}is the outlet pressure, and the lower the σ

_{v}is, the higher is the potential. In general, when the σ

_{v}is lower than 1.0, the cavitation will occur. When the σ

_{v}is lower than 0.5, the cavitation phenomenon will be stable.

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

p | pressure (MPa) |

p_{v} | saturation pressure of water (MPa) |

t | time (s) |

v | mass average velocity (m/s) |

V_{v} | total vapor volume (m^{3}) |

R_{b} | bubble radius (m) |

R_{c} | rates of breaking of vapor bubbles |

α | vapor volume fraction |

n | bubble number density |

ρ_{m} | mixture density (kg/m³) |

ρ_{l} | liquid density (kg/m³) |

ρ_{v} | vapor density (kg/m³) |

μ_{m} | mixture dynamic viscosity (Pa·s) |

μ_{l} | liquid dynamic viscosity (Pa·s) |

μ_{v} | vapor dynamic viscosity (Pa·s) |

μ_{t} | turbulent viscosity (Pa·s) |

v_{v} | vapor phase velocity (m/s) |

L | valve core displacement (mm) |

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**Figure 2.**Mesh of the sleeve regulating valve with maximum valve core displacement of 60 mm (

**a**) overall view; (

**b**) mesh in the sleeve.

**Figure 3.**Pressure and velocity contours inside the sleeve regulating valve with valve core displacement of 60 mm and 30 mm (

**a**) pressure, 60 mm; (

**b**) pressure, 30 mm; (

**c**) velocity, 60 mm; (

**d**) velocity, 30 mm.

**Figure 4.**Pressure and velocity variation along the horizontal direction for different valve core displacements (

**a**) pressure; (

**b**) velocity.

**Figure 5.**Vapor distributions inside the sleeve regulating valve for different valve core displacements (

**a**) 60 mm; (

**b**) 30 mm.

**Figure 6.**Pressure contours inside the sleeve regulating valve with valve core displacement of 60 mm and 30 mm (MPa) (

**a**) 2 MPa, 60 mm; (

**b**) 2 MPa, 30 mm; (

**c**) 5 MPa, 60 mm; (

**d**) 5 MPa, 30 mm; (

**e**) 8 MPa, 60 mm; (

**f**) 8 MPa, 30 mm.

**Figure 7.**Pressure variation along the horizontal direction for different pressure differences (

**a**) L = 60 mm; (

**b**) L = 30 mm.

**Figure 8.**Velocity contours inside the sleeve regulating valve with valve core displacement of 60 mm and 30 mm (m/s) (

**a**) 2 MPa, 60 mm; (

**b**) 2 MPa, 30 mm; (

**c**) 5 MPa, 60 mm; (

**d**) 5 MPa, 30 mm; (

**e**) 8 MPa, 60 mm; (

**f**) 8 MPa, 30 mm.

**Figure 9.**Velocity variation along the horizontal direction for different pressure differences (

**a**) L = 60 mm; (

**b**) L = 30 mm.

**Figure 11.**Vapor distributions inside the sleeve regulating valve for different pressure difference with the valve core displacement of 60 mm (

**a**) 2 MPa; (

**b**) 5 MPa; (

**c**) 8 MPa.

**Figure 12.**Vapor distributions inside the sleeve regulating valve for different pressure difference with the valve core displacement of 30 mm (

**a**) 2 MPa; (

**b**) 5 MPa; (

**c**) 8 MPa.

**Figure 13.**Total vapor volumes inside the valve for different pressure differences with the valve core displacement of 60 mm and 30 mm.

**Figure 14.**Total vapor volumes inside the valve for different cavitation index with the valve core displacement of 60 mm and 30 mm.

Grids | Flow Rate (kg/s) | Volume Fraction |
---|---|---|

1,451,696 | 162.72 | 0.1296 |

1,705,067 | 162.14 | 0.2272 |

2,055,352 | 168.31 | 0.2676 |

2,407,840 | 167.74 | 0.2829 |

2,708,138 | 167.37 | 0.2585 |

3,138,669 | 167.01 | 0. 2323 |

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**MDPI and ACS Style**

Qiu, C.; Jiang, C.-H.; Zhang, H.; Wu, J.-Y.; Jin, Z.-J.
Pressure Drop and Cavitation Analysis on Sleeve Regulating Valve. *Processes* **2019**, *7*, 829.
https://doi.org/10.3390/pr7110829

**AMA Style**

Qiu C, Jiang C-H, Zhang H, Wu J-Y, Jin Z-J.
Pressure Drop and Cavitation Analysis on Sleeve Regulating Valve. *Processes*. 2019; 7(11):829.
https://doi.org/10.3390/pr7110829

**Chicago/Turabian Style**

Qiu, Chang, Cheng-Hang Jiang, Han Zhang, Jia-Yi Wu, and Zhi-Jiang Jin.
2019. "Pressure Drop and Cavitation Analysis on Sleeve Regulating Valve" *Processes* 7, no. 11: 829.
https://doi.org/10.3390/pr7110829