# Flow Field and Gas Field Distribution of Non-Submerged Cavitation Water Jet Based on Dual-Nozzle with Concentric Configuration

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## Abstract

**:**

## 1. Introduction

## 2. Numerical Simulation

#### 2.1. Geometric Model

_{h}(20 MPa) into a low-speed water jet with a pressure of p

_{w}(0.08 MPa) to form a cavitation water jet.

_{H}= 9 mm and d

_{L}= 70 mm, respectively. The standoff distance is H = 25 mm, which is the same for the inner and external nozzle. The outer diameter of the inner nozzle is 32 mm, the linear transition segment of the outer wall is 30 mm, and the length of the outer wall constriction segment is 45 mm; the straight segment of the outer nozzle is 20 mm and the inner wall constriction segment is 55 mm. For the inner nozzle, the length of the constriction segment is L = 7 mm, the height is s = 4 mm, and the angle of the contraction segment is α = 30°. The length of the expansion segment is w = 3.5 mm and the expansion angle is β = 45°. The diameter of the throat is d = 1 mm and the length is 7.5 mm.

#### 2.2. Meshing and Boundary Condition

^{−6}s. When the residual error is controlled within 1 × 10

^{−6}, the calculation is considered to be basically convergent. The CPU used for the calculation is Intel(R) Xeon(R) Gold 6242R. The simulation calculation in this paper used a total of 2000 core hours.

#### 2.3. Control Equation

#### 2.3.1. Multiphase Flow Model

#### 2.3.2. Turbulence Model

_{k}is the generating term of turbulent kinetic energy; G

_{ω}is the generating term of dissipation rate ω; Y

_{k}and Y

_{ω}represent the dissipation of k and ω caused by turbulence, respectively; Γ

_{k}and Γ

_{ω}are the effective diffusivity of k and ω, respectively; and σ

_{k}and σ

_{ω}are the turbulent Prandtl numbers of k and ω, respectively. μ

_{t}represents the turbulent viscosity, which is calculated by the following equation.

#### 2.3.3. Cavitation Model

- $v$ = vapor phase;
- $\alpha $ = vapor volume fraction;
- ${\rho}_{v}$ = vapor density;
- ${\overrightarrow{V}}_{v}$ = vapor phase velocity;
- ${R}_{e},{R}_{c}$ = mass transfer source terms connected to the growth and collapse of the vapor bubbles, respectively.

- $\alpha $ = vapor volume fraction;
- ${\rho}_{v}$ = vapor density;
- ${R}_{b}$ = bubble radius;
- ${P}_{b}$ = bubble surface pressure;
- $P$ = local far-field pressure;
- ${\rho}_{l}$ = liquid density.

- ${P}_{v}$ = saturation vapor pressure;
- ${F}_{vap}$ (evaporation coefficient) = 50;
- ${\alpha}_{nuc}$ (volume fraction of gas nuclei) = 5 × 10
^{−4}; - ${\rho}_{v}$ = vapor density;
- ${R}_{b}$ (bubble radius) = 1 × 10
^{−6}m; - $P$ = local far-field pressure;
- ${\rho}_{l}$ = liquid density;
- ${F}_{cond}$ (condensation coefficient) = 0.01.

#### 2.4. Mesh Refinement Analysis

#### 2.5. Model Experimental Validation

## 3. Results and Discussions

#### 3.1. Analysis of Flow Field Characteristics

#### 3.1.1. The Gas Phase Distribution

#### 3.1.2. The Velocity Distribution

#### 3.1.3. The Pressure Distribution

#### 3.2. Effects of Geometric Parameters of Inner Nozzle

#### 3.2.1. The Gas Phase Distribution

#### 3.2.2. The Velocity Distribution

#### 3.2.3. The Pressure Distribution

#### 3.3. Effects of Pressure Ratio of Inner Nozzle to External Nozzle

#### 3.3.1. The Gas Phase Distribution

_{1}is the upstream pressure of the jet, p

_{2}is the downstream pressure, and p

_{v}is the saturated vapor pressure of the environment in which it is located.

#### 3.3.2. The Velocity Distribution

#### 3.3.3. The Pressure Distribution

#### 3.4. Discussions

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**(

**a**) Schematic diagram of cavitation water jet device. (

**b**) Schematic diagram of the geometric size of the nozzle structure.

**Figure 4.**Cloud map of gas phase distribution in the flow field with different number of grids: (

**a**) 14,860, (

**b**) 22,200, (

**c**) 79,200, (

**d**) 122,840, (

**e**) 245,400.

**Figure 5.**Comparison of cavitation jet morphology from high-speed photography (

**a**) and numerical simulation (

**b**).

**Figure 9.**Conical composite nozzle structure and grid schematic: (

**a**) nozzle B, (

**b**) nozzle C, (

**c**) nozzle D, (

**d**) nozzle E.

**Figure 10.**Cloud diagram of gas phase distribution in the flow fields of five nozzles: (

**a**) nozzle A, (

**b**) nozzle B, (

**c**) nozzle C, (

**d**) nozzle D, (

**e**) nozzle E.

**Figure 13.**Flow field gas phase distribution clouds at different incident pressures: (

**a**) 20 MPa:0.08 MPa, (

**b**) 20 MPa:0.04 MPa, (

**c**) 20 MPa:0 Pa, (

**d**) 30 MPa:0 Pa, (

**e**) 40 MPa:0 Pa.

Mesh-1 | Mesh-2 | Mesh-3 | Mesh-4 | Mesh-5 | |
---|---|---|---|---|---|

Number of grids | 14,860 | 22,200 | 79,200 | 122,840 | 245,400 |

Contraction Segment | Expansion Segment | Throat Diameter d | Target Distance H | |
---|---|---|---|---|

Nozzle A | L = 7 mm, s = 4 mm (α = 30°) | w = 3.5 mm, β = 45° | 1 mm | 25 mm |

Nozzle B | L = 6.125 mm, s = 3.5 mm (α = 30°) | w = 3.5 mm, β = 45° | 2 mm | 25 mm |

Nozzle C | L = 12 mm, s = 4 mm (α = 18°) | w = 3.5 mm, β = 45° | 1 mm | 25 mm |

Nozzle D | L = 7 mm, s = 4 mm (α = 30°) | No expansion segment | 1 mm | 25 mm |

Nozzle E | No contraction segment | No expansion segment | 1 mm | 25 mm |

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**MDPI and ACS Style**

Luo, Y.; Zang, J.; Zheng, H.
Flow Field and Gas Field Distribution of Non-Submerged Cavitation Water Jet Based on Dual-Nozzle with Concentric Configuration. *Water* **2023**, *15*, 2904.
https://doi.org/10.3390/w15162904

**AMA Style**

Luo Y, Zang J, Zheng H.
Flow Field and Gas Field Distribution of Non-Submerged Cavitation Water Jet Based on Dual-Nozzle with Concentric Configuration. *Water*. 2023; 15(16):2904.
https://doi.org/10.3390/w15162904

**Chicago/Turabian Style**

Luo, Yun, Jingyu Zang, and Hongxiang Zheng.
2023. "Flow Field and Gas Field Distribution of Non-Submerged Cavitation Water Jet Based on Dual-Nozzle with Concentric Configuration" *Water* 15, no. 16: 2904.
https://doi.org/10.3390/w15162904