# Effect of Fuel Mass Flow at the End of Injection on Cavitation and Gas Ingestion in the Nozzle

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## Abstract

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## Featured Application

**Diesel engine injector.**

## Abstract

## 1. Introduction

## 2. Experiment

## 3. Mathematical Model

#### 3.1. Governing Equations

#### 3.2. Cavitation Model

#### 3.3. Computational Domain and Boundary Condition

^{−8}s, the maximum time step was 1 × 10

^{−6}s, the maximum Courant number (the ratio of time step to space step) was 0.3, and the maximum maxAlphaCo was also 0.3.

## 4. Results and Discussion

#### 4.1. End of Injection (EOI)

#### 4.2. After Injection (AI)

#### 4.3. Influence of Mass Flux

#### 4.4. Analyzing the Cavitation Mechanism of Different Mass Fluxes

^{9}iso-surface, streamline, and α = 0.25 vapor iso-surface in the nozzle at different mass fluxes. From left to right are cloud pictures of Q = 2 × 10

^{9}iso-surface, streamlines, and α = 0.25 vapor iso-surface, respectively. As can be seen, regardless of whether the mass flux was 12 mg/str, 14 mg/str, or 18 mg/str, the orifice always occurred cavitation first, the cavitation in the nozzle had similar morphology, and the sac was dominated by annular cavitation, while the orifice was bulk. In addition, the annular cavitation in the sac was mainly concentrated at the fuel inlet, then developed from the inlet toward the sac downstream but never reached the bottom of the sac.

## 5. Conclusions

- (1)
- Cavitation and gas ingestion occurred sequentially in the nozzle, starting with the orifice and finishing in the sac. The sac played a major role in affecting the total amount of ingestion gas and cavitation. The maximum fuel inertial outflow and cavitation in the nozzle were crucial in determining the total fuel outflow.
- (2)
- The pressure difference between the pressure of the cavitation bubble and that of atmospheric pressure caused the cavitation collapse after the EOI, further generating external air to flow back into the nozzle. In addition, the gas ingestion bubbles in the nozzle began to fuse under the action of the surface tension after the EOI, and finally, its shape became regular.
- (3)
- The cavitation in the sac was mainly annular, and the orifice was mainly bulk cavitation. The cavitation in the sac concentrated on the nozzle inlet and developed downward. This was attributed to the fact that larger fuel mass increased the amount of gas ingestion and cavitation, and resulted in a longer deformation and fusion time for ingestion bubbles.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**The experimental visualization platform. 1. Oil tank; 2. High-pressure oil pump; 3. High-pressure common-rail pipe; 4. Pressure sensor; 5. Fuel injector; 6. Experimental nozzle; 7. Electronic control unit (ECU); 8. High-speed framing camera; 9. Long focal distance microscope; 10. LED light; 11. Computer.

**Figure 5.**Volume fraction of diesel in the nozzle at the end of injection (EOI) (volume fraction of diesel means the volume of diesel as a percentage of the fluid volume in the nozzle).

**Figure 12.**Q = 2 × 10

^{9}iso-surface, streamline, and α = 0.25 vapor iso-surface in the nozzle at different mass fluxes.

Parameters | Value | Unit |
---|---|---|

Density of diesel/ρ | 840 | kg·m^{−3} |

Dynamic viscosity of diesel/μ | 0.0065 | Pa·s |

Density of air/ρ | 1.21 | kg·m^{−3} |

Dynamic viscosity of air/μ | 1.85 × 10^{−5} | Pa·s |

Density of diesel vapor/ρ | 0.14 | kg·m^{−3} |

Dynamic viscosity of diesel vapor/μ | 4.25 × 10^{−5} | Pa·s |

Saturated vapor pressure of diesel/p_{v} | 2000 | Pa |

Surface tension/σ | 0.03 | kg·s^{−2} |

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**MDPI and ACS Style**

Wen, H.; Jiang, Y.; Ma, J.
Effect of Fuel Mass Flow at the End of Injection on Cavitation and Gas Ingestion in the Nozzle. *Appl. Sci.* **2021**, *11*, 258.
https://doi.org/10.3390/app11010258

**AMA Style**

Wen H, Jiang Y, Ma J.
Effect of Fuel Mass Flow at the End of Injection on Cavitation and Gas Ingestion in the Nozzle. *Applied Sciences*. 2021; 11(1):258.
https://doi.org/10.3390/app11010258

**Chicago/Turabian Style**

Wen, Hua, Yulong Jiang, and Jinglong Ma.
2021. "Effect of Fuel Mass Flow at the End of Injection on Cavitation and Gas Ingestion in the Nozzle" *Applied Sciences* 11, no. 1: 258.
https://doi.org/10.3390/app11010258