Flash boiling atomization (FBA) is a promising approach for enhancing spray atomization, which can generate a fine and more evenly distributed spray by increasing the fuel injection temperature or reducing the ambient pressure. However, when the outlet speed of the nozzle exceeds 400 m/s, investigating high-speed flash boiling atomization (HFBA) becomes quite challenging. This difficulty arises from the involvement of many complex physical processes and the requirement for a very fine mesh in numerical simulations. In this study, an HFBA model for gasoline direct injection (GDI) is established. This model incorporates primary and secondary atomization, as well as vaporization and boiling models, to describe the development process of the flash boiling spray. Compared to low-speed FBA, these physical processes significantly impact HFBA. In this model, the Eulerian description is utilized for modeling the gas, and the Lagrangian description is applied to model the droplets, which effectively captures the movement of the droplets and avoids excessive mesh in the Eulerian coordinates. Under various conditions, numerical solutions of the Sauter mean diameter (SMD) for GDI show good agreement with experimental data, validating the proposed model’s performance. Simulations based on this HFBA model investigate the influences of fuel injection temperature and ambient pressure on the atomization process. Numerical analyses of the velocity field, temperature field, vapor mass fraction distribution, particle size distribution, and spray penetration length under different superheat degrees reveal that high injection temperature or low ambient pressure significantly affects the formation of small and dispersed droplet distribution. This effect is conducive to the refinement of spray particles and enhances atomization.

Over the last few decades, significant efforts have been made to increase the efficiency of internal combustion engines and simultaneously reduce tailpipe emissions. The spray atomization process in internal combustion engines directly affects the engine’s thermal efficiency and emissions [

Many researchers have studied FBA from theoretical, experimental, and numerical aspects. The theoretical studies have investigated the flash boiling process’s theories, including flashing inception, nucleation, bubble growth [

Since the theory of FBA is quite complicated, covering many physical processes, and experiments under high temperature and high pressure are hard to control, more investigations have been achieved through numerical simulations [

In order to save computational costs, more simulations of flash boiling spray resort to Eulerian-Lagrangian methods. Models based on Eulerian-Lagrangian descriptions include primary atomization models [

When the outlet speed of the nozzle exceeds 400 m/s, the high-speed FBA requires a very dense mesh to trace the flow field information of the gas and droplets and the gas-liquid interfaces. Millions or even billions of grids should be introduced, and the data post-processing becomes quite burdensome [

This study establishes a high-speed flash boiling atomization (HFBA) model for fuel atomization, catering to scenarios where the outlet speed exceeds 400 m/s, reaching up to approximately 700 m/s. This model encompasses the processes of primary atomization, secondary atomization, and the interaction between gas and liquid during atomization. The Eulerian method is employed for modeling the gas, while the Lagrangian method is utilized for simulating the liquid. These methods enable effective capture of the droplets and gas-liquid interfaces. Implementing an adaptive mesh enhances the resolution of the gas-liquid interfaces, improving the model’s accuracy. The model operates with fewer than one hundred thousand grids, maintaining a solution error below 10% compared to experimental data [

Considering the computational costs, the Eulerian-Lagrangian method is adopted for fuel atomization simulations. Compared to the Eulerian-Eulerian method, this method simplifies capturing the flow field, particle size, and other information post-atomization and facilitates the design and optimization of the numerical model [

The flash boiling spray of fuel is a complex gas-liquid two-phase flow process, encompassing turbulent flow, gas-liquid heat transfer, and mass transfer processes. These physical processes adhere to basic conservation laws, including mass and momentum conservation. For the heat transfer problem, the law of energy conservation and the equation of state of the ideal gas are also applicable [

(1) Mass conservation equation

In this study, the three-dimensional problem is simplified to be a 2D axisymmetric problem, where

where

(2) Momentum conservation equations

For the 2D axisymmetric problem, the momentum conservation equation is given by

where

(3) Energy conservation equation

The energy conservation equation can be expressed as

where

(4) Vapor-liquid equilibrium equation

The vapor-liquid equilibrium equation is described as follows:

where

(5) Equation of state of the ideal gas

For the ideal gas, the equation of state can be expressed by

where

This study simulates the FBA and evaporation processes of fuel using the discrete phase model (DPM) in the Lagrangian coordinate system. The DPM model captures various physical processes in the FBA process, including liquid spraying into the combustion chamber, droplet formation, and the exchange of momentum, mass, energy, and species transfer between droplets and gas [

The droplet is considered a discrete particle, and the particle trajectory can be predicted by solving the equation of motion under the Lagrangian reference system. The equation of motion is given as follows [

where

where

(1) Droplet heating and cooling

When the temperature of the droplet is below the defined evaporation temperature

where

where

(2) Evaporation of droplets

The evaporation law can be utilized to evaluate the evaporation of a droplet in the discrete phase when the temperature of the droplet satisfies the following conditions

where

where

During the evaporation of the droplet, the reduction of the mass of the droplet is according to the following equation:

where

When

where

(3) Boiling of droplets

When the boiling condition

where

In the interactions between gas and droplets, exchanges of mass and momentum occur, as illustrated in

(1) Momentum exchange

The transfer of momentum from the gas to the droplets can be calculated by examining the change in momentum of the droplets when they pass through each control volume. The change in momentum can be described as follows [

where

(2) Mass exchange

The mass transfer from the droplets to the gas can be evaluated by computing the change in mass of the droplets when they pass through each control volume. The mass change

where

Turbulence is a nonlinear and complex flow that induces turbulent fluctuations, resulting in mass and momentum exchange and concentration changes between fluid media. Common numerical methods for modeling turbulence include the direct simulation method (DNS), large eddy simulation (LES), and Reynolds-averaged Navier-Stokes (RANS) method. DNS directly solves the Navier-Stokes equation without a turbulence model, encompassing the flow field from the turbulent dissipation scale (Kolmogorov scale) to the large eddy scale, requiring a very small time step and refined grid scale [

where

In the HFBA process, the fuel undergoes intense heat and momentum exchange with surrounding air during the primary atomization period. As a critical component of the atomization process, the accuracy of the entire simulation depends on the model selection for this period [

Effervescent atomization is a process where a jet of superheated liquid is injected, and upon leaving the nozzle, the volatile liquid rapidly boils and undergoes phase change. This sudden phase change effectively breaks the continuous liquid stream into small droplets with a wide atomization angle, forming a droplet group. In the model, the initial droplet velocity is calculated using the law of conservation of mass. It is assumed that the nozzle exit’s cross-sectional area is

where

The maximum droplet diameter is set to be the effective diameter of the nozzle

where

where

and

where

Post-primary atomization, large droplets may further fragment in subsequent motions. The WAVE model, which is applicable to high Weber number problems, is introduced in this paper to simulate the HFBA process of fuel [

where

The most unstable growth rate

where

The radius of the newly-formed droplets is proportional to the wavelength of the fastest-growing unstable surface wave on the parent droplet

where

In this section, several examples of numerical simulations for the HFBA process are presented. The experimental data from Li et al.’s study [

Parameter (unit) | Value |
---|---|

Fuel temperature (K) | 293, 333, 379 |

Ambient pressure (kPa) | 5, 10, 20, 30, 60, 100 |

Ambient temperature (K) | 298 |

Injection pressure (bar) | 350 |

Nozzle diameter (mm) | 0.143 |

Fuel | n-pentane |

In the numerical simulations, a 2D axisymmetric geometry problem is studied, as depicted in

Boundary conditions | Pressure inlet (kPa) | 5, 10, 20, 30, 60, 100 |

Pressure outlet (kPa) | 5, 10, 20, 30, 60, 100 | |

Component | n-pentane | |

Temperature (K) | 298 | |

Droplet properties | Position (mm) | (0.1, 0) |

Temperature (K) | 293, 313, 333, 343, 353, 379 | |

Vaporization temperature (K) | 223 | |

Boiling point (K) | 309 | |

Atomization model | Primary atomization | Effervescent atomizer model |

Secondary atomization | WAVE | |

Numerical algorithm | Scheme | SIMPLEC |

Pressure | PRESTO! | |

Momentum | Second order upwind | |

Density | Second order upwind | |

Turbulent kinetic energy | Second order upwind | |

Turbulence dissipation rate | Second order upwind | |

n-pentane | Second order upwind |

For the finite volume method, the accuracy of simulation results depends on mesh distribution. Near the nozzle, where a large number of liquids boil and vaporize instantaneously, forming an extremely high-velocity jet stream with drastic changes in temperature, momentum, and species concentration, mesh refinement is crucial. As shown in

In order to validate the proposed atomization model, experimental results of n-pentane fuel atomization from the literature [

where

For the FBA, the ambient-to-saturation pressure and the degree of superheating can be utilized as characteristic parameters to describe the phase transformation of the flash boiling spray [

(1) Solutions of gas under different ambient pressures

As depicted in

As shown in

As the spray continues to move, the maximum velocity and vapor concentration along the x-axis direction gradually decrease while the mass fraction increases in the y-axis direction (radial direction). This phenomenon occurs since work is required to overcome air resistance during the spray motion, resulting in energy consumption. As a result, the velocity decays in both the axial and radial directions, accompanied by the diffusion of vapor in the radial direction.

(2) Solutions of droplets under different ambient pressures

In order to investigate the influence of ambient pressure on the size of atomized droplets, the SMD of droplets under an injection temperature of 333 K and ambient pressures of 5, 10, 20, 30, 60, and 100 kPa are compared, as shown in

The size distribution of the droplets under ambient pressures of 5, 10, 20, 30, 60, and 100 kPa is presented in

Furthermore, as displayed in

(1) Solutions of gas under different injection temperatures

As presented in

(2) Solutions of droplets under different injection temperatures

In order to investigate the differences in atomized droplet size at 50 mm from the nozzle under different injection temperatures, the droplet SMD at an ambient pressure of 60 kPa and injection temperatures of 293, 313, 333, 343, 353, and 397 K are compared, as presented in

As shown in

As displayed in

This study proposes an HFBA model to simulate the atomization process under high outlet speed. Compared to the experimental results, the maximum SMD error from the proposed model is less than 8% when the numerical model’s boundary conditions align with the experiments’ operating conditions [

The results demonstrate that HFBA can generate extremely fine and uniformly distributed spray. During flash evaporation, vapor generation and bubble growth stem from mass transfer induced by interphase heat transfer, with the vapor generation rate being regulated by thermal imbalance. Increasing the initial injection temperature or decreasing the ambient pressure enhances the liquid’s superheat, intensifies the thermal imbalance, and amplifies energy instability within the liquid, thus accelerating vapor generation. Additionally, higher superheat fosters bubble nucleation density and frequency, precipitates the onset of flash vaporization, and reduces droplet size, thereby driving the flash vapor. Incremental increases in injection temperature or reductions in ambient pressure lead to a gradual increase in the proportion of smaller droplets and a corresponding decrease in D10, D30, D50, and SMD, culminating in finer and more uniform atomized droplets. Furthermore, lowering the ambient pressure diminishes the axial velocity of atomized droplets, enhancing their combustion efficiency in the chamber. This HFBA model shows significant potential for extensive application in simulating high-velocity fuel atomization challenges.

The authors express their sincere gratitude to Professor Xuesong Li of the School of Mechanical Engineering, Shanghai Jiao Tong University, for providing invaluable insights and details crucial to the success of the experimental work in this paper. Special thanks also extend to the dedicated staff at Beijing Mechanical Equipment Research Institute for their valuable input and guidance, which contributed to the enhancement of this research. Their collaborative efforts have greatly enriched the quality and depth of their work.

This work is supported by the National Natural Science Foundation of China (Project Nos. 12272270, 11972261).

The authors confirm their contribution to the paper as follows: Study conception and design: Wei Zhong, Lihua Wang; data collection: Wei Zhong, Zhenfang Xin, Lihua Wang, Haiping Liu; analysis and interpretation of results: Wei Zhong, Lihua Wang; draft manuscript preparation: Wei Zhong, Lihua Wang. All authors reviewed the results and approved the final version of the manuscript.

The material data utilized in this study have been sourced from Google, which provides a comprehensive platform for various datasets, and the experimental data [

The authors declare that they have no conflicts of interest to report regarding the present study.