# Review on the Recent Numerical Studies of Liquid Atomization
## 3 Interface Capturing
### Application Cases  
[PERSON] et al. [38] combined direct numerical simulation (DNS) and large eddy simulation (LES) turbulence model, respectively, in the dense and sparse regions of a pre-filming atomization. A total number of 84 million cells were used with a time step of \(5\times 10^{-8}\) s. VOF in the OpenFOAM was employed, resulting in comparable gas-liquid patterns and droplet distribution with the visual measurement. [PERSON] and [PERSON] [39] considered evaporation in their simulation of liquid fuel jet. In their VOF method, ghost fluid method (GFM) was used to solve the discretizing problem of the jumping interface, and 130 million cells were created in a region of 4 mm \(\times\) 4 mm \(\times\) 16 mm. [PERSON] et al. [40] studied the influence of gas pressure on the droplet size distribution of metal powder production. The instantaneous and local complexity of the gas-liquid interface was captured using the VOF method integrated in the OpenFOAM, and a clear increment of the atomization effectiveness was found with the increasing gas pressure. The LES model was adopted to capture the turbulence vortex. In order to keep track of both primary and secondary breakup, a quarter cylindrical domain with radius and length of 20 mm and 100 mm, respectively, was simulated. Due to the demand of Courant number with a gas velocity more than 1500 m/s, 11.8 million cells as well as a time step of \(10^{-8}\) s had to be used. [PERSON] et al. [41] analyzed the unclosed terms stemming from filtering of the two-phase flow LES equations, which have not been fully covered in the single phase LES method. An idealized jet imitating diesel injection with both density ratio and viscosity ratios equal to 40 has been simulated with the VOF method in the PARIS solver. As no experimental results were available, the LES results were verified in comparison with the DNS results. In a cuboid region in the dimension of 10 mm, 2 million cells were adopted in the LES method and 900 million cells for the DNS method. The studied sub-grid scale (SGS) closure models include convective term, surface tension term, Favre filtered velocity divergence and flux in the interface advection equation. They showed the closures for each unknown term strongly interact with the other terms and as well with the numerical scheme. [PERSON] et al. [21] used an entropy stable conservative method to overcome the inefficiencies of the LS method. The comparison of LES results with DNS reference data indicated a good agreement in aspects of interface concentration and void fraction. Liquid jet into moderate gas pressure was used in their simulation, and only an atomization duration of 45 \(\upmu\)s was calculated with 60 million cells. [PERSON] et al. [42] simulated the air-assisted pre-filming atomizer of kerosene. The VOF in commercial software Fluent 2021 R1 was used along with the DNS turbulence model. They focused on the different droplet size distributions between 2D and 3D simulation. The VOF from Fluent was also adopted by [PERSON] et al. [43] to investigate the effect of wall roughness on atomization of diesel injected from a hole of 0.1 mm. Only a realizable \(k\)-\(\varepsilon\) turbulence model was used since they focused on the injection angle and penetration length. [PERSON] et al. [8] cooperated the heat transfer and solidification models into the VOF of Fluent to predict the droplet size distribution formed from a centrifugal atomizer, and the turbulence was accounted for by the SST \(k\)-\(\omega\) model. The atomization during coughing and sneezing resembles that of air-assisted pre-filming atomization and has gained major concern during the COVID pandemic. [PERSON] et al. [44] performed one expensive DNS simulation using the VOF method. In a region of 50 mm \(\times\) 20 mm \(\times\) 10 mm, 500 billion cells have to be created, so as to resolve the Kolmogorov turbulence scale.