## 1 Introduction
The complex nature of the internal flow does not allow for a simple conclusion about whether the flow is turbulent or laminar, and many authors claim the opposite. A theoretical evaluation of turbulence evolution within the swirl chamber was made by [PERSON] and [PERSON] [9; 10] who suggest that the flow is laminar even for very high \(Re\) due to the laminarization effect of the swirl dominant flow itself and also due to the very short length scale where the turbulence has no time to develop. A comparison of Large Eddy Simulation (LES) and laminar models was performed by [PERSON] et al. [11]. They used a scaled atomizer and operated it in the range of \(Re=12\),000-41,000. Under these operating regimes, the laminar model had a slightly better agreement with the experimental data than LES. The authors also examined simple turbulence models represented by RNG (renormalization group) and realizable \(k\)-\(\varepsilon\) models. However, these models were unable to predict the internal air-core. [PERSON] et al. [12] compared the LES simulation with RNG \(k\)-\(\varepsilon\) and RSM (Reynolds Stress model). They found an insignificant variation among the used models when compared to the deviation in the results from published empirical correlations. They also noted that the flow field was consistent for the LES and \(k\)-\(\varepsilon\) model, while, surprisingly, the RSM had some discrepancies. Note here that the authors claim that the internal flow is fully turbulent based on Walzel Reynolds number, \(Re_{w}\), defined as: \(Re_{w}=\sqrt{2\rho_{l}p_{l}}d_{o}/\mu_{l}\), since it was much larger than a critical value of 5000. However, the calculated \(Re=1700\)-3800 rather suggests laminar flow. [PERSON] [3] found RSM to be superior over the laminar model at \(Re=16\),000, while [PERSON] [13] found opposite conclusions for even larger \(Re\) in the range of 18,000-40,000. [PERSON] et al. [14] examined several schemes to capture the liquid-air interface using a 2D simulation with the RNG \(k\)-\(\varepsilon\) turbulence model. A geo-reconstruct scheme was found to be the most suitable for capturing the air-core. They also discussed the necessity to include surface tension and found that it has an effect only for a Weber number smaller than 204. From a practical point of view, it had a negligible effect on the developed flow. However, it affects the flow development process. The difference between 2D and 3D computational models was examined by [PERSON] et al. [15]. They used the laminar solver and found that the air-core diameter was about 5% smaller in the case of the 3D model. However, the frequency of waves on the air-core surface was predicted by both models closely and in good agreement with the experimental data. [PERSON] et al. [16] compared RANS (Reynolds-averaged Navier-Stokes) models \(k\)-\(\varepsilon\) and \(k\)-\(\omega\). The \(k\)-\(\omega\) outperforms the \(k\)-\(\varepsilon\) in the \(SCA\) prediction and convergence speed. From the overview in Table 1, no clear conclusion can be made on the physical model selection, as both laminar and turbulence approaches were used by different authors for the entire range of \(Re\). The most commonly used turbulence models are from the \(k\)-\(\varepsilon\) family and represented by realizable and renormalization group theory, RNG, models. The RSM is also widely used; the authors reported contradictory conclusions. The air-core interface is usually captured by Volume of Fluid (VOF) models. Both the 2D and 3D simulations seem to provide accurate results; however, no comparison of the periodic 3D and full-scale 3D mesh was found. The majority of the 3D simulations used meshes, which contain tangential ports. This slows the mesh creation process since the cells near the wall are usually very skewed. To overcome this, a no-port version is introduced here with the aim to provide a simpler and faster mesh creation process. Moreover, steady and transient approaches are compared here.