## 3 Results and Discussion
### Physical Models
Both versions of steady \(k\)-\(\varepsilon\), RNG and Realizable, performed almost identically and their results were close to the experimental data. The steady RSM reached the largest deviation from the experimental data since it was unable to predict the air-core within the swirl chamber. This model also failed in the mesh with a prismatic layer using Enhanced wall treatment. The same model, but omega-based RSM, properly captured the air-core but underestimated the \(C_{D}\). Similar results were obtained by the steady \(k\)-\(\omega\)-SST model. Both the \(k\)-\(\omega\)-SST and omega-based RSM predicted \(C_{D}\) accurately in the transient simulation, where all the turbulence models return virtually identical results including LES. Only the omega-based RSM converged in the transient simulations, other variants of RSM diverged. An improper setup of the wall function results in failure of the air-core prediction. The wall \(y^{+}\) must be carefully checked before selecting the proper wall function as the standard wall function failed in all investigated cases. The turbulent models were able to closely predict flow characteristics even for \(Re=1000\), which is in good agreement with [12], where the \(k\)-\(\varepsilon\) model returns reliable results for \(Re=1600\). Note here that the RSM model underperformed other turbulence models, similarly as in [12]. This result was not expected, since the RSM should be superior for flows with anisotropic turbulence, which is the case with swirl atomizers. It predicts the air-core only in the case of omega-based RSM, but its results were practically identical to the simpler \(k\)-\(\omega\). The suitable models from Table 4 were compared in the range of \(Re\) and the results are presented in Figure 10. No RSM model was able to predict the air-core for \(Re=1000\), thus these models are not presented here. The measured \(C_{D}\) decreased slightly with \(Re\) as \(C_{D}\propto Re^{-0.035}\), respectively with \(p_{l}\) as \(C_{D}\propto p_{l}{}^{-0.016}\). It is in good agreement with several authors [31; 32] who found a similar  
Figure 10: Effect of \(Re\) on \(C_{D}\), \(SCA\), liquid sheet velocity, \(v_{l}\), and \(d_{acc}\) from various numerical setups. decrease in \(C_{D}\) but some authors [33] claimed rather ascending \(C_{D}\) with \(p_{l}\). Nevertheless, all CFD models predicted the same downward trend, yet minor differences were observed. The steady \(k\)-\(\omega\) model underpredicted the \(C_{D}\), particularly for \(Re=1000\). The \(k\)-\(\varepsilon\) also suffers from difficulties with this regime, where it severely overpredicts the \(C_{D}\) and underpredicts the air-core dimension. The LES model returns the closest results of \(C_{D}\), followed by the transient laminar model, which slightly diverts from the experimental data at \(Re=4000\). Nevertheless, the mean absolute percentage error (MAPE) of both laminar simulations, LES and \(k\)-\(\varepsilon\) was below 2.5%. This indicates that the prediction of \(C_{D}\) is robust regardless of the model used. Note here that the empirical correlation for \(C_{D}\) proposed by [PERSON] and [PERSON] [34] gives a constant value of \(C_{D}\) of 0.41, which is in perfect agreement with the experimental data for \(Re=2000\). The \(C_{D}\) value is usually related to the air-core diameter. Therefore, a decrease in \(C_{D}\) should be accompanied by the growing air-core diameter, which is true for both experimental data and all the CFD models, see Figure 10, right. Only the \(k\)-\(\varepsilon\) model diverts for \(Re=1000\). Other models tend to slightly overestimate the air-core size for low \(Re\). The MAPE of \(d_{acc}\) prediction of all the models is below 4.5%. The relative velocity of discharged liquid sheet, \(v_{l}/v_{p}\) (combined radial and axial velocity divided by the inlet velocity) is slightly increasing with \(Re\). All CFD models captured the trend from the experiment well, but most of them overestimated the velocity values.