# Impact of Mesh Resolution and Temperature Effects in Jet Ejector CFD Calculations
## 2 Materials and Methods
### Software and Modeling Approach  
The calculation of the jet eject model is achieved using Star CCM+ software, version 18.06.007. Geometry has been represented in the 2D axisymmetric configuration. It is a \begin{table}
\begin{tabular}{c c c c} \hline
**Symbol** & **Name** & **Value** & **Unit** \\ \hline \(T_{p}\) & Temp. at primary inlet & 362.85 & K \\ \(T_{s}\) & Temp. at secondary inlet & 273.15 & K \\ \(P_{p}\) & Pressure at primary inlet & 30.6 & bar \\ \(p_{s}\) & Pressure at a secondary inlet & 3.2 & bar \\ \(P_{out}\) & Pressure at outlet & 10.7 & bar \\ \hline \end{tabular}
\end{table} 
Table 2: The design conditions of the used jet eject. Figure 3: A schematic representation of the working map of an ejector. common technique for shortening the calculation time [19; 20]. The ideal gas assumption has been used to simplify this study. It is a simplification present in the literature [21], which is shown to provide reliable results [22]. The chosen solver was the steady density-based coupled implicit available in Star CCM+, since it is more appropriate for highly compressible flows. The discretization of the convective term was a 3 rd order MUSCL (Monotonic Upstream-centered Scheme for Conservation Laws). This high-order scheme leads to a better description of the shock wave discontinuities without oscillations of the solution thanks to the flux limiters. In the current state-of-the-art literature, no definitive consensus exists on the most suitable turbulence modeling for jet ejector simulations. When conducting complex simulations, a balance must always be struck between computational efficiency and accuracy. Various studies have analyzed different solvers, each with their own advantages. For instance, [PERSON] et al. [23] found that the k-\(\varepsilon\) model was best suited for capturing shockwaves, while [PERSON] [24] argued that the RSM (Reynolds Stress Model) was more appropriate. Both studies, however, also identified the k-\(\omega\) model as one of the best-performing options. Each approach to turbulence modeling has distinct strengths depending on the simulation's focus. The RSM is particularly effective for capturing anisotropic turbulence in the mixing layers but is computationally expensive due to its five-equation framework. The k-\(\varepsilon\) model, on the other hand, captures better wall friction effects and internal duct flows. [PERSON] et al. [25] conducted a study comparing the k-\(\varepsilon\) and k-\(\omega\) models, demonstrating that both provided similar levels of accuracy, aligning well with experimental results within the desired error range. Other studies support the use of the k-\(\omega\) solver. The results from [PERSON] et al. [26] show that the k-\(\omega\) SST (shear stress transport) turbulence model performs better than the other models in predicting the flow behavior of a supersonic air ejector, especially under different operating conditions. They have found that although k-\(\varepsilon\) models are more accurate at low motive pressures, they are less reliable overall. The k-\(\omega\) SST model stood out because it handled near-wall effects, shock interactions, and recirculation zones more accurately, and those are key factors in supersonic ejector flows. Although global parameters, like mass flow rates and entrainment ratios, do not vary much between models, those studies have found that k-\(\omega\) SST model provides more accurate local flow predictions, particularly in off-design conditions. In our simulations, we prioritized precision, yet we also needed to manage a significant number of computational cells. Given these considerations and taking into account the relevance of the mixing layers in the modeling of the ejectors, we selected the k-\(\omega\) solver, as used in [PERSON] et al. 's study and confirmed by the work of [PERSON] et al., to achieve a balance between accuracy and computational feasibility.