## 4 Results and Discussion
### Numerical Simulation Results
(**a**) Numerical simulation results for pressure field along the symmetry plane for four turbulent models. (**b**) Pressure distribution curve along line Z1 for four turbulent models. (**c**) Pressure distribution curve along line Z2 for four turbulent models. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Cases** & **Case 1** & **Case 2** & **Case 3** & **Case 4** \\ (**Turbulent Model**) & \(k-\epsilon\) (**Reliable**) & \(k-\epsilon\) (**Standard**) & \(k-\epsilon\) (**RNG**) & \(k-\omega\) \\ \hline No. of iterations & 5418 & 3876 & 6848 & 5284 \\ Computation time (s) & 8474 & 2887 & 5412 & 4149 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Simulation cases with different turbulent models. and the number of fluctuations corresponds with each other. Figure 9c shows the presence of the high Mach number region in these low-pressure and high-velocity regions. The flow behavior shown by the pressure and velocity curves corresponds with the simulation results for all turbulent models studied in this work. However, on close comparison of these models, the standard \(k\)-\(\varepsilon\) turbulent model has low fluctuation in the flow field, and the intensity of the flow field dampens very shortly after the gas exits from the nozzle. The shock wave intensity predicted by this model is comparatively lower than all other turbulence models. The standard \(k\)-\(\varepsilon\) model is incapable of capturing the subtler relationships between the turbulent energy production and the turbulent stresses caused by the anisotropy of the normal stress, and therefore it results in poor performance in cases of near-wall flow [27]. While they were suitable for modeling a free stream jet flow, the model used for the numerical simulation in this study consisted of a cut kerr that had an inclination angle. The flow from the nozzle was directed toward the inclined surface inside the kerr slot, which produces an adverse pressure gradient, which results in the substantial deterioration of the solution. The RNG model, however, predicted that the shock Mach disks will occur at closer distances, compared to all other models, and the fluctuation in both the pressure and velocity fields is comparatively high. This model predicts that Mach shock disks that are formed in the low-pressure zone will be of higher intensity than those predicted by any other models. The \(k\)-\(\varepsilon\) (realizable) model and \(k\)-\(\omega\) turbulent model, on the other hand, exhibited remarkable similarities in flow behavior. Both models predicted the location of the Mach shock disk at almost the same position. The extended \(k\)-\(\varepsilon\) models (RNG and realizable) were designed to overcome the shortcomings of the standard \(k\)-\(\varepsilon\) model by introducing wall damping functions for the model coefficients. This helps them to perform better in near-wall flow conditions. However, several researchers have mentioned in their work that these wall damping functions are not reliable [25; 27] and can lead to wrongly predicted flow behavior. The high sensitivity of the RNG model is possibly due to the choice of a less reliable damping function for the given geometry. In addition, several studies have mentioned that the RNG turbulence model provides better performance with swirling flows, and can make wrong predictions when the flow is not rotating [31]. Unlike the RNG and realizable \(k\)-\(\varepsilon\) models, the \(k\)-\(\omega\) turbulent model does not require wall dampening functions to predict the flow at the viscous sublayer near the wall, and can give a comparatively accurate prediction [25]. The results obtained from the CFD simulation were validated by comparison with the experimental results carried out using the Schlieren method, which indicates the model is comparatively stable and reliable for simulating flow inside a cut kerr, similar to this study. From the results of the realizable \(k\)-\(\varepsilon\) model, it can be concluded that the performance of this model is similar to that of the \(k\)-\(\omega\) turbulence model.