## 4 Results and Discussion
### Numerical Simulation Results  
The velocity, Mach number distribution, and pressure fields along the symmetry plane of the computational domain were mapped as individual turbulence models to evaluate their validity with respect to the experimental results. The gas flow direction along the kerf slot was inclined at an angle with respect to the axis of the nozzle. Therefore, the distribution curves are partially shown in two sections: at the nozzle section where the gas flow direction is along the nozzle axis (Z1); and at the inclined section in the kerf slot and under the cutting plate (Z2). The two sections are shown with dotted lines in Figure 7. Line Z1 passes through the axis of the nozzle from the inlet to the top surface of the cutting plate and line Z2 starts from the top surface of the cutting plate at 0.5 mm offset from the cut kerf end and runs parallel to the inclined cut kerf surface. Figures 8-10 show the velocity, Mach number, and pressure distribution respectively for all the turbulence models tested in this study. In Figure 8a, the velocity field maps for the four turbulence models are shown. Figure 8b,c shows the velocity distribution curve of the turbulence models along the lines Z1 and Z2, respectively. From the velocity field figure, it can be seen that the flow exhibits an under-expansion characteristic, which is expected for the convergent subsonic nozzles operating at high exit pressure. Figure 6: Grid dependency for maximum velocity of the flow. Figure 8: Velocity field. (**a**) Numerical simulation results for velocity field along the symmetry plane for four turbulent models. (**b**) Velocity distribution curve along the line Z1 for four turbulent models. (**c**) Velocity distribution curve along line Z2 for four turbulent models. Figure 7: Sections showing lines Z1 and Z2, where the flow field distribution is studied. Figure 9a shows the Mach number distribution map of the four turbulence models. Mach number distribution curves along lines Z1 and Z2 for each model are given in Figures 9b and 9c, respectively. Similarly, Figure 10a shows the pressure field maps of the four turbulence models, and the pressure distribution curves along lines Z1 and Z2 for each model are given in Figures 10b and 10c, respectively. Table 3 shows the number of iterations and the computational time taken for each case to converge. The flow distribution along the nozzle and kerf slot for the tested turbulent models show uniformity and have good flow distribution. The velocity and pressure distribution curve in Figures 8b and 10b shows high pressure and low-velocity flow at the inlet and as the geometry of the nozzle converges gradually, the flow becomes low pressure and high-velocity flow. This phenomenon is explained by Bernoulli's principle. As the flow exits the nozzle, the flow velocity continues to rise until the Mach shock disk is observed. This phenomenon is reflected by the Mach number distribution curve in Figure 9b. Figure 9: Mach number distribution. (**a**) Numerical simulation results for Mach number distribution along the symmetry plane for four turbulent models. (**b**) Mach number distribution curve along the line Z1 for four turbulent models. (**c**) Mach number distribution curve along line Z2 for four turbulent models. The pressure distribution curve shown in Figure 10c along the flow direction inside the cut kerr shows fluctuations and follows a harmonic wave pattern, which dampens as the flow propagates further downstream. The high- and low-pressure regions are formed along the flow direction and are shown with the crest and trough in the pressure curve. These fluctuations indicate the presence of a Mach shock disk along the flow propagation, as observed in the Schlieren experiment. Similarly, the velocity curves in Figure 8c exhibit a similar fluctuation pattern in the flow. It is evident from the velocity and pressure distribution curves that the fluctuations in these fields occur at corresponding positions  
Figure 10: Pressure field.