## 5 Conclusions  
The gas flow behavior inside the cut kerf slot affects the cutting quality and the performance of the gas-assisted thermal cutting process to a great extent. Therefore, studying the dynamic behavior of the flow inside the kerf can help operators effectively determine the optimum operating conditions. A kerf slot was measured using an actual sample which was cut using a thermal cutting process. Then, a representative kerf slot was fabricated per the measurement using transparent glass and a 3D-printed part. The fabricated cut kerf was used in Schlieren experiments to visualize the gas flow through the kerf slot. In addition to the experimental study, a numerical study was carried out to investigate the gas flow in the kerf slot. For precise measurement of such gas flow dynamics, accurate numerical modeling is necessary. In this research, several Reynolds-averaged Navier-Stokes (RANS) turbulence models were used for numerical modeling of the gas flow pattern inside cut kerf: the realizable \(k\)-\(\epsilon\) model, the standard \(k\)-\(\epsilon\) model, the RNG \(k\)-\(\epsilon\) model, and the \(k\)-\(\omega\) model. Using these models, a CFD analysis was conducted, and the results were presented in this work. The numerical results revealed that the \(k\)-\(\omega\) model and the realizable \(k\)-\(\epsilon\) model gave the best results compared with the other models, for predicting shock waves position and the separation points. The superior performance of these models may be attributed to the formulation of these models. The realizable \(k\)-\(\epsilon\) model incorporates some near-wall turbulence anisotropy with wall damping functions, while the \(k\)-\(\omega\) turbulence model uses a specific dissipation rate of turbulent kinetic energy and hence can perform well in near-wall conditions without introducing a wall damping function. Nevertheless, the \(k\)-\(\omega\) model showed a great advantage over the realizable \(k\)-\(\epsilon\) model in computational cost. Further analysis after refining the mesh resolution in stand-off  
Figure 18: Comparison graph between simulation result and experiment (distance between the line of gas flow and line Z2; velocity; Mach number; and pressure). distance, the \(k\)-\(\omega\) turbulent model outperformed the realizable \(k\)-\(\varepsilon\) model in modeling the shockwave structure accurately. The validation of the proposed model was carried out by comparing the numerical simulation results with the results obtained from the Schlieren experiment. The results of the Schlieren experiment were consistent to a great extent with the predicted results from the proposed model. The position of shock waves and the separation points of the flow predicted by the proposed model strongly resembled the experimental results. The dampening of the Mach shock disk due to repeated contact with the inclined kerf slot was remarkably similar in the two results. An image processing technique was used to further support the validation of the proposed model. The plot representing the outline of the gas flow obtained from the Schlieren image showed good resemblance to the velocity, Mach number, and pressure distribution curves from the numerical simulation results, validating the proposed model for use in the study of gas flow inside the cut kerf slot. Conceptualization, D.-W.C., U.T. and S.-H.A. ; methodology, U.T., S.-H.A. and S.K. ; numerical modeling, U.T. ; numerical simulation, U.T., image processing, S.-H.A., S.-H.B. ; validation, D.-W.C. and T.-K.P. ; investigation, U.T. and S.-H.A. ; resources, D.-W.C. and D.-H.K. ; data curation, U.T. and S.-H.A. ; writing--original draft preparation, U.T. and S.-H.A. ; writing--review and editing, U.T., S.-H.A. and D.-W.C.; visualization, U.T. and S.-H.A. ; supervision, D.-W.C. and S.A.; project administration, D.-W.C.; funding acquisition, D.-W.C. and S.A. All authors have read and agreed to the published version of the manuscript.