## 4 Results and Discussion
### Experimental Result from Schlieren Method
(**a**) Image before gas injection, (**b**) image after gas injection, (**c**) subtracted image, and (**d**) filtered image. Figure 13: Image processing algorithm. In Figure 15a, the region where gas flow experienced a high flow speed and reached the sound barrier, Mach shock disks are observed as shown in Figure 15b. The larger the Mach number, the wider the size of the Mach disks [32]. As a result, the flow is deflected around these Mach disks, and the patterns shown in Figure 15 were observed. In the region where the velocity is seen to be on the rise, the density of air is found to be low, and as the sound barrier is reached the Mach shock disk is formed. In the region behind the Mach shock disk, the velocity becomes subsonic, and the density of the air builds up. This phenomenon can be clearly seen in Figure 15a-c. Thus, there should be a relationship between the flow velocity (Mach number) and the degree of flow expansion as seen in the image captured with the Schlieren technic. For a closer examination, the outline of the flow along the kerf was plotted with respect to the reference line (line Z2) passing along the kerf slot. Figure 16a shows the reference line Z2 along the cut kerf and Figure 16b shows the outline of gas flow marked with a red curve using edge detection. Then, the distance from the reference line to the outline of gas flow was calculated as shown in Figure 16c. After a series of image processing operations, the graph was synchronized with the density gradient fluctuation curve obtained from the simulation result of four tested turbulent models. In the position where the expansion and contraction were seen in the gas flow, low- and high-density regions can be observed from the density gradient map in Figure 11. This can be further validated by comparing the density gradient curve and the outline curve of the gas flow pattern observed in the Schlieren experiment. The comparison is given in Figure 17.  
As can be seen in Section 1, in the regions indicated by lines 1, 3, and 3 where expansion in the gas flow is seen, the density gradient fluctuation curve shows a low-density region. Similarly, for regions 2 and 4 where the contraction in flow pattern was seen, the density gradient curve shows a rise in the density. However, in Section 2, the plot obtained from the processed image includes a high amount of noise and could not be used for a meaningful comparison with the numerical simulation results. The resemblance in the results is consistent for all the turbulent models; however, the density gradient fluctuation shown by the standard \(k\)-\(\epsilon\) turbulent model is not noticeably high, whereas for the RNG model, the gas flow fluctuation is comparatively higher in intensity and the positions of high- and low-density regions are predicted closer to each other as discussed in the previous section. Moreover, expansion and contraction in gas flow predicted by the  
Figure 15: Comparison of flow pattern. (a) Numerical simulation result for \(k\)–\(\omega\) turbulence model (velocity field), (b) numerical simulation result for \(k\)–\(\omega\) turbulence model (Mach number), (c) numerical simulation result for \(k\)–\(\omega\) turbulence model (density gradient), (d) Schlieren experiment result, and (e) image processed result. RNG model are higher in number which was not visible during the Schlieren experiment. The comparison between results shows that the realizable \(k\)-\(\epsilon\) turbulent model and \(k\)-\(\omega\) turbulence model give better prediction among all the tested turbulence models. As discussed in previous the section, the selection of the \(k\)-\(\omega\) turbulence model was made based on the cost effectiveness in the performance. Therefore, further comparisons were made with the numerical simulation results predicted by the \(k\)-\(\omega\) turbulence model.