# Numerical Analysis of Cold Spray Process for Creation of Pin Fin Geometries
## 3 Results  
The gas pressure, velocity, and temperature contours are shown in the figures below. Figures 6 and 7 show the medium- and high-pressure cases for Mask 2. Figures 8 and 9 show the medium- and high-pressure cases for Mask 4. The medium- and high-pressure cases for Mask 1 and Mask 3 are shown in Appendix C.  
In these figures, the first row illustrates the variation in static pressure across different masks and SODs. It is evident that changes in the inlet conditions, mask type, and mask and substrate SODs significantly alter the pressure distribution. The second row depicts the velocity magnitude of the gas flow, while the third row shows the temperature distribution. Similar to the pressure, both the velocity and temperature are greatly influenced by the inlet conditions, the mask type, and the mask and substrate SODs. In general, the typical shock diamond structures seen in cold spray processes [34; 43] or the simple bow shock formed near a flat substrate [30; 31; 32] are replaced by highly complex supersonic jets when a mask is placed between the nozzle exit and the substrate. As can be seen, the gas pressure, velocity, and temperature are significantly higher for the higher-pressure cases compared to the medium-pressure cases. Due to the higher inlet pressure and temperature, the flow is accelerated to greater gas velocities. There appears to be a bow shock upstream of the mask, which creates a high-pressure zone, as well as increasing the gas temperature and decreasing the gas velocity. In addition to this, there also appears to be a pressure rise in the stagnation zone at the substrate surface. The reduction in gas velocity due to the mask can potentially decrease the particle velocity and, hence, the deposition efficiency. A study performed by [PERSON] et al. [30] found that the bow shock caused by small substrate SODs had a significant adverse effect, causing a reduction in the particle impact velocity and deposition efficiency. Therefore, the shock experienced due to the mask could significantly impact the particle deposition, especially for small mask SODs. The gas pressure and velocity profiles are analyzed along the jet centerline from the nozzle exit to the substrate surface. The gas pressure and velocity profiles for the medium-pressure case are shown in Figures 10 and 11, respectively. Likewise, the gas pressure and velocity profiles for the high-pressure case are shown in Appendix D. The figures show the gas profile along the centerline for each of the four masks, for all the test cases. The mask location and approximate size are overlayed on each plot. The gas temperature profiles along the centerline are presented in Appendix E.  
From the profiles, the bow shock that is formed upstream of the mask is evident by the sudden rise in the gas pressure, decrease in the gas velocity, and rise in the gas temperature. Interestingly, the bow shock appears to be of a consistent magnitude for the medium-pressure case. Irrespective of the test case, the pressure rise, velocity decrease, and temperature rise are of a similar size and shape along the centerline where the majority of the particles move. It should be noted that Masks 1 and 2 (red and blue) experience bow shock earlier in the flow due to their larger rod diameters, compared to Masks 3 and 4 which have smaller rod diameter. For the high-pressure case, the magnitude of the bow shock formed upstream of the mask varies based on the mask and mask location. The bow shock also appears to be more severe compared to the medium-pressure case, resulting in a higher gas velocity decrease. The bow shock that is formed in the stagnation zone at the substrate surface is also evident, as indicated by the rise in pressure near the substrate. However, the bow shock at the substrate is of a lesser magnitude compared to that at the mask. Figure 6: Flow contours for Mask 2 (medium-pressure case). Figure 7: Flow contours for Mask 2 (high-pressure case). Figure 8: Flow contours for Mask 4 (medium-pressure case).