# Numerical Analysis of Cold Spray Process for Creation of Pin Fin Geometries
## 3 Results
In this figure, Mask 1 is used, with a mask SOD of 16 mm and a substrate SOD of 20 mm. The corresponding particle dispersion and velocity for the high-pressure case are provided in Appendix G. The results indicate that minor dispersion occurs before the mask, corresponding to the region where the main shock wave and pressure rise are observed. However, after the mask, no significant particle dispersion is detected. Only very small particles (-20 um) exhibit slight dispersion under medium-pressure conditions, attributed to their lower Stokes number [49; 50; 51; 52]. Figure 7:0 Average particle velocity after exiting mask and before impacting substrate (medium-pressure case). Figure 7:1 Average particle velocity after exiting mask and before impacting substrate (high-pressure case). To determine whether a particle will adhere to the substrate surface, the particle's impact velocity from numerical simulations must be compared with the critical velocity, either calculated or experimentally measured. If the particle's impact velocity exceeds this critical threshold, it is likely to be deposited on the substrate. [PERSON] et al. (2019) utilized Finite Element Analysis (FEA) to estimate the critical impact velocity for nickel powder on a mild steel substrate. To the best of the authors' knowledge, these are the only available critical velocity data for nickel powder that account for the effects of both the particle diameter and temperature. Therefore, we analyze the deposition rate and efficiency by comparing our CFD-simulated particle impact velocities with the critical velocity data from [PERSON] et al. (2019). This comparison is expected to be valuable for readers interested in the topic, and also underscores the need for further research to develop critical velocity correlations for a broader range of powder and substrate materials. The critical velocity correlation for nickel powder (Equation (1)) is developed in the current study based on the data presented in the work of [PERSON] et al. (2019), as follows:  
Figure 7:2  
where \(\text{T}_{\text{P}}\) (K) is the particle temperature upon impact and \(\text{d}_{\text{P}}\) (m) is the particle diameter. Figure 7:3 Particle distribution at different locations: Mask 1, 16 mm Mask SOD, 20 mm substrate SOD, medium-pressure case. The fitted critical velocity correlation provides a decent interpolation and extrapolation of the FEM data. The fitted equation is compared with the FEM data [53] and is shown in Figure 7:4 Since [PERSON] et al. 's study analyzed nickel particles ranging from 25 to 75 \(\upmu\)m, the data needed to be extrapolated for this study to include the present particle diameter range (from 17 to 77 \(\upmu\)m). The curve fitted Equation (1) has an R\({}^{2}\) of 0.964 with respect to the original study data [53]. As mentioned, if the particle velocity upon impact on the substrate is greater than the critical velocity, it is assumed that the particle deposits on the substrate. The particle deposition and distribution on the substrate surface are visualized in Figure 20 for the medium-pressure case. The deposited and undeposited particles that landed on the substrate are shown for all four different masks, for each mask SOD and substrate SOD. As can be seen, the particles primarily deposit in the central opening of the mask that is in line with the nozzle centerline. It can also be seen that the masks with smaller rod diameters (Masks 3 and 4) have a wider particle distribution, with a significant number of particles in the adjacent mask openings. However, most of these particles do not deposit. In the high-pressure scenario, nearly all particles are successfully deposited across all test cases (see Figure 21). This emphasizes that the inlet pressure has a dominant impact on the particle velocity and deposition, while other parameters exert secondary effects. Figure 7:5 Fitted critical velocity correlation (Equation (1)) vs. original study data [53]. Figure 7:6 Deposited vs. undeposited particles for each test case (medium pressure case).