# Interferometry of Gas-Phase Flows during Selective Laser Melting
## 4 Discussion  
The interferometry clearly visualizes optical inhomogeneities. It made possible the calculation of the average velocity of the jet outflow for all the processing modes (Figure 7). The obtained data correlate with the previously obtained results when observing the gas-phase flow [5; 9]. The effect of power on the flow rate is obvious: an increase in the energy input leads to more intense evaporation of the material. Moreover, flow acceleration common for all the observed modes starting from 90 W and above is observed at a distance of 3-4 mm from the substrate. Laser power of 50 W seems to be insufficient for stable evaporation of the metal in the treatment zone; thus, no gas-phase flow was observed. \begin{table}
\begin{tabular}{c c} \hline
**Laser Power, W** & **Average Velocity, m/s** \\ \hline
50 & 0.35 \(\pm\) 0.1 \\
90 & 1.8 \(\pm\) 0.4 \\
130 & 2.3 \(\pm\)0.4 \\
170 & 2.6 \(\pm\) 0.5 \\ \hline \end{tabular}
\end{table} 
Table 2: Gas-phase flow velocity. Figure 6: Sequential frames of a steady-state vapor-gas jet at laser power of (**a**) 50 and (**b**) 130 W.  
It is known that submerged jets with moderate Reynolds numbers are laminar in the initial flow segment, and, starting from a certain critical distance, go into turbulent mode [29]. In the laminar zone, the jet is thin, and upon transition to turbulence, it begins to expand sharply. It is possible that the maxima in the interferograms arise in the turbulence zone (Figure 4). The laminar zone can be so thin that the image resolution is not enough. The works on the denuded zone in the SLM indicate a collective motion of powder particles from the periphery to the melt pool [5; 8; 14]. The movement itself is caused by the emerging Bernoulli effect when the vapor jet creates a zone of reduced pressure, which entrains ambient gas. The gas flows drag particles and transfers them to the molten pool. To evaluate the pressure change, a gas flow model was developed for SLM for various Reynolds numbers taking into account the presence of a solid surface and allowing calculating the shear stresses on this surface (Appendix A). The stresses are responsible for the detachment of particles of the powder layer and the formation of the denuded zone. The numerically calculated flow (Figure 8) qualitatively corresponds to the obtained experimental data. It should be mentioned that a fast jet flow is formed near the axis and a much slower-induced flow in the rest of the half-space. With an increase in the Reynolds number Re, the jet becomes less divergent and extends further along the axis. The velocity of the induced entrainment flow at a certain point, increases with increasing Reynolds number. It can be noted that at a large distance from the origin, the velocity vector of the induced flow is directed approximately along the radius (see blue flags in Figure 8). In the axial region, the flow  
[PERSON] et al. [28] numerically solved the system of mass, momentum and energy conservation laws for the laser plume and calculated the fields of temperature and flow velocities of vapor and ambient gas. Their results reviled the formation of a slender high-velocity vapor jet surrounded with a low-velocity induced entrainment flow of ambient gas. The estimated maximum vapor temperature ranged from approximately 3000 K to approximately 6000 K, depending on the laser power. The maximum was attained in the laser spot on the surface. Vapor temperature gradually decreased downstream the  
Figure 8: Calculated gas-dynamic fields of the absolute value of flow velocity (left: **a,c,e**) and pressure (right: **b,d,f**) at Reynolds number Re: (**a,b**) 10; (**c,d**) 20; (**e,f**) 30. Blue flags indicate the direction of the flow velocity vector. Contour lines: numerical calculation (black curves); [PERSON]’s similarity solution (green dashed lines). slender jet. The estimated temperature rise in the ambient gas was much less.