## 2 Development of a Local Shielding Gas Concept
### Design of the Shielding Gas Nozzle Geometry  
Due to the similar requirements, design guidelines for subsonic wind tunnels were incorporated in the final design of the shielding gas nozzle [44; 45]. The shielding gas device was designed in two parts, which had both manufacturing and functional reasons (see Section 2.4). These two parts will be referred to as adapter and nozzle in the following. The inner contours of the adapter and the nozzle were designed as sequential contraction cones corresponding to those used in wind tunnels before the test section. According to [PERSON] and [PERSON] [46], a wind tunnel contraction leads to a uniform velocity profile across the outlet area and reduces the degree of turbulence of the flow. The most important parameter determining these properties is the contraction ratio \(\sigma\), which is defined as the ratio of the nozzle inlet area to the nozzle outlet area [47]. It was shown that axial velocity differences in the flow profile are reduced to the same extent as the mean velocity increases due to the contraction effect [48]. However, for the given application, the contraction ratio must not be too high, as this would contradict the required shielding gas coverage over a large area. In addition, a high gas velocity could negatively affect the melt pool stability. Considering these aspects, contraction ratios between 5 and 7 were found to be a reasonable compromise. In addition to the contraction ratio, the contour of the contractions had to be determined. It is noteworthy that the exact shape of the contour has only a minor influence on the flow profile as long as basic requirements are met [46]. For describing the contour, various analytical approaches were proposed in the literature [47; 49; 50; 51; 52; 53]. In this work, the contraction contour was designed according to [PERSON] [54] and can be described by  
\[\frac{r-r_{1}}{r_{2}-r_{1}}=\Big{(}\frac{x}{L}\Big{)}^{3}\bigg{[}2-\Big{(} \frac{x}{L}\Big{)}^{3}\bigg{]}, \tag{1}\]  
where \(r\) is the radius at a distance \(x\) from the nozzle outlet; \(r_{2}\) and \(r_{1}\) refer to the inlet and outlet radius, respectively; and \(L\) is the length of the contraction. Thereby, the maximum wall angle to the axis \(\alpha\) should satisfy the condition \(\alpha_{\text{max}}\leq 43^{\circ}\)[55]. The contour is illustrated in Figure 2 together with the relevant parameters. Figure 2: Contour of the contractions according to [PERSON] [54] with the inlet radius \(r_{2}\), the outlet radius \(r_{1}\), the length of the contraction \(L\), the maximum wall angle to the axis \(\alpha\), and the radius \(r\) at a distance \(x\) from the nozzle outlet. Considering the given requirements and spatial constraints, the parameters listed in Table 1 were chosen to describe the contours of the two sequential contractions. One appealing feature of the selected contour is that it resembles the tapered shape of the conical laser beam, thus enabling a highly compact design. It should be noted that, because the inert gas needs to be fed into the adapter from the side, there is no continuous flow profile over the entire cross-section at the adapter inlet. However, this approach yielded satisfactory results in the simulation regarding the uniformity of the flow profile at the inlet of the nozzle. In order to extend the area covered by the shielding gas without introducing turbulence, a flow straightener in the form of circular channels [45] was added to the nozzle, superimposed on the contraction cone. This provides an additional laminar outer flow curtain, which protects the center region from atmospheric diffusion. For this purpose, additional holes were inserted into the nozzle. The arrangement as illustrated in Figure 3, consisting of 54 holes with diameters of 2 mm and 3 mm, resulted in a significant improvement of the shielding gas coverage, while at the same time a robust design and good manufacturability were ensured. Since a honeycomb-like structure did not improve the flow condition beyond this, it was not considered further.