## 3 Results and Discussion
### Geometric and Surface Texture Characterization  
Figure 11 shows the difference in equivalent and nominal diameters for the nine investigated channels, together with unobstructed views of the five investigated channels with different diameters. Figure 11: _Cont._  
Figure 11a shows how the difference (\(D_{\alpha}-D_{nom}\)) is close to being constant for channel diameters of \(D_{nom}\geq 3\) mm. The reduction in the unobstructed cross-sectional area follows a power law with increasing channel diameter, which is also to be expected since \(A=\left(\frac{D}{2}\right)^{2}\times\pi\). Figure 11b shows the unobstructed cross-sectional area of the investigated channel sizes. The cross-sectional views show a similar mass formation trend, how it is different for \(D_{nom}\) = 1 mm, and how the peak-valley-peak signature of cross formation is becoming decreasingly apparent from \(D_{nom}\) = 2 mm to \(D_{nom}\) = 9 mm. Figure 12a shows the overall channel average \(Pa\)-values calculated for all investigated channels. The average \(Pa\)-values divided the channels into two distinctive groups: 1 mm \(\leq D_{nom}\leq\) 3 mm and 6 mm \(\leq D_{nom}\leq\) 9 mm. The calculated channel averages are similar within the two groups indicating a shift in the magnitude of average roughness between \(D_{nom}\) = 3 mm and \(D_{nom}\) = 6 mm. Apart from this size effect, it was found that within the group separated into \"small\" and \"large\" channels, a similar average roughness can be expected, irrespective of the nominal channel diameter. Figure 12b shows the results obtained from the five repeated X-ray CT scans of the 6 mm A channel. The results can then be compared to the other five 6 mm channels (Figure 12a), to investigate the repeatability of the production process. Figure 11: Difference in equivalent and nominal diameters at 4.5 mm length. (**a**) (\(D_{\alpha}-D_{nom}\)) for each of the investigated channels showing how the deviation from the nominal diameter is close to being constant for \(D_{nom}\geq 3\) mm. (**b**) Through view of the image stacks. Notice the differently scaled axes. The overall average \(Pa\)-value together with the associated standard deviation, together with the corresponding values of the repeatability investigations, can be seen in Table 2. By comparing the standard deviations of the \(Pa\)-values, it can be seen how the process and analysis repeatability are not significantly different, although when comparing the standard deviation of the obtained \(D_{eq}\)-values, the standard deviation of the repeated CT scans is half that of the process-induced standard deviation. Part of the process repeatability discrepancy may be attributed to build platform positioning effects, which have been found in other works to affect the roughness of produced parts and may therefore also affect the diameter [39]. The estimation of the equivalent diameter for the investigated channels as a function of channel length can be seen in Figure 13. As discussed in Section 2.4, the reduction in \(D_{eq}\) closely follows a logarithmic trend for all the investigated channel sizes. \begin{table}
\begin{tabular}{c c c c c} \hline  & **Avg. \(Pa\) [\(\mathbf{\mu}\)m]** & **STD of \(Pa\) [\(\mathbf{\mu}\)m]** & **Avg. \(D_{eq}\) [\(\mathbf{mm}\)]** & **STD of \(D_{eq}\) [\(\mathbf{mm}\)]** \\ \hline All channels & 41.40 & 2.20 & - & - \\
6 mm A, B, C, D, E & 40.57 & 0.56 & 5.559 & 0.025 \\
6 mm A 1, 2, 3, 4, 5 & 40.09 & 0.62 & 5.507 & 0.012 \\ \hline \end{tabular}
\end{table} 
Table 2: Average \(Pa\)-values and repeatability investigation by comparison of \(D_{eq}\). Figure 12: Average \(Pa\)-values. (**a**) Average \(Pa\)-values for all investigated channels showing a distinct grouping of channel sizes based on similar \(Pa\)-values. (**b**) \(Pa\)-values obtained from the repeated X-ray CT scans of channel 6 mm A. The influence of stack size was investigated for all channel sizes to test the estimation methodology.