## 3 Results and Discussion
### Correlation of Surface Profile Parameters and Dross Formation  
This subsection is dedicated to the investigation of the possible correlations between the selected surface profile parameters (see Section 2.3) and the dress formation. Figure 14 shows an overview of polar plots visualizing the computed profile parameters at every local orientation (\(\beta\)) for the investigated channel, 6 mm A. For each of the other investigated channel sizes, the polar plots together with the corresponding generated surface deviation map may be found in Figure A1 in the Appendix A. The average value of the profile parameter shown in each polar plot is given at the top right corner of the plots. The channels 6 mm B, 6 mm C, 6 mm D, and 6 mm E are not reported as their results are very similar to those obtained for channel 6 mm A.  
Figure 14: Polar plots showing the calculated profile parameters together with surface deviation maps showing the observed roughness and dress formation for channel 6 mm A. The scale is radial and the unit for each profile parameter is given together with the overall average value in the top right corner. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Channel**} & \multirow{2}{*}{\(D_{eq}^{N}\) **(1000 mm) [mm]**} & \multirow{2}{*}{\(D_{eq}^{L}\) **(1000 mm) [mm]**} & \multirow{2}{*}{**ABS (\(D_{eq}^{N}-D_{eq}^{L}\))**} & \multirow{2}{*}{**The Mean Difference over**} \\  & & & **[mm]** & **50 mm Length [\%]** \\ \hline
1 mm & 0.189 & 0.234 & 0.045 & 7.0 \\
2 mm & 1.371 & 1.288 & 0.083 & 2.9 \\
3 mm & 2.161 & 2.213 & 0.052 & 1.4 \\
6 mm A & 5.102 & 5.066 & 0.036 & 0.8 \\
9 mm & 8.197 & 8.223 & 0.026 & 0.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Estimation of \(D_{eq}\). Comparison of normal (\(N\)) and large (\(L\)) image stacks. Figure 14 shows a profile parameter comparison for the \(D_{nom}\) = 6 mm channel. Polar plots for \(Pa\), \(P10z\), \(Pq\), \(Pz\), \(Pp\), \(Pmc\), and \(Pvc\) show similar trends. This observation was found to be true for all investigated channels but is more evident in the larger channels with \(D_{nom}\geq 3\) mm. By comparing the abovementioned parameters with the surface deviation map shown in Figure 14, it becomes apparent that the magnitude of the calculated parameters can be considered connected to the magnitude of the surface deviation maps, which in essence shows the level of dress formation in the channels. This observation indicates that it can be expected that areas with higher dress formation will also have higher surface roughness. The seven parameters mentioned above can all be considered as suited to characterize the variation of the magnitude of surface texture in different axial profiles of internal channels, especially \(Pa\), \(P10z\), and \(Pq\) are practically interchangeable for this purpose. For convenience, it was decided to use \(Pa\) as the main parameter for characterizing the variation of surface texture magnitude as a function of the local orientation \(\beta\). _Pmp_ and \(Pvv\) were found to be close to inversely related as would be expected from the definitions. \(Pvv\) even showed resemblance to the seven parameters mentioned earlier that were found usable in the characterization of the roughness magnitude. \(Pmp\) allows determining if a profile had maxima relative to the general roughness of the surface. Two examples of this can be found in Figure 14 around \(\beta\) = 5\({}^{\circ}\), \(\beta\) = 185\({}^{\circ}\), and \(\beta\) = 270\({}^{\circ}\) where \(Pmp\) spikes and indicates that the extracted profile at that local orientation has large peaks relative to the profile heights. This inference can be confirmed by inspection of the surface deviation map at the same \(\beta\)-orientations, where generally \"flat\" sections are found with a few agglomerations acting as local maxima on an extracted profile. _Psk_, or the \"skewness\" of the profile, is used to characterize the bias of the profile around the mean line.