## 4 Conclusions  
In this work, nine LPBF aluminum channels were characterized in terms of equivalent channel diameters and surface topography, using X-ray CT and image analysis. The work presents a simple methodology for estimating the equivalent diameter (\(D_{eq}\)) of the unobstructed cross-sectional area as a function of channel length, enabling the optimization of channel designs. An overview of surface deviation maps allowed for the description of a distinct roughness and dress formation trend in the observed channels. The trend might have been formed due to the use of different process parameters at surfaces identified as down skin/overhanging surfaces. The cross formation at overhanging areas was found to follow a reverse \"camelback\" trend with low to no dress formation around \(\beta=180^{\circ}\) within an angular width of approximately \(10^{\circ}\) and high dress formation on both sides of the low dress area. The total reduction in \(D_{eq}\) at the investigated length was found to be close to constant for the channel sizes \(D_{nom}\geq 3\) mm. Furthermore, it was found that \(D_{eq}\) could be estimated as a function of the channel length and that the reduction followed a logarithmic trend for all investigated channel sizes. The analysis of surface texture using different surface profile parameters resulted in the following key findings:  
Figure 15: Simple geometry and roughness prediction following the approach of [26]. (**a**) Model \(Pa\) (\(\beta\), D) with linear interpolation between points along the “Diameter”; (**b**) prediction of 6 mm channel according to the \(Pa\) (\(\beta\), D) model; (**c**) surface deviation map of 6 mm A. * _Pa_, _P10z_, and _Pq_ are interchangeable for the specific purpose of quantifying the variations in the surface texture level depending on the angular local orientation \(\beta\), hence describing the dress variation around the channel periphery, with only a scaling factor separating the parameters quantitatively;
* _Pz_, _Pp_, _Pmc_, and _Pvc_ are closely related to the above;
* _Pku_ and _Pmp_ are useful parameters for the characterization of the peak-valley nature of the profiles. _Pmp_ and the fractal dimension of a profile may be used to characterize the degree to which a surface is affected by local distributions of sintered particles and agglomerations;
* The channels could be divided into a group for smaller channels \(D_{nom}\leq 3\) mm and a group for larger channels \(D_{nom}\geq 6\) mm in terms of quantitative characterization of the observed roughness. The group with smaller channels had an average _Pa_ of around 10% higher than that of the larger channels. While the current work did not intend to develop new parameters, the use of existing parameters and their appropriateness was sought to be investigated. The possible connections observed in this work between the selected surface profile parameters and cross formations and the presence of particles and agglomerations on the internal channel surface could help move towards a better understanding of the appropriate parameters for characterizing dorsal formation and surface texture in all AM channels. The appropriateness of using _Pa_ as the measure for variations in the surface texture level depending on the angular local orientation, while being correlated with cross formation, was validated by the generation of a simple roughness prediction model _Pa_ (\(\beta\), \(D\)). The roughness model was successfully used to generate a modified CAD design of a \(D_{nom}=6\) mm with information on the predicted roughness and dress formation. Future work is planned to (i) investigate the applicability of the proposed methods on channels with different geometries and made under different processing conditions and (ii) determine the uncertainty of CT surface texture measurements. Conceptualization, C.G.K., F.Z. and S.M. ; methodology, C.G.K. ; software, C.G.K. ; validation, C.G.K. ; formal analysis, C.G.K. ; investigation, C.G.K. and F.Z. ; resources, F.Z. and S.C.; data curation, C.G.K.