## 3 Results and Discussion  
In Table 2, the simulation results for the matrices are listed, comparing the \(k-\varepsilon\) realizable with EWT and \(k-\omega\) SST schemes. This initial part of the analysis was primarily useful for comprehending the effects of the parameters discussed in Section 2.4, as well as for selecting the appropriate turbulence model. The \(k-\omega\) mostly provided an overestimation of pressure drop, which increases alongside the mass flow rate. With the \(k-\varepsilon\), lower \(\Delta P\) values were observed, along with smaller errors that remained nearly constant at higher Reynolds numbers. This differing behavior was also detected in the work of [PERSON] et al. (2013), who attributed it to the so-called \"dead zone\" that forms behind the brazing points. They suggested that the effect is due to the larger volume of the region predicted when employing the \(k-\omega\) model. Looking at these locations, as the flow passes around the obstacles, a wake develops and evolves into a complex structure due to the expanding cross-sectional area downstream. This is illustrated in Figure 9a. Figure 8: Dependence of numerical results on mesh density for S1 whole plate. Some fluid particles exhibit a helical upward movement as they fill the channel, while others merge with the mainstream flow between the rows of the brazed points, as depicted in Figure 9b. This pattern is intentional and characterizes the current technology, distinguishing it from the flow in herringbone PHEs, because it features fewer three-dimensional wavy paths having higher velocities magnitude. A clearer comparison of the results from the two turbulence approaches is achieved by introducing a quantity that more meaningfully represents the losses within a channel, the total pressure \(P_{0}\), namely the sum of the static and dynamic components. Figure 10 shows \(P_{0}\) relative to its maximum value \(P_{0,max}\), extracted as a function of the width position \(w\), scaled by the pitch, on a channel cross-section located midway between two consecutive rows of brazed points, for sample S1. The peaks are associated with the preferential flow paths illustrated in Figure 9b, while the minima correspond to the wake cores. In these regions, the dissipation predicted by \(k-\omega\) is higher and remains significant further downstream from the brazed points, unlike the \(k-\varepsilon\), which determines a more pronounced tendency toward pressure uniformity, as indicated by the local valleys at the top of the chart. The greater accuracy provided by the \(k-\varepsilon\) realizable with EWT model, along with its ability to align with matrix experimental trends and enable more stable calculations in terms of residuals, led to the decision to use this method for analyzing the entire channels. Figure 11 presents these calculation results which align with those derived from the matrices, as the HP sample with the lowest profile height (S2) again exhibits positive errors, suggesting a slight overestimation of \(\Delta P\). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sample** & \(Re\) & \
\begin{tabular}{c} _Error_ [\%] \\ \(k-\varepsilon\) \\ \end{tabular} &
\begin{tabular}{c} _Error_ [\%] \\ \(k-\omega\) \\ \end{tabular} \\ \hline \multirow{3}{*}{S1} & \(514\) & \(-5.4\) & \(-3.7\) \\  & \(1025\) & \(-2.1\) & \(7.2\) \\  & \(1275\) & \(-2.0\) & \(9.1\) \\ \hline \multirow{3}{*}{S2} & \(466\) & \(-2.5\) & \(6.4\) \\  & \(626\) & \(1.0\) & \(7.6\) \\  & \(1046\) & \(1.1\) & \(9.9\) \\ \hline \multirow{3}{*}{S3} & \(545\) & \(-2.2\) & \(2.5\) \\  & \(706\) & \(-2.0\) & \(6.7\) \\ \cline{1-1}  & \(1132\) & \(-3.0\) & \(11.0\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Pressure drops results for matrices. Figure 9: Flow field: (**a**) streamlines passing around the brazed point; (**b**) flow pattern on the mid-plane.