## 3 Results and Discussion
### Thermal-Mechanical Test  
In order to evaluate the structural integrity of the channel, a thermal-mechanical-coupled analysis was subsequently conducted to investigate the distribution of the deformation and thermal stresses. Fixed boundary conditions were applied at the end faces (inlet  
Figure 27: TKE distribution on streamwise–spanwise plane (x-y plane) for Schemes A1, A2, B1-M, and B2-M.  
and outlet) of all the channel configurations, disregarding aerodynamic forces but considering the operational pressure on the inner surfaces and global solid temperature field. A preliminary thermal-mechanical analysis using the parallel arrangement was conducted under the first-round test condition, with an inlet flow rate of 1 g/s and an inlet temperature of 300 K. The results indicate that the maximum displacements of category A and category B exhibit similarity, as presented in Table 5. However, they demonstrate distinct deformation patterns, which are illustrated in Figure 28 for category A(represented by Scheme A1) and category B (represented by Scheme B1). The deformations in category A resemble bending deformations, with the maximum displacement occurring at the tip of the leading edge. Conversely, the deformations in category B resemble bulking deformations, with the maximum displacement observed at the junction of the inclined segment and horizontal segment. Category A and B also exhibited very different maximum von Mises stresses, as shown in Table 5. The magnitude of the stresses suggests that the operating pressure applied on the inner wall of the channel had a negligible impact on the stress results, with thermal stresses induced by temperature gradients being the primary contributing factor. Figure 29 illustrates the locations where the maximum stresses occurred in category A (represented by Scheme A2) and category B(represented by Scheme B2-M). For category A, the maximum von Mises stresses were observed at the inner wall of the channel front, reaching 98.83 MPa and 104.25 MPa for A1 and A2, respectively, which are significantly lower than the acceptable limit of 600 MPa. In the case of category B, the peak values of the Mises stresses were consistently observed at joints between the inclined channel and core channel. These excessive stresses resulted not only from thermal effects but were also due to the stress concentration caused by the geometric factors (R4 = 0.25 mm for category B, as  
Figure 28: The contours of deformation obtained from the thermal-mechanical analysis. (**a**) Scheme A1; (**b**) Scheme B1. (Note that “E” in the legend represents “exponent” in scientific notation, indicating the power of 10 which a number is multiplied). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Scheme** & **A1** & **A2** & **B1** & **B1-M** & **B2** & **B2-M** \\ \hline \(D_{\text{max}}\), mm & 0.449 & 0.420 & 0.415 & 0.416 & 0.414 & 0.410 \\ \(\sigma_{\text{max}}\), MPa & 98.83 & 104.25 & 463.04 & 467.65 & 463.21 & 453.83 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The maximum displacements and von Mises stresses of the various cooling schemes. shown in Figure 11) at these locations. The maximum stresses for category B all exceed 450 MPa, yet they remain below the threshold of 600 MPa. To address concerns about the stress concentration in the B configuration, a small test was conducted where R4 was extended to 0.5 mm and 0.75 mm. The results are shown in Figure 30. As observed, increasing R4 leads to a significant reduction in the maximum structural stress. When R4 is increased to 0.5 mm, the maximum stress decreases to 336.28 MPa. With R4 extended to 0.75 mm, the maximum stress further decreases to 290.74 MPa. The additional weight introduced by these modifications is negligible. Therefore, concerns regarding the structural integrity of the B2-M configuration can be dismissed. The findings suggest that both Schemes A2 and B2-M exhibit superior cooling performances and maintain sufficient structural integrity.