## 3 Results and Discussion  
### Model Validation  
To the best of our knowledge, there is a lack of experimental studies investigating the flow and heat transfer characteristics of supercritical n-decane in channels similar to those depicted in Figures 6 and 7. Hence, comparisons between the simulation results and experimental data obtained from the flow of supercritical n-decane through a vertical circular tube [41] as well as aviation kerosene RP-3 flowing through a U-turn tube [42] were carried out to validate our simulation method and turbulence model.  
The first validation example involves a vertical tube with an inner diameter of 0.95 mm, an outer diameter of 2 mm, and a length of 977.5 mm. These analysis cases, referred to as Cases 1-8 in Ref. [43], operate at a pressure of 3 MPa and an inlet temperature of 423.15 K. Among these cases, Cases 1-4 have an inlet Reynolds number of 2700, while Cases 5-8 have a higher Reynolds number of 4000. The wall heat flux ranges from 72 kW/m\({}^{2}\) to 393 kW/m\({}^{2}\). Table 4 summarizes the detailed operating conditions. In the second example, the curved section of the U-turn pipe has a radius of 20 mm, while the tube features an inner diameter of 1.82 mm and a wall thickness of 0.19 mm. The experimental conditions include an operating pressure of 4 MPa, an inlet temperature of 523 K, and a mass flow rate of 1178 kg/(m\({}^{2}\cdot\)s). Four different heat flux conditions are considered: 200 kW/m\({}^{2}\), 400 kW/m\({}^{2}\), 500 kW/m\({}^{2}\), and 600 kW/m\({}^{2}\). Thermo-physical data for aviation kerosene can refer to the ten-component surrogate model in Ref. [44].  
The findings depicted in Figures 14 and 15 suggest that the CFD model employing the SST k-\(\omega\) turbulence model yielded accurate outcomes for both Reynolds numbers, with only minor deviations observed in the inlet region. The disparities, except for Case 3 and Case 4, are negligible, ranging from approximately 3% to 6%. Even with variances of 6.56% and 11.62% for Case 3 and Case 4, respectively, these values still fall within acceptable engineering limits. The prediction of the wall temperature in Figure 16 exhibits excellent agreement with the experimental data for three different heat fluxes of 200, 500, and 600 kW/m\({}^{2}\). For a wall heat flux of 400 kW/m\({}^{2}\), the average and maximum deviations are 4.22% and 5.83%, respectively.  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Cases** & \(T_{\text{in}}\) **(K)** & \(p_{\text{in}}\) **(MPa)** & \(u_{\text{in}}\) **(m/s)** & \(Re_{\text{in}}\)** & \(q_{\text{w}}\) **(kW/m\({}^{2}\))** \\ \hline
1 & 423.15 & 3 & 1.1474 & 2700 & 72 \\
2 & & & & & 114 \\
3 & & & & & 163 \\
4 & & & & & 294 \\ \hline
5 & 423.15 & 3 & 1.7 & 4000 & 154 \\
6 & & & & & 240 \\
7 & & & & & 319 \\
8 & & & & & 393 \\ \hline \end{tabular}
\end{table}
Table 4: Operating conditions of Cases 1 to 8 in the first validation example.  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Mesh Resolution** & **Number** & \(T_{\text{w,le}}\), K & \(\varepsilon\), \% & \(\Delta P\), kPa & \(\varepsilon\), \% \\ \hline Coarse & 3.26 million & 799.43 & 1.00 & 2.60 & 6.47 \\ Medium & 5.33 million & 792.92 & 0.18 & 2.77 & 0.36 \\ Fine & 11.18 million & 791.51 & - & 2.78 & - \\ \hline \end{tabular}
\end{table}
Table 3: Mesh sensitivity tests of the flow and heat transfer of Scheme A1.  
Figure 14: Comparison of calculated wall temperatures with experimental data [41] for Cases 1–4 of a vertical circular pipe (simulation results of Xu can be found in Ref. [43]).  
Figure 15: Comparison of calculated wall temperatures with experimental data [41] for Cases 5–8 of a vertical circular pipe (simulation results of Xu can be found in Ref. [43]).