# Conjugate Heat Transfer Advancements and Applications in Aerospace Engine Technology
## 3 Case Study of Conjugate Heat Transfer
### Results and Discussion  
The comparison of the pressure distribution at mid-span across four different density flow field meshes with NASA experimental results reveals that the trend in pressure distribution for all four mesh densities closely aligns with the experimental data, as shown in Figure 13. The pressure drop along the surface is relatively gradual, with an increase in the rate of decrease observed near the trailing edge. On the suction surface, the pressure drops rapidly in the intake region, followed by a more gradual acceleration of the flow after the midsection (approximately \(p/p_{0}\) = 0.5-0.6). The calculation results exhibit a sharp rise in pressure at the leading-edge stagnation point, which may be attributed to the accumulation of flow due to an excessive lack of uniformity in the grid relative to the surrounding area at the stagnation point. Consequently, the largest pressure surge is observed in the finest mesh with 9.3 million cells. Beyond the midsection of the suction surface, pressure fluctuations occur, accompanied by an inverse pressure gradient, indicating the complexity of the flow characteristics in this region, which can lead to shockwave formation and separation phenomena. In areas of complex flow, denser meshes yield calculations that are closer to the experimental data, although overall discrepancies remain minor. \begin{table}
\begin{tabular}{c c c} \hline
**Boundary Conditions** & **Parameter/Unit** & **Value** \\ \hline \multirow{4}{*}{Inlet boundary conditions} & Working medium & Ideal gas \\  & Total pressure/Pa & 413,286 \\  & Total temperature/K & 818 \\  & Mach/Ma & 0.17 \\  & Turbulence intensity/\% & 8.3 \\  & Viscosity ratio & 30 \\ \hline \multirow{2}{*}{Outlet boundary conditions} & Average static pressure/Pa & 254,172 \\  & Temperature/K & 800 \\ \hline \end{tabular}
\end{table} 
Table 1: Working condition. \begin{table}
\begin{tabular}{c c c} \hline
**Name/Unit** & **Value** \\ \hline \multirow{2}{*}{
\begin{tabular}{c} Black material \\ Thermal conductivity coefficient/W/(m\(\cdot\)K) \\ Heat capacity/J/(kg\(\cdot\)K) \\ External wall temperature/K \\ Coolant initial temperature/K \\ \end{tabular} } & 310 SS \\  & 19.1 \\  & 502 \\  & 400 \\  & 300 \\ \hline \end{tabular}
\end{table} 
Table 2: Blade material properties and initial conditions. \begin{table}
\begin{tabular}{c c c c} \hline
**\#** & **Diameter/mm** & **Flow Mass/kg/s** & **Inlet Temperature/K** \\ \hline
1 & 6.3 & 0.0222 & 342 \\
2 & 6.3 & 0.0221 & 344 \\
3 & 6.3 & 0.0218 & 335 \\
4 & 6.3 & 0.0228 & 336 \\
5 & 6.3 & 0.0225 & 330 \\
6 & 6.3 & 0.0225 & 355 \\
7 & 6.3 & 0.0216 & 336 \\
8 & 3.1 & 0.00744 & 350 \\
9 & 3.1 & 0.00477 & 377 \\
10 & 1.98 & 0.00256 & 387 \\ \hline \end{tabular}
\end{table} 
Table 3: Radial coolant flow conditions for the C3X vane. Figure 14 illustrates the average dimensionless pressure values at mid-span, revealing that as the mesh density increases, the calculated average pressure values converge towards the experimentally obtained mean pressures. Given this convergence, for the sake of accuracy in our numerical simulations, a mesh count of 9.3 million grids was selected for subsequent testing. Figure 15 illustrates the isentropic Mach number distribution along the mid-span section of the C3X blade. It is evident that the flow within the blade channel is predominantly subsonic. Notably, a faint shockwave (Mach > 1) is discernible on the suction side at approximately 40% axial chord (Figure 16). Additionally, the leading edge of the blade is characterized by a relatively large arc shape, and the curvature radius exhibits minimal variation. Such a design minimizes energy loss when the incidence angle at the inlet varies significantly. Meanwhile, the influence of these shockwaves on both the pressure and suction sides appears to be minimal. As depicted in Figure 17, the flow state at the trailing edge of the blade is relatively regular, with the vortex growth reaching approximately 1.5 times the diameter of the trailing edge.