## 4 Application Examples for Turbomachinery
### Hybrid RANS/LES Model Menter SST-SAS
#### 4.2.2 Simulation of Film Cooling Based on C3X Cascade  
The simulation of flat-plate film cooling on a turbine blade was compared with the experimental results obtained by [PERSON] [38] in 1998 on C3X turbine blade film cooling. The experimental turbine blade operated at approximate chord-based Reynolds numbers of 800,000 and 500,000 at exit Mach numbers of about 0.27 and 0.17, respectively. And the coolant hole diameter was \(D=1.59\) mm. These Reynolds numbers fall within the relevant numerical range for medium-sized gas turbines. This study compared the experimental data for suction-side single-row holes. The turbine blade geometry data and computational setup parameters are detailed in Tables 5 and 6. The cascade computational domain adopts an HOH topology to ensure grid orthogonality, with a minimum grid spacing at the wall of 0.0015 mm. The first layer of the wall grids satisfies \(\Delta y^{+}<1\). The total number of grids in a single airfoil passage is 6.5 million, with each individual film hole having 30,000 grids. The grid domain of the airfoil and film holes is depicted in Figure 13. The calculation employs the SST-MSAS turbulence model, and the fifth-order novel WENO-ZQ high-precision format reconstructs the interface conservation quantities. The RANS equations are solved using the implicit LU-SGS method. At the inlet boundary, the total temperature, total pressure, and inflow angle are specified. The outlet boundary is designed as a subsonic outflow boundary. The blade surface is modeled as a no-slip adiabatic boundary, while the film hole outlet participates directly in \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \(\mathbf{Ma_{\text{in}}}\) & \(\mathbf{T_{\text{inl}}^{*}}(\mathbf{K})\) & \(\mathbf{P_{\text{inl}}^{*}}(\mathbf{Pa})\) & \(\mathbf{Ma_{\text{ex}}}\) & \(\mathbf{P_{\text{out}}}(\mathbf{Pa})\) & \(\mathbf{T_{\text{cool}}}(\mathbf{K})\) & \(\mathbf{\text{VR}}\) & \(\mathbf{\text{DR}}\) \\ \hline
0.0793 & 297.34 & 97262 & 0.2702 & 92451 & 317.39 & 0.49 & 0.94 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Boundary conditions of C3X cooling film. Figure 12: Comparison of numerical Schlieren calculation results under different WENO schemes. (a) WENO_ZQ_; (b) WENO_JS. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Chord length (mm) & 144.93 \\ Axial chord length (mm) & 78.16 \\ Pitch-to-chord ratio (-) & 0.812 \\ Throat-to-chord ratio (-) & 0.227 \\ Flow inlet angle (degree) & 0 \\ Stagger angle (degree) & 55.47 \\ Exit flow angle (degree) & 72.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Characteristic dimensions of C3X. the flow field solution using area-weighted average interpolation. The film hole walls are modeled as no-slip adiabatic boundaries. The prediction of cooling efficiency near film cooling holes has long been a challenge for scholars, due to the highly complex flow field generated by the continuous injection of jets into the mainstream. According to the jet mechanism reported in the relevant literature, the presence of jets resembles flow around a cylinder, forming a stagnation point at the jet's leading edge, thereby creating a horseshoe vortex around the leading edge. As the jet enters the mainstream, it forms kidney-shaped vortex pairs downstream of the hole. The momentum of the jet entering the mainstream determines the strength of these kidney-shaped vortex pairs, and excessive jet momentum can lead to the phenomenon of jet lifting near the hole. This series of complex flow phenomena renders the prediction of film cooling efficiency near the holes a challenging task. This case study employs a fifth-order improved finite-volume WENO scheme, significantly enhancing the predictive accuracy of the simulation code. Figure 14 compares the calculated and experimental results of the centerline film cooling efficiency \(\left|\eta_{aw}=\left(T_{aw}-T_{r}\right)/\left(T_{c}-T_{r}\right)\right|\) along the suction surface, where \(T_{aw}\) is the adiabatic wall temperature and \(T_{r}\) is the recovery temperature.