# Multidisciplinary Design Optimization of Cooling Turbine Blade: An Integrated Approach with R/ICSM
## 3 Multidisciplinary Design and Optimization of Turbine Stage Blade
### Subject Analysis of Turbine Stage Blade  
#### 3.2.1 Fidelity CFD Simulation Analysis  
The ANSYS (2020 R1) CFX software, renowned for its high accuracy in solving turbine aerodynamic problems and demonstrating robust convergence stability, was employed in this study for high-fidelity CFD simulation [22]. It resolved the steady-state compressible Reynolds Average Navier-Stokes (RANS) equation via the finite volume method, utilizing the Shear Stress Transport (SST) turbulence model to simulate the viscous term. Each blade row's rotor static interface was configured as \"Stage\", and the Advance Scheme and Turbulence Numbers were set to \"High Resolution\".  
A single blade channel served as the computational domain, with periodic boundary conditions applied on both sides. The flow working fluid in the main channel of this article was gas, with a molar mass of 28.94 kg/kmol. The Dynamic Viscosity was set to 1.831 \(\times\) 10\({}^{-5}\) kg/(m * s). The inlet boundary conditions encompassed total temperature,  
Figure 5: Parametric modeling of blade cavity with variable wall thickness.  
Figure 6: Parametric model of cooling turbine blade.  
total pressure, and airflow angle direction. Inlet turbulence was moderated at 5%, while outlet boundary conditions were specified in terms of average static pressure. Solid wall boundaries were treated as adiabatic and no slip wall.  
Grid partitioning was performed using ANSYS (2020 R1) TurboGrid software, with the grid topology structure set to ATM Optimized. The total number of grids and the number of spanwise grids in the meridian channel were separately adjusted to regulate overall grid quality, ensuring a value less than or approximately equal to 1 (as depicted in Figure 7) to meet the SST turbulence model grid quality requirements. The rotor blade tip clearance was set at 0.3 mm, with over 13 grid layers at the clearance to capture flow details. To verify grid independence and mitigate the flow field calculation result dependency on grid accuracy, five grid partitioning schemes with varying grid numbers were established: 0.6 million, 1.2 million, 2.4 million, 4.8 million, and 9.6 million. Figure 8 illustrates the radial distribution of the total expansion ratio of high-pressure turbines across these five grid schemes, revealing the following: (1) A trend towards consistent radial distribution with increasing grid numbers. (2) When the grid number reaches 2.4 million, the impact on flow field calculation results is relatively minor, indicating grid independence.  
Considering both computational accuracy and efficiency, this paper ultimately selected a grid partitioning scheme comprising 2.4 million grids (illustrated in Figure 9) for numerical calculations and optimization design.  
Figure 8: Spanwise distribution of total expansion ratio for turbine blade with different mesh schemes (0.6 million, 1.2 million, 2.4 million, 4.8 million, and 9.6 million).  
Figure 7: The distribution of dimensionless distance Yplus values near the walls of turbine blades.