# Multidisciplinary Design Optimization of Cooling Turbine Blade: An Integrated Approach with R/ICSM
## 3 Multidisciplinary Design and Optimization of Turbine Stage Blade  
This study focuses on optimizing the turbine blade. To enhance isentropic efficiency within the constraints of aerodynamic and strength performance, an efficient multidisciplinary integrated design optimization method for the cooling turbine blade is proposed. This method combines a parametric modeling approach for the cooling turbine blade with cooperative coupling characteristics, numerical simulation analysis methods from various disciplines, and a regression/interpolation combination surrogate model (Figure 2). The specific steps involved in this method are as follows:  
1. Select appropriate design variables and determine their ranges. 2. Select a suitable Design of Experiments (DOE) technique to generate a design matrix representing a set of sample points. Considering the precision required for the surrogate model and the time constraints for aerodynamic and strength analysis, an initial set of 200 sample points was generated using the \"hhsdesign\" program in MATLAB (v.2011). 3. Employ the blade modeling approach outlined in Section 3.1.1. A custom MATLAB (v.2011) program was utilized to produce blade profile curves for the tip, middle, and root sections of the first-stage rotor blade across the 200 samples from step (2). The scatter coordinates of these blade profile curves were exported in various formats to facilitate blade modeling within the aerodynamic domain and parameterized modeling of the cooling blade within the structural domain. 4. Utilize the parameterized modeling approach outlined in Section 3.1.2 for the cooling blade. The UG macro command was employed to automatically generate the geometric model of the first-stage rotor blade for strength analysis across the 200 samples from step (2). 5. Use the aerodynamic analysis method detailed in Section 3.2.1. A high-fidelity Computational Fluid Dynamics (CFD) simulation of the two-stage high-pressure turbine blade was conducted using ANSYS (2020 R1) CFX software across all samples. Subsequently, pertinent response parameters were extracted, namely \(W_{41}\), \(\pi\), \(\eta\) and \(\alpha\). 6. Employ the strength analysis method outlined in Section 3.2.2. Finite element simulation analyses of the first-stage rotor blade were conducted across all samples using the APDL language within ANSYS (2020 R1) software. Subsequently, the relevant response parameters were extracted. 7. Combine sampling points with their respective response parameters to create the initial sample database. 8. Utilizing existing sample data, integrate the advantages of two different surrogate models, and construct a regression/interpolation combination surrogate model. 9. Select a suitable optimization algorithm for the optimization process. The optimization objectives and constraint parameters are approximated by the regression/interpolation combination surrogate model developed in step (8). Details of the constructed optimization model will be presented in Section 3.4. A Genetic Algorithm (GA) was employed to solve the constrained optimization problem in this study. * Generate a new blade profile curve for the tip, middle, and root sections of the first-stage rotor blade based on the optimized design obtained in step (9). Output the scatter coordinates of the curve in different formats. * Employ UG macro commands to automatically generate the geometric models of the first-stage rotor blade for the new design scheme obtained in step (9). * Utilizing ANSYS CFX software, conduct high-fidelity CFD simulations for the two-stage high-pressure turbine blade based on the new design scheme. Then extract relevant response parameters. * Using the APDL language within ANSYS (2020 R1) software, conduct finite element simulation analyses of the first-stage rotor blade for the new design scheme. Extract relevant response parameters \(e_{\text{eq,max}}\). * Verify the fulfillment of convergence criteria. If satisfied, conclude the loop and acquire an improvement plan.