Surrogate-assisted multi-objective optimization of effusion cooling configurations for turbine shroud rings

Effusion cooling is an effective technique for turbine shroud thermal management. However, achieving high-performance cooling structures remains challenging due to the competing requirements between thermal protection, structural integrity, and limited coolant supply. In full-scale turbine systems, complex blade-flow interactions lead to prohibitively high computational cost, which limits the generation of sufficient training data for design optimization. To address this issue, a simplified flat-plate model is developed to represent the essential thermal-fluid characteristics of turbine shroud effusion cooling. A surrogate-assisted framework combining CFD simulations, support vector machine surrogate modeling, NSGA-II optimization, and Sobol global sensitivity analysis is employed for efficient design and analysis. Experimental validation demonstrates good agreement between predictions and measurements for representative optimized configurations. Sensitivity analysis identifies spacing ratio, number of hole rows, and hole diameter as the dominant parameters governing overall cooling effectiveness and coolant consumption. Multi-objective optimization results show that, under a fixed thermal constraint, comparable cooling performance can be achieved through different combinations of mass flow ratio ( MR ) and effusion-hole porosity. As thermal requirements increase, the Pareto front shifts toward higher MR and effusion-hole porosity levels. Thermal-fluid analysis of representative Pareto-optimal configurations shows that as MR decreases from 0.069 to 0.039, the contribution of internal heat transfer decreases from 64.3% to 57.8%, while η ave increases from 0.063 to 0.130. The corresponding effective effusion-hole porosity varies from 0.0115 to 0.0154. These results demonstrate that different optimized configurations achieve similar thermal protection through redistribution between internal convection and external film cooling mechanisms.