This paper discusses the approach of cooling design optimization of a high-pressure turbine (HPT) endwall with applied 3D conjugate heat transfer (CHT) computational fluid dynamics (CFD). This study involved the optimization of the spacing of impingement jet array and the exit width of shaped holes, which are different for each cooling cavity. The optimization objectives were to reduce the wall-temperature level and to increase the aerodynamic performance. The optimization methodology consisted of an in-house parametric design and CFD mesh generation tool, a CHT CFD solver, a database of CFD results, a metamodel, and an algorithm for multi-objective optimization. The CFD tool was validated against experimental data of an endwall at CHT conditions. The metamodel, which could efficiently estimate the optimization objectives of new individuals without CFD runs, was developed and coupled with nondominated sorting genetic algorithm II (NSGA II) to accelerate the optimization process. Through the optimization search, the Pareto front of the problem was found in each iteration. The accuracy of metamodel with more iterations was improved by enriching database. But optimal designs found by the last iteration are almost identical with those of the first iteration. Through analyzing extra CFD results, it was demonstrated that the design variables in the Pareto front successfully reached the optimal values. The optimal pitches of impingement arrays could be decided accommodating the local thermal load while avoiding jet lift-off of film coolant. It was also suggested that cylindrical film holes near throat should be beneficial to both aerodynamic and cooling performances.

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