In spite of a myriad of researches on the optimal shape of film cooling holes, only a few attempts have been made to optimize the hole arrangement for film cooling so far. Moreover, although the general scale of film cooling hole is so small that manufacturing tolerance has substantial effects on the cooling performance of turbine, the researches on this issue are even scarcer. If it is possible to obtain optimal hole arrangement which not only improve the film cooling performance but also is robust to the manufacturing tolerance, then overall cooling performance of a turbine would become more reliable and useful from the practical point of view. To this end, the present study proposed a robust design optimization procedure which takes the manufacturing uncertainties into account. The procedure was subsequently applied to the film cooling holes on high pressure turbine nozzle pressure side to obtain the robust array shape under the uncertainty of the manufacturing tolerance. First, the array of the holes was parameterized by 5 design variables using the newly suggested shape functions, and 2 representative factors were considered for the manufacturing tolerance of the film cooling hole. Probabilistic process that consists of Kriging surrogate model and Monte Carlo Simulation with descriptive sampling method was coupled with the design optimization process using Genetic Algorithm. Through this, film cooling hole array which shows the high performance, yet robust to the manufacturing tolerance was obtained, and the effects of the manufacturing tolerance on the cooling performance was carefully investigated. As a result, the region where the film cooling effectiveness is noticeable, as well as the maximum width of the variation of the film cooling effectiveness were reduced through optimization, and it is also confirmed that the tolerance of the holes near the leading edge is more influential to the cooling performance because the film cooling effectiveness is more sensitive to the manufacturing tolerance of the leading edge than that of the trailing edge.

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