Shape optimization of a laidback fan-shaped film-cooling hole has been performed by surrogate-based optimization techniques using three-dimensional Reynolds-averaged Navier-Stokes analysis. Spatially-averaged film-cooling effectiveness has been maximized for the optimization. The injection angle of the hole, the lateral expansion angle of the diffuser, the forward expansion angle of the hole, and the ratio of the length to the diameter of the hole are chosen as design variables, and thirty-five experimental points within design space are selected by Latin hypercube sampling. Basic surrogate models, such as second-order polynomial response approximation (RSA), Kriging meta-modeling technique, radial basis neural network (RBNN), are constructed using the analysis results, and the PBA model is composed from these basic surrogate models with the weights being calculated for each basic surrogate. The optimal points are searched from the above constructed surrogates by sequential programming (SQP). It is shown that use of multiple surrogates increases the robustness in prediction of better design with minimum computational cost.

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