Surrogate based optimization of a laidback fan-shaped hole for film-cooling

The present work has been performed to evaluate the effects of geometric variables of a laidback fan-shaped hole on the film-cooling effectiveness using a Reynolds-averaged Navier–Stokes analysis, and to optimize the shape of the hole using the Kriging meta-modeling technique. The shape of the laidback fan-shaped hole is defined by four geometric design variables, namely, 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. From the results of a parametric study, effects of design variables on the film-cooling effectiveness are evaluated. The objective function, which is defined as the spatially averaged film-cooling effectiveness, is numerically evaluated through a RANS analysis at design points selected through Latin hypercube sampling. The Kriging model is used to approximate these objective function values at the design points, and sequential quadratic programming is used to search for the optimal point from the constructed Kriging model. The optimizations are carried out for two different blowing ratios, 0.5 and 2.5. The film-cooling effectiveness has been successfully improved with the optimization as compared to the reference geometry.