In the present work, multi-objective shape optimization of a row of laidback fan shaped film cooling holes has been performed using a hybrid multi-objective evolutionary approach in order to achieve an acceptable compromise between two competing objectives, i.e., enhancement of the film cooling effectiveness and reduction of the aerodynamic loss. In order to perform comprehensive optimization of film-cooling hole shape, the injection angle of the hole, the lateral expansion angle of the diffuser, the forward expansion angle of the hole and the pitch to hole diameter ratio, are chosen as design variables. Forty experimental designs within design spaces are selected by Latin hypercube sampling method. The response surface approximation method is used to construct the surrogate with objective function values for the experimental designs calculated through Reynolds-averaged Navier-Stokes analysis. The shear stress transport turbulence model is used as a turbulence closure. The optimization results are processed by the Pareto-optimal method. The Pareto optimal solutions are obtained using a combination of the evolutionary algorithm NSGA-II and a local search method. The optimum designs are grouped by k-means clustering technique and the six optimal points selected in the Pareto optimal solutions are evaluated by numerical analysis. The different trends in the variations of the design variables for each blowing ratios were found, and the optimum designs show enhanced objective function values.

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