Optimization of the configuration of the laidback fan-shaped film cooling hole with a lateral expansion angle of 10 degrees

Highlights: • Optimized hole by the Kriging method performed better than that by the RSM. • Generally, smaller injection angle cases resulted in higher film cooling effectiveness. • Hole with higher area ratio generally gave a better cooling performance. • In optimization, all hole shape configurations must be considered simultaneously. -- Abstract: Film cooling techniques have been widely applied to gas turbine engines to protect the components from hot combustion gas. In this study, the shape of the laidback fan-shaped hole with a lateral expansion angle of 10 degrees was optimized through the Reynolds Averaged Navier-Stokes (RANS) analysis. Results by numerical analysis were validated with the corresponding experimental results obtained by the pressure sensitive paint technique (PSP). For optimal hole shape derivation, the design points were selected through the Latin Hypercube Sampling (LHS) method for three design variables: injection angle, metering length, and forward expansion angle. The overall averaged effectiveness was used as the objective function. Results showed that the overall film cooling effectiveness of the optimal holes derived by the response surface method and the Kriging method were higher than that of the reference hole by 4.5% and 7.5%, respectively. Generally, holes with a higher area ratio (AR) showed higher overall film cooling effectiveness. However, the interaction between each shape parameter should be considered to derive the optimal hole shape.