Global optimization of a laidback fan-shaped film-cooling hole regarding multiple blowing ratios and pressure-sensitive paint experimental validation

Designing an optimal film-cooling hole that can provide superior cooling performance at various blowing ratios considering the off-design working conditions, rather than just being limited to a single-blowing ratio, constitutes a considerable challenge. Our study introduces a new optimal objective function to assess global cooling performance. This function represents an integral expression of spatially averaged cooling effectiveness encompassing the range of interest for blowing ratios. An iterative optimization procedure was conducted to determine the optimal shape of a typical laidback fan-shaped hole. Two function objectives were implemented: one at a fixed blowing ratio of M = 1.0 and the other across a range of blowing ratios from M = 0.5 to 2.5. The influences of three key geometrical variables were assessed using Sobol's sensitivity analysis. The analysis indicated that the impacts of individual geometrical variables differ depending on the specific evaluation objective. The following optimization yielded two hole shapes, each characterized by an equal metering length and lateral expansion angle but a differing forward expansion angle. The superiority of optimal holes was demonstrated in a validation experimental test in the low-speed wind tunnel using pressure-sensitive paint technology. Two optimal holes yielded improvements of 12.07% and 24.62% for their respective objective functions compared to the reference hole. The detailed vortex structures were analyzed to explore the flow mechanism for enhancing cooling performance.