This paper describes a multi-objective optimization method for round-to-slot shaped film-holes (RTSH) using computational fluid dynamic analysis and surrogate model approximation. The physical model is a single-row of film cooling holes on a flat surface. Three design variables relating to the main RTSH geometric parameters are investigated: the film-hole inclination angle (θ), slot width (s), and film-hole height (t). The slot length (l) and hole-to-hole pitch (P) are fixed as 2d and 2.4d, respectively, where d is the film-hole diameter. The optimal model is constructed by selecting the discharge coefficient ($C_{\mathrm{d}}$) and spatially-averaged adiabatic film cooling effectiveness (η_ad,av) as independent objective functions. From the Pareto front of optimal solutions, the optimized round-to-slot holes are obtained under blowing ratios of $M=0.5$ and 1.5. Numerical assessments corresponding to the maximum η_ad,av (Opt-A), maximum $C_{\mathrm{d}}$ (Opt-B), and a compromise between the two objective functions (Opt-C) are performed, and the mechanisms influencing the optimal film-hole shapes in terms of film cooling performance are analyzed in depth.

本文介绍了一种使用计算流体动力学分析和替代模型逼近的圆形至缝隙形膜孔（RTSH）的多目标优化方法。物理模型是在平坦表面上的单行薄膜冷却孔。研究了与主要RTSH几何参数有关的三个设计变量：膜孔倾斜角（θ），缝隙宽度（s）和膜孔高度（t）。缝隙长度（l）和孔间间距（P）分别固定为2 d和2.4 d，其中d是膜孔直径。通过选择排放系数（$C_{\mathrm{d}}$）和空间平均绝热膜的冷却效率（ηad _，av）作为独立的目标函数。从最佳解决方案的帕累托角出发，在吹塑比为的情况下获得了最佳的圆孔到槽孔$\mathrm{中号}=0.5$和1.5。对应于最大ηad _，av（Opt-A）最大值的数值评估$C_{\mathrm{d}}$ （Opt-B），并折衷了两个目标函数（Opt-C），并深入分析了影响薄膜冷却性能的最佳薄膜孔形状的机理。