This paper investigates film cooling flow over a flat plate with five different cooling hole configurations. These configurations include a combined arrangement of cylindrical and fan-shaped holes. Numerical simulations are performed using the open-source computational fluid dynamics (CFD) platform OpenFOAM. The study is performed at two different mainstream Mach numbers ( \(Ma=0.4\) and \(0.6\) ) and three different blowing ratios ( \(BR=1.0\) , \(1.5\) , and \(2.0\) ), while maintaining a coolant density ratio of approximately \(2.0\) . To enable accurate and physically consistent boundary conditions, a mathematical equation is presented to compute the total pressure of the coolant at the inlet as a function of blowing ratio, density ratio, and mainstream Mach number. Across all conditions, staggered fan-shaped configurations exhibited the highest cooling effectiveness. At the higher Mach number ( \(Ma = 0.6\) ) and higher blowing ratio ( \(BR = 2.0\) ), an asymmetric coolant distribution was observed for the fan-shaped hole geometries. This asymmetry was attributed to flow separation within the fan-shaped coolant channel. This asymmetric coolant distribution leads to a significant drop in cooling performance, resulting in an approximate 60% reduction in the averaged film cooling effectiveness for staggered fan-shaped compared with \(Ma=0.4\) at the same blowing ratio.
