This study numerically investigates the influences of cooling hole surface roughness in a laidback fan-shaped hole on the flow structure and film-cooling effectiveness. The three-dimensional compressible LES approach (large eddy simulation) is conducted in a baseline 7-7-7 laidback fan-shaped hole. The cooling hole is located on a flat plate surface with a 30-degree injection angle at a constant density ratio DR = 1.5 and two blowing ratios M = 1.5 and 3. The computational results were validated by the measurements in terms of velocity and thermal fields for both the smooth and rough holes. In order to numerically consider the influences of the surface roughness on cooling hole side, the equivalent sand grain roughness method was utilized. Different correlations between the equivalent sand grain roughness height and arithmetic average roughness height were numerically tested to find an accurate correlation in comparison to the measurements. The computational data revealed that the surface roughness of the hole interior walls increases the thickness of the boundary layers within the hole. This leads to a higher jet core flow at the hole exit and lower film-cooling performance at the surface of flat plate compared to those of the smooth cooling hole. The minimum area-averaged film-cooling performance was observed in the case of the highest blowing ratio and the largest surface roughness height. The present work reveals that the current LES approach by considering the proper equivalent sand grain roughness height is a powerful tool to obtain the accurate solution in the prediction of the heat transfer characteristics and the flow structures in the fan-shaped cooling holes.

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