Impact of a Crossflow-to-Jet Velocity Ratio on Cooling Effectiveness for Shaped Holes

The study of film cooling fed by internal crossflow is critical for advancing high-efficiency cooling technologies. Crossflow within the coolant induces asymmetric flow structures inside the cooling holes, significantly affecting the coolant jet distribution at the hole exit and the resulting cooling effectiveness. In this study, a surrogate model is constructed using a convolutional neural network (CNN) to predict the cooling effectiveness field based on selected flow parameters, with a laid-back fan-shaped hole configuration. An active subspace (AS) method is further employed to conduct a sensitivity analysis of selected flow parameters, identifying dominant factors affecting cooling effectiveness. The results indicate that the distribution of cooling effectiveness at the hole exit can be classified into three distinct modes, depending on flow conditions: a unimodal distribution aligned with the crossflow, a bimodal distribution, and a unimodal distribution opposing the crossflow. The velocity ratio between the coolant crossflow and the jet at the hole exit, referred to as the crossflow-to-jet velocity ratio [Formula: see text], is found to govern the modal behavior. The AS analysis identifies the blowing ratio and cooling channel Reynolds number as the dominant parameters, both of which are incorporated in the definition of [Formula: see text]. Additionally, the influence of the blowing ratio on cooling effectiveness is examined at fixed [Formula: see text]. It is found that increasing the blowing ratio does not result in a continuous improvement in cooling effectiveness. In fact, when [Formula: see text] is relatively low, a higher blowing ratio may even reduce the cooling performance. This dimensionless velocity ratio [Formula: see text] proves to be an effective and practical parameter for characterizing film cooling performance under internal crossflow conditions.