Effect of the Key Geometry and Flow Parameters on Discharge Coefficient of Laidback Fan-Shaped Hole Under Coolant Crossflow Condition

Abstract

Abstract A laidback fan-shaped hole is commonly used due to its superior lateral film coverage. Its discharge coefficient is significantly influenced by internal crossflow owing to its complex geometrical structure. In this paper, the authors numerically investigate the flow mechanisms of the laidback fan-shaped hole under the influence of internal crossflow. The numerical simulations utilize the validated SST k–ω turbulence model, with the Reynolds number of internal crossflow ranging from 20,000 to 160,000 and the ratio of pressure ranging from 1 to 1.6. The results show that the different orientations of internal crossflow cause varying degrees of in-hole separation that led to a discrepancy in the discharge coefficient. The larger the Reynolds number of the crossflow is, the more drastic the change in the discharge coefficient. Furthermore, a comparison between the results obtained with and without internal crossflow has shown that the length of the cylindrical section is the primary factor determining the discharge coefficient of the laidback fan-shaped hole. The magnitude of the discharge coefficient depended on the extent of flow separation within the cylindrical section. Additionally, the numerical simulations obtained the discharge coefficient under a high internal crossflow Reynolds number of internal crossflow and a wall with a constant thickness and compared it with the predictions of a low-dimensional model of the discharge coefficient (based on our previous experimental data). The discrepancy between the results is within 10%, thus verifying the scalability of the low-dimensional model.