Film cooling behavior from shaped holes on a curved wall under nonuniform pressure gradients

Film cooling over curved surfaces subjected to variable pressure gradients exhibits complex near-wall flow dynamics, which are strongly influenced by the local pressure gradient distribution and the mainstream flow structure. In this study, the film cooling response of different hole geometries on a single curved surface exposed to a highly nonuniform three-dimensional mainstream is investigated using numerical simulations, with particular emphasis on the coolant-to-mainstream pressure ratio (R_P). The upstream region is dominated by a strong adverse pressure gradient (SAPG), which suppresses coolant discharge, induces near-wall recirculation, and leads to unstable and direction-sensitive jets' behavior for cylindrical holes. As R_P increases, several holes remain susceptible to jet bifurcation, lift-off, and reverse entrainment, indicating the limited effectiveness of increasing R_P alone. Analysis of boundary layer characteristics and coolant trajectories reveals three distinct flow-response modes: attached plate-like jets under mild adverse or favorable pressure gradients, forked distributions caused by separation and reattachment under moderate adverse pressure gradients, and reverse entrainment under SAPG conditions. Based on these mechanisms, two modified hole geometries—a racetrack-shaped (RS) hole and a forward-inclined fan-shaped hole—are proposed. Both geometries stabilize the coolant trajectory and mitigate SAPG-induced recirculation, with the RS hole providing the most robust near-wall attachment under SAPG conditions.