Impact of Streamwise Pressure Gradient on Shaped Film Cooling Hole Using Large Eddy Simulation

In turbine blade environments, the combination of blade curvature and accelerating flow gives rise to streamwise pressure gradients (SPGs), which substantially impact coolant–mainstream interactions. This study investigates the effect of SPGs on film cooling performance using Large Eddy Simulation (LES) for a shaped cooling hole at a density ratio of DR=1.5 under two blowing ratios: M=0.5 and M=1.6. Both favorable pressure gradient (FPG) and zero pressure gradient (ZPG) conditions are examined. LES predictions are validated against experimental data in the high blowing ratio case, confirming the accuracy of the numerical method. Comparative analysis of the time-averaged flow fields indicates that, at M=1.6, FPG enhances wall attachment of the coolant jet, reduces boundary layer thickness, and suppresses vertical dispersion. Counter-rotating vortex pairs (CVRPs) are also compressed in this process, leading to improved downstream cooling. At M=0.5, however, the ZPG promotes greater lateral coolant spread near the hole exit, resulting in superior near-field cooling performance. Instantaneous flow structures are also analyzed to further explore the unsteady dynamics governing film cooling. The Q criterion exposes the formation and evolution of coherent vortices, including hairpin vortices, shear-layer vortices, and horseshoe vortices. Compared to ZPG, the FPG case exhibits a greater number of downstream hairpin vortices identified by density gradient, and this effect is particularly pronounced at the lower blowing ratio. The shear layer instability is evaluated using the local gradient Ri number, revealing widespread Kelvin–Helmholtz instability near the jet interface. In addition, Fast Fourier Transform (FFT) analysis shows that FPG shifts disturbance energy to lower frequencies with higher amplitudes, indicating enhanced turbulent dissipation and intensified coolant mixing at a low blowing ratio.