Unsteady flow and heat-transfer characteristics of transpiration cooling under shock-wave sweeping

Transpiration cooling is a promising active thermal-protection technology, and shock-wave sweeping may arise in certain practical applications. This study numerically investigates the unsteady flow and heat-transfer behavior of a porous plate with transpiration cooling subjected to an oscillating inflow and periodic shock-wave sweeping. A Darcy-Brinkman-Forchheimer model with a local thermal equilibrium assumption is employed inside the porous medium. For the baseline case with a 1000 Hz inflow oscillation and a 1.2% blowing ratio, the incident shock sweeps over roughly half of the plate, substantially altering the external flow temperature, pressure, turbulent kinetic energy, surface heat flux, and wall shear stress. In contrast, the wall-temperature distribution remains nearly unchanged in time: the average wall temperature varies by about 10 K, and the temperature-based cooling effectiveness remains close to 0.6 across most of the surface. By decomposing the heat-transfer process into time-averaged and fluctuating components and applying POD analysis together with periodic unsteady conduction theory, the underlying mechanism of shock-wave-sweeping effects on transpiration cooling is elucidated. The analyses reveal that the wall-temperature distribution is primarily governed by the mean thermal mode, while the strong damping and thermal inertia of the transpiration-cooling configuration attenuate the transmission of temperature fluctuations into the porous medium. As the sweep frequency increases, wall-temperature fluctuations diminish and the system approaches a quasi-steady state. Variations in inflow Mach-number amplitude primarily affect the outer-wall temperature, exerting nearly negligible influence on the internal temperature field, and the wall temperature amplitude exhibits a nearly linear dependence on the inflow Mach-number amplitude.