Pressure-Velocity Coupling in Transpiration Cooling

Abstract

Transpiration cooling is an active thermal protection system of increasing interest in aerospace applications wherein a coolant is effused through a porous wall into a hot external flow. The wall is cooled due to convection within the porous structure and the formation of a coolant buffer layer between the wall and the main flow. In order to design an effective transpiration cooling system, it is necessary to understand the complex interaction between the high-temperature turbulent boundary layer and the pressure-driven coolant flow through the porous wall. However, high fidelity simulations of this interaction are rare and computationally limited to simple problems when accounting for both fluid domains. In the present work, two shallow convolutional neural networks (CNN) were trained on pore-network simulations of flow through a pressure-driven porous wall. CNN were used due to their ability to consider spatial correlations, meaning they can capture the influence of flow between neighbouring pores. The CNN are coupled with direct numerical simulations of a turbulent boundary layer over a massively-cooled flat plate. The coolant flow inside the porous medium is thus indirectly coupled to the near-wall pressure in the boundary layer, allowing the interaction between the two flow domains to be considered. Linear expressions that do not account for flow interactions between neighbouring pores were also coupled with direct numerical simulations in order to investigate the significance of this effect. With the incorporation of the pressure-coolant injection velocity coupling, the streamwise variation in mean pressure was found to have a significant impact on the local coolant injection. Blowing was reduced near the beginning of the transpiration region due to the high pressure region formed by the incoming boundary layer flow encountering the injected coolant. This effect reduced as the flow recovered and eventually reversed as the coolant film accumulated in the boundary layer, lifting it off of the wall. A corresponding trend was observed in the local cooling effectiveness, while the inverse was found in the local friction coefficient. The incorporation of lateral flow between neighbouring pores via the neural network was found to greatly attenuate these coupling effects. In all coupled cases, the turbulent kinetic energy was reduced at the beginning of the transpiration region due to the more gradual introduction of coolant. However, further downstream the rapid increase in coolant injection in the cases coupled using linear expressions resulted in increased turbulent production such that the turbulent kinetic energy was greater than in the uniform injection case at the end of the transpiration region. In the neural network cases, the increase in shear due to increased coolant injection was not significant enough to overcome the modulation of the turbulence due to the coupling. An analysis of the power spectral density of the pressure fluctuations at the wall within the transpiration region revealed that the implemented pressure-coolant velocity coupling only attenuated the largest scales of the turbulence, leaving the smaller scales relatively unaffected.