Pressure–velocity coupling in transpiration cooling

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 present work focuses on the interaction between the high-temperature turbulent boundary layer and the pressure-driven coolant flow through the porous wall. A new coupling method was developed to investigate this interaction and is presented with an analysis of the results from the coupled simulations. Coupling functions relating the coolant injection velocity to the wall pressure were obtained from pore-network simulations. These were then coupled to direct numerical simulations of a turbulent boundary layer over a massively-cooled flat plate. Two different types of coupling function were used: algebraic expressions, which do not account for flow interactions between neighbouring pores, and shallow convolutional neural networks (CNN), which incorporate spatial correlations. All coupled cases demonstrated a significant variation in cooling effectiveness as a result of the variation in blowing due to the mean streamwise pressure gradient associated with the onset of coolant injection. This trend was mitigated in the CNN-coupled cases due to the incorporation of lateral flow between neighbouring pores. The distribution of turbulent kinetic energy in the coupled cases was also modified by the coupling due to the competing effects of near-wall turbulence attenuation and increased shear due to increasing blowing ratio. Finally, the coupling was shown to impact the power spectral density of the pressure fluctuations at the wall within the transpiration region, attenuating the largest scales of the turbulence whilst leaving the smaller scales relatively unaffected. These results demonstrate the importance of incorporating the pressure–velocity coupling in transpiration cooling models not only when considering transpiration cooling parameters but also when looking at the general flow structures within the boundary layer. • DNS of transpiration cooling with pressure–coupled coolant injection velocity were run. • A pressure–velocity coupling algorithm was developed for the DNS using a CNN. • Coupling effects were shown to be attenuated by lateral flow in the porous medium. • Variations in the different contributors to cooling effectiveness are discussed. • The coupling attenuates the boundary layer TKE and large scale pressure fluctuations.