The turbulence evolution of tangential supersonic cooling film using direct numerical simulation

Supersonic film cooling is a potential approach to thermally protecting hypersonic aircraft. To unveil the turbulence evolution and inherent energy transport, a direct numerical simulation (DNS) of supersonic film cooling is performed, wherein the cooling gas with a Mach number of 2.0 is tangentially injected into a turbulent boundary layer with a Mach number of 3.0. Particular attention is paid to the evolution of turbulent structures reflected by energy spectra. The overall flow response can be described as the decay of upstream wall turbulence and the re-establishment of the downstream wall shear layer. Visualizations of vortex identification clearly show that well-shaped hairpin vortices oriented to the laminar cooling film are formed in the mixing layer. The decompositions of wall skin friction reveal that the tangential film causes considerable drag reduction downstream, and this is the joint benefit of the thickening of the wall shear layer and the decaying of upstream turbulence. The turbulent statistics reveal the coexistence of two energy peaks in the flow field. One in the mixing layer is the remnant of upstream turbulence and gradually decays, while the other near the wall is newly generated and keeps growing. The conclusion is further confirmed by energy spectra, which also show that streaky structures scaling differently from those in a turbulent boundary layer are formed near the wall. It is interesting to find that the two energy sites directly exchange turbulent kinetic energy through mean convection, and they redistribute energy toward the bracketing region through turbulent transport.