Contribution of flow topology to the kinetic energy flux in hypersonic turbulent boundary layer

Abstract

The contribution of various flow topologies to the subgrid-scale (SGS) flux of kinetic energy in hypersonic turbulent boundary layer for different Mach numbers and wall temperature ratios is investigated by direct numerical simulation. In the far-wall region (approximately [Formula: see text], where y is the wall-normal location and [Formula: see text] is the viscous length scale), the volume fractions of flow topologies unstable focus/compressing (UFC) and stable focus/stretching (SFS) increase with the increase in filter width, resulting in the dominance of UFC and SFS in the inertial range; while in the near-wall region, the volume fractions of flow topologies unstable/saddle/saddle (UN/S/S), stable node/saddle/saddle (SN/S/S), stable focus/compressing (SFC), and unstable focus/stretching (UFS) increase with the increase in filter width, leading to the majority of UN/S/S and SN/S/S in the inertial range. In the inertial range, the SGS flux of kinetic energy is mainly contributed by UFC and SFS far from the wall (approximately [Formula: see text]) and is primarily contributed by UN/S/S and SN/S/S near the wall. The wall temperature has a significant effect on the contributions of various flow topologies in the near-wall region. As the wall temperature decreases, the contributions by SN/S/S and SFC to the SGS kinetic energy flux increase in the compression region, and those by UN/S/S and UFS increase in the expansion region. Moreover, the direct transfer of fluctuating kinetic energy from large scales to small scales is mainly characterized by UN/S/S, SFS, and SFC in the compression region, while the reverse transfer of fluctuating kinetic energy is primarily characterized by UFC, SN/S/S, and UFS in the expansion region.