No abstract

The effect of wall temperature on the transfer of kinetic energy in a hypersonic turbulent boundary layer for different Mach numbers and wall temperature ratios is studied by direct numerical simulation. A cold wall temperature can enhance the compressibility effect in the near-wall region through increasing the temperature gradient and wall heat flux. It is shown that the cold wall temperature enhances the local reverse transfer of kinetic energy from small scales to large scales, and suppresses the local direct transfer of kinetic energy from large scales to small scales. The average filtered spatial convection and average filtered viscous dissipation are dominant in the near-wall region, while the average subgrid-scale flux of kinetic energy achieves its peak value in the buffer layer. It is found that the wall can suppress the inter-scale transfer of kinetic energy, especially for the situation of a cold wall. A strong local reverse transfer of fluctuating kinetic energy is identified in the buffer layer in the inertial range. Helmholtz decomposition is applied to analyse the compressibility effect on the subgrid-scale flux of kinetic energy. A strong transfer of the solenoidal component of fluctuating kinetic energy is identified in the buffer layer, while a significant transfer of the dilatational component of fluctuating kinetic energy is observed in the near-wall region. It is also shown that compression motions have a major contribution to the direct transfer of fluctuating kinetic energy, while expansion motions play a marked role in the reverse transfer of fluctuating kinetic energy.

The decompositions of the skin-friction and heat-transfer coefficients based on the twofold repeated integration in hypersonic transitional and turbulent boundary layers are analysed to give some major reasons of the overshoot phenomena of the wall skin friction and heat transfer. It is shown that the overshoot of the skin-friction coefficient is mainly caused by the drastic change of the mean velocity profiles, especially the strong negative streamwise gradient of the mean streamwise velocity far from the wall; and the overshoot of the heat-transfer coefficient is primarily due to the viscous dissipation, especially the strong positive vertical gradient of the mean streamwise velocity near the wall. These observations are different from the previous observations that the Reynolds shear stress and Reynolds heat flux are the reasons, respectively. Further investigations show that the above observations are independent of the set-up of the wall blowing and suction parameters, which indicates the universality of the major reasons of the overshoot phenomena in our numerical simulations. In the hypersonic turbulent boundary layers, it is observed that the strongly cooled wall temperature and the high Mach number can slightly enhance the contribution of the Reynolds shear stress, and weaken the contribution of the mean convection, mainly due to the strong compressibility effect. Moreover, the magnitudes of the relative contributions of the mean convection, pressure dilatation, viscous dissipation and the Reynolds heat flux increase as the wall temperature increases.

No 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.