Turbulent heat flux and wall heat transfer in hypersonic turbulent boundary layers with wall disturbances

Hypersonic turbulence over disturbed walls can be encountered when the fuselage of the vehicles is ablated or installed with transpiration -cooling porous media, resulting in the variation of the wall heat transfer that complicates its accurate predictions. In this paper, we study the turbulent heat flux and wall heat transfer in hypersonic turbulent boundary layers at the free -stream Mach number of 6.0 subject to wall disturbances with different wall temperatures, with our focus on the compressibility effects. We found that the temperature fluctuation intensity and the turbulent heat flux are enhanced in the outer region, which is attributed to the higher mean temperature gradient induced by the wall disturbances. The solenoidal and dilatational components of the turbulent heat flux, obtained by the Helmholtz decomposition that splits the velocity fluctuations into the solenoidal and dilatational components, are of opposite signs, with the latter smaller in magnitude but showing the tendency of mitigating the former. The integration formula that decomposes the wall heat transfer into various physical processes reveals that the viscous dissipation generates the wall heat transfer, while the turbulent heat flux, work of pressure on dilatation and the mean flow convection transport it towards the free stream. The contribution of the dilatational motions to the viscous dissipation and turbulent heat flux is negligible compared with that of the solenoidal components.