Statistical behavior of supersonic turbulent boundary layers with heat transfer at [formula omitted

Abstract

Direct numerical simulations (DNS) of supersonic turbulent boundary layers (STBL) over adiabatic and isothermal walls are performed to investigate the effects of wall heat transfer on turbulent statistics and near wall behaviors. Four different cases of adiabatic, quasi-adiabatic, and uniform hot and cold wall temperatures are considered. Based on the analysis of the current database, it is observed that even though the turbulent Mach number is below 0.3, the wall heat transfer modifies the behavior of near-wall turbulence. These modifications are investigated and identified using both instantaneous fields (i.e. scatter plots) and mean quantities. Morkovin’s hypothesis for compressible turbulent flows is found to be valid for neither heated nor cooled case. It is further uncovered that although some near-wall asymptotic behaviors change upon using weak or strong adiabatic walls, respectively denote the isothermal and iso-flux walls, basic turbulent statistics are not affected by the thermal boundary condition itself. We also show that among different definition of Reynolds number used in STBL, the Reynolds number based on the friction velocity has some advantages data comparison regarding the first and second order statistical moments. More in depth analyses are also performed using the balance equation for turbulent kinetic energy (TKE) budget, as well as the dissipation rate. It is found that the dilatational to solenoidal dissipation ratio increases/decreases when heating/cooling the walls. The DNS of the current STBLs are available online for the community.