Numerical Study of the Turbulent Prandtl Number in Supersonic Plane-Channel Flow – the Effect of Thermal Boundary Conditions

Direct numerical simulation is used to investigate the turbulent Prandtl number Prt
above cold (isothermal) and hot (adiabatic) walls in a family of supersonic channel
flows. A range of Reynolds numbers and mean temperature/density variations is
considered. The value of Prt away from the wall approaches 0.85 above both the
isothermal and adiabatic walls, with the width of the Prt = 0.85 region increasing
with wall-variable-based Reynolds number Reτw (the latter strongly affected by
the thermal boundary condition). The variable, near-wall Prt profiles from
both the present and previous, passive-scalar simulations collapse as a function of
the semilocal y∗ wall scaling proposed by Huang et al., with the y∗-dependence
weakly parameterized by Reτw.