Internal energy balance and aerodynamic heating predictions for hypersonic turbulent boundary layers

Abstract

The internal energy equation for a compressible fluid can be cast in a form that relates the wall heat flux for a turbulent boundary layer to various terms integrated across the layer. We derive and utilize such a relation to investigate the ability of several Reynolds-averaged Navier-Stokes turbulence models to predict wall heat flux in a Mach 11 turbulent boundary layer. Data from a Direct Numerical Simulation (DNS) provide a means for assessing detailed contributions of the integrated model terms to the wall heat flux, helping to determine whether each model is able to obtain the ``right answer for the right reasons.''