Coherent structure modeling of viscous sublayer turbulence for incompressible flow with heat transfer and for compressible flow

The general objective of the present research is to develop a Navier-Stokes computational model of the time-dependent dynamics and heat transfer in a compressible viscous sublayer. The main objective is to compute the variation of turbulent Prandtl number across the sublayer. Experiments have been unable to define this variation, and existing theories differ greatly. A computational code has been developed using preliminary, relatively simple temperature and velocity boundary conditions at the outer edge of the sublayer. Computations have been made for molecular Prandtl numbers from 0.7 to 6 with zero pressure gradient, and for adverse, zero, and favorable pressure gradient, with a Prandtl number of 0.7. These preliminary results show a strong effect of molecular Prandtl number on turbulent Prandtl number near the wall; but only a relatively small effect of pressure gradient throughout the sublayer. Future computations will be made with more refined boundary conditions.