Near-wall modeling of turbulent heat fluxes

Abstract

The near-wall asymptotic behavior of the turbulent heat fluxes is analyzed and the result is used to formulate a second-moment turbulence closure for heat flux transport near a wall. The analysis shows that the pressure diffusion and viscous dissipation terms are of primary importance in the near-wall region and have to be properly modeled in the transport equations. New models satisfying the nearwall balance between viscous diffusion, viscous dissipation and pressure diffusion, and also having the characteristics of approaching their respective conventional high-Reynolds-number models far away from the wall are proposed. Fully-developed pipe flows with constant wall heat flux are chosen to validate the proposed models. The calculations show that the new models are capable of capturing the near-wall behavior very well. However, they also point to the rather immature status of the present high-Reynolds-number heat flux models. The modeling of the pressure-scrambling term is shown to have significant effects on the calculated heat flux and it is believed that this term is influenced by more than one turbulent time scale. Finally, the analysis also verifies the notion that the turbulent Prandtl number is not constant near a wall. If the turbulent Prandtl number is assumed constant, the results obtained are at variance with measurements.