IJTP Home Issue Contents

A Geometry Independent Near-wall Heat Flux Model for Fluids with Different Prandtl Numbers
C. Y. Zhao and R. M. C. Soy

Near-wall modeling of the turbulent temperature field is more complicated, because the boundary conditions are not as well defined as those for the velocity field. Up to now, most computational and theoretical investigations are based on the hypothesis of a constant turbulent Prandtl number in order to remove the uncertainty of the turbulent thermal boundary condition. However, strictly speaking, the physical arguments for these assumptions are applicable only for fluids whose molecular Prandtl number, Pr, is approximately one. Near-wall asymptotes of the turbulence statistics show that they are Pr dependent. Another difficulty in the modeling of near-wall heat transfer is the irregular geometry often encountered in heat transfer problems. If the heat-flux models fail to reflect the Pr dependence and are geometry dependent, they would not be able to replicate the thermal asymptotes correctly as a wall is approached. The main objective of this paper is to develop a geometry independent near-wall two-equation heat-flux model for fluids with different Pr. As a first attempt, the proposed model and two other geometry dependent heat flux models are assessed against fully developed turbulent channel/pipe flows with variable Pr, with different thermal boundary conditions and with different Reynolds number. In all these investigations, a geometry independent near-wall Reynolds-stress turbulence model is used to calculate the velocity field. The mean temperature and turbulence statistics, such as temperature variance, heat flux and the turbulent time scale ratio, are calculated and compared with direct numerical simulation (DNS) results. Furthermore, the near wall characteristics are investigated and compared with DNS calculations.

full text (IP)