Turbulent Prandtl Number Distribution within the Constant Stress/Heat-Flux Region of a Near-Wall Flow

摘要

The turbulent Prandtl number variation within the near-wall region of fully-developed boundary layers is obtained by using profile analysis. This is achieved by deriving expressions for the eddy diffusivities from Spalding's inner layer formula and its thermal analogue. The analysis is performed over two orders of magnitude of the molecular Prandtl number, encompassing most of the common, non-metallic fluids. It ensures that the limiting conditions at high and low turbulence Reynolds numbers are satisfied explicitly. The turbulent Prandtl number distribution is found to be complex, and dependent on its molecular counterpart within the diffusive sublayer. It is compared with the distributions implied by several phenomenological models, and the consequences for the treatment of the near-wall region in numerical calculation procedures for thin shear layers are discussed.