Near-wall determination of the turbulent prandtl number based on experiments, numerical simulation and analytical models

Abstract

The Reynolds-averaged computation of turbulent flow with heat transfer most commonly introduces the turbulent Prandtl number to relate the turbulent fluxes of momentum and heat. Its significant deviation from a uniform bulk flow value for high molecular Prandtl numbers requires a reliable description of this parameter for predicting accurately the heat transfer. The present study proposes a model for the near-wall variation of this important quantity for use in an analytically computed solution of heated turbulent pipe flow. The comparison of the predictions against results from Direct Numerical Simulation (DNS) and experiments proves the proposed analytical approach as a computationally efficient alternative to the much costlier numerical approach with still acceptable accuracy. The analytically obtained results do not only demonstrate the reliability of the proposed model for the near-wall behavior of the turbulent Prandtl number, but also highlight the significance of the dependence of the material properties on the temperature. Numerical simulations mostly neglect this effect to avoid a further increase of the already high computational costs associated with the discretized solution of the heated/cooled flow field.