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 models the turbulent heat flux as directly related to the turbulent flux of momentum through the turbulent Prandtl number. Its significant deviation from a uniform bulk flow value for high molecular Prandtl numbers needs to be adequately described to predict accurately the heat transfer. The present study derives a model for the near-wall variation of this important parameter, used as input into an analytical solution of heated turbulent pipe flow. The basic functional form of the profile of the turbulent Prandtl number is determined from direct numerical simulations (DNS), and experimental data are used for model calibration. The analytically predicted Nusselt numbers agree very well with experimental measurements, proving the reliability of the proposed model for the turbulent Prandtl number also for Reynolds numbers well beyond the scope of DNS. The validation against experiments further highlights the significant effect of the temperature-dependent material properties of the considered high Prandtl number liquids. Numerical simulations often discard this aspect to reduce the computational effort. The present combination of DNS, analytical solution, and experiments appears as a convenient approach for modeling turbulent key quantities such as the turbulent Prandtl number, which is well applicable to other convective flow conditions and Prandtl number regimes, as well.