Passive scalar profiles in wall-bounded turbulent flows*

Understanding and predicting the passive scalar (here, we consider temperature with small differences) transfer between a solid wall and a turbulent flow has long been studied. However, due to the inherent complexity of the dual-parameter system (characterized by Reynolds number Re_τ and molecular Prandtl number Pr), predictions for mean scalar profiles have been limited to specific regions (e.g., the log region, which is of general interest). Here, using online direct numerical simulation (DNS) databases for turbulent channel and pipe flows with passive scalar, we quantify the mean scalar profiles over the entire region for a wide range of Pr (0.25 to 16) and Re_τ (500 to 6000). A multi-layer thermal mixing length model is applied to solve the mean thermal balance equation and approximate the DNS profiles. With slight parameter adjustments compared to the parameters of momentum mixing length, our model profiles demonstrate uniformly accurate predictions from the wall to the pipe or channel centerline with an error of no more than 4%, valid for both constant heat flux and constant heating source driving conditions. A model for the turbulent Prandtl number is further developed, providing a better description of its distribution than before and yielding excellent predictions from mean velocity profiles to mean temperature profiles. The turbulent heat and mass transfer coefficients are also discussed based on the new model.