An analysis of spatially varying turbulent Prandtl number in a flow with local acceleration and deceleration

The turbulent Prandtl number (Pr$_{t}$) is an important parameter in turbulent flows used in many engineering models for heat transfer. In the present study, spatial variation of Pr$_{t}$ in a wall-bounded turbulent flow is investigated using DNS. We derived a form of Pr$_{t}$ applicable to a general flow configuration, using the least-square method in a manner consistent with the turbulent viscosity model in LES. For a flow subject to local acceleration and deceleration induced by the wall geometry, we performed a parametric study for the Reynolds number, Prandtl number and a geometric factor using DNS. A comparison of the data from DNS and RANS with a constant Pr$_{t}$ indicates the potential of improved RANS predictions using the present variable Pr$_{t}$ subject to the local flow field. Also, it is observed that the local pressure gradient has an important effect on the Pr$_{t}$ field. From the flow statistics, a few flow variables showing higher correlations with Pr$_{t}$ are identified. An elementary model for Pr$_{t}$ is devised, and used for RANS prediction producing a more accurate prediction of the heat transfer rate.