Investigation of turbulent Prandtl number subject to local acceleration and deceleration

The main objective of the present study is to analyze the turbulent Prandtl number ($\Pr_{t} )$ varying over space in a wall-bounded turbulent flow under local acceleration and deceleration. The $\Pr_{t} $ shows the opposite trends for the conditions of acceleration and deceleration. In order to explain these phenomena, the convection velocity from the space-time correlation is investigated. It is shown that small-scale motions experience larger acceleration and deceleration compared to large-scale ones. Also, a discrepancy between the momentum and heat transfer at small scales results in the spatially varying $\Pr_{t} $. The budgets of the turbulent kinetic energy and temperature variance show a hint for the variation of $\Pr_{t} $. The results from DNS and RANS with a constant $\Pr _{t} $ are compared and show that RANS prediction can be improved by using a modeled $\Pr_{t} $. From the turbulent statistics, a few flow variables showing higher correlations with $\Pr_{t} $ are identified. Based on this, simple phenomenological models are devised and the corresponding simulations show a more accurate prediction of the heat transfer rate.