Lattice Boltzmann simulations of turbulent channel flow and heat transport by incorporating the Vreman model

In this article, the Vreman model with a dynamic procedure is applied for subgrid scale modeling of turbulent channel flow and heat transport, under the Lattice Boltzmann framework. Numerical simulations of channel flow at Re_τ=180 with a constant temperature difference at the upper and bottom boundaries are presented and verified via comparisons with existing data of direct numerical simulations and large eddy simulations with the dynamic Smagorinsky model. Additionally, in the same flow and thermal system, the effect of natural convection along the vertical direction is investigated both qualitatively and quantitatively. Results indicate that the bulk velocity is decreased whereas the heat transfer is substantially enhanced. Meanwhile, the vertical thermal convection also alters the profiles of first and second-order statistics, especially in that the temperature fluctuation is flattened in the central region of the channel. Overall, our work offers a useful extension of the current Lattice Boltzmann method in complex situations and will facilitate researches involving turbulent flow and heat transport.