Wall-modeled large-eddy simulation of a square duct at high Reynolds number

Turbulent flows in a square duct at high Reynolds number are studied, using a conventional Smagorinsky model in the center of the duct and a self-adaptive Smagorinsky model near the walls which allows to recover correct velocity profiles close to the wall. At the wall, a wall stress model is used as a boundary condition. A modified log law, which describes the distribution of the normalized mean velocity along the wall bisector, is proposed. This provides a better match than the classic log law with the experimental data. Wall-modeled LES are then conducted for the duct flows at a Reynolds number of 250000. The results are compared with the experimental results. The modified log law results in a better prediction of the skin friction, while the self-adaptive Smagorinsky model provides a overall better prediction of both skin friction and the mean velocity profiles. Moreover, the self-adaptive Smagorinsky model captures the acceleration of the mean streamwise velocity near the corner, while the conventional Smagorisnky model fails to capture this phenomenon. The methodology developed in this study provides a pragmatic wall-modeled LES methodology for the simualtion of a square duct at high Reynolds numbers.