Direct numerical simulation of turbulent flow over a wall-mounted cube placed inside a channel

Abstract

Direct numerical simulation (DNS) of a developing flow over a wall-mounted cube placed in a channel has been carried out at five different Reynolds numbers ($R{e}_H$) ranging from 500 to 5000 (based on the cube size and average streamwise velocity). The governing equations have been discretized using second-order spatial and temporal schemes. The influence of Reynolds number on separating shear layer transition caused by Kelvin$-$Helmholtz ($KH$) instabilities and the horseshoe vortices is addressed. We examine the topological characteristics of flow separation and reattachment phenomena at different Reynolds numbers and observe that the number of nodes and saddle points increases as the Reynolds number increases, resulting in the formation of additional recirculation regions. A large-scale Kármán vortex shedding is clearly discerned at $R{e}_H\ge 1000$, the frequency of which is found to drop with increasing Reynolds number. The analysis of turbulent kinetic energy production uncovers the presence of negative turbulence production, especially over the top/side surfaces as well as in the horseshoe vortex regime, which diminishes as the Reynolds number increases. Finally, the effect of the Reynolds number on the mean and fluctuating components of wall-shear stresses on each surface of the cube is discussed, and the results demonstrate that the Kelvin$-$Helmholtz rolls contribute significantly to the augmentation of the wall-shear stresses, particularly on the top and side surfaces.