The dynamics of the transitional flow over a backward-facing step

Abstract

The internal flow over a backward-facing step in the transitional regime (ReD = 6000) was studied based on direct numerical simulations. The predictions were carried out with the help of a finite-volume Navier–Stokes solver equipped with a co-visualization facility which allows one to investigate the flow dynamics at high temporal resolution. First, grid-induced oscillations were precluded by a careful grid design. Second, the strong influence of the velocity profile approaching the step was studied and outlined. The main objective, however, was to provide a comprehensive insight into the dynamic flow behaviour, especially oscillations of the reattachment length of the primary recirculation region. The origin of this well-known flapping behaviour of the reattachment line is not yet completely understood. In the present work, the mechanisms leading to the oscillations of the reattachment length were extensively investigated by analysing the time-dependent flow. Besides the oscillations of the primary recirculation region, oscillations of the separation and the reattachment line of the secondary recirculation bubble at the upper channel wall were also observed. The results clearly show that in the present flow case the flapping of the primary reattachment and the secondary separation line is due to vortical structures in the unstable shear layers between the main flow and the recirculation bubbles. Vortices emerging in the shear layers and sweeping downstream convectively induce small zones of backward-flowing fluid at the channel walls while passing the recirculation regions. In the case of the primary recirculation region, the rotational movement of the shear-layer vortices impinging on the lower channel wall was found to cause zones of negative fluid velocity at the end of the recirculation bubble and thus flapping of the reattachment line. In contrast, in the case of the secondary recirculation region, the shear-layer vortices moved away from the upper channel wall so that their rotational movement did not reach the boundary. In this case, the pressure gradients originating from local pressure minima located in the shear-layer vortices were identified as being responsible for the oscillations of the separation line at the upper channel wall. While moving downstream with the shear-layer vortices, the pressure gradients were found to influence the top boundary of the channel and create alternating zones of forward- and backward-flowing fluid along the wall. All of these unsteady processes can best be seen from animations which are provided on the Journal of Fluid Mechanics website: journals.cambridge.org/FLM.