Instability and Transition of a Boundary Layer over a Backward-Facing Step

Abstract

The development of secondary instabilities in a boundary layer over a backward-facing step is investigated numerically. Two step heights are considered, h/δ∗o = 0.5 and 1.0 (where δ∗o is the displacement thickness at the step location), in addition to a reference flat-plate case. A case with a realistic freestream-velocity distribution is also examined. A controlled K-type transition is initiated using a narrow ribbon upstream of the step, which generates small and monochromatic perturbations by periodic blowing and suction. A well-resolved direct numerical simulation is performed. The step height and the imposed freestream-velocity distribution exert a significant influence on the transition process. The results for the h/δ∗o = 1.0 case exhibit a rapid transition primarily due to the Kelvin–Helmholtz instability downstream of step; non-linear interactions already occur within the recirculation region, and the initial symmetry and periodicity of the flow are lost by the middle stage of transition. In contrast, case h/δ∗o = 0.5 presents a transition road map in which transition occurs far downstream of the step, and the flow remains spatially symmetric and temporally periodic until the late stage of transition. A realistic freestream-velocity distribution (which induces an adverse pressure gradient) advances the onset of transition to turbulence, but does not fundamentally modify the flow features observed in the zero-pressure gradient case. Considering the budgets of the perturbation kinetic energy, both the step and the induced pressure-gradient increase, rather than modify, the energy transfer.