Computational analysis of the two-dimensional–three-dimensional transition in forward-facing step flow

Abstract

Results are presented from a computational study of the flow over a forward-facing step in a plane channel. The aim of the study is to gain better insight into the three-dimensionality that is typically observed in the separation region of flows over steps and ribs, and in similar configurations. We consider laminar flow at a Reynolds number of 330, based on step height and bulk velocity of the oncoming flow, and the step is assumed to be infinitely extended in the spanwise direction. High-resolution simulations are undertaken using a mixed spectral/spectral-element code. Moreover, a linear stability study of the flow at the step is performed. The results show that, in the case considered, the three-dimensionality is not related to some absolute instability of the separation bubble in front of the step; rather, it is a sensitive reaction of the flow to three-dimensional perturbations present in the oncoming stream. It is demonstrated that disturbance amplitudes of less than 1% of the mean flow (at, say, 10 step heights ahead of the step) already suffice to produce a visibly three-dimensional structure of the separation zone. If the disturbance level is systematically decreased, the three-dimensional state evolves to an almost two-dimensional recirculation. Here, the key finding is that the intensity of the flow response is proportionate to the amplitude of the inflow disturbance, meaning that the breakup of the flow in the step region is a linear (i.e. small) perturbation of the two-dimensional base flow. A comparison of the present simulation results with experimental data shows close agreement concerning, for example, the flow topology in the step region, and the spanwise spacing of the characteristic streaks that form further downstream.

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“…flow-path constriction), is a fundamental and widely investigated flow process characterized by a wide range of three-dimensional instabilities. Hence, complex, perturbationsensitive, recirculating-flow topologies are common to arise even in the laminar-flow regime and concerning simplified geometrical configurations (Wilhelm et al 2003). In reference to high-velocity, turbulent liquid flows, onset of a recirculating-flow pattern having a significant vorticity magnitude is possible to cause enough tension at its core, so as to force the liquid to nucleate, hence, giving rise to a vortical cavity.…”

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“…The three-dimensional nature of separated flows in the case of a geometrical confinement generates a complex velocity field manifested by the formation of distinct vortex structures [8][9][10][11]. Stüer et al [8] used the hydrogen bubble technique and particle tracking velocimetry to visualize the laminar three-dimensional flow ahead of a forward facing step.…”

“…They noticed a structure similar to a horseshoe vortex in front of the step and came to the conclusion that the flow passes the step over paths of approximately the same spanwise distance. Wilhelm et al [10] performed a computational analysis of the three-dimensional, laminar, incompressible flow of a Newtonian fluid over an infinite, in the spanwise direction, forward-facing step. The simulation was initialized with a two-dimensional solution and three-dimensional perturbations of different kind and intensity were superimposed.…”