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Flow instability in a channel obstructed by an infinite array of equi-spaced circular cylinders has been numerically studied. An immersed boundary method was employed to facilitate the placement of the cylinders within a Cartesian grid system. This flow configuration is relevant to a heat exchanger in which vortex generators play an important role in enhancing its heat-transfer capacity. The presence of the circular cylinders arranged periodically in the streamwise direction causes a significant topological change of the flow, leading to increasing susceptibility to flow instability. A parametric study has been carried out to investigate the effects of Reynolds number (Re) and the gap (G) between the cylinders and the channel wall not only on the primary instability for Hopf bifurcation, but also on the secondary instability leading to three-dimensional flow. The blockage ratio (d/H) and the distance between two neighboring cylinder centers were fixed as 0.2 and 3.333H, respectively, where d and H represent the cylinder diameter and the channel height, respectively. The Stuart-Landau equation was used to compute the growth rate of the primary instability. The characteristics of the primary instability, including the critical Reynolds numbers and the patterns of the subsequent unsteady flow, were identified. In particular, the crossover of flow topology from flow separation on the channel wall to separated free shear layers from the cylinders turned out to be the key point to explain the flow characteristics of an obstructed channel flow. In addition, the effects of Re and G on the flow-induced forces and the frequency of vortex shedding are also reported. A Floquet stability analysis was employed to study the secondary instability at a higher Reynolds number. It reveals the critical Reynolds number for the three-dimensional instability along with the most unstable spanwise wave number associated with each G considered here. The dependency of the secondary instability on G is also addressed. |
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