The flow past large numbers of cylinders in tandem

Abstract

The present study investigates the flow in a multi-cylinder tandem array. A primary aim is to build a framework for understanding the flow as the number of cylinders becomes large. Two-dimensional numerical simulations have been conducted of the flow past a row of identical and equispaced cylinders, at Reynolds number Re≤200, while the distance between cylinders or pitch varies in the range 1.1≤p≤10. The number of cylinders n in the array varies between n=2 and n=100. Three main regimes are identified as a function of p which are delineated by the behavior of the flow in the gap between the two most upstream cylinders, similar to the regimes in a two-cylinder array. These are a short-pitch or attached regime, with a fully attached and apparently steady flow in this gap, a medium-pitch or fluctuating regime, with some fluctuation in this gap, and a large-pitch or shedding regime, with full vortex formation similar to the wake of single-cylinder system in this gap. Large arrays show that these regimes actually occur as a geometric series, i.e. with progression downstream, the attached regime begins to fluctuate, and then form and shed vortices. This shedding regime is then followed by a region of convective instability which breaks the feedback of information upstream. The flow downstream of this convectively unstable region then goes through the same series of regimes with further downstream progression, but on a longer length scale. There is a self-similar “cascade” – development of fluctuation, established vortex shedding, convectively unstable flow – the self-similar units of which are separated by the regions of convective instability. While the length of each unit is a function of p and Re, the appearance of these units is common.