Paths of stable configurations resulting from the interaction of two disks falling in tandem

Abstract

We investigate the interaction of two identical disks falling in tandem in a fluid at rest, at Reynolds numbers Re varying between 80 and 300. Wake visualization with fluorescent dyes was used to capture the interaction process: the trailing body accelerates until it catches up with the leading body. Thick disks ( χ = diameter / thickness = 3 ) then lose their initial wakes, separate laterally and eventually fall side by side. In contrast, the wakes of thinner disks ( χ ⩾ 6 ) merge into a single wake and the bodies continue their fall together, adopting a Y-configuration. The paths associated with this stable configuration were investigated in detail by three-dimensional trajectography. Three regimes were identified. At the lowest Re the Y-configuration falls along a rectilinear non-vertical path, but at higher Re the centre of gravity of the pair describes a periodic path contained in a plane slightly tilted relative to the vertical, and the orientations of the bodies exhibit planar in-phase oscillations. In both cases, the two bodies behave like a single rigid body. When Re is further increased, the configuration becomes flexible, the relative distance and relative inclination of the bodies fluctuate in time and the inclined periodic motion becomes irregular.