Centrifugal instability of Stokes layers in crossflow: the case of a forced cylinder wake

Abstract

The wake flow around a circular cylinder at Re ≈ 100 performing rotatory oscillations has been thoroughly discussed in the literature, mostly focusing on the modifications to the natural Bénard-von Kármán vortex street that result from the forced shedding modes locked to the rotatory oscillation frequency. The usual experimental and theoretical frameworks at these Reynolds numbers are quasi-two-dimensional, because the secondary instabilities bringing a threedimensional structure to the cylinder wake flow occur only at higher Reynolds numbers. In this paper, we show that a three-dimensional structure can appear below the usual three-dimensionalization threshold, when forcing with frequencies lower than the natural vortex shedding frequency, at high amplitudes, as a result of a previously unreported mechanism: a pulsed centrifugal instability of the oscillating Stokes layer at the wall of the cylinder. The present numerical investigation lets us in this way propose a physical explanation for the turbulence-like features reported in the recent experimental study by the present authors.

Wakes and Instabilities of Static and Freely Vibrating Cylinders

“…These structures form and dissipate periodically twice every cycle depending on the position of the cylinder (see also figure 8) and can be seen as counter-rotating vortical structures covering the whole span. Similar structures have been observed before in cylinders with forced oscillations in a fluid at rest [33,34], in the flow over a rotating cylinder [35] and in the flow over a cylinder performing rotating oscillations [36], but have never been reported on the VIV context.…”

Experimental investigation of flow-induced vibration of a rotating circular cylinder

“…One question of interest is whether this mode-switching signature of the upper branch still prevails when the cylinder is undergoing forced vibration. Indeed, the action of rotating fixed cylinders modifies the wake stability, whether the rotation is oscillatory (Tokumaru & Dimotakis 1991;Lo Jacono et al 2010;D'Adamo, Godoy-Diana & Wesfreid 2015) or uniform (El Akoury et al 2008;Rao et al 2013Rao et al , 2015. Thus, given that the cylinder is under uniform rotation, hence biasing the vorticity production towards one side and therefore biasing the wake topology, the question of how this affects the wake dynamics of the upper branch is of interest.…”

Topological colouring of fluid particles unravels finite-time coherent sets

“…This free software program combines an adaptive multigrid finite-volume method with immersed boundary and volume of fluid methods. Gerris was previously used by D'Adamo, Godoy-Diana & Wesfreid (2015) to analyse the centrifugal instabilities that may appear at higher Reynolds number in ROCs. Numerical data validation is presented in Appendix C.…”