Experimental and numerical study of the shear layer instability between two counter-rotating disks

Abstract

International audienceThe shear layer instability in the flow between two counter-rotating disks enclosed by a cylinder is investigated experimentally and numerically, for radius-to-height ratio Γ=R/h between 2 and 21. For sufficiently large rotation ratio, the internal shear layer that separates two regions of opposite azimuthal velocities is prone to an azimuthal symmetry breaking, which is investigated experimentally by means of visualization and particle image velocimetry. The associated pattern is a combination of a sharp-cornered polygonal pattern, as observed by Lopez et al. (2002) for low aspect ratio, surrounded by a set of spiral arms, first described by Gauthier et al. (2002) for high aspect ratio. The spiral arms result from the interaction of the shear layer instability with the Ekman boundary layer over the faster rotating disk. Stability curves and critical modes are experimentally measured for the whole range of aspect ratios, and are found to compare well with numerical simulations of the three-dimensional time-dependent Navier–Stokes equations over an extensive range of parameters. Measurements of a local Reynolds number based on the shear layer thickness confirm that a shear layer instability, with only weak curvature effect, is responsible for the observed patterns. This scenario is supported by the observed onset modes, which scale as the shear layer radius, and by the measured phase velocities

Crossflow instability of finite Bödewadt flows: Transients and spiral waves

“…This related problem consists of a rotating disk and a stationary disk, shrouded by a cylindrical sidewall, and there may also be an inner cylindrical hub. [37][38][39][40][41][42] However, the motivation for these studies comes from applications in turbomachinery rather than interests in crossflow boundary layer instabilities, and the setups studied typically have the gap between the two disks being a very small fraction of their radius and the cylindrical shroud is stationary. These characteristics of the rotor-stator setup lead to the boundary layer on the rotating disk being turned into the interior by the presence of the stationary shroud, forming a free shear layer that under some conditions becomes unstable to azimuthal waves 43 or the free shear layer may be drawn ͑via Ekman suction type processes͒ into either the boundary layer on the rotating or stationary disk or even periodically flipping between the two.…”

A local sensor for joint temperature and velocity measurements in turbulent flows

“…We detail two situations more particularly: (i) the case of flows where changes in local flow direction may occur [12], and (ii) the case of thermally-inhomogeneous flows where warm or cold fluid parcels could significantly bias the signal. Indeed, hot-wire anemometers are based on the measurement of the heat-transfer efficiency from the wire to the surrounding fluid.…”

Direction reversal of a rotating wave in Taylor–Couette flow

“…Such states arise from cylindrical flows between rotating disks (Serre, Crespo del Arco & Bontoux 2001;Marques, Lopez & Shen 2002;and Moisy et al 2004) or rotating spheres (Marcus & Tuckerman 1987) (see also Egbers & Pfister 2000). One of the most famous rotating waves in a shear flow is the so-called wavy vortex flow, that occurs in the viscous fluid in the gap between two concentric rotating cylinders, i.e.…”