Jac. Humphrey et D. Gor, EXPERIMENTAL-OBSERVATIONS OF AN UNSTEADY DETACHED SHEAR-LAYER IN ENCLOSED COROTATING DISK FLOW, Physics of fluids. A, Fluid dynamics, 5(10), 1993, pp. 2438-2442
The flow in the unobstructed space between a pair of disks corotating
at high speed in a fixed cylindrical enclosure can be divided into fiv
e regions amenable to theoretical analysis [C. A. Schuler, Ph.D. Thesi
s, University of California at Berkeley (1990); C. A. Schuler et al.,
Phys. Fluids A 2, 1760 (1990)]. One of these, region III in Fig. 2, is
an axially-aligned detached shear layer predicted by the analysis to
be located at r(III)/R2 almost-equal-to GAMMA1/2 and of thickness delt
a(III)/R2 almost-equal-to (2 Re)-1/4, where R2 is the radius of the di
sks, Re is the Reynolds number based on R2 and the tip speed of rotati
on of the disks (omegaR2), and GAMMA is an experimentally determined c
onstant. Through viscous diffusion, the detached shear layer allows th
e transition that must take place between the bulk of the three-dimens
ional flow in the interdisk space (region II) and the two-dimensional
flow in solid body rotation surrounding the hub that spins the disks (
region IV). Present findings, based on flow visualization, confirm the
se hitherto untested theoretical expressions and reveal that beyond a
critical value of the Reynolds number the detached shear layer oscilla
tes in the cross-stream (r-z) plane of the flow. The unsteadiness appe
ars to originate at the enclosure side wall where the disk Ekman layer
s collide as a result of being redirected from the radial into the axi
al direction. These observations agree with the direct numerical simul
ations of Schuler [Ph.D. Thesis, University of California at Berkeley
(1990)] which also show that the onset of flow unsteadiness in the cro
ss-stream plane coincides with the appearance of an integer number of
circumferentially-periodic large-scale flow structures with large comp
onent of axial vorticity, of the type found by Hide and Titman [J. Flu
id Mech. 29, 39 (1967)] in a similar flow configuration as of a critic
al value of the Reynolds number.