Experimental observations of an unsteady detached shear layer in enclosed corotating disk flow

Abstract

The flow in the unobstructed space between a pair of disks corotating at high speed in a fixed cylindrical enclosure can be divided into five regions amenable to theoretical analysis [C. A. Schuler, Ph.D. Thesis, 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 rIII/R2≊Γ1/2 and of thickness δIII/R2≊(2 Re)−1/4, where R2 is the radius of the disks, Re is the Reynolds number based on R2 and the tip speed of rotation of the disks (ωR2), and Γ is an experimentally determined constant. Through viscous diffusion, the detached shear layer allows the transition that must take place between the bulk of the three-dimensional 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 these hitherto untested theoretical expressions and reveal that beyond a critical value of the Reynolds number the detached shear layer oscillates in the cross-stream (r-z) plane of the flow. The unsteadiness appears to originate at the enclosure side wall where the disk Ekman layers collide as a result of being redirected from the radial into the axial direction. These observations agree with the direct numerical simulations of Schuler [Ph.D. Thesis, University of California at Berkeley (1990)] which also show that the onset of flow unsteadiness in the cross-stream plane coincides with the appearance of an integer number of circumferentially-periodic large-scale flow structures with large component of axial vorticity, of the type found by Hide and Titman [J. Fluid Mech. 29, 39 (1967)] in a similar flow configuration as of a critical value of the Reynolds number.