Revisiting the two first instabilities of the flow in an annular rotor-stator cavity

• Published in: Physics of fluids (1994) 2009-06, Vol.21 (6), p.064106-064106-8
• Main Authors: Poncet, Sébastien, Serre, Éric, Le Gal, Patrice
• Format: Article
• Language: English
• Subjects: Applied fluid mechanics; Exact sciences and technology; Fluid Dynamics; Fundamental areas of phenomenology (including applications); Hydraulic and pneumatic machinery; Hydrodynamic stability; Nonlinearity (including bifurcation theory); Physics; Transition to turbulence; Turbulent flows, convection, and heat transfer
• ISSN: 1070-6631; 1089-7666
• DOI: 10.1063/1.3156859

The stability of the flow enclosed between a stationary and a rotating disk with a central hub is revisited by experimental visualizations and direct numerical simulations in the case of unmerged boundary layers. The first instability appears as circular rolls, denoted by CRs (type 2 instability), which propagate along the stator before vanishing in the vicinity of the hub. The calculations highlight the convective nature of these rolls, which is in agreement with previous experimental results ( P. Gauthier , P. Gondret , and M. Rabaud , J. Fluid Mech. 386 , 105 ( 1999 ) ). It proves in particular that the CR instability observed in the experiment under permanent conditions is noise sustained. Above a second threshold, spiral rolls, denoted SR1 (type 1 instability), appear at the periphery of the cavity and can coexist with the circular rolls. The DNS shows that they appear through a supercritical Hopf bifurcation. The SR1 patterns appear to be very close to those emitted by the corner vortices obtained by Lopez and Weidman [ J. Fluid Mech. 326 , 373 ( 1996 ) ] during the spin-down of a rotating disk in a fixed cylinder.