Instability patterns between counter-rotating disks

Abstract

Abstract. The instability patterns in the flow between counter-rotating disks (radius to heigh ratio R/ h from 3.8 to 20.9) are investigated experimentally by means of visualization and Particle Image Velocimetry. We restrict ourselves to the situation where the boundary layers remain stable, focusing on the shear layer instability that occurs only in the counter-rotating regime. The associated pattern is a combination of a circular chain of vortices, as observed by Lopez et al. (2002) at low aspect ratio, surrounded by a set of spiral arms, first described by Gauthier et al. (2002) in the case of high aspect ratio. Stability curve and critical modes are measured for the whole range of aspect ratios. From the measurement of a local Reynolds number based on the shear layer thickness, evidence is given that a free shear layer instability, with only weak curvature effect, is responsible for the observed patterns. Accordingly, the number of vortices is shown to scale as the shear layer radius, which results from the competition between the centrifugal effects of each disk.

Spiral patterns in swirling flows

“…The particles are illuminated by a pulsed laser sheet synchronised with a high-resolution video camera. In Figure Sb, obtained for the same angular velocities as in Figure Sa, we can see the circular chain of 5 vortices surrounded by the negative spiral arms, similar to the pattern visualised using the flakes [8]. The colours encode the levels ofvorticity, i.e., oflocal rotation rate of the fluid particles, from blue (counter-clockwise) to red (clockwise).…”

“…In order to study the instabilities of the flow between two rotating disks, the experimental set-up shown in Figure 2 has been built [6][7][8]. It consists oftwo coaxial disks, each of radius R=14 cm and separated by a distance h, which can be varied between a few mm up to several cm.…”

“…(b) Corresponding velocity field, as measured from Particle Image Velocimetry (PIV). Colors are coding the levels of vertical vorticity, i.e., the 2D local rotation rate of fluid particles [8].…”

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

“…This pattern was given the name of 'negative' spirals, because they roll up to the centre in the direction of the slower disk. Although the morphology of the funnel-like vortices and the negative spirals patterns strongly differs, the issue of a possible continuity between them was first raised by Gauthier et al (2002) and Moisy, Pasutto & Rabaud (2003). The purpose of this paper is to address this issue from a detailed analysis of the instability patterns for a wide range of aspect ratio Γ , between 2 and 21.…”

Rotating and modulated rotating waves in transitions of an enclosed swirling flow

“…Schouveiler et al 1999;Gauthier, Gondret & Rabaud 1999;Gauthier et al 2002;Serre, Tuliszka-Sznitko & Bontoux 2004); in these cases the transition process is dominated by the instability of the boundary layers on the endwalls (which are thought of as disks), which results in spiral modes of very large azimuthal wavenumber. The case of independently rotating endwalls introduces new phenomena associated with internal shear layers (Lopez 1998;Lopez et al 2002a;Moisy, Pasutto & Rabaud 2003) and in the exactly counter-rotating endwalls case, near-heteroclinic behaviour associated with the extra symmetry has been reported (Nore et al 2003;Nore, Moisy & Quartier 2005). In the present study, we shall focus on moderate values of Γ and a single rotating endwall where the transition process is dominated by the internal redistribution of angular momentum.…”