Near-wall vortical structures in domains with and without curved surfaces

Abstract

Taylor–Couette flow is a canonical flow to study Taylor–Görtler (TG) instability or centrifugal instability and the associated vortices. TG instability has been traditionally associated with flow over curved surfaces or geometries. In the computational study, we confirm the presence of TG-like near-wall vortical structures in two lid-driven flow systems, the Vogel–Escudier (VE) and the lid-driven cavity (LDC) flows. The VE flow is generated inside a circular cylinder by a rotating lid (top lid in the present study), while the LDC flow is generated inside a square or rectangular cavity by the linear movement of the lid. We look at the emergence of these vortical structures through reconstructed phase space diagrams and find that the TG-like vortices are seen in the chaotic regimes in both flows. In the VE flow, these vortices are seen when the side-wall boundary layer instability sets in at large R e . The VE flow is observed to go to a chaotic state in a sequence of events from a steady state at low R e . In contrast to VE flows, in the LDC flow with no curved boundaries, TG-like vortices are seen at the emergence of unsteadiness when the flow exhibits a limit cycle. The LDC flow is observed to have transitioned to chaos from the steady state through a periodic oscillatory state. Various aspect ratio cavities are examined in both flows for the presence of TG-like vortices. This article is part of the theme issue ‘Taylor–Couette and related flows on the centennial of Taylor’s seminal Philosophical transactions paper (Part 2)’.

Vortex breakdown in the small Mach number regimes

“…The azimuthal perturbation in the 3D instability analysis was observed by Lugt & Abboud [28] and Gelfgat et al [29]. In a recent work [30], the presence of Taylor-like vortices is reported in VE flows, which corresponds to the chaotic state of the flow. This paper examines the effect of small density changes due to compressibility on the flow topology and vortex breakdown in the subsonic regime.…”

“…A weak turbulence, where flow is in a chaotic state due to multiple azimuthal waves, was observed for Re = 5000 for incompressible flows ( [30,52]). The various modes present can be obtained from the velocity magnitude, u, at a point (θ, r * , z * ):(0, 0.5, 0.1784) for various Mach numbers shown in the signal in figures 12(a)-(d) and the power spectrum is shown in figure 12(c).…”