Investigation of the structures in the unstable rotating-cone boundary layer

Abstract

This work reports on the unstable region and the transition process of the boundary-layer flow induced by a rotating cone with a half apex angle of 60 degrees using the probability density function (PDF) contour map of the azimuthal velocity fluctuation, which was first used by Imayama et al. [Phys. Fluids 24, 031701 (2012)] for the similar boundary-layer flow induced by a rotating disk. The PDF shows that the transition behavior of the rotatingcone flow is similar to that on the rotating disk. The effects of roughness elements on the cone surface have been examined. For the cone with roughnesses, we reconstructed the most probable vortex structure within the boundary layer from the hot-wire anemometry time signals. The results show that the PDF clearly describes the overturning process of the high-momentum upwelling of the spiral vortices, which due to vortex meandering cannot be detected in the phase-averaged velocity field reconstructed from the point measurements. At a late stage of the overturning process, our hot-wire measurements captured high-frequency oscillations, which may be related to secondary instability.

Boundary-layer transition over a rotating broad cone

“…[10,11]), similar to the one for the disk as suggested by Lingwood [4]. However, since the stationary corotating vortices always exist in a physical experiment the role or importance of this absolute instability with respect to transition is not clear [12]. As shown in Fig.…”

“…The basic-flow characteristics of the cone flow are similar to that of the rotating disk (see Ref. [12]) except the most unstable wave number for the primary stationary disturbance, at the critical Reynolds numbers, is 22 for the disk and 19 for the 60 • cone. The corresponding critical x values are 286 and 268, respectively.…”

“…13045) was used, for the roughness, each was circular with a diameter of approximately 2 mm. The deterministically introduced disturbance gives a fixed fundamental wave number on the entire cone [12] and its initial development compares well with linear stability analysis. In the case without deterministic disturbances, e.g., a clean cone or with randomly distributed roughness elements, the wave number may vary but the disturbance development is still well predicted by linear theory [13].…”

Instability and transition in the boundary layer driven by a rotating slender cone

“…ψ = 0 • ), giving rise to counter-rotating vortices. Recent works provide further quantitative data for broad cones (Imayama, Alfredsson & Lingwood 2012, 2013Kato, Alfredsson & Lingwood 2019a;Kato et al 2019b). However, such detailed experimental data on slender cones have up to now not been available.…”

Boundary layer instability over a rotating slender cone under non-axial inflow

“…This pressure gradient results in an inflectional profile of the mean streamwise velocity that leads to cross-flow instability (Kohama 1984b;Garrett et al 2010). Recent experiments by Kato, Alfredsson & Lingwood (2019a) and Kato et al (2019b) also show the existence of co-rotating spiral vortices (relating to the cross-flow instability) over a broad cone (ψ = 60 • ) rotating in still fluid. Overall, past research provides detailed insights into the formation, growth and breakdown of spiral vortices over a rotating cone, but all of these detailed studies are limited to axisymmetric inflow conditions.…”