Curvature- and rotation-induced instabilities in channel flow

Abstract

In a curved channel streamwise vortices, often called Dean vortices, may develop above a critical Reynolds number owing to centrifugal effects. Similar vortices can occur in a rotating plane channel due to Coriolis effects if the axis of rotation is normal to the mean flow velocity and parallel to the walls. In this paper the flow in a curved rotating channel is considered. It is shown from linear stability theory that there is a region for which centrifugal effects and Coriolis effects almost cancel each other, which increases the critical Reynolds number substantially. The flow visualization experiments carried out show that a complete cancellation of Dean vortices can be obtained for low Reynolds number. The rotation rate for which this occurs is in close agreement with predictions from linear stability theory. For curved channel flow a secondary instability of travelling wave type is found at a Reynolds number about three times higher than the critical one for the primary instability. It is shown that rotation can completely cancel the secondary instability.

Relative velocity profile and flow‐rate in sedimentation field‐flow fractionation

“…This result can be shown to be identical to that previously obtained using a different coordinate system [17].…”

Secondary instability of a swept-wing boundary layer disturbed by controlled roughness elements

“…As a result, high-frequency (secondary) instabilities start to grow dominating the laminar-turbulent transition. In 2D boundary layers and channel flows, such a path of the transition was previously observed by Elofsson et al (1999), Matsson and Alfredsson (1990) and Matsubara and Alfredsson (2001).…”

Numerical Simulation of Multiplicity and Stability of Mixed Convection in Rotating Curved Ducts

“…More comprehensive studies have been made in recent years by Wang and Cheng [4], and Daskopoulos and Lenhoff [9] for a circular tube; Matsson and Alfredsson [10,11], and Guo and Finlay [12] for a high-aspect-ratio rectangular duct; and Wang and Cheng [5,13,14,15], Wang [6,7,8], Selmi et al [17], and Selmi and Nandakumar [16] for the square and rectangular ducts with a low-aspect ratio. All the works are for the steady fully developed flows.…”

“…Daskopoulos and Lenhoff [9] made the first bifurcation study numerically under the small curvature and the symmetry condition imposed along the tube's horizontal central plane. Matsson and Alfredsson [10] presented the first and comprehensive linear stability analysis. Matsson and Alfredsson [11] reported an experimental study, by hotwire measurements and smoke visualization, of the effect of rotation on both primary and secondary instabilities.…”