The absolute instability of the boundary layer on a rotating cone

Abstract

This paper is concerned with the existence of local absolute instability in the boundary-layer flow over the outer surface of a rotating cone, thereby extending earlier work by Lingwood who considered the rotating disk. Both still outer fluids and non-zero axial flow are considered, viscous and streamline-curvature effects are included, and the analysis is conducted for a wide range of cone half-angles, ψ. In still outer fluid our predicted local Reynolds numbers at the onset of absolute instability is relatively insensitive to the value of ψ, and is in reasonable agreement with experimental data for the onset of turbulence when ψ > 50 • . For ψ < 50 • the discrepancy increases, suggesting that some other mechanism may be responsible for transition on more slender cones. The introduction of axial flow is found to significantly increase the Reynolds number for local absolute instability for each half-angle. Crown

Boundary-Layer Transition on Broad Cones Rotating in an Imposed Axial Flow

“…Although numerous flow-visualization studies due to Kobayashi et al [7][8][9][10][11][12][13][14][15][16][17] and recent theoretical studies due to Garrett & Peake [18][19][20][21][22] have been published on the boundary-layer flows over rotating spheres and cones, a complete understanding of the stability characteristics of such boundary layers with regards to these applications is still a long way off. This current paper is part of a series by the present authors 23,24 which considers the convective instability of the boundary-layer flow over a family of rotating cones (including the disk as the limiting half angle), both in and out of an imposed axial flow.…”

“…This current paper is part of a series by the present authors 23,24 which considers the convective instability of the boundary-layer flow over a family of rotating cones (including the disk as the limiting half angle), both in and out of an imposed axial flow. Particular emphasis is placed on the above applications.…”

“…The series presents complementing numerical and asymptotic studies and commenced with an investigation into a family of cones rotating in an otherwise still fluid. 23 This was then followed by an investigation into the disk rotating in an imposed axial flow. 24 As we shall see in §II.A, the mathematical formulation of the rotating-disk problem in axial flow is necessarily different to that for the rotating cone in axial flow, and this motivates separate publication.…”

Quantifying non-Newtonian effects in rotating boundary-layer flows

“…Hall [8] demonstrated that in the limit of large Reynolds number the upper and lower branches of the neutral curve can be described (with excellent agreement) using asymptotic theory. More recently, the aforementioned pioneering studies have been extended to include rotating spheres, see Garrett & Peake [9] and rotating cones, see Garrett et al [10] and Hussain et al [11]. In all cases the flow can be stabilised (or destabilised) with control of the governing parameter, that being the spin rate, in the case of the sphere, and the half-angle, in the case of the cone.…”

Instability of flow around a rotating, semi-infinite cylinder

“…Such flows are often due to rotating bodies as, for example, disks [3,4], cones [5,6], or spheres [7]. Here, we consider a semi-infinite cylinder, rotating about its axis and placed in a high-Reynolds-number axial stream, thus inducing a steady, axisymmetric, three-velocity-component boundary layer whose flow field depends on rotation and curvature of the cylinder, as we have already described in an earlier paper [8], henceforth referred to as I.…”