Experimental investigation of absolute instability of a rotating-disk boundary layer

Othman, Hesham; Corke, Thomas

doi:10.1017/s0022112006001546

Cited by 48 publications

(92 citation statements)

References 17 publications

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“…Othman & Corke (2006) used a stronger perturbation too, in order to investigate the nonlinear behaviour. However, this proved less conclusive than the linear case, and they conclude that 'they do not have sufficient evidence to address the question of whether the higher-amplitude condition triggered a global mode.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

The elephant mode between two rotating disks

2008

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Spectral direct numerical simulations (DNS) are carried out for a source-sink flow in an annular cavity between two co-rotating disks. When the Reynolds number based on the forced inflow is increased, a self-sustained crossflow instability of finite amplitude is observed. We show that this nonlinear global mode is made up of a front located at the upstream boundary of the absolutely unstable domain, followed by a saturated spiral mode, and that its properties are in good agreement with results of the local stability theory. This structure is characteristic of the so-called elephant mode of Pier & Huerre (J. Fluid Mech. vol. 435, 2001, p. 145). The global bifurcation is subcritical since only large-amplitude initial perturbations are found to trigger the elephant mode. Small-amplitude perturbations induce a long-lasting transient growth but lead eventually to a damped linear global mode, showing that non-parallel effects counteract the absolute instability and restabilize the flow. A similar linear global stabilization due to non-parallel effects has been found in the case of the flow above a single rotating disk. For the single-disk geometry, the existence of an elephant mode would imply, together with results of Davies & Carpenter (2003) a subcritical global instability, which has not yet been demonstrated. Although the present geometry differs from the single-disk case, the existence of a subcritical global bifurcation is now established, allowing a precise analysis of the transition scenarios.

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Section: Conclusion and Discussionmentioning

confidence: 99%

The elephant mode between two rotating disks

2008

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“…However, non-stationary modes (i.e., those where γ 0) can also exist, and some have lower critical Re and higher growth rates than the stationary modes. Corke and co-workers 18,28,29 have shown that non-stationary modes can be important in the transition process over smooth disks, but these tend not to be naturally excited where roughnesses are present. In order to safely predict a stabilization of the boundary layer by surface roughness though, some calculations for travelling modes are included.…”

Section: Travelling Modes and Absolute Instabilitymentioning

confidence: 99%

The effect of anisotropic and isotropic roughness on the convective stability of the rotating disk boundary layer

et al. 2015

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A theoretical study investigating the effects of both anisotropic and isotropic surface roughness on the convective stability of the boundary-layer flow over a rotating disk is described. Surface roughness is modelled using a partial-slip approach, which yields steady-flow profiles for the relevant velocity components of the boundary-layer flow which are a departure from the classic von Kármán solution for a smooth disk. These are then subjected to a linear stability analysis to reveal how roughness affects the stability characteristics of the inviscid Type I (or cross-flow) instability and the viscous Type II instability that arise in the rotating disk boundary layer. Stationary modes are studied and both anisotropic (concentric grooves and radial grooves) and isotropic (general) roughness are shown to have a stabilizing effect on the Type I instability. For the viscous Type II instability, it was found that a disk with concentric grooves has a strongly destabilizing effect, whereas a disk with radial grooves or general isotropic roughness has a stabilizing effect on this mode. In order to extract possible underlying physical mechanisms behind the effects of roughness, and in order to reconfirm the results of the linear stability analysis, an integral energy equation for three-dimensional disturbances to the undisturbed three-dimensional boundary-layer flow is used. For anisotropic roughness, the stabilizing effect on the Type I mode is brought about by reductions in energy production in the boundary layer, whilst the destabilizing effect of concentric grooves on the Type II mode results from a reduction in energy dissipation. For isotropic roughness, both modes are stabilized by combinations of reduced energy production and increased dissipation.

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“…For the von Kármán rotating-disc boundary layer, no unequivocal evidence for the presence of a linearly unstable global mode has, as yet, been adduced using data obtained from physical experiments [19,20]. Disturbances with such a form might have been expected to have arisen in conjunction with the onset of absolute instability.…”

Section: Global Stability Behaviourmentioning

confidence: 99%

Global stability behaviour for the BEK family of rotating boundary layers

Davies

Thomas

2016

Theor. Comput. Fluid Dyn.

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Numerical simulations were conducted to investigate the linear global stability behaviour of the Bödewadt, Ekman, von Kármán (BEK) family of flows, for cases where a disc rotates beneath an incompressible fluid that is also rotating. This extends the work reported in recent studies that only considered the rotating-disc boundary layer with a von Kármán configuration, where the fluid that lies above the boundary layer remains stationary. When a homogeneous flow approximation is made, neglecting the radial variation of the basic state, it can be shown that linearised disturbances are susceptible to absolute instability. We shall demonstrate that, despite this prediction of absolute instability, the disturbance development exhibits globally stable behaviour in the BEK boundary layers with a genuine radial inhomogeneity. For configurations where the disc rotation rate is greater than that of the overlying fluid, disturbances propagate radially outwards and there is only a convective form of instability. This replicates the behaviour that had previously been documented when the fluid did not rotate beyond the boundary layer. However, if the fluid rotation rate is taken to exceed that of the disc, then the propagation direction reverses and disturbances grow while convecting radially inwards. Eventually, as they approach regions of smaller radii, where stability is predicted according to the homogeneous flow approximation, the growth rates reduce until decay takes over. Given sufficient time, such disturbances can begin to diminish at every radial location, even those which are positioned outwards from the radius associated with the onset of absolute instability. This leads to the confinement of the disturbance development within a finitely bounded region of the spatial-temporal plane.

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Experimental investigation of absolute instability of a rotating-disk boundary layer

Cited by 48 publications

References 17 publications

The elephant mode between two rotating disks

The elephant mode between two rotating disks

The effect of anisotropic and isotropic roughness on the convective stability of the rotating disk boundary layer

Global stability behaviour for the BEK family of rotating boundary layers

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