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

Garrett, S. D.; Hussain, Zahir; Stephen, Sharon

doi:10.2514/6.2009-3810

Cited by 14 publications

(26 citation statements)

References 26 publications

(27 reference statements)

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“…Importantly, we note that this is not a single unsteady problem but rather a sequence of steady ones, each of which characterised by a different strength of oncoming axial flow. Existing studies have computed the basic flow for this problem, with [7] displaying accurate solutions for 50…”

Section: Justification Of the Centrifugal Mode And Updated Basic Flowmentioning

confidence: 99%

“…While the current authors have conducted cross-flow stability analyses of the effects of enforced axial flow over broad rotating cones and disks (see [5,7,12,13]), this paper represents the first such study to apply a centrifugal Görtler stability analysis to a slender cone rotating within an axial flow. As such, the investigation extends the work of [15], which presents a full description of the still fluid problem.…”

Section: Introductionmentioning

confidence: 99%

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The centrifugal instability of the boundary-layer flow over a slender rotating cone in an enforced axial free stream

et al. 2015

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In this study, a new centrifugal instability mode, which dominates within the boundary-layer flow over a slender rotating cone in still fluid, is used for the first time to model the problem within an enforced oncoming axial flow. The resulting problem necessitates an updated similarity solution to represent the basic flow more accurately than previous studies in the literature. The new mean flow field is subsequently perturbed leading to disturbance equations that are solved via numerical and short-wavelength asymptotic approaches, importantly yielding favourable comparison with existing experiments. Essentially, the boundary-layer flow undergoes competition between the streamwise flow component, due to the oncoming flow, and the rotational flow component, due to effect of the spinning cone surface, which can be described mathematically in terms of a control parameter, namely the ratio of streamwise to axial flow. For a slender cone rotating in sufficiently strong axial flow rates, the instability mode breaks down to Görtler-type counter-rotating spiral vortices, governed by an underlying centrifugal mechanism, which is consistent with experimental and theoretical studies for a slender rotating cone in otherwise-still fluid.

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Section: Justification Of the Centrifugal Mode And Updated Basic Flowmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The centrifugal instability of the boundary-layer flow over a slender rotating cone in an enforced axial free stream

et al. 2015

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“…The crossflow instability for broader rotating cones in axial flow has been considered and discussed in Garrett et al (2010). Meanwhile, an investigation into the centrifugal instability for more slender rotating cones within an imposed axial flow is currently underway and we hope to report on this in the near future.…”

Section: Resultsmentioning

confidence: 99%

“…However, this work should be considered as a further step towards fully classifying the instability mechanics within the general class of flows. Indeed, studies of the effects of enforced axial flow over broad cones and disks have already been published, Garrett & Peake (2007), Garrett et al (2010), Hussain (2010), Hussain et al (2011), Towers & Garrett (2013a,b).…”

Section: Introductionmentioning

confidence: 99%

The centrifugal instability of the boundary-layer flow over slender rotating cones

2014

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Existing experimental and theoretical studies are discussed which lead to the clear hypothesis of a hitherto unidentified convective instability mode that dominates within the boundary-layer flow over slender rotating cones. The mode manifests as Görtler-type counter-rotating spiral vortices, indicative of a centrifugal mechanism. Although a formulation consistent with the classic rotating-disk problem has been successful in predicting the stability characteristics over broad cones, it is unable to identify such a centrifugal mode as the half-angle is reduced. An alternative formulation is developed and the governing equations solved using both short-wavelength asymptotic and numerical approaches to independently identify the centrifugal mode.

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“…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.…”

Section: Introductionmentioning

confidence: 99%

Instability of flow around a rotating, semi-infinite cylinder

2016

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Stability of flow around a rotating, semi-infinite cylinder placed in an axial stream is investigated. Assuming large Reynolds number, the basic flow is computed numerically as described by Derebail Muralidhar et al. [Proc. R. Soc. London, Ser. A 472, 20150850 (2016)], while numerical solution of the local stability equations allows calculation of the modal growth rates and hence determination of flow stability or instability. The problem has three nondimensional parameters: the Reynolds number Re, the rotation rate S, and the axial location Z. Small amounts of rotation are found to strongly affect flow stability. This is the result of a nearly neutral mode of the nonrotating cylinder which controls stability at small S. Even small rotation can produce a sufficient perturbation that the mode goes from decaying to growing, with obvious consequences for stability. Without rotation, the flow is stable below a Reynolds number of about 1060 and also beyond a threshold Z. With rotation, no matter how small, instability is no longer constrained by a minimum Re nor a maximum Z. In particular, the critical Reynolds number goes to zero as Z → ∞, so the flow is always unstable at large enough axial distances from the nose. As Z is increased, the flow goes from stability at small Z to instability at large Z. If the critical Reynolds number is a monotonic decreasing function of Z, as it is for S between about 0.0045 and 5, there is a single boundary in Z, which separates the stable from the unstable part of the flow. On the other hand, when the critical Reynolds number is nonmonotonic, there can, depending on the choice of Re, be several such boundaries and flow stability switches more than once as Z is increased. Detailed results showing the critical Reynolds number as a function of Z for different rotation rates are given. We also obtain an asymptotic expansion of the critical Reynolds number at large Z and use perturbation theory to further quantify the behavior at small S.

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

Cited by 14 publications

References 26 publications

The centrifugal instability of the boundary-layer flow over a slender rotating cone in an enforced axial free stream

The centrifugal instability of the boundary-layer flow over a slender rotating cone in an enforced axial free stream

The centrifugal instability of the boundary-layer flow over slender rotating cones

Instability of flow around a rotating, semi-infinite cylinder

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