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An experimental study of edge effects on rotating-disk transition
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. (Henrik Alfredsson)
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. (Henrik Alfredsson)ORCID iD: 0000-0002-1146-3241
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. (Mekanik, Lingwood)
2013 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 716, 638-657 p.Article in journal (Refereed) Published
Abstract [en]

The onset of transition for the rotating-disk flow was identified by Lingwood (J. Fluid. Mech., vol. 299, 1995, pp. 17-33) as being highly reproducible, which motivated her to look for absolute instability of the boundary-layer flow; the flow was found to be locally absolutely unstable above a Reynolds number of 507. Global instability, if associated with laminar-turbulent transition, implies that the onset of transition should be highly repeatable across different experimental facilities. While it has previously been shown that local absolute instability does not necessarily lead to linear global instability: Healey (J. Fluid. Mech., vol. 663, 2010, pp. 148-159) has shown, using the linearized complex Ginzburg-Landau equation, that if the finite nature of the flow domain is accounted for, then local absolute instability can give rise to linear global instability and lead directly to a nonlinear global mode. Healey (J. Fluid. Mech., vol. 663, 2010, pp. 148-159) also showed that there is a weak stabilizing effect as the steep front to the nonlinear global mode approaches the edge of the disk, and suggested that this might explain some reports of slightly higher transition Reynolds numbers, when located close to the edge. Here we look closely at the effects the edge of the disk have on laminar-turbulent transition of the rotatingdisk boundary-layer flow. We present data for three different edge configurations and various edge Reynolds numbers, which show no obvious variation in the transition Reynolds number due to proximity to the edge of the disk. These data, together with the application (as far as possible) of a consistent definition for the onset of transition to others' results, reduce the already relatively small scatter in reported transition Reynolds numbers, suggesting even greater reproducibility than previously thought for 'clean' disk experiments. The present results suggest that the finite nature of the disk, present in all real experiments, may indeed, as Healey (J. Fluid. Mech., vol. 663, 2010, pp. 148-159) suggests, lead to linear global instability as a first step in the onset of transition but we have not been able to verify a correlation between the transition Reynolds number and edge Reynolds number.

Place, publisher, year, edition, pages
2013. Vol. 716, 638-657 p.
Keyword [en]
absolute/convective instability, boundary layer stability, transition to turbulence
National Category
Engineering and Technology
URN: urn:nbn:se:kth:diva-119043DOI: 10.1017/jfm.2012.564ISI: 000314422800038ScopusID: 2-s2.0-84878344317OAI: diva2:609915
Swedish Research Council

QC 20130308

Available from: 2013-03-08 Created: 2013-03-05 Last updated: 2015-01-19Bibliographically approved
In thesis
1. Studies of the rotating-disk boundary-layer flow
Open this publication in new window or tab >>Studies of the rotating-disk boundary-layer flow
2014 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The rotating-disk boundary layer is not only a simpler model for the study of cross-flow instability than swept-wing boundary layers but also a useful simplification of many industrial-flow applications where rotating configurations are present. For the rotating disk, it has been suggested that a local absolute instability, leading to a global instability, is responsible for the small variation in the observed laminar-turbulent transition Reynolds number however the exact nature of the transition is still not fully understood. This thesis aims to clarify certain aspects of the transition process. Furthermore, the thesis considers the turbulent rotating-disk boundary layer, as an example of a class of three-dimensional turbulent boundary-layer flows.

The rotating-disk boundary layer has been investigated in an experimental apparatus designed for low vibration levels and with a polished glass disk that gave a smooth surface. The apparatus provided a low-disturbance environment and velocity measurements of the azimuthal component were made with a single hot-wire probe. A new way to present data in the form of a probability density function (PDF) map of the azimuthal fluctuation velocity, which gives clear insights into the laminar-turbulent transition region, has been proposed. Measurements performed with various disk-edge conditions and edge Reynolds numbers showed that neither of these conditions a↵ect the transition process significantly, and the Reynolds number for the onset of transition was observed to be highly reproducible.

Laminar-turbulent transition for a ‘clean’ disk was compared with that for a disk with roughness elements located upstream of the critical Reynolds number for absolute instability. This showed that, even with minute surface roughness elements, strong convectively unstable stationary disturbances were excited. In this case, breakdown of the flow occurred before reaching the absolutely unstable region, i.e. through a convectively unstable route. For the rough disk, the breakdown location was shown to depend on the amplitude of individual stationary vortices. In contrast, for the smooth (clean-disk) condition, the amplitude of the stationary vortices did not fix the breakdown location, which instead was fixed by a well-defined Reynolds number. Furthermore, for the clean-disk case, travelling disturbances have been observed at the onset of nonlinearity, and the associated disturbance profile is in good agreement with the eigenfunction of the critical absolute instability.

Finally, the turbulent boundary layer on the rotating disk has been investigated. The azimuthal friction velocity was directly measured from the azimuthal velocity profile in the viscous sublayer and the velocity statistics, normalized by the inner scale, are presented. The characteristics of this three-dimensional turbulent boundary-layer flow have been compared with those for the two-dimensional flow over a flat plate and close to the wall they are found to be quite similar but with rather large differences in the outer region. 

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2014. viii, 58 p.
TRITA-MEK, ISSN 0348-467X ; 2014:27
Fluid mechanics, laminar-turbulent transition, convective instability, absolute instability, secondary instability, hot-wire anemometry
National Category
Other Physics Topics
Research subject
Engineering Mechanics
urn:nbn:se:kth:diva-158973 (URN)978-91-7595-416-5 (ISBN)
Public defence
2015-01-30, F3, Lindstedsv. 26, KTH, Stockholm, 10:15 (English)
Swedish Research Council, 76324

QC 20150119

Available from: 2015-01-19 Created: 2015-01-16 Last updated: 2015-01-19Bibliographically approved

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