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On the laminar-turbulent transition of the rotating-disk flow: the role of absolute instability
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0002-1146-3241
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
2014 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 745, p. 132-163Article in journal (Refereed) Published
Abstract [en]

This paper describes a detailed experimental study using hot-wire anemometry of the laminar-turbulent transition region of a rotating-disk boundary-layer flow without any imposed excitation of the boundary layer. The measured data are separated into stationary and unsteady disturbance fields in order to elaborate on the roles that the stationary and the travelling modes have in the transition process. We show the onset of nonlinearity consistently at Reynolds numbers, R, of similar to 510, i.e. at the onset of Lingwood's (J. Fluid Mech., vol. 299, 1995, pp. 17-33) local absolute instability, and the growth of stationary vortices saturates at a Reynolds number of similar to 550. The nonlinear saturation and subsequent turbulent breakdown of individual stationary vortices independently of their amplitudes, which vary azimuthally, seem to be determined by well-defined Reynolds numbers. We identify unstable travelling disturbances in our power spectra, which continue to grow, saturating at around R = 585, whereupon turbulent breakdown of the boundary layer ensues. The nonlinear saturation amplitude of the total disturbance field is approximately constant for all considered cases, i.e. different rotation rates and edge Reynolds numbers. We also identify a travelling secondary instability. Our results suggest that it is the travelling disturbances that are fundamentally important to the transition to turbulence for a clean disk, rather than the stationary vortices. Here, the results appear to show a primary nonlinear steep-fronted (travelling) global mode at the boundary between the local convectively and absolutely unstable regions, which develops nonlinearly interacting with the stationary vortices and which saturates and is unstable to a secondary instability. This leads to a rapid transition to turbulence outward of the primary front from approximately R = 565 to 590 and to a fully turbulent boundary layer above 650.

Place, publisher, year, edition, pages
2014. Vol. 745, p. 132-163
Keywords [en]
absolute/convective instability, boundary layer stability, transition to turbulence
National Category
Other Physics Topics
Identifiers
URN: urn:nbn:se:kth:diva-145087DOI: 10.1017/jfm.2014.80ISI: 000333907700007OAI: oai:DiVA.org:kth-145087DiVA, id: diva2:716200
Funder
Swedish Research Council
Note

QC 20140508

Available from: 2014-05-08 Created: 2014-05-08 Last updated: 2017-12-05Bibliographically 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. p. viii, 58
Series
TRITA-MEK, ISSN 0348-467X ; 2014:27
Keywords
Fluid mechanics, laminar-turbulent transition, convective instability, absolute instability, secondary instability, hot-wire anemometry
National Category
Other Physics Topics
Research subject
Engineering Mechanics
Identifiers
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)
Opponent
Supervisors
Funder
Swedish Research Council, 76324
Note

QC 20150119

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

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