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Studies of the rotating-disk boundary-layer flow
KTH, School of Engineering Sciences (SCI), Mechanics, Fluid Physics.
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.
Series
TRITA-MEK, ISSN 0348-467X ; 2014:27
Keyword [en]
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: urn:nbn:se:kth:diva-158973ISBN: 978-91-7595-416-5 (print)OAI: oai:DiVA.org:kth-158973DiVA: diva2:781517
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
List of papers
1. A new way to describe the transition characteristics of a rotating-disk boundary-layer flow
Open this publication in new window or tab >>A new way to describe the transition characteristics of a rotating-disk boundary-layer flow
2012 (English)In: Physics of fluids, ISSN 1070-6631, E-ISSN 1089-7666, Vol. 24, no 3, 031701- p.Article in journal (Refereed) Published
Abstract [en]

A new method of graphically representing the transition stages of a rotating-disk flow is presented. The probability density function contour map of the fluctuating azimuthal disturbance velocity is used to show the characteristics of the boundary-layer flow over the rotating disk as a function of Reynolds numbers. Compared with the variation of the disturbance amplitude (rms) or spectral distribution, this map more clearly shows the changing flow characteristics through the laminar, transitional, and turbulent regions. This method may also be useful to characterize the different stages in the transition process not only for the rotating-disk flow but also for other flows.

National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-93941 (URN)10.1063/1.3696020 (DOI)000302224600001 ()2-s2.0-84859347277 (Scopus ID)
Funder
Swedish Research CouncilStandUp
Note

QC 20120503

Available from: 2012-05-03 Created: 2012-05-03 Last updated: 2017-12-07Bibliographically approved
2. An experimental study of edge effects on rotating-disk transition
Open this publication in new window or tab >>An experimental study of edge effects on rotating-disk transition
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.

Keyword
absolute/convective instability, boundary layer stability, transition to turbulence
National Category
Engineering and Technology
Identifiers
urn:nbn:se:kth:diva-119043 (URN)10.1017/jfm.2012.564 (DOI)000314422800038 ()2-s2.0-84878344317 (Scopus ID)
Funder
Swedish Research Council
Note

QC 20130308

Available from: 2013-03-08 Created: 2013-03-05 Last updated: 2017-12-06Bibliographically approved
3. On the laminar-turbulent transition of the rotating-disk flow: the role of absolute instability
Open this publication in new window or tab >>On the laminar-turbulent transition of the rotating-disk flow: the role of absolute instability
2014 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 745, 132-163 p.Article 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.

Keyword
absolute/convective instability, boundary layer stability, transition to turbulence
National Category
Other Physics Topics
Identifiers
urn:nbn:se:kth:diva-145087 (URN)10.1017/jfm.2014.80 (DOI)000333907700007 ()
Funder
Swedish Research Council
Note

QC 20140508

Available from: 2014-05-08 Created: 2014-05-08 Last updated: 2017-12-05Bibliographically approved
4. Experimental study of the rotating-disk boundary-layer flow with surface roughness
Open this publication in new window or tab >>Experimental study of the rotating-disk boundary-layer flow with surface roughness
2014 (English)Report (Other academic)
Publisher
34 p.
Series
TRITA-MEK, ISSN 0348-467X ; 2014:27
National Category
Other Physics Topics
Identifiers
urn:nbn:se:kth:diva-158970 (URN)
Note

QC 20150116

Available from: 2015-01-16 Created: 2015-01-16 Last updated: 2015-01-19Bibliographically approved
5. Linear disturbances in the rotating-disk flow: a comparison between results from simulations, experiments and theory
Open this publication in new window or tab >>Linear disturbances in the rotating-disk flow: a comparison between results from simulations, experiments and theory
Show others...
2014 (English)Report (Other academic)
Series
TRITA-MEK, ISSN 0348-467X
National Category
Other Physics Topics
Identifiers
urn:nbn:se:kth:diva-158971 (URN)
Note

QC 20150119

Available from: 2015-01-16 Created: 2015-01-16 Last updated: 2015-01-19Bibliographically approved
6. The turbulent rotating-disk boundary layer
Open this publication in new window or tab >>The turbulent rotating-disk boundary layer
2014 (English)In: European journal of mechanics. B, Fluids, ISSN 0997-7546, E-ISSN 1873-7390, Vol. 48, 245-253 p.Article in journal (Refereed) Published
Abstract [en]

The turbulent boundary layer on a rotating disk is studied with the aim of giving a statistical description of the azimuthal velocity field and to compare it with the streamwise velocity of a turbulent two-dimensional flat-plate boundary layer. Determining the friction velocity accurately is particularly challenging and here this is done through direct measurement of the velocity distribution close to the rotating disk in the very thin viscous sublayer using hot-wire anemometry. Compared with other flow cases, the rotating-disk flow has the advantage that the highest relative velocity with respect to a stationary hot wire is at the wall itself, thereby limiting the effect of heat conduction to the wall from the hot-wire probe. Experimental results of mean, rms, skewness and flatness as well as spectral information are provided. Comparison with the two-dimensional boundary layer shows that turbulence statistics are similar in the inner region, although the rms-level is lower and the maximum spectral content is found at smaller wavelengths for the rotating case. These features both indicate that the outer flow structures are less influential in the inner region for the rotating case.

Keyword
Near-wall turbulence, Hot-wire anemometer, Skin friction
National Category
Fusion, Plasma and Space Physics
Identifiers
urn:nbn:se:kth:diva-153238 (URN)10.1016/j.euromechflu.2014.03.009 (DOI)000341549300023 ()2-s2.0-84951882787 (Scopus ID)
Note

QC 20141016

Available from: 2014-10-16 Created: 2014-10-03 Last updated: 2017-12-05Bibliographically approved

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