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Revisiting the stability analysis of the flow over a rotating disk
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
2014 (English)Report (Other academic)
Abstract [en]

Local linear stability analysis applied to the rotating-disk flow is discussed.This flow case is an exact similarity solution to the cylindrical incompressibleNavier–Stokes equations also called the von Karman flow. The laminar mean velocity profiles are obtained by solving the resulting ordinary differential equa-tions assuming the flow is axisymmetric and time independent. Two stability-analyses methods are used to investigate the local linear stability of this flow: i)the ‘shooting method’; and ii) the ‘Chebyshev polynomial method’. This the-oretical investigation focuses on convectively unstable disturbances. Resultsobtained from the two methods are compared and the methods are shown togive similar results. These theoretical results are also compared with directnumerical simulations and experimental results showing good agreement.

Place, publisher, year, edition, pages
2014. , 128 p.
Keyword [en]
Fluid mechanics, boundary layer, rotating disk, laminar-turbulent transition
National Category
Mechanical Engineering
Research subject
Engineering Mechanics
Identifiers
URN: urn:nbn:se:kth:diva-146079OAI: oai:DiVA.org:kth-146079DiVA: diva2:722139
Note

QC 20140617

Available from: 2014-06-05 Created: 2014-06-05 Last updated: 2017-02-03Bibliographically approved
In thesis
1. Direct numerical simulations of the rotating-disk boundary-layer flow
Open this publication in new window or tab >>Direct numerical simulations of the rotating-disk boundary-layer flow
2014 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis deals with the instabilities of the incompressible boundary-layer flow that is induced by a disk rotating in otherwise still fluid. The results presented are mostly limited to linear instabilities derived from direct numerical simulations (DNS) but with the objective that further work will focus on the nonlinear regime, providing greater insights into the transition route to turbulence.

The numerical code Nek5000 has been chosen for the DNS using a spectral-element method in an effort to reduce spurious effects from low-order discretizations. Large-scale parallel simulations have been used to obtain the present results.

The known similarity solution of the Navier–Stokes equation for the rotating-disk flow, also called the von Karman flow, is investigated and can be reproduced with good accuracy by the DNS. With the addition of small roughnesses on the disk surface, convective instabilities appear and data from the DNS are analysed and compared with experimental and theoretical data. A theoretical analysis is also presented using a local linear-stability approach, where two stability solvers have been developedbased on earlier work. A good correspondence between DNS and theory is found and the DNS results are found to explain well the behaviour of the experimental boundary layer within the range of Reynolds numbers for small amplitude (linear) disturbances. The comparison between the DNS and experimental results, presented for the first time here, shows that the DNS allows (for large azimuthal domains) a range of unstable azimuthal wavenumbers β to exist simultaneously with the dominantβ varying, which is not accounted for in local theory, where β is usually fixed for each Reynolds number at which the stability analysis is applied.

Furthermore, the linear impulse response of the rotating-disk boundary layer is investigated using DNS. The local response is known to be absolutely unstable. The global response is found to be stable if the edge of the disk is assumed to be at infinity, and unstable if the domain is finite and the edge of the domain is placed such that there is a large enough pocket region for the absolute instability to develop. The global frequency of the flow is found to be determined by the edge Reynolds number.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2014. viii, 30 p.
Series
TRITA-MEK, ISSN 0348-467X ; 2014:17
Keyword
Fluid mechanics, boundary layer, rotating disk, laminar-turbulent transition, convective instability, absolute instability, secondary instability, crossflow instability, direct numerical simulations
National Category
Engineering and Technology
Research subject
Engineering Mechanics
Identifiers
urn:nbn:se:kth:diva-146087 (URN)978-91-7595-202-4 (ISBN)
Presentation
2014-09-03, Faxen, Teknikringen 8, KTH, Stoockholm, 10:15 (English)
Opponent
Supervisors
Note

QC 20140708

Available from: 2014-07-08 Created: 2014-06-05 Last updated: 2014-07-08Bibliographically approved

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