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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.ORCID iD: 0000-0002-9859-6169
KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
(English)Manuscript (preprint) (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 incompressible Navier–Stokes equations also called the von K ́arm ́an flow. The laminar mean velocity profiles are obtained by solving the resulting ordinary differential equations 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 theoretical investigation focuses on convectively unstable disturbances. Results obtained from the two methods are compared and the methods are shown togive similar results. These theoretical results are also compared with direct numerical simulations and experimental results showing good agreement.

National Category
Applied Mechanics
Identifiers
URN: urn:nbn:se:kth:diva-200908OAI: oai:DiVA.org:kth-200908DiVA: diva2:1071222
Note

This is the second edition of the same paper appearing in Appelquist (Direct numerical simulations of the rotating-disk boundary-layer flow. Licentiate thesis, 2014, Royal Institute of Technology, ISBN: 978-91-7595-202-4). A figure of the Chebyshev polynomials has been taken away, there has been a correction to a typographical error in equation (79), and the result section has been modified. This is mainly due to a mistake that appears in oneof the transformed variables for Mack (1985) which was the basis of an error analysis. Also the introduction is modified appropriately.

QC 20170203

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

This thesis deals with the instabilities of the incompressible boundary-layer flow thatis induced by a disk rotating in otherwise still fluid. The results presented include bothwork in the linear and nonlinear regime and are derived from direct numerical sim-ulations (DNS). Comparisons are made both to theoretical and experimental resultsproviding new insights into the transition route to turbulence. The simulation codeNek5000 has been chosen for the DNS using a spectral-element method (SEM) witha high-order discretization, and the results were obtained through large-scale paral-lel simulations. The known similarity solution of the Navier–Stokes equations for therotating-disk flow, also called the von K ́arm ́an rotating-disk flow, is reproduced by theDNS. With the addition of modelled small simulated roughnesses on the disk surface,convective instabilities appear and data from the linear region in the DNS are anal-ysed and compared with experimental and theoretical data, all corresponding verywell. A theoretical analysis is also presented using a local linear-stability approach,where two stability solvers have been developed based on earlier work. Furthermore,the impulse response of the rotating-disk boundary layer is investigated using DNS.The local response is known to be absolutely unstable and the global response, onthe contrary, is stable if the edge of the disk is assumed to be at radius infinity. Herecomparisons with a finite domain using various boundary conditions give a globalbehaviour that can be both linearly stable and unstable, however always nonlinearlyunstable. The global frequency of the flow is found to be determined by the Rey-nolds number at the confinement of the domain, either by the edge (linear case) or bythe turbulence appearance (nonlinear case). Moreover, secondary instabilities on topof the convective instabilities induced by roughness elements were investigated andfound to be globally unstable. This behaviour agrees well with the experimental flowand acts at a smaller radial distance than the primary global instability. The sharpline corresponding to transition to turbulence seen in experiments of the rotating diskcan thus be explained by the secondary global instability. Finally, turbulence datawere compared with experiments and investigated thoroughly.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2017. 47 p.
Series
TRITA-MEK, ISSN 0348-467X ; 2017:01
Keyword
laminar-turbulent transition, convective instability, absolute instability, crossflow instability, direct numerical simulations
National Category
Engineering and Technology Physical Sciences
Research subject
Physics
Identifiers
urn:nbn:se:kth:diva-200827 (URN)978-91-7729-269-2 (ISBN)
Public defence
2017-02-24, F3, Lindstedtsvägen 26, Stockholm, 10:15 (English)
Opponent
Supervisors
Note

QC 20170203

Available from: 2017-02-03 Created: 2017-02-03 Last updated: 2017-02-03Bibliographically approved

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