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Global linear instability of the rotating-disk flow investigated through simulations
KTH, School of Engineering Sciences (SCI), Mechanics, Fluid Physics. 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), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0001-9627-5903
KTH, School of Engineering Sciences (SCI), Mechanics, Fluid Physics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.ORCID iD: 0000-0002-1146-3241
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. nstitute of Continuing Education, University of Cambridge, Madingley Hall, Madingley Cambridge, United Kingdom .
2015 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 765, 612-631 p.Article in journal (Refereed) Published
Abstract [en]

Numerical simulations of the flow developing on the surface of a rotating disk are presented based on the linearized incompressible Navier-Stokes equations. The boundary-layer flow is perturbed by an impulsive disturbance within a linear global framework, and the effect of downstream turbulence is modelled by a damping region further downstream. In addition to the outward-travelling modes, inward-travelling disturbances excited at the radial end of the simulated linear region, r(end), by the modelled turbulence are included within the simulations, potentially allowing absolute instability to develop. During early times the flow shows traditional convective behaviour, with the total energy slowly decaying in time. However, after the disturbances have reached r(end), the energy evolution reaches a turning point and, if the location of r(end) is at a Reynolds number larger than approximately R = 594 (radius non-dimensionalized by root v/Omega*, where v is the kinematic viscosity and Omega* is the rotation rate of the disk), there will be global temporal growth. The global frequency and mode shape are clearly imposed by the conditions at r(end). Our results suggest that the linearized Ginzburg-Landau model by Healey (J. Fluid Mech., vol. 663, 2010, pp. 148-159) captures the (linear) physics of the developing rotating-disk flow, showing that there is linear global instability provided the Reynolds number of r(end) is sufficiently larger than the critical Reynolds number for the onset of absolute instability.

Place, publisher, year, edition, pages
2015. Vol. 765, 612-631 p.
National Category
Mechanical Engineering
Identifiers
URN: urn:nbn:se:kth:diva-164479DOI: 10.1017/jfm.2015.2ISI: 000351543600011Scopus ID: 2-s2.0-84922021920OAI: oai:DiVA.org:kth-164479DiVA: diva2:806428
Funder
Swedish Research CouncilSwedish e‐Science Research Center
Note

QC 20150420

Available from: 2015-04-20 Created: 2015-04-17 Last updated: 2017-12-04Bibliographically 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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