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Linear disturbances in the rotating-disk flow: A comparison between results from simulations, experiments and theory
KTH, School of Engineering Sciences (SCI), Mechanics, Fluid Physics.
KTH, School of Engineering Sciences (SCI), Mechanics, Fluid Physics.
KTH, School of Engineering Sciences (SCI), Mechanics, Fluid Physics.ORCID iD: 0000-0002-1146-3241
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.ORCID iD: 0000-0001-9627-5903
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2016 (English)In: European journal of mechanics. B, Fluids, ISSN 0997-7546, E-ISSN 1873-7390, Vol. 55, 170-181 p.Article in journal (Refereed) Published
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Text
Abstract [en]

The incompressible Navier-Stokes equations have an exact similarity solution for the flow over an infinite rotating disk giving a laminar boundary layer of constant thickness, also known as the von Kármán flow. It is well known now that there is an absolute instability of the boundary layer which is linked to transition to turbulence, but convective routes are also observed. It is these convective modes that we focus on here. A comparison of three different approaches to investigate the convective, so called Type-I, stationary crossflow instability is presented here. The three approaches consist of local linear stability analysis, direct numerical simulations (DNS) and experiments. The ’shooting method’ was used to compute the local linear stability whereas linear DNS was performed using a spectral-element method for a full annulus of the disk, a quarter and 1/32 of an annulus, each with one roughness element in the computational domain. These correspond to simulating one, four and 32 roughness elements on the full disk surface and in addition a case with randomly-distributed roughnesses was simulated on the full disk. Two different experimental configurations were used for the comparison: i) a clean-disk condition, i.e. unexcited boundary-layer flow; and ii) a rough-disk condition, where 32 roughness elements were placed on the disk surface to excite the Type-I stationary vortices. Comparisons between theory, DNS and experiments with respect to the structure of the stationary vortices are made. The results show excellent agreement between local linear stability analysis and both DNS and experiments for a fixed azimuthal wavenumber (32 roughnesses). This agreement clearly shows that the three approaches capture the same underlying physics of the setup, and lead to an accurate description of the flow. It also verifies the numerical simulations and shows the robustness of experimental measurements of the flow case. The effects of the azimuthal domain size in the DNS and superposition of multiple azimuthal wavenumbers in the DNS and experiments are discussed.

Place, publisher, year, edition, pages
Elsevier, 2016. Vol. 55, 170-181 p.
Keyword [en]
Direct numerical simulations, Hot-wire anemometry, Linear stability theory, Rotating-disk boundary layer
National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:kth:diva-181460DOI: 10.1016/j.euromechflu.2015.09.010ISI: 000367762900016Scopus ID: 2-s2.0-84948457564OAI: oai:DiVA.org:kth-181460DiVA: diva2:899710
Funder
Swedish Research Council, 2013-5786
Note

QC20160202

Available from: 2016-02-02 Created: 2016-02-02 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)
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Note

QC 20170203

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

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