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The rotating-disk boundary-layer flow studied through numerical simulations
KTH, School of Engineering Sciences (SCI), Mechanics.ORCID iD: 0000-0002-9859-6169
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. , p. 47
Series
TRITA-MEK, ISSN 0348-467X ; 2017:01
Keywords [en]
laminar-turbulent transition, convective instability, absolute instability, crossflow instability, direct numerical simulations
National Category
Engineering and Technology Physical Sciences
Research subject
Physics
Identifiers
URN: urn:nbn:se:kth:diva-200827ISBN: 978-91-7729-269-2 (print)OAI: oai:DiVA.org:kth-200827DiVA, id: diva2:1070906
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
List of papers
1. Revisiting the stability analysis of the flow over a rotating disk
Open this publication in new window or tab >>Revisiting the stability analysis of the flow over a rotating disk
(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:nbn:se:kth:diva-200908 (URN)
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
2. 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...
2016 (English)In: European journal of mechanics. B, Fluids, ISSN 0997-7546, E-ISSN 1873-7390, Vol. 55, p. 170-181Article in journal (Refereed) Published
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
Keywords
Direct numerical simulations, Hot-wire anemometry, Linear stability theory, Rotating-disk boundary layer
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-181460 (URN)10.1016/j.euromechflu.2015.09.010 (DOI)000367762900016 ()2-s2.0-84948457564 (Scopus ID)
Funder
Swedish Research Council, 2013-5786
Note

QC20160202

Available from: 2016-02-02 Created: 2016-02-02 Last updated: 2017-11-30Bibliographically approved
3. Global linear instability of the rotating-disk flow investigated through simulations
Open this publication in new window or tab >>Global linear instability of the rotating-disk flow investigated through simulations
2015 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 765, p. 612-631Article 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.

National Category
Mechanical Engineering
Identifiers
urn:nbn:se:kth:diva-164479 (URN)10.1017/jfm.2015.2 (DOI)000351543600011 ()2-s2.0-84922021920 (Scopus ID)
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
4. On the global nonlinear instability of the rotating-disk flow over a finite domain
Open this publication in new window or tab >>On the global nonlinear instability of the rotating-disk flow over a finite domain
2016 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 803, p. 332-355Article in journal (Refereed) Published
Abstract [en]

Direct numerical simulations based on the incompressible nonlinear Navier-Stokes equations of the flow over the surface of a rotating disk have been conducted. An impulsive disturbance was introduced and its development as it travelled radially outwards and ultimately transitioned to turbulence has been analysed. Of particular interest was whether the nonlinear stability is related to the linear stability properties. Specifically three disk-edge conditions were considered; (i) a sponge region forcing the flow back to laminar flow, (ii) a disk edge, where the disk was assumed to be infinitely thin and (iii) a physically realistic disk edge of finite thickness. This work expands on the linear simulations presented by Appelquist el al. (J. Fluid. Mech., vol. 765, 2015, pp. 612-631), where, for case (i), this configuration was shown to be globally linearly unstable when the sponge region effectively models the influence of the turbulence on the flow field. In contrast, case (ii) was mentioned there to he linearly globally stable, and here, where nonlinearity is included, it is shown that both cases (ii) and (iii) are nonlinearly globally unstable. The simulations show that the flow can he globally linearly stable if the linear wavepacket has a positive front velocity. However, in the same flow field, a nonlinear global instability can emerge, which is shown to depend on the outer turbulent region generating a linear inward-travelling mode that sustains a transition front within the domain. The results show that the front position does not approach the critical Reynolds number for the local absolute instability, R = 507. Instead, the front approaches R = 583 and both the temporal frequency and spatial growth rate correspond to a global mode originating at this position.

Place, publisher, year, edition, pages
Cambridge University Press, 2016
Keywords
absolute/convective instability, boundary layer stability, rotating flows
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-193985 (URN)10.1017/jfm.2016.506 (DOI)000382894700015 ()2-s2.0-84983391118 (Scopus ID)
Funder
Swedish Research Council, 621-2011-4526Swedish e‐Science Research Center
Note

QC 20161018

Available from: 2016-10-18 Created: 2016-10-14 Last updated: 2017-11-29Bibliographically approved
5. Transition to turbulence in the rotating-disk boundary-layer flow with stationary vortices
Open this publication in new window or tab >>Transition to turbulence in the rotating-disk boundary-layer flow with stationary vortices
(English)Article in journal (Refereed) Submitted
National Category
Applied Mechanics
Identifiers
urn:nbn:se:kth:diva-200906 (URN)
Note

QC 20170203

Available from: 2017-02-03 Created: 2017-02-03 Last updated: 2017-02-03Bibliographically approved
6. Turbulence in the rotating-disk boundary layer investigated through direct numerical simulations
Open this publication in new window or tab >>Turbulence in the rotating-disk boundary layer investigated through direct numerical simulations
(English)Article in journal (Refereed) Submitted
National Category
Engineering and Technology
Identifiers
urn:nbn:se:kth:diva-200907 (URN)
Note

QC 20170203

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

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