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Global linear and nonlinear stability of viscous confined plane wakes with co-flow
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0001-9627-5903
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
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2011 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 675, 397-434 p.Article in journal (Refereed) Published
Abstract [en]

The global stability of confined wakes is studied numerically, using two-dimensionallinear global modes and nonlinear direct numerical simulations (DNS).The wake inflow velocity is varied between different amounts of co-flow (basebleed), while the density and viscosity are assumed to be constant everywherein the flow domain. In accordance with previous studies, we find that thefrequencies of both the most unstable linear and the saturated nonlinear globalmode increase with confinement. Here, we also find that for wake Reynoldsnumber Re = 100, the confinement is stabilising. It decreases both the growthrate of the linear and the saturation amplitude of the nonlinear modes. Weconclude that the dampening effect is connected to the streamwise developmentof the base flow, and for higher Reynolds numbers this effect decreases, sincethe flow becomes more parallel. The linear analysis reveals that the criticalwake velocities below which the flow becomes unstable are almost identicalfor unconfined and confined wakes at Re ≈ 400. Also, the present resultsare compared with literature data for an inviscid parallel wake due to thesimilarity of inflow profile. The confined wake is found to be more stable thanits inviscid counterpart, while the unconfined wake is more unstable than theinviscid wake. The main reason to both can be explained by the base flowdevelopment. A detailed comparison of the linear and nonlinear results revealsthat the most unstable linear global mode gives an excellent prediction of theinitial nonlinear behaviour and therefore the stability boundary, in all cases.However, the nonlinear saturated state is quite different in particular for higherReynolds numbers. For Re = 100, the saturated frequency also differs less than5% from the linear frequency, and trends regarding confinement observed in thelinear analysis are confirmed.141

Place, publisher, year, edition, pages
2011. Vol. 675, 397-434 p.
National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:kth:diva-34141DOI: 10.1017/jfm.2011.24ISI: 000290491500016Scopus ID: 2-s2.0-79959199912OAI: oai:DiVA.org:kth-34141DiVA: diva2:419288
Funder
Swedish e‐Science Research Center
Note
QC 20110530Available from: 2011-05-26 Created: 2011-05-26 Last updated: 2017-12-11Bibliographically approved
In thesis
1. Numerical stability studies of one-phase and immiscible two-phase jets and wakes
Open this publication in new window or tab >>Numerical stability studies of one-phase and immiscible two-phase jets and wakes
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The initial linear instability growth of two-dimensional plane wakes and jetsis investigated, by temporal two-dimensional global modes, and local spatialstability analysis. Comparisons are also made to experiments, direct numericalsimulations, and methods designed for weakly-non-parallel flows. The studiesproceed through three different flow setups with increasing complexity.The first flow analysed is a convectively unstable liquid sheet surroundedby a stagnant or co-flowing gas. The experimentally measured growth rates arefound to be in excellent agreement with spatial stability calculations, if the airboundary layer is taken into account, and not otherwise. The stabilizing effectof moderate air co-flow is quantified in the numerical study, and the governingparameters found to be the speed difference between water and air, and theshear from air at the water surface (inversely proportional to the air boundarylayer thickness).The second flow case is a one-phase confined wake, i.e. a wake in a channel.The effect of confinement (wall distance) on the global stability of wakes isanalysed by linear global modes, and compared to the results from DNS andweakly-non-parallel theory. At Re = 100, confinement is globally stabilizing,mostly due to a faster development towards a parabolic profile for confinedflows. The stabilizing effect of confinement almost disappears at Re ≈ 400.However, when the structural sensitivity of the wakes is analysed by an adjointbasedapproach, fundamental differences are seen in the global wavemakers ofconfined and unconfined wakes at Re ≈ 400.The third and most complex flow case is immiscible two-fluid wakes andjets. A parallel multi-domain spectral code is developed, where the kinematicand dynamic conditions on the interface are imposed as coupling conditions. Itis shown that intermediate values of surface tension can destabilize stable wakesand jets. In addition, surface tension has a considerable influence on the globaloscillation frequency and spatial shape of the global mode for unstable wakes.The character of the mode is gradually changed from a wake instability to aglobal shear layer instability. Both symmetric and antisymmetric modes areencountered for both wakes and jets, depending on the strength of the surfacetension (value of the Weber number) and the flow case.iii

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2011. ix, 93 p.
Series
Trita-MEK, ISSN 0348-467X ; 11:07
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-34149 (URN)978-91-7501-051-9 (ISBN)
Public defence
2011-06-13, F3, Lindstedsvägen 206, KTH, Stockholm, 10:15 (English)
Opponent
Supervisors
Funder
Swedish e‐Science Research Center
Note
QC 20110530Available from: 2011-05-30 Created: 2011-05-26 Last updated: 2012-05-24Bibliographically approved

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