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Numerical stability studies of one-phase and immiscible two-phase jets and wakes
KTH, School of Engineering Sciences (SCI), Mechanics.
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: urn:nbn:se:kth:diva-34149ISBN: 978-91-7501-051-9OAI: oai:DiVA.org:kth-34149DiVA: diva2:419319
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
List of papers
1. Stabilizing effect of surrounding gas flow on a plane liquid sheet
Open this publication in new window or tab >>Stabilizing effect of surrounding gas flow on a plane liquid sheet
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2011 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 672, 5-32 p.Article in journal (Refereed) Published
Abstract [en]

The stability of a plane liquid sheet is studied experimentally and theoretically, with an emphasis on the effect of the surrounding gas. Co-blowing with a gas velocity of the same order of magnitude as the liquid velocity is studied, in order to quantify its effect on the stability of the sheet. Experimental results are obtained for a water sheet in air at Reynolds number Re-t = 3000 and Weber number We = 300, based on the half-thickness of the sheet at the inlet, water mean velocity at the inlet, the surface tension between water and air and water density and viscosity. The sheet is excited with different frequencies at the inlet and the growth of the waves in the streamwise direction is measured. The growth rate curves of the disturbances for all air flow velocities under study are found to be within 20% of the values obtained from a local spatial stability analysis, where water and air viscosities are taken into account, while previous results from literature assuming inviscid air overpredict the most unstable wavelength with a factor 3 and the growth rate with a factor 2. The effect of the air flow on the stability of the sheet is scrutinized numerically and it is concluded that the predicted disturbance growth scales with (i) the absolute velocity difference between water and air (inviscid effect) and (ii) the square root of the shear from air on the water surface (viscous effect).

Keyword
instability control, interfacial flows (free surface), jets
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-32620 (URN)10.1017/S0022112010006087 (DOI)000289005200002 ()
Note
QC 20110419Available from: 2011-04-19 Created: 2011-04-18 Last updated: 2011-05-30Bibliographically approved
2. Global linear and nonlinear stability of viscous confined plane wakes with co-flow
Open this publication in new window or tab >>Global linear and nonlinear stability of viscous confined plane wakes with co-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

National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-34141 (URN)10.1017/jfm.2011.24 (DOI)000290491500016 ()2-s2.0-79959199912 (ScopusID)
Funder
Swedish e‐Science Research Center
Note
QC 20110530Available from: 2011-05-26 Created: 2011-05-26 Last updated: 2012-05-24Bibliographically approved
3. Effect of surface tension on global modes of confined wake flows
Open this publication in new window or tab >>Effect of surface tension on global modes of confined wake flows
2011 (English)In: Physics of fluids, ISSN 1070-6631, E-ISSN 1089-7666, Vol. 23, no 1, 014108- p.Article in journal (Refereed) Published
Abstract [en]

Many wake flows are susceptible to self-sustained oscillations, such as the well-known von Karman vortex street behind a cylinder that makes a rope beat against a flagpole at a distinct frequency on a windy day. One appropriate method to study these global instabilities numerically is to look at the growth rates of the linear temporal global modes. If all growth rates for all modes are negative for a certain flow field then a self-sustained oscillation should not occur. On the other hand, if one growth rate for one mode is slightly positive, the oscillation will approximately obtain the frequency and shape of this global mode. In our study, we first introduce surface tension between two fluids to the wake-flow problem. Then we investigate its effects on the global linear instability of a spatially developing wake with two co-flowing immiscible fluids. The inlet profile consists of two uniform layers, which makes the problem easily parametrizable. The fluids are assumed to have the same density and viscosity, with the result that the interface position becomes dynamically important solely through the action of surface tension. Two wakes with different parameter values and surface tension are studied in detail. The results show that surface tension has a strong influence on the oscillation frequency, growth rate, and shape of the global mode(s). Finally, we make an attempt to confirm and explain the surface-tension effect based on a local stability analysis of the same flow field in the streamwise position of maximum reverse flow.

National Category
Mechanical Engineering
Identifiers
urn:nbn:se:kth:diva-31601 (URN)10.1063/1.3540686 (DOI)000287424200043 ()2-s2.0-79551558463 (ScopusID)
Funder
Swedish Research Council
Note
QC 20110325Available from: 2011-03-25 Created: 2011-03-21 Last updated: 2011-05-30Bibliographically approved
4. The local and global stability of confined planar wakes at intermediate Reynolds number
Open this publication in new window or tab >>The local and global stability of confined planar wakes at intermediate Reynolds number
2011 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 686, 218-238 p.Article in journal (Refereed) Published
Abstract [en]

At high Reynolds numbers, wake flows become more globally unstable whenconfined within a duct or between two flat plates. At Reynolds numbers around100, however, global analyses suggest that such flows become more stable whenconfined, while local analyses suggest that they become more unstable. Theaim of this paper is to resolve this apparent contradiction. In this theoreticaland numerical study, we combine global and local stability analyses of planarwake flows at Re = 100 to determine the effect of confinement. We find thatconfinement acts in three ways: it modifies the length of the recirculation zoneif one exists, it brings the boundary layers closer to the shear layers, and itcan make the flow more locally absolutely unstable. Depending on the flowparameters, these effects work with or against each other to destabilize orstabilize the flow. In wake flows at Re = 100 with free slip boundaries, flowsare most globally unstable when the outer flows are 50% wider than the halfwidthof the inner flow because the first and third effects work together. Inwake flows at Re = 100 with no slip boundaries, confinement has little overalleffect when the flows are weakly confined because the first two effects workagainst the third. Confinement has a strong stabilizing effect, however, whenthe flows are strongly confined because all three effects work together. Bycombining local and global analyses, we have been able to isolate these threeeffects and resolve the apparent contradictions in previous work.1.

National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-34144 (URN)10.1017/jfm.2011.324 (DOI)000297295900009 ()2-s2.0-84855508019 (ScopusID)
Available from: 2011-05-26 Created: 2011-05-26 Last updated: 2011-12-28Bibliographically approved
5. Oscillatory sensitivity patterns for global modes in wakes
Open this publication in new window or tab >>Oscillatory sensitivity patterns for global modes in wakes
2012 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 701, 251-277 p.Article in journal (Refereed) Published
Abstract [en]

Globally unstable wakes with co-flow at intermediate Reynolds numbers are studied, to quantify important spatial regions for the development and control of the global instability. One region of high structural sensitivity is found close to the inlet for all wakes, in agreement with previous findings for cylinder wakes. A second, elongated region of high structural sensitivity is seen downstream of the first one for unconfined wakes at Re = 400. When base-flow modifications are considered, a spatially oscillating sensitivity pattern is found inside the downstream high-structural-sensitivity region. This implies that the same change in the base flow can either destabilize or stabilize the flow, depending on the exact position where it is applied. It is shown that the sensitivity pattern remains unchanged for different choices of streamwise boundary conditions and numerical resolution. The actual base-flow is modified in selected configurations, and the linear global modes recomputed. It is confirmed that the linear global eigenvalues move according to the predicted sensitivity pattern for small-amplitude base-flow modifications, for which the theory applies. We also look at the implications of a small control cylinder for the flow. Only the upstream high-sensitivity region proves to be robust in terms of control, but one should be careful not to disturb the flow in the downstream high-sensitivity region, in order to achieve control. The findings can have direct implications for the numerical resolution requirements for wakes at higher Reynolds numbers. Furthermore, they provide one more possible explanation for why confined wakes have a more narrow frequency spectrum than unconfined wakes.

Keyword
absolute/convective instability, instability control, wakes
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-34145 (URN)10.1017/jfm.2012.156 (DOI)000304914400009 ()2-s2.0-84864251767 (ScopusID)
Funder
Swedish Research Council
Note
QC 20120703. Updated from submitted to published.Available from: 2011-05-26 Created: 2011-05-26 Last updated: 2012-07-03Bibliographically approved
6. Surface tension induced global destabilization of plane jets and wakes
Open this publication in new window or tab >>Surface tension induced global destabilization of plane jets and wakes
(English)Manuscript (preprint) (Other academic)
Abstract [en]

The effect of surface tension on global stability of confined co-flow jets andwakes at a moderate Reynolds number is studied. The flow cases under studyare globally stable without surface tension. It is found that surface tensioncan cause the flow to be unstable if the inlet shear is strong enough. For evenstronger surface tension, the flow is re-stabilized. As long as there is no changeof the most unstable mode, increasing surface tension seems to decrease the oscillationfrequency and increase the wavelength of the mode. The critical shear(minimum shear at which an instability is found) is found to occur for antisymmetricdisturbances for the wakes and symmetric disturbances for the jets.However, at stronger shear, the opposite symmetry might be the most unstableone, in particular for wakes at high surface tension. The results show strongeffects of surface tension that should be possible to reproduce experimentallyas well as numerically.

Identifiers
urn:nbn:se:kth:diva-34146 (URN)
Available from: 2011-05-26 Created: 2011-05-26 Last updated: 2011-05-30Bibliographically approved

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