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Optimal linear growth in the asymptotic suction boundary layer
KTH, Superseded Departments, Mechanics.ORCID iD: 0000-0002-3251-8328
2003 (English)In: European journal of mechanics. B, Fluids, ISSN 0997-7546, E-ISSN 1873-7390, Vol. 22, no 3, 259-270 p.Article in journal (Refereed) Published
Abstract [en]

A variational technique in the temporal framework is used to study initial configurations of disturbance velocity which maximize perturbation kinetic energy in the asymptotic suction boundary layer (ASBL). These optimal perturbations (OP) excite significant and remarkably persistent transient growth, on the order of that which occurs in the Blasius boundary layer (BBL). In contrast, classical modal analysis of the ASBL predicts a critical Reynolds number two orders of magnitude larger than that for the BBL. As in other two-dimensional boundary layer flows, disturbances undergoing maximum amplification are infinitely elongated in the direction of the flow and take the form of streamwise-oriented vortices which induce strong variations in the streamwise perturbation velocity (streaks). The Reynolds number dependence of the maximum growth, and the best choice of scaling for the spanwise wavenumber of the perturbation causing it, are elucidated. There is good agreement between the streak resulting from OP and disturbances measured in experiments in which the asymptotic suction boundary layer is subject to free stream turbulence (FST). This agreement is shown to improve as the level of FST increases.

Place, publisher, year, edition, pages
2003. Vol. 22, no 3, 259-270 p.
Keyword [en]
transient growth, boundary layer, asymptotic suction, optimal perturbations, streaks, DISTURBANCE GROWTH, BYPASS TRANSITION, ENERGY GROWTH, FLOW-CONTROL, INSTABILITY, TURBULENCE, STABILITY
National Category
Mechanical Engineering
Identifiers
URN: urn:nbn:se:kth:diva-13237DOI: 10.1016/S0997-7546(03)00033-5ISI: 000184383400004OAI: oai:DiVA.org:kth-13237DiVA: diva2:322552
Note
QC 20100607Available from: 2010-06-07 Created: 2010-06-07 Last updated: 2017-12-12Bibliographically approved
In thesis
1. Flow control of boundary lagers and wakes
Open this publication in new window or tab >>Flow control of boundary lagers and wakes
2003 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [en]

Both experimental and theoretical studies have beenconsidered on flat plate boundary layers as well as on wakesbehind porous cylinders. The main thread in this work iscontrol, which is applied passively and actively on boundarylayers in order to inhibit or postpone transition toturbulence; and actively through the cylinder surface in orderto effect the wakecharacteristics.

An experimental set-up for the generation of the asymptoticsuction boundary layer (ASBL) has been constructed. This studyis the first, ever, that report a boundary layer flow ofconstant boundary layer thickness over a distance of 2 metres.Experimental measurements in the evolution region, from theBlasius boundary layer (BBL) to the ASBL, as well as in theASBL are in excellent agreement with boundary layer analysis.The stability of the ASBL has experimentally been tested, bothto Tollmien-Schlichting waves as well as to free streamturbulence (FST), for relatively low Reynolds numbers (Re). For the former disturbances good agreement is foundfor the streamwise amplitude profiles and the phase velocitywhen compared with linear spatial stability theory. However,the energy decay factor predicted by theory is slightlyoverestimated compared to the experimental findings. The latterdisturbances are known to engender streamwise elongated regionsof high and low speeds of fluid, denoted streaks, in a BBL.This type of spanwise structures have been shown to appear inthe ASBL as well, with the same spanwise wavelength as in theBBL, despite the fact that the boundary layer thickness issubstantially reduced in the ASBL case. The spanwise wavenumberof the optimal perturbation in the ASBL has been calculated andis β = 0.53, when normalized with the displacementthickness. The spanwise scale of the streaks decreases withincreasing turbulence intensity (Tu) and approaches the scale given by optimalperturbation theory. This has been shown for the BBL case aswell.

The initial energy growth of FST induced disturbances hasexperimentally been found to grow linearly as Tu2Rexin the BBL, the transitional Reynolds numberto vary as Tu-2, and the intermittency function to have a relativelywell-defined distribution, valid for all Tu.

The wake behind a porous cylinder subject to continuoussuction or blowing has been studied, where amongst other thingsthe Strouhal number (St) has been shown to increase strongly with suction,namely, up to 50% for a suction rate of 2.5% of the free streamvelocity. In contrast, blowing shows a decrease ofStof around 25% for a blowing rate of 5% of the freestream velocity in the considered Reynolds number range.

Keywords:Laminar-turbulent transition, asymptoticsuction boundary layer, free stream turbulence,Tollmien-Schlichting wave, stability, flow control, cylinderwake.

Place, publisher, year, edition, pages
Stockholm: KTH, 2003. viii, 60 p.
Series
Trita-MEK, ISSN 0348-467X ; 2003:18
Keyword
Laminar-turbulent transition, asymptotic suction boundary layer, free stream turbulence, Tollmien-Schlichting wave, stability, flow control, cylinder wake
National Category
Mechanical Engineering
Identifiers
urn:nbn:se:kth:diva-3664 (URN)
Public defence
2003-12-12, 00:00
Note
QC 20100607Available from: 2003-12-05 Created: 2003-12-05 Last updated: 2010-06-07Bibliographically approved

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Fransson, Jens H.M.

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