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Global stability of a jet in crossflow
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0002-8209-1449
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0001-9627-5903
Laboratoire d'Hydrodynamique (LadHyX), CNRS-Ecole Polytechnique.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0001-7864-3071
2009 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 624, 33-44 p.Article in journal (Refereed) Published
Abstract [en]

A linear stability analysis shows that the jet in crossflow is characterized by self-sustained global oscillations for a jet-to-crossflow velocity ratio of 3. A fully three-dimensional unstable steady-state solution and its associated global eigenmodes are computed by direct numerical simulations and iterative eigenvalue routines. The steady flow, obtained by means of selective frequency damping, consists mainly of a (steady) counter-rotating vortex pair (CVP) in the far field and horseshoe-shaped vortices close to the wall. High-frequency unstable global eigenmodes associated with shear-layer instabilities on the CVP and low-frequency modes associated with shedding vortices in the wake of the jet are identified. Furthermore, different spanwise symmetries of the global modes are discussed. This work constitutes the first simulation-based global stability analysis of a fully three-dimensional base flow.

Place, publisher, year, edition, pages
2009. Vol. 624, 33-44 p.
Keyword [en]
Baseflows, Counter-rotating Vortex Pair, Crossflow velocities, Eigen modes, Eigen-value, Far field, Global stability, Global stability analysis, High frequency HF, Jet in crossflow, Low-frequency modes, Shedding vortex, Simulation-based, Steady state solution, Direct numerical simulation, Flow separation, Flow simulation, Groundwater flow, Jets, Linear stability analysis, Three dimensional
National Category
Fluid Mechanics and Acoustics
URN: urn:nbn:se:kth:diva-8501DOI: 10.1017/S0022112009006053ISI: 000265754000003ScopusID: 2-s2.0-65649120402OAI: diva2:13844
QC 20101103Available from: 2008-05-23 Created: 2008-05-23 Last updated: 2010-11-03Bibliographically approved
In thesis
1. Analysis and control of transitional shear flows using global modes
Open this publication in new window or tab >>Analysis and control of transitional shear flows using global modes
2010 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In this thesis direct numerical simulations are used to investigate two phenomenain shear flows: laminar-turbulent transition over a flat plate and periodicvortex shedding induced by a jet in cross flow. The emphasis is on understanding and controlling the flow dynamics using tools from dynamical systems and control theory. In particular, the global behavior of complex flows is describedand low-dimensional models suitable for control design are developed; this isdone by decomposing the flow into global modes determined from spectral analysisof various linear operators associated with the Navier–Stokes equations.Two distinct self-sustained global oscillations, associated with the sheddingof vortices, are identified from direct numerical simulations of the jet incrossflow. The investigation is split into a linear stability analysis of the steadyflow and a nonlinear analysis of the unsteady flow. The eigenmodes of theNavier–Stokes equations, linearized about an unstable steady solution revealthe presence of elliptic, Kelvin-Helmholtz and von K´arm´an type instabilities.The unsteady nonlinear dynamics is decomposed into a sequence of Koopmanmodes, determined from the spectral analysis of the Koopman operator. Thesemodes represent spatial structures with periodic behavior in time. A shearlayermode and a wall mode are identified, corresponding to high-frequency andlow-frequency self-sustained oscillations in the jet in crossflow, respectively.The knowledge of global modes is also useful for transition control, wherethe objective is to reduce the growth of small-amplitude disturbances to delaythe transition to turbulence. Using a particular basis of global modes, knownas balanced modes, low-dimensional models that capture the behavior betweenactuator and sensor signals in a flat-plate boundary layer are constructed andused to design optimal feedback controllers. It is shown that by using controltheory in combination with sensing/actuation in small, localized, regionsnear the rigid wall, the energy of disturbances may be reduced by an order of magnitude.

Place, publisher, year, edition, pages
Stockholm: KTH, 2010. viii, 82 p.
Trita-MEK, ISSN 0348-467X ; 2010:01
Fluid mechanics, flow control, hydrodynamic stability, global modes, jet in crossflow, flat-plate boundary layer, laminar-turbulent transition, Arnoldi method, Koopman modes, balanced truncation, direct numerical simulations.
National Category
Fluid Mechanics and Acoustics
urn:nbn:se:kth:diva-11894 (URN)978-91-7415-540-2 (ISBN)
Public defence
2010-02-12, F3, Lindsedsv, 26, KTH, Stockholm, 10:15 (English)
Available from: 2010-01-26 Created: 2010-01-20 Last updated: 2010-11-03

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