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Global optimal disturbances in the Blasius flow using time-steppers
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: 0000-0002-4346-4732
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0001-7864-3071
(English)Manuscript (preprint) (Other academic)
Abstract [en]

The stability of the Blasius flat-plate boundary-layer flow to three-dimensional disturbances is studied by means of optimisation methods at relatively high Reynolds numbers. We consider both the optimal initial condition leading to the largest growth at finite times and the optimal time-periodic forcing leading to the largest asymptotic response. Both optimisation problems are solved using a Lagrange multiplier technique, where the objective function is the kinetic energy of the flow perturbations and the constraints involve the linearised Navier-Stokes equations. In both cases the evolution equations for the Lagrange multiplier are the adjoint Navier-Stokes equations. The approach proposed here is particularly suited to examine convectively unstable flows, where single global eigenmodes of the system do not capture the downstream growth of the disturbances. The optimal initial condition for spanwise wavelengths of the order of the boundary layer thickness are streamwise vortices exploiting the lift-up mechanism to create streaks. For long spanwise wavelengths it is the Orr mechanism combined with oblique wave packet propagation that dominates. It is found that the latter mechanism is dominant for the relatively high Reynolds number and the long computational domain considered here. The spatial structure of the optimal forcing is similar to the that of the optimal initial condition, and the response to forcing is also dominated by the Orr/oblique wave mechanism, however less so than in the former case. The lift-up mechanism is, as in the local approach using the Orr-Sommerfeld squire equations, most efficient at zero frequency and degrades slowly for increasing frequencies.

National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:kth:diva-9545OAI: oai:DiVA.org:kth-9545DiVA: diva2:117427
Note
QC 20100924Available from: 2008-12-03 Created: 2008-11-12 Last updated: 2010-09-24Bibliographically approved
In thesis
1. Global stability and feedback control of boundary layer flows
Open this publication in new window or tab >>Global stability and feedback control of boundary layer flows
2008 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [en]

In this thesis the stability of generic boundary layer flows is studied from a global viewpoint using optimization methods. Global eigenmodes of the incompressible linearized Navier-Stokes equations are computed using the Krylov subspace Arnoldi method. These modes serve as a tool both to study asymptotic stability and as a reduced basis to study transient growth. Transient growth is also studied using adjoint iterations. The knowledge obtained from the stability analysis is used to device systematic feedback control in the Linear Quadratic Gaussian framework. The dynamics is assumed to be described by the linearized Navier-Stokes equations. Actuators and sensors are designed and a Kalman filtering technique is used to reconstruct the unknown flow state from noisy measurements. This reconstructed flow state is used to determine the control feedback which is applied to the Navier-Stokes equations through properly designed actuators. Since the control and estimation gains are obtained through an optimization process, and the Navier-Stokes equations typically forms a very high-dimensional system when discretized there is an interest in reducing the complexity of the equations. A standard method to construct a reduced order model is to perform a Galerkin projection of the full equations onto the subspace spanned by a suitable set of vectors, such as global eigenmodes and balanced truncation modes.

Place, publisher, year, edition, pages
Stockholm: KTH, 2008. viii, 58 p.
Series
Trita-MEK, ISSN 0348-467X ; 2008:09
Keyword
Stability, Global Stability, Feedback Control, Control, Estimation, Absolute/Convective Instabilities, Model Reduction
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-9547 (URN)978-91-7415-176-3 (ISBN)
Public defence
2008-12-05, E1, Lindstedtsvägen 3, Stockholm, 10:30 (English)
Opponent
Supervisors
Note
QC 20100924Available from: 2008-11-13 Created: 2008-11-12 Last updated: 2010-09-24Bibliographically approved

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Brandt, LucaHenningson, Dan S.

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