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Global stability analysis of three-dimensional boundary layer flows
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.ORCID iD: 0000-0001-9446-7477
2015 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis considers the stability and transition of incompressible boundary layers. In particular, the Falkner–Skan–Cooke boundary layer subject to a cylindrical surface roughness, and the Blasius boundary layer with applied localized suction are investigated. These flows are of great importance within the aviation industry, feature complex transition scenarios, and are strongly three-dimensional in nature. Consequently, no assumptions regarding homogeneity in any of the spatial directions are possible, and the stability of the flow is governed by an extensive three-dimensional eigenvalue problem.

The stability of these flows is addressed by high-order direct numerical simulations using the spectral element method, in combination with a Krylov subspace projection method. Such techniques target the long-term behavior of the flow and can provide lower limits beyond which transition is unavoidable. The origin of the instabilities, as well as the mechanisms leading to transition in the aforementioned cases are studied and the findings are reported.

Additionally, a novel method for computing the optimal forcing of a dynamical system is developed. This type of analysis provides valuable information about the frequencies and structures that cause the largest energy amplification in the system. The method is based on the inverse power method, and is discussed in the context of the one-dimensional Ginzburg–Landau equation and a two-dimensional flow case governed by the Navier–Stokes equations.

Place, publisher, year, edition, pages
KTH Royal Institute of Technology, 2015. , x, 30 p.
Series
TRITA-MEK, ISSN 0348-467X ; 2015:07
Keyword [en]
Hydrodynamic stability, transition to turbulence, global analysis, boundary layers, roughness, laminar flow control, Stokes/Laplace preconditioner, optimal forcing, crossflow vortices, Ginzburg-Landau, Falkner-Skan-Cooke, Blasius, lid-driven cavity
National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:kth:diva-175353ISBN: 978-91-7595-725-8 (print)OAI: oai:DiVA.org:kth-175353DiVA: diva2:860490
Presentation
2015-10-30, D3, Lindstedtsvägen 5, KTH, Stockholm, 13:00 (English)
Opponent
Supervisors
Note

QC 20151015

Available from: 2015-10-15 Created: 2015-10-12 Last updated: 2015-10-15Bibliographically approved
List of papers
1. A method for computing optimal forcing of convectively unstable flows using Laplace preconditioning
Open this publication in new window or tab >>A method for computing optimal forcing of convectively unstable flows using Laplace preconditioning
(English)Manuscript (preprint) (Other academic)
Abstract [en]

For problems governed by a non-normal operator, the leading eigenvalue of the operator is of limited interest and a more relevant measure of the stability is obtained by considering the harmonic forcing causing the largest system response. Various methods for determining this so-called optimal forcing exist, but they all suffer from great computational expense and are hence not practical for large-scale problems. In the present paper a new method is presented, which is applicable to problems of arbitrary size. The method does not rely on timestepping, but on the solution of linear systems, in which the inverse Laplacian acts as a preconditioner. By formulating the problem of finding the optimal forcing as an eigenvalue problem based on the resolvent operator, repeated system solves amount to power iterations, in which the dominant eigenvalue is seen to correspond to the energy amplification in a system for a given frequency, and the eigenfunction to the optimal forcing function. Implementation of the method requires only minor modifications of an existing time-stepping code, and is applicable to any partial differential equation containing the Laplacian, such as the Navier-Stokes equations. We discuss it in the context of the linear Ginzburg-Landau equation.

National Category
Fluid Mechanics and Acoustics Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-175352 (URN)
Note

QS 2015

Available from: 2015-10-12 Created: 2015-10-12 Last updated: 2015-10-15Bibliographically approved
2. Onset of global instability behind distributed surface roughness in a Falkner–Skan–Cooke boundary layer
Open this publication in new window or tab >>Onset of global instability behind distributed surface roughness in a Falkner–Skan–Cooke boundary layer
Show others...
2015 (English)Report (Other academic)
Abstract [en]

A three-dimensional linear global stability analysis of a Falkner–Skan–Cooke boundary layer with distributed three-dimensional surface roughness is performed. The Falkner–Skan–Cooke boundary layer models the flow over swept airplane wings, and investigation of the critical roughness size for which a global instability emerges is thus of great importance within aeronautical applications. The study considers high-order direct numerical simulations and shows that such a critical roughness height exists for the Falkner–Skan–Cooke boundary layer. The roughness Reynolds number and roughness element aspect ratio for which this happens is comparable to the transition data reported in the literature for two-dimensional boundary layers. This demonstrates the importance of the local flow conditions in the vicinity of the roughness for triggering a global instability, although the resulting breakdown scenario is completely different from that of two-dimensional boundary layers. This breakdown scenario is studied in detail, and a global energy analysis is used to reveal the structures and mechanisms responsible for production and dissipation of perturbation energy.

Publisher
33 p.
National Category
Fluid Mechanics and Acoustics Aerospace Engineering
Research subject
Engineering Mechanics; Aerospace Engineering
Identifiers
urn:nbn:se:kth:diva-175347 (URN)
Note

QC 20151015

Available from: 2015-10-12 Created: 2015-10-12 Last updated: 2015-10-15Bibliographically approved
3. On the stability of flat plate boundary layers subject to localized suction
Open this publication in new window or tab >>On the stability of flat plate boundary layers subject to localized suction
Show others...
2015 (English)Report (Other academic)
Abstract [en]

The stability of the Blasius boundary layer subject to localized suction is revisited. Using tools of global stability analysis, the leading direct and adjoint eigenpairs are determined, and novel insight into the sensitivity and receptivity of the flow is obtained. The problem is addressed through high-order spectral element simulations, which enables the inclusion of a suction pipe into the domain. Due to this, a detailed investigation of the connection between the pipe flow and the boundary layer flow is possible. For all cases investigated, the former always turns out to transition for a lower Reynolds number and suction rate than the latter, and the transition scenario is found to be due to a global instability originating inside a separation bubble at the pipe inlet. Identification of such regions, provides information that is valuable in further development of algorithms for laminar flow control.

Publisher
20 p.
National Category
Fluid Mechanics and Acoustics Aerospace Engineering
Research subject
Aerospace Engineering; Engineering Mechanics
Identifiers
urn:nbn:se:kth:diva-175350 (URN)
Note

QC 20151015

Available from: 2015-10-12 Created: 2015-10-12 Last updated: 2017-08-15Bibliographically approved

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Brynjell-Rahkola, Mattias

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