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Stability and Receptivity of Three-Dimensional Boundary Layers
KTH, School of Engineering Sciences (SCI), Mechanics. (Stability and Control)
2009 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

The stability and the receptivity of three-dimensional flat plate boundary layers is studied employing parabolised stability equations. These allow for computationally efficient parametric studies. Two different sets of equations are used. The stability of modal disturbances in the form of crossflow vortices is studied by means of the well-known classical parabolised stability equations (PSE). A new method is developed which is applicable to more general vortical-type disturbances. It is based on a modified version of the classical PSE and describes both modal and non-modal growth in three-dimensional boundary layers. This modified PSE approach is used in conjunction with a Lagrange multiplier technique to compute spatial optimal disturbances in three-dimensional boundary layers. These take the form of streamwise oriented tilted vortices initially and develop into streaks further downstream. When entering the domain where modal disturbances become unstable optimal disturbances smoothly evolve into crossflow modes. It is found that non-modal growth is of significant magnitude in three-dimensional boundary layers. Both the lift-up and the Orr mechanism are identified as the physical mechanisms behind non-modal growth. Furthermore, the modified PSE are used to determine the response of three-dimensional boundary layers to vortical free-stream disturbances. By comparing to results from direct numerical simulations it is shown that the response, including initial transient behaviour, is described very accurately. Extensive parametric studies are performed where effects of free-stream turbulence are modelled by filtering with an energy spectrum characteristic for homogeneous isotropic turbulence. It is found that a quantitative prediction of the boundary layer response to free-stream turbulence requires detailed information about the incoming turbulent flow field. Finally, the adjoint of the classical PSE is used to determine the receptivity of modal disturbances with respect to localised surface roughness. It is shown that the adjoint approach yields perfect agreement with results from Finite-Reynold-Number Theory (FRNT) if the boundary layer is assumed to be locally parallel.  Receptivity is attenuated if nonlocal and non-parallel effects are accounted for. Comparisons to direct numerical simulations and extended parametric studies are presented.

Place, publisher, year, edition, pages
Stockholm: KTH , 2009. , 20 p.
Series
Trita-MEK, ISSN 0348-467X ; 2009:19
Keyword [en]
Receptivity, stability, optimal growth, three-dimensional boundary layers, parabolised stability equations, adjoint PSE, crossflow instability
National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:kth:diva-11579ISBN: 978-91-7415-505-1 (print)OAI: oai:DiVA.org:kth-11579DiVA: diva2:277820
Presentation
2009-12-14, E35, Lindstedtsvägen 3, KTH, 10:15 (English)
Opponent
Supervisors
Available from: 2009-11-24 Created: 2009-11-20 Last updated: 2010-11-02Bibliographically approved
List of papers
1. Spatial optimal growth in three-dimensional boundary layers
Open this publication in new window or tab >>Spatial optimal growth in three-dimensional boundary layers
2010 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 646, 5-37 p.Article in journal (Refereed) Published
Abstract [en]

A parabolized set of linear equations is derived, which, in combination with the proposed solution procedure, allows for the study of both non-modal and modal disturbance growth in three-dimensional boundary layers. The method is applicable to disturbance waves whose lines of constant phase are closely aligned with the external streamline. Moreover, strongly growing disturbances may fall outside the scope of application. These equations are used in conjunction with a variational approach to compute optimal disturbances in Falkner Skan Cooke boundary layers subject to adverse and favourable pressure gradients. The disturbances associated with maximum energy growth initially take the form of streamwise vortices which are tilted against the mean crossflow shear. While travelling downstream these vortical structures rise into an upright position and evolve into bent streaks. The physical mechanism responsible for non-modal growth in three-dimensional boundary layers is therefore identified as a combination of the lift-up effect and the Orr mechanism. Optimal disturbances smoothly evolve into crossflow modes when entering the supercritical domain of the flow. Non-modal growth is thus found to initiate modal instabilities in three-dimensional boundary layers. Optimal growth is first studied for stationary disturbances. Influences of parameters such as sweep angle, spanwise wavenumber and position of inception are studied, and the initial optimal amplification of stationary crossflow modes because of non-modal growth is investigated. Finally, general disturbances are considered, and envelopes yielding the maximum growth at each position are computed. In general, substantial growth is already found upstream of the first neutral point. The computations show that at supercritical conditions, maximum growth of optimal disturbances in accelerated boundary layers can exceed the growth predicted for modal instabilities by several orders of magnitude.

Keyword
parabolized stability equations, optimal perturbations, disturbance, growth, bypass transition, transient growth, algebraic growth, shear, flows, instability
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-19371 (URN)10.1017/s0022112009993260 (DOI)000276267200002 ()2-s2.0-77952333911 (Scopus ID)
Note
QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2017-12-12Bibliographically approved
2. Receptivity to Free-Stream Disturbances in Three-Dimensional Boundary Layers
Open this publication in new window or tab >>Receptivity to Free-Stream Disturbances in Three-Dimensional Boundary Layers
2009 (English)Report (Other academic)
Place, publisher, year, edition, pages
Stockholm: KTH, 2009
Series
Internal Report KTH Mechanics
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-25853 (URN)
Note
QC 20101102Available from: 2010-11-02 Created: 2010-11-02 Last updated: 2010-11-02Bibliographically approved
3. Receptivity to Roughness in Three-Dimensional Boundary Layers
Open this publication in new window or tab >>Receptivity to Roughness in Three-Dimensional Boundary Layers
2009 (English)Report (Other academic)
Place, publisher, year, edition, pages
Stockholm: KTH, 2009
Series
Internal Report KTH Mechanics
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-25856 (URN)
Note
QC 20101102Available from: 2010-11-02 Created: 2010-11-02 Last updated: 2010-11-02Bibliographically approved

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