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Spatial optimal growth in three-dimensional boundary layers
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0002-5913-5431
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0001-7864-3071
2010 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 646, p. 5-37Article 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.

Place, publisher, year, edition, pages
2010. Vol. 646, p. 5-37
Keywords [en]
parabolized stability equations, optimal perturbations, disturbance, growth, bypass transition, transient growth, algebraic growth, shear, flows, instability
National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:kth:diva-19371DOI: 10.1017/s0022112009993260ISI: 000276267200002Scopus ID: 2-s2.0-77952333911OAI: oai:DiVA.org:kth-19371DiVA, id: diva2:337418
Note
QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2017-12-12Bibliographically approved
In thesis
1. Stability and Receptivity of Three-Dimensional Boundary Layers
Open this publication in new window or tab >>Stability and Receptivity of Three-Dimensional Boundary Layers
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. p. 20
Series
Trita-MEK, ISSN 0348-467X ; 2009:19
Keywords
Receptivity, stability, optimal growth, three-dimensional boundary layers, parabolised stability equations, adjoint PSE, crossflow instability
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-11579 (URN)978-91-7415-505-1 (ISBN)
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
2. Receptivity of crossflow-dominated boundary layers
Open this publication in new window or tab >>Receptivity of crossflow-dominated boundary layers
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis deals with receptivity mechanisms of three-dimensional, crossflow-dominated boundary layers. The receptivity of two model problems, a swept-flat-plate and a swept-wing boundary layer, is investigated by solving the parabolised stability equations (PSE) as well as by performing direct numerical simulations (DNS).Both flow cases are known to exhibit strong inflectional instabilities, the crossflow disturbances, whose excitation by external disturbances such as surface roughness or free-stream vorticity is studied. One focus is on worst-case scenarios. This involves the determination of optimal conditions, i.e. those disturbance environments yielding the largest possible response inside the boundary layer.

A new method on the basis of the PSE is presented which allows to study optimal disturbances of swept-flat-plate boundary layers. These take the form of tilted streamwise vortices. While convected downstream they develop into streamwise streaks experiencing strong non-modal growth. Eventually, they turn into crossflow disturbances and undergo exponential growth. Non-modal growth is thus found to optimally excite crossflow disturbances and can be related to a receptivity mechanism of three-dimensional boundary layers. Evaluating effects of compressibility reveals that the potential for both non-modal and modal growth increases for higher Mach numbers. It is shown that wall cooling has diverse effects on disturbances of non-modal and modal nature. While destabilising the former it attenuates the growth of modal disturbances. Concave curvature on the other hand is found to be equally destabilising for both types of disturbances.

The adjoint of the linearised Navier-Stokes equations is solved for a swept-wing boundary layer by means of DNS. The adjoint solution of a steady crossflow disturbance is computed in the boundary layer as well as in the free-stream upstream of the leading edge. This allows to determine receptivity to incoming free-stream disturbances and surface roughness as well as the corresponding worst-case scenarios. Upstream of a swept wing the optimal initial free-stream disturbance is found to be of streak-type which convects downstream towards the leading edge. It entrains the boundary layer a short distance downstream of the stagnation line. While minor streamwise vorticity is present the streak component is dominant all the way into the boundary layer where the optimal disturbance turns into a crossflow mode. Futher, the worst-case surface roughness is determined. It takes a wavy shape and is distributed in the chordwise direction. It is shown that, under such optimal conditions, the swept-wing boundary layer is more receptive to surface roughness than to free-stream disturbances.

Another focus of this work has been the development and evaluation of tools for receptivity prediction. Both DNS and direct and adjoint solutions of the PSE are used to predict the receptivity of a swept-wing boundary layer to localised surface roughness. The configuration conforms to wind tunnel experiments performed by Saric and coworkers at the Arizona State University. Both the DNS and the PSE are found to predict receptivity amplitudes which are in excellent agreement with each other. Though the predicted disturbance amplitudes are slightly lower than experimental measurements the overall agreement with experimental results is very satisfactory.

Finally, a DNS of the stabilisation of a transitional swept-wing boundary layer by means of discrete roughness elements is presented. This control approach is found to completely suppress transition to turbulence within the domain studied and confirms experimental results by Saric & coworkers.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2011. p. x, 60
Series
Trita-MEK, ISSN 0348-467X ; 2011:13
Keywords
Receptivity, three-dimensional boundary layers, optimal growth, adjoint solutions, swept wing
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-48467 (URN)978-91-7501-177-6 (ISBN)
Public defence
2011-12-09, F3, Lindstedtsvägen 26, KTH, Stockholm, 10:15 (English)
Opponent
Supervisors
Funder
Swedish e‐Science Research Center
Note
QC 20111124Available from: 2011-11-24 Created: 2011-11-18 Last updated: 2012-05-24Bibliographically approved

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Hanifi, ArdeshirHenningson, Dan S.

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