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Receptivity of Boundary Layers under Pressure Gradient
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.
2008 (English)Licentiate thesis, comprehensive summary (Other scientific)
Abstract [en]

Boundary-layer flow over bodies such as aircraft wings or turbine blades is characterized by a pressure gradient due to the curved surface of the body. The boundary layer may experience modal and non-modal instability, and the type of dominant instability depends on whether the body is swept with respect to the oncoming flow or not. The growth of these disturbances causes transition of the boundary-layer flow to turbulence. Provided that they are convective in nature, the instabilities will only arise and persist if the boundary layer is continuously exposed to a perturbation environment. This may for example consist of turbulent fluctuations or sound waves in the free stream or of non-uniformities on the surface of the body. In engineering, it is of relevance to understand how susceptive to such perturbations the boundary layer is, and this issue is subject of receptivity analysis.


In this thesis, receptivity of simplified prototypes for flow past a wing is studied. In particular, the three-dimensional swept-plate boundary layer and the boundary layer forming on a flat plate with elliptic leading edge are considered. The response of the boundary layer to vortical free-stream disturbances and surface roughness is analyzed, receptivity mechanisms are identified and their efficiency is quantified.

Place, publisher, year, edition, pages
Stockholm: KTH , 2008. , vi, 23 p.
Trita-MEK, ISSN 0348-467X ; 2008:08
Keyword [en]
Leading-edge effects
URN: urn:nbn:se:kth:diva-9379ISBN: 978-91-7415-155-8OAI: diva2:113762
2008-10-29, K1, Teknikringen 56, KTH Campus Valhallavägen, Stockholm, 10:15 (English)
76218 VR Receptivity
QC 20101022Available from: 2008-10-30 Created: 2008-10-27 Last updated: 2012-02-23Bibliographically approved
List of papers
1. Receptivity mechanisms in three-dimensional boundary-layer flows
Open this publication in new window or tab >>Receptivity mechanisms in three-dimensional boundary-layer flows
2009 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 618, 209-241 p.Article in journal (Refereed) Published
Abstract [en]

Receptivity in three-dimensional boundary-layer flow to localized surface roughness and free-stream vorticity is studied. A boundary layer of Falkner–Skan–Cooke type with favourable pressure gradient is considered to model the flow slightly downstream of a swept-wing leading edge. In this region, stationary and travelling crossflow instability dominates over other instability types. Three scenarios are investigated: the presence of low-amplitude chordwise localized, spanwise periodic roughness elements on the plate, the impingement of a weak vortical free-stream mode on the boundary layer and the combination of both disturbance sources. Three receptivity mechanisms are identified: steady receptivity to roughness, unsteady receptivity to free-stream vorticity and unsteady receptivity to vortical modes scattered at the roughness. Both roughness and vortical modes provide efficient direct receptivity mechanisms for stationary and travelling crossflow instabilities. We find that stationary crossflow modes dominate for free-stream turbulence below a level of about 0.5%, whereas higher turbulence levels will promote the unsteady receptivity mechanism. Under the assumption of small amplitudes of the roughness and the free-stream disturbance, the unsteady receptivity process due to scattering of free-stream vorticity at the roughness has been found to give small initial disturbance amplitudes in comparison to the direct mechanism for free-stream modes. However, in many environments free-stream vorticity and roughness may excite interacting unstable stationary and travelling crossflow waves. This nonlinear process may rapidly lead to large disturbance amplitudes and promote transition to turbulence.

tollmien-schlichting waves, free-stream disturbances, orr-sommerfeld, equation, continuous-spectrum, localized receptivity, pressure-gradient, leading-edge, transition, roughness, vortices
National Category
Fluid Mechanics and Acoustics
urn:nbn:se:kth:diva-9407 (URN)10.1017/S0022112008004345 (DOI)000262741500010 ()2-s2.0-57749172676 (ScopusID)
Uppdaterad från in Press till Published 2009 QC 20101022 Available from: 2008-10-30 Created: 2008-10-30 Last updated: 2010-11-23Bibliographically approved
2. Transition to turbulence in the boundary layer over a smooth and rough swept plate exposed to free-stream turbulence
Open this publication in new window or tab >>Transition to turbulence in the boundary layer over a smooth and rough swept plate exposed to free-stream turbulence
2010 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 646, 297-325 p.Article in journal (Refereed) Published
Abstract [en]

Receptivity, disturbance growth and transition to turbulence of the three-dimensional boundary layer developing on a swept flat plate are studied by means of numerical simulations. The flow is subject to a favourable pressure gradient and represents a model for swept-wing flow downstream of the leading edge and upstream of the pressure minimum of the wing. The boundary layer is perturbed by free-stream turbulence and localized surface roughness with random distribution in the spanwise direction. The intensity of the turbulent free-stream fluctuations ranges from conditions typical for free flight to higher levels usually encountered in turbo-machinery applications. The free-stream turbulence initially excites non-modal streak-like disturbances as in two-dimensional boundary layers, soon evolving into modal instabilities in the form of unsteady crossflow modes. The crossflow modes grow faster than the streaks and dominate the downstream disturbance environment in the layer. The results show that the receptivity mechanism is linear for the disturbance amplitudes under consideration, while the subsequent growth of the primary disturbances rapidly becomes affected by nonlinear saturation in particular for free-stream fluctuations with high intensity. Transition to turbulence occurs in the form of localized turbulent spots randomly appearing in the flow. The main features of the breakdown are presented for the case of travelling crossflow vortices induced by free-stream turbulence. The flow is also receptive to localized roughness strips, exciting stationary crossflow modes. The mode with most efficient receptivity dominates the downstream disturbance environment. When both free-stream fluctuations and wall roughness act on the boundary layer at the same time, transition is dominated by steady crossflow waves unless the incoming turbulence intensity is larger than about 0.5 % for roughness amplitudes of about one tenth of the boundary-layer displacement thickness. The results show that a correct prediction of the disturbance behaviour can be obtained considering the receptivity and evolution of individual modes. In addition, we provide an estimate for the amplitudes of the external disturbance sources above which a fully nonlinear receptivity analysis is necessary.

National Category
Fluid Mechanics and Acoustics
urn:nbn:se:kth:diva-25452 (URN)10.1017/S0022112009993284 (DOI)000276267200012 ()2-s2.0-77952326881 (ScopusID)
QC 20101022Available from: 2010-10-22 Created: 2010-10-22 Last updated: 2011-01-19Bibliographically approved
3. Receptivity to free-stream vorticity of flow past a flat plate with elliptic leading edge
Open this publication in new window or tab >>Receptivity to free-stream vorticity of flow past a flat plate with elliptic leading edge
2010 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 653, 245-271 p.Article in journal (Refereed) Published
Abstract [en]

Receptivity of the two-dimensional boundary layer on a flat plate with elliptic leading edge is studied by numerical simulation. Vortical perturbations in the oncoming free stream are considered, impinging on two leading edges with different aspect ratio to identify the effect of bluntness. The relevance of the three vorticity components of natural free-stream turbulence is illuminated by considering axial, vertical and spanwise vorticity separately at different angular frequencies. The boundary layer is most receptive to zero-frequency axial vorticity, triggering a streaky pattern of alternating positive and negative streamwise disturbance velocity. This is in line with earlier numerical studies on non-modal growth of elongated structures in the Blasius boundary layer. We find that the effect of leading-edge bluntness is insignificant for axial free-stream vortices alone. On the other hand, vertical free-stream vorticity is also able to excite non-modal instability in particular at zero and low frequencies. This mechanism relies on the generation of streamwise vorticity through stretching and tilting of the vertical vortex columns at the leading edge and is significantly stronger when the leading edge is blunt. It can thus be concluded that the non-modal boundary-layer response to a free-stream turbulence field with three-dimensional vorticity is enhanced in the presence of a blunt leading edge. At high frequencies of the disturbances the boundary layer becomes receptive to spanwise free-stream vorticity, triggering Tollmien-Schlichting (T-S) modes and receptivity increases with leading-edge bluntness. The receptivity coefficients to free-stream vortices are found to be about 15% of those to sound waves reported in the literature. For the boundary layers and free-stream perturbations considered, the amplitude of the T-S waves remains small compared with the low-frequency streak amplitudes.

National Category
Fluid Mechanics and Acoustics
urn:nbn:se:kth:diva-25447 (URN)10.1017/S0022112010000376 (DOI)000279322000008 ()2-s2.0-77953609890 (ScopusID)
Uppdaterad till Artikel 2010 QC 20101022Available from: 2010-10-22 Created: 2010-10-22 Last updated: 2010-12-17Bibliographically approved

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