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Receptivity of crossflow-dominated boundary layers
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.
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. , x, 60 p.
Series
Trita-MEK, ISSN 0348-467X ; 2011:13
Keyword [en]
Receptivity, three-dimensional boundary layers, optimal growth, adjoint solutions, swept wing
National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:kth:diva-48467ISBN: 978-91-7501-177-6 (print)OAI: oai:DiVA.org:kth-48467DiVA: diva2:457686
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
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. Spatial optimal growth in three-dimensional compressible boundary layers
Open this publication in new window or tab >>Spatial optimal growth in three-dimensional compressible boundary layers
2012 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 704, 251-279 p.Article in journal (Refereed) Published
Abstract [en]

This paper represents a continuation of the work by Tempelmann et al. (JFM 2010) on spatial optimal growth in incompressible boundary layers over swept flat plates . We present an extension of the methodology to compressible flow. Also we account for curvature effects. Spatial optimal growth is studied for boundary layers over both flat and curved swept plates with adiabatic and cooled walls. We find that optimal growth increases for higher Mach numbers. In general, extensive non-modal growth is observed for all boundary layer cases even in subcritical regions, i.e. where the flow is stable with respect to modal crossflow disturbances. Wall cooling, though stabilising crossflow modes, destabilises disturbances of non-modal nature. Curvature acts similarly on modal as well as non-modal disturbances. Convex walls have a stabilising effect on the boundary layer whereas concave walls act destabilising. The physical mechanisms of optimal growth in all studied boundary layers are found to be similar to those identified for incompressible flat-plate boundary layers.

Keyword
compressible boundary layers, boundary layer stability, boundary layer receptivity
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-48463 (URN)10.1017/jfm.2012.235 (DOI)000306528700011 ()2-s2.0-84865459695 (Scopus ID)
Funder
Swedish e‐Science Research Center
Note

QC 20120817. Updated from submitted to published.

Available from: 2011-11-18 Created: 2011-11-18 Last updated: 2017-12-08Bibliographically approved
3. Swept-wing boundary-layer receptivity to localised surface roughness
Open this publication in new window or tab >>Swept-wing boundary-layer receptivity to localised surface roughness
Show others...
2011 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645Article in journal (Other academic) Submitted
Abstract [en]

The receptivity to localised surface roughness of a swept-wing boundary layer is studied by direct numerical simulation (DNS) and computations using the parabolised stability equations (PSE). The DNS is laid out to reproduce wind tunnel experiments performed by Saric & coworkers, where micron-sized cylinders were used to trigger steady crossflow modes. The amplitudes of the roughness-induced fundamental crossflow wave and its superharmonics obtained from nonlinear PSE solutions agree excellently with the DNS results. A receptivity model using the direct and adjoint PSE is shown to provide reliable predictions of the receptivity to roughness cylinders of different heights and chordwise locations. Being robust and computationally efficient, the model is well suited as a predictive tool of receptivity in flows of practical interest. The crossflow mode amplitudes obtained based on both DNS and PSE are 40% of those measured in the experiments.Additional comparisons between experimental and PSE data for various disturbance wavelengths reveal that the measured disturbance amplitudes are consistently larger than those predicted by the PSE-based receptivity model by a nearly constant factor. Supplementary DNS and PSE computations suggest that possible natural leading-edge roughness and free-stream turbulence in the experiments are unlikely to account for this discrepancy. It is more likely that experimental uncertainties in the streamwise location of the roughness array and cylinder height are responsible for the additional receptivity observed in the experiments.

National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-48464 (URN)
Note
QS 2011 QS 20120316Available from: 2011-11-18 Created: 2011-11-18 Last updated: 2017-12-08Bibliographically approved
4. Swept-wing boundary-layer receptivity
Open this publication in new window or tab >>Swept-wing boundary-layer receptivity
2012 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 700, 490-501 p.Article in journal (Refereed) Published
Abstract [en]

Adjoint solutions of the linearized incompressible Navier-Stokes equations are presented for a cross-flow-dominated swept-wing boundary layer. For the first time these have been computed in the region upstream of the swept leading edge and may therefore be used to predict receptivity to any disturbances of the incoming free stream as well as to surface roughness. In this paper we present worst-case scenarios, i.e. those external disturbances yielding maximum receptivity amplitudes of a steady cross-flow disturbance. In the free stream, such an 'optimal' disturbance takes the form of a streak which, while being convected downstream, penetrates the boundary layer and smoothly turns into a growing cross-flow mode. The 'worst-case' surface roughness has a wavy shape and is distributed in the chordwise direction. It is shown that, under such optimal conditions, the boundary layer is more receptive to surface roughness than to incoming free stream disturbances.

Keyword
boundary layer receptivity
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-48465 (URN)10.1017/jfm.2012.152 (DOI)000304211700021 ()2-s2.0-84864151045 (Scopus ID)
Funder
Swedish e‐Science Research Center
Note

QC 20120619

Available from: 2011-11-18 Created: 2011-11-18 Last updated: 2017-12-08Bibliographically approved
5. Stabilisation of a swept-wing boundary layer by localised surface roughness
Open this publication in new window or tab >>Stabilisation of a swept-wing boundary layer by localised surface roughness
2011 (English)Report (Other academic)
Place, publisher, year, edition, pages
KTH Royal Institute of Technology, 2011. 27 p.
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-48466 (URN)
Note
QC 20111118Available from: 2011-11-18 Created: 2011-11-18 Last updated: 2011-11-24Bibliographically approved

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