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Receptivity of Boundary-Layer Flows over Flat and Curved Walls
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.
2010 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Direct numerical simulations of the receptivity and instability of boundary layers on flat and curved surfaces are herein reported. Various flow models are considered with the aim to capture aspects of flows over straight and swept wings such as wall curvature, pressure variations, leading-edge effects, streamline curvature and crossflow. The first model problem presented, the flow over a swept flat plate, features a crossflow inside the boundary layer. The layer is unstable to steady and traveling crossflow vortices which are nearly aligned with the free stream. Wall roughness and free-stream vortical modes efficiently excite these crossflow modes, and the associated receptivity mechanisms are linear in an environment of low-amplitude perturbations. Receptivity coefficients for roughness elements with various length scales and for free-stream vortical modes with different wavenumbers and frequencies are reported. Key to the receptivity to free-stream vorticity is the upstream excitation of streamwise streaks evolving into crossflow modes. This mechanism is also active in the presence of free-stream turbulence.

The second flow model is that of a Görtler boundary layer. This flow type forms on surfaces with concave curvature, e.g. the lower side of a turbine blade. The dominant instability, driven by a vertically varying centrifugal force, appears as pairs of steady, streamwise counter-rotating vortical rolls and streamwise streaks. The Görtler boundary layer is in particular receptive to free-stream vortical modes with zero and low frequencies. The associated mechanism builds on the excitation of upstream disturbance streaks from which the Görtler modes emerge, similar to the mechanism in swept-plate flows. The receptivity to free-stream vorticity can both be linear and nonlinear. In the presence of free-stream turbulence, nonlinear receptivity is more likely to trigger steady Görtler vortices than linear receptivity unless the frequencies of the free-stream fluctuations are very low.

The third set of simulations considers the boundary layer on a flat plate with an elliptic leading edge. This study aims to identify the effect of the leading edge on the boundary-layer receptivity to impinging free-stream vortical modes. Three types of modes with streamwise, vertical and spanwise vorticity are considered. The two former types trigger streamwise disturbance streaks while the latter type excites Tollmien-Schlichting wave packets in the shear layer. Simulations with two leading edges of different bluntness demonstrate that the leading-edge shape hardly influences the receptivity to streamwise vortices, whereas it significantly enhances the receptivity to vertical and spanwise vortices. It is shown that the receptivity mechanism to vertical free-stream vorticity involves vortex stretching and tilting - physical processes which are clearly enhanced by blunt leading edges.

The last flow configuration studied models an infinite wing at 45 degrees sweep. This model is the least idealized with respect to applications in aerospace engineering. The set-up mimics the wind-tunnel experiments carried out by Saric and coworkers at the Arizona State University in the 1990s. The numerical method is verified by simulating the excitation of steady crossflow vortices through micron-sized roughness as realized in the experiments. Moreover, the receptivity to free-stream vortical disturbances is investigated and it is shown that the boundary layer is most receptive, if the free-stream modes are closely aligned with the most unstable crossflow mode

Place, publisher, year, edition, pages
Stockholm: KTH , 2010. , vii, 50 p.
Series
Trita-MEK, ISSN 0348-467X ; 2010:08
Keyword [en]
Boundary-layer receptivity, laminar-turbulent transition, swept-plate boundary layer, Görtler flow, leading-edge effects, swept-wing flow, crossflow vortices, Görtler rolls, disturbance streaks, wall roughness, free-stream turbulence
National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:kth:diva-25439ISBN: 978-91-7415-779-6 (print)OAI: oai:DiVA.org:kth-25439DiVA: diva2:358440
Public defence
2010-11-12, F 3, Lindstedtsvägen 26, KTH, Stockholm, 10:00 (English)
Opponent
Supervisors
Note
QC 20101025Available from: 2010-10-25 Created: 2010-10-21 Last updated: 2010-10-25Bibliographically approved
List of papers
1.
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2.
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3. Receptivity, instability and breakdown of Görtler flow
Open this publication in new window or tab >>Receptivity, instability and breakdown of Görtler flow
2011 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 682, 362-396 p.Article in journal (Refereed) Published
Abstract [en]

Receptivity, disturbance growth and breakdown to turbulence in Gortler flow are studied by spatial direct numerical simulation (DNS). The boundary layer is exposed to free-stream vortical modes and localized wall roughness. We propose a normalization of the roughness-induced receptivity coefficient by the square root of the Gortler number. This scaling removes the dependence of the receptivity coefficient on wall curvature. It is found that vortical modes are more efficient at generating Gortler vortices than localized roughness. The boundary layer is most receptive to zero- and low-frequency free-stream vortices, exciting steady and slowly travelling Gortler modes. The associated receptivity mechanism is linear and involves the generation of boundary-layer streaks, which soon evolve into unstable Gortler vortices. This connection between transient and exponential amplification is absent on flat plates and promotes transition to turbulence on curved walls. We demonstrate that the Gortler boundary layer is also receptive to high-frequency free-stream vorticity, which triggers steady Gortler rolls via a nonlinear receptivity mechanism. In addition to the receptivity study, we have carried out DNS of boundary-layer transition due to broadband free-stream turbulence with different intensities and frequency spectra. It is found that nonlinear receptivity dominates over the linear mechanism unless the free-stream fluctuations are concentrated in the low-frequency range. In the latter case, transition is accelerated due to the presence of travelling Gortler modes.

Keyword
boundary layer receptivity, transition to turbulence
National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-25488 (URN)10.1017/jfm.2011.229 (DOI)000294775800016 ()2-s2.0-80052174354 (Scopus ID)
Funder
Swedish Research CouncilSwedish e‐Science Research Center
Note
QC 20101025. Updated from submitted to published.Available from: 2010-10-25 Created: 2010-10-25 Last updated: 2017-12-12Bibliographically approved
4.
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5. Nonlinear receptivity of leading-edge ow to oblique free-stream vortical modes
Open this publication in new window or tab >>Nonlinear receptivity of leading-edge ow to oblique free-stream vortical modes
2010 (English)Report (Other academic)
Abstract [en]

Boundary-layer receptivity to pairs of unsteady oblique free-stream vortical modes is studied for flat-plate flow using direct numerical simulation (DNS). This kind of forcing gives rise to steady boundary-layer streaks and the associated receptivity mechanism is nonlinear in the forcing amplitude. The flat plates considered feature elliptic leading edges with two different aspect ratios, allowing for the study of leading-edge bluntness effects on the receptivity. The free stream is perturbed by three types of unsteady oblique Fourier modes upstream of the leading edge. These modes differ in the magnitude of the three vorticity components. It is found that the bluntness of the leading edge hardly affects the streak amplitudes obtained. This observation also holds for oblique waves with vertical vorticity alone and is in contrast to the linear receptivity to this kind of modes, which is known to depend strongly on the leading-edge shape. While being irrelevant at low frequencies the nonlinear receptivity mechanism becomes important for high-frequency free-stream vortices to which the boundary layer is linearly non-receptive. Although the linear receptivity mechanism for zero- or low-frequency forcing is more efficient in producing disturbance streaks than the nonlinear receptivity to high-frequency disturbances, the nonlinear mechanism is expected to contribute significantly to the boundary-layer receptivity to free-stream turbulence.

Place, publisher, year, edition, pages
Stockholm: KTH, 2010. 15 p.
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-25504 (URN)
Note
QC 20101025Available from: 2010-10-25 Created: 2010-10-25 Last updated: 2010-10-25Bibliographically approved
6. Numerical study of boundary-layer receptivity on a swept wing
Open this publication in new window or tab >>Numerical study of boundary-layer receptivity on a swept wing
Show others...
2010 (English)Report (Other academic)
Abstract [en]

Direct numerical simulations (DNS) of the flow over a wing with 45◦ sweep and −4◦ angle-of-attack are presented. This flow configuration was investigated in a series of wind-tunnel experiments at the Arizona State University (ASU). On the upper wing side, the flow develops a substantial crossflow and is therefore ideally suited for a study of the receptivity mechanisms of crossflow vortices. Here, we examine the boundary-layer receptivity to surface roughness and to single vortical free-stream modes. The roughness is modeled by a shallow circular disk and is identical with one single element of the spanwise roughness array considered in the ASU experiments. The boundary layer develops a steady crossflow mode downstream of the roughness. The spatial evolution of the modal amplitude obtained by the DNS is in excellent agreement with a solution to the nonlinear parabolized stability equations (NPSE) while being lower than that measured in the experiments. The reasons for this discrepancy are yet to be determined. Possible explanations are the idealization of the roughness array by spanwise periodic boundary conditions in our simulations, or the presence of traveling crossflow waves due to background free-stream turbulence in the experiments. We demonstrate that the boundary-layer receptivity to roughness can be successfully predicted by a nonlocal, adjoint-based receptivity model. Stationary crossflow vortices can also be triggered by zero-frequency free-stream vortical modes. We consider two types of mode, carrying stream wise and chordwise vorticity. Both modes give rise to nonmodal disturbances near the leading edge, which soon evolve into a steady crossflow mode. The boundary layer is found to be somewhat more receptive to the streamwisevorticity mode than to the chordwise vorticity.

Place, publisher, year, edition, pages
Stockholm: KTH, 2010. 19 p.
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-25507 (URN)
Note
QC 20101025Available from: 2010-10-25 Created: 2010-10-25 Last updated: 2010-10-25Bibliographically approved

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