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Receptivity and sensitivity of the leading-edge boundary layer of a swept wing

Published online by Cambridge University Press:  18 June 2015

Gianluca Meneghello ,
Peter J. Schmid  and
Patrick Huerre
Gianluca Meneghello
Affiliation:
Laboratoire d’Hydrodynamique (LadHyX), CNRS-École Polytechnique, F-91128 Palaiseau, France
Peter J. Schmid
Affiliation:
Department of Mathematics, Imperial College London, London SW7 2AZ, UK
Patrick Huerre
Affiliation:
Laboratoire d’Hydrodynamique (LadHyX), CNRS-École Polytechnique, F-91128 Palaiseau, France
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Abstract

A global stability analysis of the boundary layer in the leading edge of a swept wing is performed in the incompressible flow regime. It is demonstrated that the global eigenfunctions display the features characterizing the local instability of the attachment line, as in swept Hiemenz flow, and those of local cross-flow instabilities further downstream along the wing. A continuous connection along the chordwise direction is established between the two local eigenfunctions. An adjoint-based receptivity analysis reveals that the global eigenfunction is most responsive to forcing applied in the immediate vicinity of the attachment line. Furthermore, a sensitivity analysis identifies the wavemaker at a location that is also very close to the attachment line where the corresponding local instability analysis holds: the local cross-flow instability further along the wing is merely fed by its attachment-line counterpart. As a consequence, global mode calculations for the entire leading-edge region only need to include attachment-line structures. The result additionally implies that effective open-loop control strategies should focus on base-flow modifications in the region where the local attachment-line instability prevails.

JFM classification

Boundary Layers: Boundary layer receptivity Boundary Layers: Boundary layer stability Boundary Layers: Boundary layer structure
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 775 , 25 July 2015 , R1
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Copyright
© 2015 Cambridge University Press 

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