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

Abstract

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

Secondary instability and subcritical transition of the leading-edge boundary layer

“…While Fransson et al (2004) and White, Rice & Gökhan Ergin (2005) suggest that such perturbations do not have the character of optimal perturbations, they were shown to be even less stable than optimal ones and to exhibit secondary instability for lower streak amplitudes (Denissen & White 2013). Meneghello, Schmid & Huerre (2015) demonstrate that a strong receptivity is observed in particular for perturbations applied in the immediate vicinity of the attachment line. Finally, Thomas, Hall & Davies (2015) report that wall suction significantly alters the receptivity of the cross-flow velocity in the swept Hiemenz flow.…”

Receptivity and stability of hypersonic leading-edge sweep flows around a blunt body

“…Similar to the incompressible cases (Lin & Malik 1996; Meneghello et al. 2015), symmetric () and antisymmetric () modes alternate from the most unstable to the most stable. The leading symmetric mode has the highest growth rate.…”

“…(2008) and Meneghello et al. (2015). For larger (CASE P8), despite the similar mode structure at the attachment-line plane, marked in figure 4( b ) and shown in figure 4( d ), the perturbations at the downstream plane, marked in figure 4( b ) and shown in figure 4( f ), exhibit the behaviour of the second Mack mode instability with perturbations mainly located below the sonic line.…”

Domain reduction strategy for the stability analysis of complex aerodynamic flows

“…Interested readers may note the resemblance between Equation (and analogously ) and the structural sensitivity in equation (8.4) of Giannetti and Luchini . The sensitivity region of an eigenmode is that area of the computational domain where a small perturbation induces the largest drift in its corresponding eigenvalue . Note that, on the other hand, in Reference , the structural sensitivity is expressed in terms of the product of direct and adjoint eigenfunctions; in the present analysis, the sensitivity is obtained from the product of the right and left eigenmodes at each computational node.…”

“…As a side benefit, the DR technique allows to increase resolution into the region of interest, balancing the overall computational effort. Several works have employed DR techniques to address the study of, initially unfeasible, stability analysis …”