https://hal-polytechnique.archives-ouvertes.fr/hal-01023366Guégan, AlanAlanGuéganLadHyX - Laboratoire d'hydrodynamique - X - École polytechnique - CNRS - Centre National de la Recherche ScientifiqueSchmid, PeterPeterSchmidLadHyX - Laboratoire d'hydrodynamique - X - École polytechnique - CNRS - Centre National de la Recherche ScientifiqueUniversity of Washington [Seattle]Huerre, PatrickPatrickHuerreLadHyX - Laboratoire d'hydrodynamique - X - École polytechnique - CNRS - Centre National de la Recherche ScientifiqueOptimal energy growth and optimal control in swept Hiemenz flowHAL CCSD2006[PHYS.MECA.MEFL] Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph][SPI.MECA.MEFL] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph]Roura, Denis2014-07-20 21:16:392023-02-08 17:10:552014-07-21 10:46:24enJournal articleshttps://hal-polytechnique.archives-ouvertes.fr/hal-01023366/document10.1017/s0022112006001303application/pdf1The objective of the study is first to examine the optimal transient growth of Görtler-Hämmerlin perturbations in swept Hiemenz flow. This configuration constitutes a model of the flow in the attachment-line boundary layer at the leading-edge of swept wings. The optimal blowing and suction at the wall which minimizes the energy of the optimal perturbations is then determined. An adjoint-based optimization procedure applicable to both problems is devised, which relies on the maximization or minimization of a suitable objective functional. The variational analysis is carried out in the framework of the set of linear partial differential equations governing the chordwise and wall-normal velocity fluctuations. Energy amplifications of up to three orders of magnitude are achieved at low spanwise wavenumbers(k ~ 2000) and large sweep Reynolds number (Re ~ 2000) Optimal perturbations consist of spanwise travelling chordwise vortices, with a vorticity distribution which is inclined against the sweep. Transient growth arises from the tilting of the vorticity distribution by the spanwise shear via a two-dimensional Orr mechanism acting in the basic flow dividing plane. Two distinct regimes have been identified: for k ? 0.25, vortex dipoles are formed which induce large spanwise perturbation velocities; for k ? 0.25, dipoles are not observed and only the Orr mechanism remains active. The optimal wall blowing control yields for instance an 80% decrease of the maximum perturbation kinetic energy reached by optimal disturbances at Re = 550 and k = 0.25 The optimal wall blowing pattern consists of spanwise travelling waves which follow the naturally occurring vortices and qualitatively act in the same manner as a more simple constant gain feedback control strategy. © 2006 Cambridge University Press.