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Open AccessFeature PaperArticle

Optimal Transient Growth in an Incompressible Flow past a Backward-Slanted Step

1
Centro de Matemática (Faculdade de Ciências) da Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal
2
Aix Marseille Université, CNRS, Centrale Marseille, M2P2 UMR 7340, 13451 Marseille, France
*
Author to whom correspondence should be addressed.
Fluids 2019, 4(1), 33; https://doi.org/10.3390/fluids4010033
Received: 6 February 2019 / Revised: 12 February 2019 / Accepted: 14 February 2019 / Published: 20 February 2019
(This article belongs to the Special Issue Multiscale Turbulent Transport)
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Abstract

With the aim of providing a first step in the quest for a reduction of the aerodynamic drag on the rear-end of a car, we study the phenomena of separation and reattachment of an incompressible flow by focusing on a specific aerodynamic geometry, namely a backward-slanted step at 25 of inclination. The ensuing recirculation bubble provides the basis for an analytical and numerical investigation of streamwise-streak generation, lift-up effect, and turbulent-wake and Kelvin–Helmholtz instabilities. A linear stability analysis is performed, and an optimal control problem with a steady volumic forcing is tackled by means of a variational formulation, adjoint methods, penalization schemes, and an orthogonalization algorithm. Dealing with the transient growth of spanwise-periodic perturbations, and inspired by the need of physically-realizable disturbances, we finally provide a procedure attaining a kinetic-energy maximal gain on the order of 10 6 , with respect to the power introduced by the external forcing. View Full-Text
Keywords: linear stability analysis; separation and reattachment; optimal control; streak lift-up; turbulent-wake and Kelvin–Helmholtz instabilities; incompressibility; 3D perturbations of 2D steady base flow; structural sensitivity; recirculation bubble; 25° backward-slanted step linear stability analysis; separation and reattachment; optimal control; streak lift-up; turbulent-wake and Kelvin–Helmholtz instabilities; incompressibility; 3D perturbations of 2D steady base flow; structural sensitivity; recirculation bubble; 25° backward-slanted step
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Martins Afonso, M.; Meliga, P.; Serre, E. Optimal Transient Growth in an Incompressible Flow past a Backward-Slanted Step. Fluids 2019, 4, 33.

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