Optimal Transient Growth in an Incompressible Flow past a Backward-Slanted Step
Centro de Matemática (Faculdade de Ciências) da Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal
Aix Marseille Université, CNRS, Centrale Marseille, M2P2 UMR 7340, 13451 Marseille, France
Author to whom correspondence should be addressed.
Received: 6 February 2019 / Revised: 12 February 2019 / Accepted: 14 February 2019 / Published: 20 February 2019
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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
, with respect to the power introduced by the external forcing.
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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.
Martins Afonso M, Meliga P, Serre E. Optimal Transient Growth in an Incompressible Flow past a Backward-Slanted Step. Fluids. 2019; 4(1):33.
Martins Afonso, Marco; Meliga, Philippe; Serre, Eric. 2019. "Optimal Transient Growth in an Incompressible Flow past a Backward-Slanted Step." Fluids 4, no. 1: 33.
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