Optimal transient growth in an incompressible flow past a backward-slanted step
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 focusing on a specific aerodynamic geometry, namely a backward-slanted step at 25 degrees 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 variational formulation, adjoint method, penalization scheme and 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 of the order of one million with respect to the power introduced by the external forcing.
Keywords
Cite
@article{arxiv.1902.10629,
title = {Optimal transient growth in an incompressible flow past a backward-slanted step},
author = {Marco Martins Afonso and Philippe Meliga and Eric Serre},
journal= {arXiv preprint arXiv:1902.10629},
year = {2019}
}
Comments
17 figures