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.
Highlights
The research field of hydrodynamic stability has the objective of elucidating how the structures of some specific temporal frequency and spatial scale are selected and emerge, owing to the amplification of small-magnitude perturbations
Typical expected benefits consist of the reduction of the operational cost of vehicles by decreasing skin friction or aerodynamic drag, or the extension of the operating conditions of turbomachinery by increasing the surface heat flux
It is evident that this eigenvector is a physically meaningful one, because it is concentrated in the recirculation bubble, which is the zone where instability develops
Summary
The research field of hydrodynamic stability has the objective of elucidating how the structures of some specific temporal frequency and spatial scale are selected and emerge, owing to the amplification of small-magnitude perturbations. For boundary-layer-like flows exhibiting a marginal separation, as occurs at the rear-end of a vehicle with small slant angle, a non-modal theoretical analysis can identify flow regions where the transient amplification of streamwise streaks (by the lift-up effect) is most sensitive to steady spanwise periodic disturbances [6]. In the experiments, such disturbances can result from either steady jets or roughness elements positioned upstream of the separation location, reproducing a parietal or a volumic forcing, respectively. The Appendix A is devoted to showing some further details about boundary conditions and adjoint equations
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
