Non-linear modulation of a boundary layer induced by vortex generators Thomas Duriez * PMMH UMR 7636 CNRS , ESPCI, Universities Paris 6 and Paris 7, Paris, 75005, France Jean-Luc Aider † PMMH UMR 7636 CNRS, ESPCI, Universities Paris 6 and Paris 7, Paris, 75005, France Jose Eduardo Wesfreid ‡ PMMH UMR 7636 CNRS, ESPCI, Universities Paris 6 and Paris 7, Paris, 75005, France A novel approach, based on Non-Linear analysis of the flow, is proposed to study the modification of flat-plate boundary layer by bluff-body Vortex Generators (VGs). Small cylinders in a flat-plate boundary layer are used to create a set of counter-rotating stream- wise vortices (CRSVs) which modify the global properties of the boundary layer. From the harmonic modulation and the mean flow distortion of the global mode (or zeroth mode), one can define some physical properties which can be used to quantify the efficiency of a given set of VGs. A first parametric study for a given Reynolds number shows a clear dependance of these properties on the spacing between the VGs. Some of these properties should be useful, for instance, to choose the right parameters to control a separated flow without having to run a full and tedious parametric study. I. Introduction Vortex generators are well known as efficient tools for the control of flow separation. They are commonly used in various industrial application e.g. in aeronautics, to enhance airplane lift force in near stall situa- tions, 15 in automotive aerodynamics to reduce the drag of a vehicle 4 or in chemical industry to increase the efficiency of static mixers. 7 Nevertheless, the question of the choice and design of the proper VG for a given application is still an open issue. Moreover the physical processes involved in the effect of Vortex Generators is still to be fully understood. Klebanoff et al. 8 have shown the existence of a tridimensional instability in the boundary layer. This instability gives birth to high and low longitudinal velocity streaks. Theses structures are thought to be responsible for a by-pass transition to turbulence, which is independent of the classical process involving Tolmienn-Schlichting waves derived from a bidimensional linear study. The recent focus on transient growth due to the non-normality of several stable modes 13 was at the origin of a renewed interest in the counter- rotating streamwise vortices since they are the most amplified perturbations in a boundary layer. 17 While, if large enough, they can trigger the transition to turbulence, the streamwise vorticity and the generation of high and low velocity streaks can also delay the transition to turbulence through the classical Tolmienn- Schlichting waves. 5, 6 If streamwise vorticity seems to be a proper perturbation for a boundary layer, the question of its generation and control remains. As a matter of fact, many different perturbations of the boundary layer can create streamwise vortices, but the efficiency of the system will depend on many parameters. For instance, one can choose to use jet vortex generators which will imply the choice of the jet diameter and velocity together with the forcing frequency if we deal with pulsed jets. In the case of solid blade vortex generators, it will * Ph. D. Student, Laboratoire PMMH, 10, rue Vauquelin, 75231 Paris cedex 05. † Research Director, Laboratoire PMMH, 10, rue Vauquelin, 75231 Paris cedex 05. email: aider@pmmh.espci.fr ‡ Research Director & Head of the Laboratoire PMMH, 10, rue Vauquelin, 75231 Paris cedex 05. 1 of 7 American Institute of Aeronautics and Astronautics