Few Remarks on the Controllability of an Aeroacoustic Model Using Piezo-Devices

Abstract

Let us consider a two-dimensional airfoil as shown in Figure 1. For small angles of attack, a turbulent boundary layer appears in the rear part of the airfoil. The sub-layer can produce transverse vortices. The mechanical advantage of this phenomenon is that it enables a drag-reduction. More precisely the airfoil, or at least its rear part, can “roll” over these vortices. But the instable feature of the sub-layer requires an active control of the vortices. Several aerodynamicists have suggested that this is the way the shark skin works. In other words, it seems necessary to energize the vortices through a resonance strategy (I have been told that shark skin would have small resonators which are magically adjusted at the right frequency!). Our strategy is to use piezo-electric actuators in order to energize the micro-vortices. But at first, modelling seems to be necessary in order to understand what happens. Let us also underline that experiments (see Wojciechowski — Szuster — Pietrucha [1998]) have proved the efficiency of the strategy. But the location and the frequency of the actuator should be adjusted carefully. Let us now sketch the method that we suggest in order to improve the efficiency of the piezo-actuators. Near the airfoil, there is a so-called “bubble” as shown in Figure 1. The mean value of the velocity is U and it is represented by a vector parallel to the boundary of the airfoil.