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The lift coefficient of a configuration made of a flat plate with a trailing-edge plain flap is maximized at post-stall conditions by driving automatically the forcing frequency of a fluidic control system to an optimal value. The flap is equipped with pulsed blowing slots whose actuation frequency can be varied at constant actuation amplitude. The post-stall flow over the deflected flap is fully separated and organized around the natural vortex shedding at $$St=0.2$$ . It appears to be sensitive to the forcing frequency so that the lift coefficient is maximized if actuation is precisely the Strouhal number. Since this frequency depends on the flap deflection angle and the upstream velocity, an extremum seeking algorithm is implemented in order to drive the forcing frequency and thus guarantees that lift remains maximum whatever the geometric configuration is. Finally, a fuzzy-logic regulator is synthesized and integrated into the extremum seeking control scheme in order to speed up the convergence while maintaining stability and accuracy.

Slope seeking control is implemented to suppress flow separation occurring on a plain flap progressively deflected at $$Re_{\mathrm{c}}=2\times 10^{6}$$ . The flap is equipped with pulsed blowing slots that are actuated by a square signal whose duty cycle is adapted by the so-called slope seeking algorithm in order to minimise the injected momentum while maintaining the flow attached whatever the flap deflection angle. Thirteen hot-film sensors are chordwise distributed on the flap. They measure the wall shear stress fluctuations that are used to calculate in real time a series of correlation coefficients. This method constitutes a way to determine whether the flow is separated or not within the context of flow separation control. Finally, a modification of basic slope seeking algorithm is proposed to improve its convergence rate without compromising stability.

This paper presents the application of Nonlinear Auto-Regressive with eXogenous input (NARX) modelling to model the flow behaviour in response of a periodic forcing. In the first part, the NARX black-box model is presented. The model coefficients are obtained by least-square fitting. The resolution of the associated linear system being ill-conditioned, a Tikhonov regularization is employed. The first application presented is the identification of a NARX model of separation control by a synthetic jet slot over a rounded ramp. It is shown that the pressure at a particular location is representative of the flow state (attached or separated). This quantity will be the output of the model, the input being the forcing signal of the synthetic jet. Then, an identification signal is designed to explore as many flow states as possible with a short signal duration. The next step is dedicated to the selection of the NARX model structure. Input/output correlations, partial output autocorrelations and the Akaike Information Criterion minimization are used. A fit coefficient of 84 % is obtained. Finally, the accuracy of the NARX model, both on the steady and on the unsteady components of the output, is checked by comparison of the results with signals not used in the identification phase. The third part deals with the application of the same methodology to an experiment of separation control by pulsed fluidic vortex generators in a highly curved duct. A fit coefficient of 60 % is obtained in this case.

Wind tunnel experiments are conducted to investigate the effect of periodic blowing over a non-slotted NACA-type flap equipped with seven pulsed slots. The tests are performed at Re ≃ 3 × 106 for different deflection angles ranging from 2° to 35°. Wall-mounted hot-films are chordwise distributed on the flap. The purpose of the experiments is to assess the ability of wall shear stress signals to detect flow separation with and without periodic control, and to be used as reliable feedback information in a closed-loop control framework. Laser beam tomoscopy is first used to visualize flow structures with and without flow control. Two separation criteria based on higher-order statistical moments of hot-film signals are proposed to detect flow separation. They present the advantage of being independent of the free-stream velocity. The two criteria are finally practised to follow the steady-state response of the system and determine its static map local gradient.