NARX modelling of unsteady separation control

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.

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