Abstract

In this article, we introduce techniques to build a reduced-order model of a fluid system that accurately predicts the dynamics of a flow from local wall measurements. This is particularly difficult in the case of noise amplifiers where the upstream noise environment, triggering the flow via a receptivity process, is not known. A system identification approach, rather than a classical Galerkin technique, is used to extract the model from time-synchronous velocity snapshots and wall shear-stress measurements. The technique will be illustrated for the case of a transitional flat-plate boundary layer, where the snapshots of the flow are obtained from direct numerical simulations. Particular attention is directed to limiting the processed data to data that would be readily available in experiments, thus making the technique applicable to an experimental set-up. The proposed approach combines a reduction of the degrees of freedom of the system by a projection of the velocity snapshots onto a proper orthogonal decomposition basis combined with a system identification technique to obtain a state-space model. This model is then used in a feedforward control set-up to significantly reduce the kinetic energy of the perturbation field and thus successfully delay transition.

We apply a data-based, linear dynamic estimator to reconstruct the velocity field from measurements at a single sensor point in the wake of an aerofoil. In particular, we consider a NACA0012 airfoil at Re = 600 and 16 • angle of attack. Under these conditions, the flow exhibits a vortex shedding limit cycle. A reduced order model (ROM) of the flow field is extracted using proper orthogonal decomposition (POD). Subsequently, a subspace system identification algorithm (N4SID) is applied to extract directly the estimator matrices from the reduced output of the system (the POD coefficients). We explore systematically the effect of the number of states of the estimator, the sensor location, the type of sensor measurements (one or both velocity components), and the number of POD modes to be recovered. When the signal of a single velocity component (in the stream wise or cross stream directions) is measured, the reconstruction of the first two dominant POD modes strongly depends on the sensor location. We explore this behaviour and provide a physical explanation based on the non-linear mode interaction and the spatial distribution of the modes. When however, both components are measured, the performance is very robust, and is almost independent of the sensor location when the optimal number of estimator states is used. Reconstruction of the less energetic modes is more difficult, but still possible.

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