Recent work has demonstrated the use of sparse sensors in combination with the proper orthogonal decomposition (POD) to produce data-driven reconstructions of the full velocity fields in a variety of flows. The present work investigates the fidelity of such techniques applied to a stalled NACA 0012 aerofoil at $ {Re}_c=75,000 $ at an angle of attack $ \alpha ={12}^{\circ } $ as measured experimentally using planar time-resolved particle image velocimetry. In contrast to many previous studies, the flow is absent of any dominant shedding frequency and exhibits a broad range of singular values due to the turbulence in the separated region. Several reconstruction methodologies for linear state estimation based on classical compressed sensing and extended POD methodologies are presented as well as nonlinear refinement through the use of a shallow neural network (SNN). It is found that the linear reconstructions inspired by the extended POD are inferior to the compressed sensing approach provided that the sparse sensors avoid regions of the flow with small variance across the global POD basis. Regardless of the linear method used, the nonlinear SNN gives strikingly similar performance in its refinement of the reconstructions. The capability of sparse sensors to reconstruct separated turbulent flow measurements is further discussed and directions for future work suggested.
In this case study, we examine the effect of airfoil shape/camber on the formation and existence of stall cells. A series of experiments using a NACA0012 wing with a trailing-edge flap has been carried out over a range of angles of attack ( $11.5^\circ$ – $21^\circ$ ), flap angles ( $0^\circ$ , $5^\circ$ , $10^\circ$ ) and chord-length-based Reynolds numbers (100 000–500 000). The influence of these parameters on stall cell formation has been explored. Tufts have been used to identify the flow behaviour near the surface, while forces have been measured to relate the surface flow behaviour and wing performance. The results from the tuft analysis on the wing indicated that two different Reynolds-number regimes exist with respect to stall cell formation criteria. A preliminary estimate of the airfoil shape influence on stall cell formation is presented. A data-driven approach is used to relate the aerodynamic parameters (lift coefficient and lift-curve slope) to the formation criteria of stall cells for the wing (and flap angles). The lift coefficient can be used to implicitly take into account the change in airfoil shape in addition to the angle of attack and the Reynolds number. It is hoped that the results presented in this case study could be extended to various other airfoil shapes and that the stall cell formation angle of attack can be deduced from just the mean lift behaviour.
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