Data-driven sparse reconstruction of flow over a stalled aerofoil using experimental data

Abstract

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.

Keywords

• Extended proper orthogonal decomposition
• separated aerofoil
• shallow neural network
• sparse reconstruction