Low-order pressure determination in the flow of a stalled airfoil from PIV

Low-order representations of velocity fields, for example using the proper orthogonal decomposition (POD), are steadily increasing in popularity due to the attractive feature of capturing most of the energy of a dynamical system with a limited subset of modes and mode coefficients. In this talk, we explore the question of how many velocity modes are required to reach a desired accuracy in pressure reconstructions from time-resolved particle image velocimetry data in the turbulent flow of a static stalled airfoil at a chord-based Reynolds number Re_c=7.1x10⁴. This is demonstrated cumulatively by retaining up to a cut-off number of modes as well as mode-by-mode through a Galerkin projection of the Poisson equation onto the POD space spanned by the modes. The number of velocity modes required to capture the pressure to a desired accuracy is quantified and discussed.