Low-order planar pressure reconstruction of stalled airfoils using particle image velocimetry data

We present planar time -resolved particle image velocimetry (PIV) measurements of flow in the streamwise surface -normal plane of a NACA 0012 airfoil at chord -based Reynolds number Rec = 7 x 104. The angles of attack alpha = 13 degrees and 15 degrees correspond to transient stall and deep stall flow regimes, respectively. A Poisson solver is utilized to reconstruct the instantaneous planar pressure fields from the PIV with satisfactory comparison in the mean pressure compared with dynamically matched Reynolds -averaged Navier-Stokes (RANS) simulations. Using the proper orthogonal decomposition (POD), a systematic reducedorder reconstruction of the velocity fields and subsequent pressure fields is used to quantify the required number of velocity modes to achieve a desired accuracy in the instantaneous pressure. Further, a Galerkin projection of the Poisson equation onto the POD subspace is used as a framework to identify the relative contribution of each velocity mode on the resulting pressure field via quadratic stochastic estimation (QSE). In both cases, the zeroth mode (corresponding to the mean) is of leading -order importance. In addition, a tendency of the zeroth mode to interact with vortex -shedding modes is identified.