Full-domain POD modes from PIV asynchronous patches

A method is proposed to obtain full-domain spatial modes based on proper orthogonal decomposition (POD) of particle image velocimetry (PIV) measurements taken at different (overlapping) spatial locations. This situation occurs when large domains are covered by multiple non-simultaneous measurements and yet the large-scale flow field organization is to be captured. The proposed methodology leverages the definition of POD spatial modes as eigenvectors of the spatial correlation matrix, where local measurements, even when not obtained simultaneously, provide each a portion of the latter, which is then analyzed to synthesize the full-domain spatial modes. The measurement domain coverage is found to require regions overlapping by 50-75% to yield a smooth distribution of the modes. The procedure identifies structures twice as large as each measurement patch. The technique, referred to as Patch POD, is applied to planar PIV data of a submerged jet flow where the effect of patching is simulated by splitting the original PIV data. Patch POD is then extended to robotic measurement around a wall-mounted cube. The results show that the patching technique enables global modal analysis over a domain covered with a multitude of non-simultaneous measurements.