Measurement of fluid rotation, dilation, and displacement in particle image velocimetry using a Fourier-Mellin cross-correlation

摘要

Traditional particle image velocimetry (PIV) uses discrete Cartesian cross correlations (CCs) to estimate the displacements of groups of tracer particles within small subregions of sequentially captured images. However, these CCs fail in regions with large velocity gradients or high rates of rotation. In this paper, we propose a new PIV correlation method based on the Fourier-Mellin transformation (FMT) that enables direct measurement of the rotation and dilation of particle image patterns. In previously unresolvable regions of large rotation, our algorithm significantly improves the velocity estimates compared to traditional correlations by aligning the rotated and stretched particle patterns prior to performing Cartesian correlations to estimate their displacements. Our algorithm, which we term Fourier-Mellin correlation (FMC), reliably measures particle pattern displacement between pairs of interrogation regions with up to +/- 180 degrees of angular misalignment, compared to 6-8 degrees for traditional correlations, and dilation/compression factors of 0.5-2.0, compared to 0.9-1.1 for a single iteration of traditional correlations.