Estimating Velocity Correlations Using Single Pixel PIV

Abstract

In this work, we analyze the possibility of determining correlations of turbulent velocity fluctuations from PIV data with improved spatial resolution. The analysis is based on the method presented by Oldenziel et al. (2023), where a joint probability density function of the velocity at two locations is calculated from the single-pixel ensemble correlation for these locations. Synthetic PIV images are used to discuss the occurrence of random and systematic errors and to derive the number of image pairs required for a determination of the correlation coefficient with desired uncertainty, depending on the particle image density. Compared to classical window correlation, the presented method can improve the spatial resolution by about one order of magnitude if a very large number of PIV image pairs are available and/or many statistically independent points with identical flow properties can be used. As an example of application, we show the spatial distribution of a two-point correlation in a compressible turbulent boundary layer flow for a reference point near the wall.