Corrections for one- and two-point statistics measured with coarse-resolution particle image velocimetry

Abstract

A theoretical model to determine the effect of the size of the interrogation window in particle image velocimetry measurements of turbulent flows is presented. The error introduced by the window size in two-point velocity statistics, including velocity autocovariance and structure functions, is derived for flows that are homogeneous within a 2D plane or 3D volume. This error model is more general than those previously discussed in the literature and provides a more direct method of correcting biases in experimental data. Within this model framework, simple polynomial approximations are proposed to provide a quick estimation of the effect of the averaging on these statistics. The error model and its polynomial approximation are validated using statistics of homogeneous isotropic turbulence obtained in a physical experiment and in a direct numerical simulation. The results demonstrate that the present formulation is able to correctly estimate the turbulence statistics, even in the case of strong smoothing due to a large interrogation window. We discuss how to use these results to correct experimental data and to aid the comparison of numerical results with laboratory data.