Methods for estimating higher order moments from PIV data

This work shows how the probability density function (PDF) of the turbulent velocity fluctuation can be estimated from the deconvolution of ensemble averaged cross-correlation and auto-correlation functions of PIV recordings. Once the PDF is known, the mean displacement, the Reynolds stresses as well as higher order moments can reliable be estimated. The approach was tested on synthetic PIV images and the results are compared to those obtained by standard window correlation as well as by deconvolution of Gaussian fit functions. The effect of the number of images pairs, the digital particle image size, and the shape of the PDF on the random error of the estimated moments was investigated. It was found that the developed method can also handle complex shaped PDF’s like an asymmetric peak or two separated peaks. The new approach is also applied to evaluate an experimental data set in order to demonstrate its suitability for real flows.