Estimation and optimization of loss-of-pair uncertainties based on PIV correlation functions

Abstract

The uncertainty quantification of particle image velocimetry (PIV) measurements is still an open problem, and to date, no consensus exists about the best suited approach. When the spatial resolution is not appropriate, the largest uncertainties are usually caused by flow gradients. But also the amount of loss-of-pairs due to out-of-plane flow motion and insufficient light-sheet overlap causes strong uncertainties in real experiments. In this paper, we show how the amount of loss-of-pairs can be quantified using the volume of the correlation function normalized by the volume of the autocorrelation function. The findings are an important step toward a reliable uncertainty estimation of instantaneous planar velocity fields computed from PIV and stereo-PIV data. Another important consequence of the analysis is that the results allow for the optimization of PIV and stereo-PIV setups in view of minimizing the total error. In particular, it is shown that the best results (concerning the relative uncertainty) can be achieved if the out-of-plane loss-of-correlation is smaller than one (F o ). The only exception is the case where the out-of-plane motion is exactly zero. The predictions are confirmed experimentally in the last part of the paper.