Uncertainty quantification in particle image velocimetry

Particle image velocimetry (PIV) has become the chief experimental technique for velocity field measurements in fluid flows. The technique yields quantitative visualizations of the instantaneous flow patterns, which are typically used to support the development of phenomenological models for complex flows or for validation of numerical simulations. However, due to the complex relationship between measurement errors and experimental parameters, the quantification of the PIV uncertainty is far from being a trivial task and has often relied upon subjective considerations. Recognizing the importance of methodologies for the objective and reliable uncertainty quantification (UQ) of experimental data, several PIV-UQ approaches have been proposed in recent years that aim at the determination of objective uncertainty bounds in PIV measurements. This topical review on PIV uncertainty quantification aims to provide the reader with an overview of error sources in PIV measurements and to inform them of the most up-to-date approaches for PIV uncertainty quantification and propagation. The paper first introduces the general definitions and classifications of measurement errors and uncertainties, following the guidelines of the International Organization for Standards (ISO) and of renowned books on the topic. Details on the main PIV error sources are given, considering the entire measurement chain from timing and synchronization of the data acquisition system, to illumination, mechanical properties of the tracer particles, imaging of those, analysis of the particle motion, data validation and reduction. The focus is on planar PIV experiments for the measurement of two- or three-component velocity fields. Approaches for the quantification of the uncertainty of PIV data are discussed. Those are divided into a-priori UQ approaches, which provide a general figure for the uncertainty of PIV measurements, and a-posteriori UQ approaches, which are data-based and aim at quantifying the uncertainty of specific sets of data. The findings of a-priori PIV-UQ based on theoretical modelling of the measurement chain as well as on numerical or experimental assessments are discussed. The most up-to-date approaches for a-posteriori PIV-UQ are introduced, highlighting their capabilities and limitations. As many PIN/ experiments aim at determining flow properties derived from the velocity fields (e.g. vorticity, time-average velocity, Reynolds stresses, pressure), the topic of PIV uncertainty propagation is tackled considering the recent investigations based on Taylor series and Monte Carlo methods. Finally, the uncertainty quantification of 3D velocity measurements by volumetric approaches (tomographic PIV and Lagrangian particle tracking) is discussed.