Assessment of the pseudo-tracking approach for the calculation of material acceleration and pressure fields from time-resolved PIV: part I. Error propagation

Pseudo-tracking refers to the construction of imaginary particle paths from PIV velocity fields and the subsequent estimation of the particle (material) acceleration. In view of the variety of existing and possible alternative ways to perform the pseudo-tracking method, it is not straightforward to select a suitable combination of numerical procedures for its implementation. To address this situation, this paper extends the theoretical framework for the approach. The developed theory is verified by applying various implementations of pseudo-tracking to a simulated PIV experiment. The findings of the investigations allow us to formulate the following insights and practical recommendations: (1) the velocity errors along the imaginary particle track are primarily a function of velocity measurement errors and spatial velocity gradients; (2) the particle path may best be calculated with second-order accurate numerical procedures while ensuring that the CFL condition is met; (3) least-square fitting of a first-order polynomial is a suitable method to estimate the material acceleration from the track; and (4) a suitable track length may be selected on the basis of the variation in material acceleration with track length. (paper)