Optimized timing schemes for multi-pulse shake-the-box particle tracking velocimetry

Abstract

Particle Tracking Velocimetry (PTV) is a non-intrusive measurement technique that is gaining increasing popularity in the experimental fluid mechanics community. The basic working principle is to determine three-dimensional Lagrangian particle tracks via multiple exposures separated by known time intervals as seen by at least three cameras. The practical extension of PTV to three-dimensional tracks was enabled by the introduction of the Shake-the-Box algorithm, which can accurately determine three-dimensional particle trajectories. However, the selected timing strategy of the multi-pulse (i.e., four in this paper) technique is not clearly defined a priori. The accuracy of the reconstructed pathline depends on the timing strategy of the four pulses and the selected temporal interpolation/fitting methods. By examining several canonical flows, this study aims to investigate the $dt$ timing strategy, whether the pulses should be symmetric or asymmetric with respect to the midpoint of the two middle pulses, and to assess the uncertainty from different pathline reconstruction methods, i.e., quadratic and cubic polynomial fitting and Radial Basis Functions (RBF). The results indicate that a symmetric timing scheme is consistently better than an asymmetric timing scheme for a fixed total track duration, and that RBF-based fitting is slightly better than polynomial fits because it provides a good compromise between accuracy and error assessment. The error scaling associated with the timing schemes is also quantified.