Material Derivative Measurements in High-Speed Flows by Four-Pulse

A tomographic PIV system is introduced for the instantaneous measurement of the material derivative of velocity (VMD). The system is able to operate with very short temporal separation and is therefore suitable for applications in high-speed flows. The method of operation consists of the imaging of a measurement volume using an array of 12 CCD cameras and two double-cavity laser systems. Four independent recordings of particle images are captured by decomposing the system into three separate tomographic PIV systems comprised of four cameras. A discussion is made that compares the present working principle with other methods used to separate the light scattered from multiple pulses, namely by polarization. Various approaches are compared to determine the optimal utilization of four-pulse data to measure the VMD: the Eulerian and Lagrangian schemes are compared with the recently introduced fluid trajectory correlation (FTC) technique from the authors (Lynch and Scarano, 2013). The comparison focuses on the behavior of the schemes with respect to truncation errors and how the error estimates for four-pulse data are modified from those typically applied to image sequence data from a time-resolved PIV experiment. The analysis of synthetic images of a translating vortex clearly shows the envelope of applicability of the different schemes and the structure of the measurement errors introduced by truncation