In situ calibrated defocusing PTV for wall-bounded measurement volumes

Abstract

In many situations, 3D velocity measurements in thin (∼1 mm) but wide (∼100 × 100 mm2) flow channels is an important task. To resolve the in-plane and out-of-plane velocity gradients properly, a precise calibration is required, since 3D measurement approaches rely strongly on the accuracy of the calibration procedure. It is likely that calibration targets do not fit domains with small depths, due to their size. Furthermore, in fields where such measurements are of interest, the accessibility of the measurement volume is often limited or even impossible. To overcome these drawbacks, this paper introduces an in situ calibrated defocusing particle tracking velocimetry approach for wall-bounded measurement domains with depths in the low millimeter range. The calibration function for the particle depth location is directly derived from the particle image geometries and their displacements between two frames. Employing only a single camera, this defocusing approach is capable of measuring the air flow between two parallel glass plates at a distance of 1 mm with an average uncertainty of 2.43% for each track, relative to the maximum velocity. A tomographic particle tracking velocimetry measurement, serving as a benchmark for the single camera technique, reaches an average uncertainty of 1.59%. Altogether, with its straightforward set-up and without requiring a calibration target, this in situ calibrated defocusing approach opens new areas of application for optical flow velocimetry. In particular, for measurement domains with small optical windows and a lack of accessibility.