Multi-Δt 3D-PTV based on Reynolds decomposition

A novel approach is investigated to extend the range of measurable velocities by 3D-PTV systems. The method is specifically conceived for robotic volumetric PTV measurements, but it has applications for other similar techniques. The multi-Δt method relies upon combining the information from two or more sets of double-frame images with pulse separation of different time duration. Measurements with a short time separation yield a robust particle velocity field estimation with a higher percentage of valid vectors, yet a low measurement precision. Conversely, measurements with longer time separation potentially offer a higher measurement precision but suffer from an increased probability of spurious particle pairing. Reynolds decomposition is used to combine the two (dual-Δt) sets where a predictor for the mean particle displacement and its statistical dispersion is used to pair particle recordings from a longer time separation. For this reason, this method is aimed at the analysis of turbulent flows where the Reynolds decomposition is meaningful (e.g. turbulent flows with steady/quasi-steady boundary conditions). The extent of the search region is selected dynamically, based on the estimate of the velocity fluctuations from the short time separation evaluation. A more advanced variant of the algorithm contemplates the progressive increase of the pulse separation (multi-Δt) until the expected dispersion of data due to turbulent fluctuations eventually exceeds the distance between neighbouring particles.

Flow measurements in the near wake of a truncated cylinder obstacle and of an Ahmed body are carried out to examine the performance of the proposed method. Reference data is taken from time-resolved multi-frame analysis based on the Shake-The-Box (STB) algorithm. The two experiments differ for the measurement principle used: the first one is conducted with a tomographic-like system (large aperture), whereas the latter uses coaxial volumetric velocimetry. The rate of correct pairing as well as the velocity dynamic range dependence upon the choice of the time separation are monitored and discussed. The results compare favourably with the STB analysis, indicating that the measurement of the time-average velocity field can be based on dual-Δt 3D-PTV measurements removing the constraint of time-resolved particle motion recording.