Multi-Δt 3D-PTV based on Reynolds decomposition

Abstract

A novel approach is introduced to enlarge the range of measurable velocities by PTV systems. The approach relies upon the acquisition of two or more sets of double-frame images with increasing pulse separation time Δt. The underlying principle is that measurements with a short Δt yield a velocity field with high percentage of valid vectors, but low measurement precision. Conversely, the measurements with longer Δt potentially offer a higher measurement precision but suffer from an increased probability of spurious particle pairing. Their combination is shown possible making use of Reynolds decomposition to form a predictor for the mean displacement and its statistical dispersion. The time-averaged velocity field produced with a short Δt is used as predictor to set the expected average displacement. Moreover, the extent of the search region is based on the estimate of the velocity fluctuations from the evaluation at short Δt. The algorithm can be applied progressively, increasing the pulse separation till truncation errors are found to limit the accuracy of the measurement. An experiment on the near wake of the Ahmed body performed with the Robotic Volumetric PIV system is used to assess the performance of the proposed method, which is compared with reference data from multi-frame measurements based on the Shake-the-Box (STB) algorithm. Results are firstly evaluated in terms of velocity pdf along the in-plane and coaxial directions. Furthermore, the vorticity field obtained by the different methods is compared.