Generic Energy Function To Predict Particle Positions In 4D-PTV

Abstract

Recent developments in time-resolved Particle Tracking Velocimetry (4D-PTV) consistently improved tracking accuracy and robustness by introducing predictive algorithms such as Shake-The-Box (STB). We propose a generic nondimensional energy function to predict particle positions by leveraging additional information from coherent neighbour motions. The proposed energy function is a combination of position history, neighbour velocity and acceleration terms. Coherent neighbours are quantified by locally utilising Finite Time Lyapunov Exponent (FTLE) as an objective Lagrangian Coherent Structure (LCS) diagnostic method. Synthetic analysis of the wake behind a smooth cylinder at Reynolds number equal to 3900 showed that the optimal solution of the minimised energy function could be modelled as a function of the measurement uncertainties. The model was assessed with the 2D homogeneous isotropic turbulent flow (HIT) as well and was found to be case and Reynolds independent. Results of the 4D-PTV experimental study of the same wake flow configurations are reported. We compared predicted positions with the optimised final positions of STB. It was found that the generic energy function succeeded in estimating particle positions with minimum deviation to the optimised positions in comparison with other techniques.