Incommensurable time intervals for multi-exposure PTV

Abstract

A novel approach to the analysis of multiply exposed particle image recordings at low source density is presented. The foundation of the method is the similarity between the time sequence of multiple light pulses and the set of positions marked along the trajectory of a Lagrangian tracer. The study discusses the properties of the time sequence to obtain unambiguous identifications of the particles trajectories and directions of motion. The identification of the particles trajectories from multi-exposed image recordings relies on the inner product between two signals, namely the time-sequence of the illumination pulses and the positions of the selected set of particle images. Considering double-frame image recordings, the origin of every track is set in the first frame, where the tracers are exposed a single time. Instead, in the second frame, the tracers are illuminated multiple times. A scaling operation (homothety) based on the estimated track velocity is performed to express the two signals in the same domain, namely time. The inner product is repeated for different values of the estimated track velocity and the signal-to-noise ratio is taken as relevant parameter for robust track identification. An ordinary sequence with regularly time separation between pulses suffers from a low signal-to-noise ratio because of the high probability of spurious matching. Instead, irregular and incommensurable intervals offer the highest signal-to-noise. The concept is demonstrated with an experimental dataset based on high-speed recordings of the turbulent flow across a cylinder obstacle. Multiply-exposed recordings are simulated superimposing instantaneous recordings, where the choice of the time sequence could be varied finely. The method detects successfully particle tracks and assigns correctly the particles time stamp in approximately 80% of the domain. At very low velocity (<3% of free stream), the superposition of the particle images over several exposures hampers the detection of individual particle images.