Shake-The-Box: Lagrangian particle tracking at high particle image densities

A Lagrangian tracking method is introduced, which uses a prediction of the particle distribution for the subsequent time-step as a mean to seize the temporal domain. Errors introduced by the prediction process are corrected by an image matching technique ('shaking' the particle in space), followed by an iterative triangulation of particles newly entering the measurement domain. The scheme was termed 'Shake-The-Box' and previously characterized as '4D-PTV' due to the strong interaction with the temporal dimension. Trajectories of tracer particles are identified at high spatial accuracy due to a nearly complete suppression of ghost particles; a temporal filtering scheme further improves on accuracy and allows for the extraction of local velocity and acceleration as derivatives of a continuous function. Exploiting the temporal information enables the processing of densely seeded flows (beyond 0.1 particles per pixel, ppp), which were previously reserved for tomographic PIV evaluations. While TOMO-PIV uses statistical means to evaluate the flow (building an 'anonymous' voxel space with subsequent spatial averaging of the velocity information using correlation), the Shake-The-Box approach is able to identify and track individual particles at numbers of tens or even hundreds of thousands per time-step. The method is outlined in detail, followed by descriptions of applications to synthetic and experimental data. The synthetic data evaluation reveals that STB is able to capture virtually all true particles, while effectively suppressing the formation of ghost particles. For the examined four-camera set-up particle image densities NI up to 0.125 ppp could be processed. For noise-free images, the attained accuracy is very high. The addition of synthetic noise reduces usable particle image density (N-I <= 0.075 ppp for highly noisy images) and accuracy (still being significantly higher compared to tomographic reconstruction). The solutions remain virtually free of ghost particles. Processing an experimental data set on a transitional jet in water demonstrates the benefits of advanced Lagrangian evaluation in describing flow details-both on small scales (by the individual tracks) and on larger structures (using an interpolation onto an Eulerian grid). Comparisons to standard TOMO-PIV processing for synthetic and experimental evaluations show distinct benefits in local accuracy, completeness of the solution, ghost particle occurrence, spatial resolution, temporal coherence and computational effort.