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Correlation based Particle Tracking Velocimetry

DOI: 10.1615/ICHMT.2006.TurbulHeatMassTransf.390
pages 231-234

K. Hoyer
Institute of Environmental Engineering, ETH - Swiss Federal Institute of Technology, CH-8093 Zurich, Switzerland

Markus Holzner
Institute of Environmental Engineering, ETH - Swiss Federal Institute of Technology, CH-8093 Zurich, Switzerland

Wolfgang Kinzelbach
Institute of Hydromechanics and Water Resources Management, Swiss Federal Institute of Technology, ETH Honggerberg, CH 8093 Zurich, Switzerland

Abstract

The present paper describes a particle tracking algorithm that is very robust in densely seeded flow fields of moderate Reynolds numbers. It first uses a local spatial (3D) correlation measure to overcome the restriction imposed by the displacement ratio, limiting the classical single trajectory tracking to small seeding densities or requiring large over-sampling in time. When this ratio of particle displacement per time step over average particle separation exceeds unity, tracking becomes increasingly difficult and erroneous. Starting with an experimentally obtained time sequence of numerous particle positions within a 3-D observation volume we first correlate lengths and angles between proximate points of two time steps to identify similar tetrahedra. Once a number of such tetrahedra are identified, each set of four corner points serves as basis for a 3-D Taylor expansion of the velocity field, which can be used to estimate expected positions of other nearby particles in a second step. A particle track is established when simultaneously a number of matching particle positions are found within a specified distance from their predictors. We use the method to analyze the physical mechanisms present in a turbulent jet like flow, where we are able to quantify the entire velocity gradient tensor (VGT) along the Lagrangian trajectories of the original data, as well as in the interpolated regular Eulerian frame. We succeeded in simultaneously tracking about 4000 particles within a (35 mm)3 volume at a scan rate of 94 Hz. We analyze joint statistics of turbulence quantities such as the 2nd and 3rd invariant of the VGT, dissipation rate, shear strain and enstrophy production rate as well as the intermediate eigenvalue of the pressure Hessian. For a given time step, we reveal the spatial relationship between said quantities.

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