Application of Photogrammetric 3D-PTV Technique to Track Particles in Porous Media

Abstract

To be able to assess the adequacy of existing theories of flow and transport in porous media, experimental methods must be able to obtain fully three-dimensional descriptions of both the Eulerian velocity field and Lagrangian particle trajectories within the system. Here, we report on matched-refractive porous media experiments that rely upon a three- camera 3D-PTV photogrammetric technique. A hexagonal test section is used for experiments. The goal in the experiment is to image a volume far away from the boundary walls, to design a photogrammetric 3D-PTV system, to lengthen the trajectories through an accurate experimental technique and improve the statistical accuracy of the method. A combination of image and object space based information is employed to establish the spatio-temporal correspondences between particle positions of consecutive time steps. The system calibration features have been examined in detail. The photogrammetric principles used by 3D Particle Tracking Velocimetry are described. First, the fundamental mathematical model of the collinearity condition and its extensions are explained. Then, the epipolar line intersection method built upon multicamera correspondences is discussed. The porous media were constructed of Pyrex and the fluid was glycerol. At the bench scale the porous media were heterogeneous, and various mean flow velocities were applied. The tracer particles were air bubbles which moved passively and were imaged as the glycerol was drained from the system. Particle trajectories, velocity covariance’s, classical dispersion tensors are obtained. Further tests on simulated data were performed to ensure the method’s operability and robustness. The great variety of data sets that were processed during the development of the matching algorithm show its general applicability for a wide range of 3D-PTV measurement tasks.