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

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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.

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References

  1. Becker J., Bosemann W., Bopp R.: Photogrammetric methods applied to fluid motion within a fluid matrix. Meas. Sci. Technol. 10, 914–920 (1999). doi:10.1088/0957-0233/10/10/312

  2. Cenedese A., Viotti P.: Lagrangian analysis of nonreactive pollutant dispersion in porous media by means of the particle image velocimetry technique. Water Resour. Res. 32(8), 2329–2343 (1996). doi:10.1029/96WR00605

  3. Chang T.P.K., Watson A.T., Tatterson G.B.: Image processing of tracer particle motions as applied to mixing and turbulent flow. I: the technique. Chem. Eng. Sci. 40, 269–275 (1985). doi:10.1016/0009-2509(85)80066-X

  4. Doh D.H., Hwang T.G., Saga T.: 3D-PTV measurements of the wake of a sphere. Meas. Sci. Technol. 15, 1059–1066 (2004). doi:10.1088/0957-0233/15/6/004

  5. Guezennec Y.G., Brodkey R.S., Trigui N., Kent J.C.: Algorithms for fully automated three-dimensional particle tracking velocimetry. Exp. Fluids 17, 209–219 (1994). doi:10.1007/BF00203039

  6. Hinsch, K.D., Hinrichs, H.: Three-dimensional particle velocimetry. In: Dracos, Th. (ed.) Three-dimensional Velocity and Vorticity Measuring and Image Analysis Technique. Kluwer Academic Publishers (1996)

  7. Kasagi, N., Nishino, K.: Probing turbulence with three-dimensional particle trecking velocimetry. In: Proceedings of International Symposium on Engineering Turbulence—Methods and Measurements (1990)

  8. Lüthi, B., Burr, U., Kinzelbach, W., Tsinober, A.: Velocity derivatives in turbulent flow from 3D-PTV measurements. In: Lindborg, E. et al. (eds.) Proceedings of the Second International Symposium on Turbulence and Shear Flow Phenomena. vol. 2, pp. 123–128 (2001)

  9. Maas H.G.: Complexity analysis for the establishment of image correspondences of dense spatial target fields. Int. Arch. Photogrammetr. Remote Sens. XXIX(B5), 102–107 (1992)

  10. Maas H.-G., Grün A., Papantoniou D.: Particle tracking in threedimensional turbulent flows—Part I: photogrammetric determination of particle coordinates. Exp. Fluids 15, 133–146 (1993). doi:10.1007/BF00190953

  11. Malik N., Dracos T., Papantoniou D.: Particle tracking in threedimensional turbulent flows—Part II: particle tracking. Exp. Fluids 15, 279–294 (1993). doi:10.1007/BF00223406

  12. Moroni M., Cenedese A.: Comparison among feature tracking and more consolidated velocimetry image analysis techniques in a fully developed turbulent channel flow. Meas. Sci. Technol. 16, 2307–2322 (2005). doi:10.1088/0957-0233/16/11/025

  13. Moroni M., Cushman J.H.: Three-dimensional particle tracking velocimetry studies of the transition from pore dispersion to Fickian dispersion for homogeneous porous media. Water Resour. Res. 37(4), 873–884 (2001a). doi:10.1029/2000WR900364

  14. Moroni M., Cushman J.H.: Statistical mechanics with 3D-PTV experiments in the study of anomalous dispersion: II. Exp. Phys. Fluids. 13(1), 81–91 (2001b). doi:10.1063/1.1328076

  15. Moroni M., Cushman J.H., Cenedese A.: A 3D-PTV two projection study of preasymptotic dispersion in porous media which are heterogeneous on the bench scale. Int. J. Eng. Sci. 2003(41), 337–370 (2003). doi:10.1016/S0020-7225(02)00237-9

  16. Papantoniou D., Dracos T.: Lagrangian statistics in open channel flow by 3-D particle tracking velocimetry. In: Rodi and Ganic (eds.) Engineering Turbulence Modeling and Experiments. Elsevier (1990)

  17. Saleh S., Thovert J.F., Adler P.M.: Measurement of two-dimensional velocity fields in porous media by particle image displacement velocimetry. Exp. Fluids 12, 210–212 (1992). doi:10.1007/BF00188261

  18. Stuer H., Mass H.G., Virant M., Becker J.: A volumetric 3D measurement tool for velocity field diagnostic in microgravity experiments. Meas. Sci. Technol. 10, 904–913 (1999). doi:10.1088/0957-0233/10/10/311

  19. Walpot R.J.E., Rosielle P.C.J.N., van der Geld C.W.M.: Design of a set-up for high-accuracy 3D PTV measurements in turbulent pipe flow. Meas. Sci. Technol. 17, 3015–3026 (2006). doi:10.1088/0957-0233/17/11/022

  20. Willert C.E., Gharib M.: Three-dimensional particle imaging with a single camera. Exp. Fluids 12, 353–358 (1992). doi:10.1007/BF00193880

  21. Willneff, J., Gruen, A.: A new spatio-temporal matching algorithm from 3D-particle tracking velocimetry. In: Proceedings of 9th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery (2002)

  22. Zhang J., Tao B., Katz J.: Turbulent flow measurement in a square duct with hybrid holographic PIV. Exp. Fluids 23, 373–381 (1997). doi:10.1007/s003480050124

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Correspondence to John H. Cushman.

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Monica, M., Cushman, J.H. & Cenedese, A. Application of Photogrammetric 3D-PTV Technique to Track Particles in Porous Media. Transp Porous Med 79, 43–65 (2009). https://doi.org/10.1007/s11242-008-9270-4

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Keywords

  • Photogrammetric
  • Particle tracking
  • Velocimetry
  • Dispersion