Myth 1: ‘Two-dimensional’ PTV – there are references that use the same name of Particle Tracking Velocimetry for the two-dimensional technique, which is the same experiment as Particle Image Velocimetry (PIV), but the displacement vectors are extracted from particle images through the cross-correlation and another step which is called ‘tracking’. In this step, the software (or a person) is selecting pairs of particles in PIV images. The technique increases the resolution of PIV vector maps, but this is NOT the three-dimensional system, that we describe here. The myth is that in few flows the particle will stay within the light sheet for more than a couple of frames. That means, that this procedure is not real ‘tracking’, which implicitly means something which needs a sequence of images of the tracked object in time.
Myth 2: The name ‘Three-dimensional particle tracking velocimetry (3D-PTV)’ is also misleading – it is much more than 3D, it is 4D. The technique is three-dimensional, nonintrusive, optical, imaging experimental technique. But, it is inherently four-dimensional and we should use 4D PTV. Let see why it so: the apparatus is four (4) cameras (see some of early references regarding 3D-PTV that explain in details why it has to be four and not three or two), sequentially (like a video) imaging tracer particles. Particles diffract a continuous illumination light while they follow a flow in an observational volume. Measurement procedure requires the following steps:
- Careful calibration, usually using multi-plane technique or using three-dimensional object. There is some idea to use a non-intrusive calibration with the laser pointer, not verified in our lab yet. Calibration feeds the software with the 16 parameters per camera, allowing for determining particle's position in three dimensions with an accuracy of few microns (we talk today about 3 micron accuracy and it is not a limit, as it was shown in the space project).
- Every particle in every frame is IDentified and its location and ID are stored. A particle could be identified with two cameras at least. However, when its image exists in less than four cameras, an accuracy of its position is relatively low. It means large uncertainty in the next tracking step.
- Tracking is an iterative, forward-prediction, backward-correction technique that uses a buffer of at least four time steps to track every particle in time. Here comes the point of the four-dimensionality – the tracking procedure is impossible in practice, if the mean travel distance of the particle is longer than the mean distance between particles in the frame. This constraining factor means that 3D-PTV is possible only when the frame rate of the cameras is compatible with the velocity of the flow.
Two cooperating institutes has been developing 3D-PTV in its current form,: Institute of Geodesy and Photogrammetry (IGP), and Institute of Environmental Engineering (before 01.01.2006 it was Institute of Hydromechanics and Water Resources Management) ETH Zurich. The history of this system is long, as one can see from the list of references. One the best references is the book:
Three-Dimensional Velocity and Vorticity Measuring and Image Analysis Techniques, Editor Th. Dracos, ERCOFTAC Series, Vol. 4, Kluwer, 1996. [link]
The book includes all the basic knowledge to build the PTV system and to develop the software that will allow to track particles. We believe that in these days, something like 10 – 20 research groups around the world are able to measure velocity fields with certain accuracy, with such a system. Locations of particles and the time separation between the frames leads to Lagrangian velocity and Lagrangian (material) derivative of velocity along the trajectory.
IfU (IHW) group has necessary knowledge and experience with this system that will, to the best of our opinion, become a milestone in the experimental fluid dynamics. In the coming years, more and more publications will come out based on the unique capabilities of measuring Lagrangian and Eulerean three-dimensional data in turbulent flows. The limit of the low Reynolds numbers is going to be solved by our new, high-speed (500 fps) imaging and recording (IO Industries real-time storage streaming) system [link].
- Papantoniou, D. 1989, 3-D Particle tracking code, Internal report, IHW, Swiss Federal Institute of Technology, ETH Zurich.
- Papantoniou, D. Dracos, Th. 1990a. Analysing 3-D turbulent motions in open channel flow by use of stereoscopy and particle tracking. Advance in Turbulence, 2, Springer Berlin, 278-285.
- Papantoniou, D. Dracos, Th. 1990b. Lagrangian statistics in open channel flow by 3-D particle tracking velocimetry, Eng. Turb. Model Expt., ed. Rodi & Garnic, Elsevier, 315-324.
- Papantoniou, D., Maas, H.-G. 1990. Recent advances in 3-D particle tracking velocimetry, Proc. 5th. Int. Symp. On Appl. Of Laser Techs in Fluid Mech., Lisbon.
- Maas, H.-G., 1991: Digital Photogrammetry for Determination of Tracer Particle Coordinates in Turbulent Flow Research Photogrammetric Engineering & Remote Sensing Vol. 57, No. 12, pp. 1593-1597
- Maas, H.-G., 1992: Digitale Photogrammetrie in der dreidimensionalen Stroemungsmesstechnik ETH Zurich – Dissertation Nr. 9665
- Maas, H.-G., 1992: Complexity analysis for the determination of image correspondences in dense spatial target fields International Archives of Photogrammetry and Remote Sensing, Vol. XXIX, Part B5, pp. 102-107
- Maas, H.-G., Gruen, A., Papantoniou, D., 1993: Particle Tracking in threedimensional turbulent flows – Part I: Photogrammetric determination of particle coordinates Experiments in Fluids Vol. 15, pp. 133-146
- Malik, N., Dracos, T., Papantoniou, D., 1993: Particle Tracking in threedimensional turbulent flows – Part II: Particle tracking Experiments in Fluids Vol. 15, pp. 279-294
- Malik N.A., Dracos Th. 1995, Interpolation schemes for 3-dimensional velocity –fields from scattered data using Taylor expansions. J. Com. Physics. 119 (2): 231-243.
- Virant, M. and Dracos , Th. 1997. 3D PTV and its application on Lagrangian motion. Measurement Science & Technology 8:1539-1552
- O. Dupont, F. Dubois, A. Vedernikov, J.-C. Legros, J. Willneff, C. Lockowandt, 1999. Photogrammetric set-up for the analysis of particle motion in aerosol under microgravity conditions. Measurement Science and Technology, Volume 10, Number 10, October 1999, Special Issue: Instrumentation and Diagnostics for Microgravtiy Experiments, pp 921-933.
- Stueer, H., Willneff J., Maas H.-G., 1999. Evaluation of image compression in 3D PTV. Videometrics VI, Proceeding of SPIE, San Jose, California, 1999, Vol. 3641, pp 228-238
- Stuer H, Maas HG, Virant M, Becker J, 1999. A volumetric 3D measurement tool for velocity field diagnostics in microgravity experiments Meas. Sci. Tech. 10 (10): 904-913.
- Stuer H, Blaser S, 2000. Interpolation of scattered 3D PTV data to a regular grid, Flow, Turbulence and Combustion, 64 (3): U1-U18.
- Stuer H, Blaser S, 2001. Assessment of spatial derivatives determined from scattered 3D PTV data, Exp. Fluids, 30 (5): 492-499.
- Willneff, J. Gruen, A. 2002, A new spatio-temporal matching algorithm for 3D-Particle Tracking Velocimetry The 9th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery Honolulu, Hawaii, USA, February 10-14, 2002
- Willneff, J. 2003 A Spatio-Temporal Matching Algorithm for 3D Particle Tracking Velocimetry, Diss., Technische Wissenschaften ETH Zurich, Nr. 15276, Zurich, Switzerland.
- Willneff, J. Lüthi, B. 2003, Particle Tracking Velocimetry measurements for Lagrangian analysis of turbulent flows Optical 3-D Measurement Techniques VI, Vol. II, p. 191-198 Zurich, Switzerland, 22.-26. September 2003
- Luthi, B., Tsinober A, Kinzelbach, W. 2005 Lagrangian Measurement of Vorticity Dynamics in Turbulent Flow, J. Fluid Mech., Vol. 528, pp 87-118.
- Liberzon A., Guala M., Lüthi B., Kinzelbach W. and Tsinober A. (2005) Dilute polymers in turbulence, Physics of Fluids.
- Guala M., Lüthi B., Liberzon A., Tsinober A. and Kinzelbach, W. (2005) On the evolution of material lines and vorticity in homogeneous turbulence, J. Fluid Mech.