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

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Abstract

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 N I 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.

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References

  • Adrian RJ (1997) Dynamic ranges of velocity and spatial resolution of particle image velocimetry. Meas Sci Technol 8:1393–1398

    Article  Google Scholar 

  • Atkinson C, Soria J (2009) An efficient simultaneous reconstruction technique for tomographic particle image velocimetry. Exp Fluids 47:563–578

    Article  Google Scholar 

  • Atkinson C, Coudert S, Foucaut JM, Stanislas M, Soria J (2011) The accuracy of tomographic particle image velocimetry for measurements of a turbulent boundary layer. Exp Fluids 50:1031–1056

    Article  Google Scholar 

  • Bastiaans RJM, van der Plas GAJ, Kieft RN (2002) The performance of a new PTV algorithm applied in super-resolution PIV. Exp Fluids 32:345–356

    Article  Google Scholar 

  • Ben-Salah R, Alata O, Tremblais B, Thomas L, David L (2015) Particle volume reconstruction based on a marked point process and application to Tomo-PIV. EUSIPCO 2015. Nice, France, 31 Aug–3 June 2015

  • Bourgoin M, Ouellette NT, Xu H, Berg J, Bodenschatz E (2006) The role of pair dispersion in turbulent flow. Science 311(5762):835–838

    Article  Google Scholar 

  • Cierpka C, Lütke B, Kähler CJ (2013) Higher order multi-frame particle tracking velocimetry. Exp Fluids 54:1533

    Article  Google Scholar 

  • Cornic P, Champagnat F, Plyer A, LeClaire B, Cheminet A, Le Besnerais G (2014) Tomo-PTV with sparse tomographic reconstruction and optical flow. In: 17th international symposium on applications of laser techniques to fluid mechanics. Lisbon, Portugal, 07–10 July 2014

  • Cornic P, Champagnat F, Cheminet A, LeClaire B, Le Besnerais G (2015) Fast and efficient particle reconstruction on a 3D grid using sparsity. Exp Fluids 56:62

    Article  Google Scholar 

  • Dalziel SB (1992) Decay of rotating turbulence: some particle tracking experiments. Appl Sci Res 49:217–244

    Article  Google Scholar 

  • Discetti S, Astarita T (2011) A fast multi-resolution approach to tomographic PIV. Exp Fluids 52:765–777

    Article  Google Scholar 

  • Discetti S, Astarita T (2012) Fast 3D PIV with direct sparse cross-correlations. Exp Fluids 53:1437–1451

    Article  Google Scholar 

  • Discetti S, Natale A, Astarita T (2013) Spatial filtering improved tomographic PIV. Exp Fluids 54:1505

    Article  Google Scholar 

  • Discetti S, Agüera N, Cafiero G, Astarita T (2015) Ensemble 3D-PTV for high resolution turbulent statistics. In: 11th international symposium on PIV–PIV15. Santa Barbara, USA, 14–16 Sept 2015

  • Earl A, Cochard S, Thomas L, Tremblais B, David L (2015) Implementation of vibration correction schemes to the evaluation of a turbulent flow in an open channel by tomographic particle image velocimetry. Meas Sci Technol 26:015303

    Article  Google Scholar 

  • Eilers PHC, Marx BD (1996) Flexible smoothing with B-splines and penalties. Stat Sci 11(2):89–121

    Article  MathSciNet  MATH  Google Scholar 

  • Elsinga GE, Tokgoz S (2014) Ghost hunting—an assessment of ghost particle detection and removal methods for tomographic-PIV. Meas Sci Technol 25:084004

    Article  Google Scholar 

  • Elsinga GE, van Oudheusden BW, Scarano F (2006b) Experimental assessment of tomographic-PIV accuracy. In: 13th international symposium on applications of laser techniques to fluid mechanics. Lisbon, Portugal, 26–29 June 2006

  • Elsinga GE, Scarano F, Wieneke B, van Oudheusden BW (2006a) Tomographic particle image velocimetry. Exp Fluids 41:933–947

    Article  Google Scholar 

  • Elsinga GE, Westerweel J, Scarano F, Novara M (2011) On the velocity of ghost particles and the bias errors in Tomographic-PIV. Exp Fluids 50:825–838

    Article  Google Scholar 

  • Gesemann S (2015) From particle tracks to velocity and acceleration fields using B-splines and penalties. arXiv 1510.09034

  • Ghaemi S, Scarano F (2011) Counter-hairpin vortices in the turbulent wake of a sharp trailing edge. J Fluid Mech 689:317–356

    Article  MATH  Google Scholar 

  • Hain R, Kähler CJ, Michaelis D (2008) Tomographic and time resolved PIV measurements on a finite cylinder mounted on a flat plate. Exp Fluids 45:715–724

    Article  Google Scholar 

  • Henningsson P, Michaelis D, Nakata T, Schanz D, Geisler R, Schröder A, Bomphrey RJ (2015) The complex aerodynamic footprint of desert locusts revealed by large-volume tomographic particle image velocimetry. J R Soc Interface 12:108

    Article  Google Scholar 

  • Herman GT, Lent A (1976) Iterative reconstruction algorithms. Comput Biol Med 6:273–294

    Article  Google Scholar 

  • Huhn F, Schanz D, Gesemannn S, Schröder A (2015) Pressure fields from high-resolution time-resolved particle tracking velocimetry in 3D turbulent flows. In: Proceedings of NIM2015 Workshop, Poitiers, France

  • Kähler CJ, Scharnowski S, Cierpka C (2012a) On the resolution limit of digital particle image velocimetry. Exp Fluids 52:1629–1639

    Article  Google Scholar 

  • Kähler CJ, Scharnowski S, Cierpka C (2012b) On the uncertainty of digital PIV and PTV near walls. Exp Fluids 52:1641–1656

    Article  Google Scholar 

  • Kasagi N, Nishino K (1990) Probing turbulence with three-dimensional particle tracking velocimetry. Exp Therm Fluid Sci 4:601–612

    Article  Google Scholar 

  • La Porta A, Voth GA, Crawford AM, Alexander J, Bodenschatz E (2001) Fluid particle accelerations in fully developed turbulence. Nature 409:1017–1019

    Article  MATH  Google Scholar 

  • Lüthi B, Tsinober A, Kinzelbach W (2005) Lagrangian measurement of vorticity dynamics in turbulent flow. J Fluid Mech 528:87–118

    Article  MATH  Google Scholar 

  • Lynch K, Scarano F (2013) A high-order time-accurate interrogation method for time-resolved PIV. Meas Sci Technol 24:035305

    Article  Google Scholar 

  • Lynch K, Scarano F (2014) Experimental determination of tomographic PIV accuracy by a 12-camera system. Meas Sci Technol 25:084003

    Article  Google Scholar 

  • Lynch K, Scarano F (2015) An efficient and accurate approach to MTE-MART for time-resolved tomographic PIV. Exp Fluids 56:66

    Google Scholar 

  • Maas HG, Grün A, Papantoniou D (1993) Particle tracking in three dimensional turbulent flows—part I: photogrammetric determination of particle coordinates. Exp Fluids 15:133–146

    Article  Google Scholar 

  • Malik N, Dracos T, Papantoniou D (1993) Particle tracking in three dimensional turbulent flows—part II: particle tracking. Exp Fluids 15:279–294

    Google Scholar 

  • Michaelis D, Wolf CC (2011) Vibration compensation for tomographic PIV using single image volume self calibration. In: 9th international symposium on particle image velocimetry—PIV11. Kobe, Japan, 21–23 July 2011

  • Neeteson NJ, Rival D (2015) Pressure-field extraction on unstructured flow data using a Voronoi tessellation-based networking algorithm: a proof-of-principle study. Exp Fluids 56:44

    Article  Google Scholar 

  • Neeteson NJ, Bhattacharya S, Rival DE, Michaelis D, Schanz D, Schröder A (2015) Pressure-field extraction from lagrangian flow measurements. In: 11th international symposium on PIV–PIV15. Santa Barbara, USA, 14–16 Sept 2015

  • Nishino K, Kasagi N, Hirata M (1989) Three-dimensional particle tracking velocimetry based on automated digital image processing. Trans ASME J Fluid Eng 111:384–390

    Article  Google Scholar 

  • Nobach H, Bodenschatz E (2009) Limitations of accuracy in PIV due to individual variations of particle image intensities. Exp Fluids 24:045302

    Google Scholar 

  • Novara M, Scarano F (2013) A particle-tracking approach for accurate material derivative measurements with tomographic PIV. Exp Fluids 54:1584

    Article  Google Scholar 

  • Novara M, Batenburg KJ, Scarano F (2010) Motion tracking-enhanced MART for tomographic PIV. Meas Sci Technol 21:035401

    Article  Google Scholar 

  • Novara M, Ianiro A, Scarano F (2013) Adaptive interrogation for 3D-PIV. Meas Sci Tech 24:024012

    Article  Google Scholar 

  • Novara M, Schanz D, Kähler CJ, Schröder A (2015) Shake-The-Box for multi-pulse tomographic systems: towards high seeding density particle tracking in high speed flows. In: 11th international symposium on PIV–IV15. Santa Barbara, USA, 14–16 Sept 2015

  • Ouellette NT, Xu H, Bodenschatz E (2006) A quantitative study of three-dimensional Lagrangian particle tracking algorithms. Exp Fluids 40(2):301–313

    Article  Google Scholar 

  • Savitzky A, Golay MJE (1964) Smoothing and differentiation of data by simplified least squares procedures. Anal Chem 36(8):1627–1639. doi:10.1021/ac60214a047

    Article  Google Scholar 

  • Scarano F (2013) Tomographic PIV: principles and practice. Meas Sci Technol 24:012001

    Article  Google Scholar 

  • Scarano F, Poelma C (2009) Three-dimensional vorticity patterns of cylinder wakes. Exp Fluids 47:69–83

    Article  Google Scholar 

  • Schanz D, Schröder A, Heine B, Dierksheide U (2012) Flow structure identification in a high-resolution tomographic PIV data set of the flow behind a backward facing step. In: 16th international symposium on applications of laser techniques to fluid mechanics, Lisbon

  • Schanz D, Gesemann S, Schröder A, Wieneke B, Novara M (2013a) Non-uniform optical transfer functions in particle imaging: calibration and application to tomographic reconstruction. Meas Sci Technol 24:024009

    Article  Google Scholar 

  • Schanz D, Schröder A, Gesemann S, Michaelis D, Wieneke B (2013b) Shake-the-Box: a highly efficient and accurate tomographic particle tracking velocimetry (TOMO-PTV) method using prediction of particle position. In: 10th international symposium on particle image velocimetry—PIV13. Delft, The Netherlands, 1–3 July 2013

  • Schanz D, Schröder A, Gesemann S (2014) Shake-the-Box—a 4D PTV algorithm: accurate and ghostless reconstruction of Lagrangian tracks in densely seeded flows. In: 17th international symposium on applications of laser techniques to fluid mechanics. Lisbon, Portugal, 07–10 July 2014

  • Schneiders JFG, Azijli I, Scarano F, Dwight RP (2015) Pouring time into space. In: 11th international symposium on particle image velocimetry—PIV15. Santa Barbara, California, 14–16 Sept 2015

  • Schröder A, Geisler R, Elsinga GE, Scarano F, Dierksheide U (2008) Investigation of a turbulent spot and a tripped turbulent boundary layer flow using time-resolved tomographic PIV. Exp Fluids 44:305–316

    Article  Google Scholar 

  • Schröder A, Geisler R, Staak K, Wieneke B, Elsinga G, Scarano F, Henning A (2011) Lagrangian and Eulerian views into a turbulent boundary layer flow using time-resolved tomographic PIV. Exp Fluids 50:1071–1091

    Article  Google Scholar 

  • Schröder A, Schanz D, Geisler R, Willert C, Michaelis D (2013) Dual-volume and four-pulse tomo PIV using polarized laser light. In: 10th international symposium on particle image velocimetry—PIV13. Delft, The Netherlands, 1–3 July 2013

  • Schröder A, Schanz D, Michaelis D, Cierpka C, Scharnovski S, Kähler CJ (2015a) Advances of PIV and 4D-PTV “Shake-The-Box” for turbulent flow analysis—the flow over periodic hills. Flow Turb Comb 95(2–3):193–209

    Article  Google Scholar 

  • Schröder A, Schanz D, Geisler R, Gesemann S, Willert C (2015b) Near-wall turbulence characterization using 4D-PTV Shake-The-Box. In: 11th international symposium on particle image velocimetry—PIV15. Santa Barbara, California, 14–16 Sept 2015

  • Sciacchitano A, Wieneke B, Scarano F (2013) PIV uncertainty quantification by image matching. Meas Sci Technol 24:045302

    Article  Google Scholar 

  • Violato D, Scarano F (2011) Three-dimensional evolution of flow structures in transitional circular and chevron jets. Phys Fluids 23:124104

    Article  Google Scholar 

  • Violato D, Moore P, Scarano F (2011) Lagrangian and Eulerian pressure field evaluation of rod-airfoil flow from time-resolved tomographic PIV. Exp Fluids 50:1057–1070

    Article  Google Scholar 

  • Violato D, Ianiro A, Cardone G, Scarano F (2012) Three-dimensional vortex dynamics and convective heat transfer in circular and chevron impinging jets. Int J Heat Fluid Flow 37:22–36

    Article  Google Scholar 

  • Wereley ST, Meinhart CD (2001) Second-order accurate particle image velocimetry. Exp Fluids 31:258–268

    Article  Google Scholar 

  • Wieneke B (2007) Volume self-calibration for stereo PIV and tomographic PIV. Exp Fluids 45:549–556

    Article  Google Scholar 

  • Wieneke B (2013) Iterative reconstruction of volumetric particle distribution. Meas Sci Technol 24:024008

    Article  Google Scholar 

  • Wieneke B (2015) PIV uncertainty quantification from correlation statistics. Meas Sci Technol 26:074002

    Article  Google Scholar 

  • Wiener N (1949) Extrapolation, interpolation, and smoothing of stationary time series, vol 2. MIT Press, Cambridge

    MATH  Google Scholar 

  • Willneff J (2003) A spatio-temporal matching algorithm for 3D particle tracking velocimetry. Swiss Federal Institute of Technology Zurich Diss. ETH No. 15276

  • Xu H (2008) Tracking Lagrangian trajectories in position-velocity space. Meas Sci Technol 19:075105

    Article  Google Scholar 

  • Xu H, Bourgoin M, Ouellette NT, Bodenschatz E (2006) High order lagrangian velocity statistics in turbulence. Phys Rev Lett 96:024503

    Article  Google Scholar 

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Acknowledgments

The work has been conducted in the scope of the DFG-project ‘Analyse turbulenter Grenzschichten mit Druckgradient bei großen Reynoldszahlen mit hochauflösenden Vielkameramessverfahren’ (Grant KA 1808/14-1 and SCHR 1165/3-1). The authors thank Dr. Daniele Violato and Dr. Matteo Novara from TU Delft for the experimental set-up and the collaboration on conducting the experiment used for the evaluation of the algorithm. Furthermore, the authors thank Bernhard Wieneke for fruitful discussions on IPR and for providing an algorithm to remove divergence from a given vector volume which served as a source for the synthetic track generation.

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  1. German Aerospace Center (DLR), Institute of Aerodynamics and Flow Technology, Göttingen, Germany

    Daniel Schanz, Sebastian Gesemann & Andreas Schröder

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  1. Daniel Schanz
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  2. Sebastian Gesemann
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Correspondence to Daniel Schanz.

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Schanz, D., Gesemann, S. & Schröder, A. Shake-The-Box: Lagrangian particle tracking at high particle image densities. Exp Fluids 57, 70 (2016). https://doi.org/10.1007/s00348-016-2157-1

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