Three-dimensional tracking of the long time trajectories of suspended particles in a lid-driven cavity flow

Stereo imaging methods are used to measure the positions of solid spherical particles suspended in a viscous liquid and enclosed in a transparent cubic cavity. The liquid and particle motions are driven at the top lid by a conveyor belt operated at constant speed. Based on sequences of stereo views of the full cavity, the particles are tracked continuously along their three-dimensional orbits. The corresponding position histories are treated as noisy stochastic data and processed using Kalman filters to fill data gaps and attenuate the effect of measurement errors. The lid-driven viscous flow is characterised by an intricate internal structure which is mirrored in the particle paths. The tracks of the solid particles align with long exposure images of laser-illuminated micro-particles in selected transverse planes. Nevertheless, their long time trajectories appear to cluster along preferential pathways of the internal circulation pattern.

[1]  R. Adrian.  Particle-Imaging Techniques for Experimental Fluid Mechanics , 1991 .

[2]  Elisabeth Guazzelli,et al.  Inertial migration of rigid spherical particles in Poiseuille flow , 2004, Journal of Fluid Mechanics.

[3]  Rangachar Kasturi,et al.  Machine vision , 1995 .

[4]  Annalisa Griffa,et al.  Prediction of particle trajectories in the Adriatic Sea using Lagrangian data assimilation , 2001 .

[5]  Tony W. H. Sheu,et al.  Flow topology in a steady three-dimensional lid-driven cavity , 2002 .

[6]  T. Dracos,et al.  3D PTV and its application on Lagrangian motion , 1997 .

[7]  Jean-Luc Guermond,et al.  Start-up flows in a three-dimensional rectangular driven cavity of aspect ratio 1:1:2 at Re = 1000 , 2002, Journal of Fluid Mechanics.

[8]  D. L. Young,et al.  Numerical solution of three‐dimensional velocity–vorticity Navier–Stokes equations by finite difference method , 2005 .

[9]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .

[10]  C. Migeon,et al.  Details on the start-up development of the Taylor-Gortler-like vortices inside a square-section lid-driven cavity for 1,000≤Re≤3,200 , 2002 .

[11]  Dan S. Henningson,et al.  Linear compensator control of a pointsource induced perturbation in a Falkner-Skan-Cooke boundary layer , 2003 .

[12]  T. P. Chiang,et al.  Numerical prediction of eddy structure in a shear-driven cavity , 1997 .

[13]  Satoru Ushijima,et al.  Three-Dimensional Particle Tracking Velocimetry With Laser-Light Sheet Scannings , 1996 .

[14]  M. Stöhr,et al.  Particle-tracking velocimetry , 1999 .

[15]  G. Segré,et al.  Behaviour of macroscopic rigid spheres in Poiseuille flow Part 2. Experimental results and interpretation , 1962, Journal of Fluid Mechanics.

[16]  Masayoshi Ito,et al.  Tracking a three-dimensional moving target with distributed passive sensors using extended Kalman filter , 2001 .

[17]  R. E. Kalman,et al.  New Results in Linear Filtering and Prediction Theory , 1961 .

[18]  Richard A. Brown,et al.  Introduction to random signals and applied kalman filtering (3rd ed , 2012 .

[19]  Roger Hermansson,et al.  Study of the phenomena affecting the accuracy of a video- based particle tracking velocimetry technique , 1997 .

[20]  N. Malik,et al.  Particle tracking velocimetry in three-dimensional flows , 1993 .

[21]  Yves Zech,et al.  Voronoï imaging methods for the measurement of granular flows , 2002 .

[22]  Robert L. Street,et al.  The Lid-Driven Cavity Flow: A Synthesis of Qualitative and Quantitative Observations , 1984 .

[23]  Minsoo Han,et al.  Particle migration in tube flow of suspensions , 1999 .

[24]  Michael Ghil,et al.  Extended Kalman filtering for vortex systems. Part 1: Methodology and point vortices , 1998 .

[25]  Benoît Macq,et al.  Stereoscopic and velocimetric reconstructions of the free surface topography of antidune flows , 2005 .

[26]  Peter J. Bosscher,et al.  MEASUREMENT OF PARTICLE MOVEMENT IN GRANULAR SOILS USING IMAGE ANALYSIS , 1999 .

[27]  A. Acrivos,et al.  Steady flows in rectangular cavities , 1967, Journal of Fluid Mechanics.

[28]  R. Adrian.  Twenty years of particle image velocimetry , 2005 .

[29]  R. Hwang,et al.  Effect of Reynolds number on the eddy structure in a lid-driven cavity , 1998 .

[30]  K. Schreel,et al.  The application of a 3D PTV algorithm to a mixed convection flow , 2002 .

[31]  M. D. Deshpande,et al.  FLUID MECHANICS IN THE DRIVEN CAVITY , 2000 .

[32]  Thomas Bewley,et al.  Performance of a linear robust control strategy on a nonlinear model of spatially developing flows , 2004, Journal of Fluid Mechanics.

[33]  D. Young,et al.  An efficient global matrix free finite element algorithm for 3D flow problems , 2004 .

[34]  J. L. Roux.  An Introduction to the Kalman Filter , 2003 .

[35]  Michele Larcher,et al.  Three-dimensional Voronoï imaging methods for the measurement of near-wall particulate flows , 2003 .

[36]  Mubarak Shah,et al.  Motion trajectories , 1993, IEEE Trans. Syst. Man Cybern..

[37]  On End-Wall Corner Vortices in a Lid-Driven Cavity , 1997 .