Particle capture by turbulent recirculation zones measured using long-time Lagrangian particle tracking

We have measured the trajectories of particles into, and around, the recirculation zone formed in water flowing through a sudden pipe expansion with radius ratio 1:3.7, at Reynolds numbers between 5,960 and 41,700 over a range of particle Stokes number (here defined as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ St = {\frac{{T_{\text{f}} }}{{\tau_{\text{p}} }}} $$\end{document}, where Tf is an appropriate mean or turbulent timescale of the fluid flow and a particle relaxation time, τp,) between 6.2 and 51 and drift parameter between 0.3 and 2.8. The particles were thus weakly inertial but nevertheless heavy with a diameter about an order of magnitude larger than the Kolmogorov scale. Trajectories of particles, released individually into the flow, were taken in a Lagrangian framework by a three-dimensional particle tracking velocimeter using a single 25 Hz framing rate intensified CCD camera. Trajectories are quantified by the axial distribution of the locations of particle axial velocity component reversal and the probability distributions of trajectory angle and curvature. The effect of increasing the drift parameter was to reduce the tendency for particles to enter the recirculation zone. For centreline release, the proportion of particles entering the recirculation zone and acquiring a negative velocity decreased from about 80% to none and from about 66% to none, respectively, as the drift parameter increased from 0.3 to 2.8. Almost half of the particles experienced a relatively large change of direction corresponding to a radius of curvature of their trajectory comparable to, or smaller than, the radius of the downstream pipe. This was due to the interaction between these particles and eddies of this size in the downstream pipe and provides experimental evidence that particles are swept by large eddies into the recirculation zone over 1.0 < \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ Z^{*} $$\end{document} < 2.5, where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ Z^{*} $$\end{document} is axial distance from the expansion plane normalized by the downstream pipe diameter, which was well upstream of the reattachment point at the wall (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ Z^{*} \approx 3. 5 $$\end{document}). Once inside the recirculation zone, the particle motion was governed more by the drift parameter than by the Stokes number.