High-speed particle image velocimetry for the efficient measurement of turbulence statistics

A high-frame-rate camera and a continuous-wave laser are used to capture long particle image sequences exceeding 100,000 consecutive frames at framing frequencies up to 20 kHz. The electronic shutter of the high-speed CMOS camera is reduced to 10μ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$10\,\upmu$$\end{document}s to prevent excessive particle image streaking. The combination of large image number and high frame rate is possible by limiting the field of view to a narrow strip, primarily to capture temporally resolved profiles of velocity and derived quantities, such as vorticity as well as higher order statistics. Multi-frame PIV processing algorithms are employed to improve the dynamic range of recovered PIV data. The recovered data are temporally well resolved and provide sufficient samples for statistical convergence of the fluctuating velocity components. The measurement technique is demonstrated on a spatially developing turbulent boundary layer inside a small wind tunnel with Reδ=4,800,Reτ=240\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Re_\delta = 4{,}800,\, Re_\tau = 240$$\end{document} and Reθ=515\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Re_\theta = 515$$\end{document}. The chosen magnification permits a reliable estimation of the mean velocity profile down to a few wall units and yields statistical information such as the Reynolds stress components and probability density functions. By means of single-line correlation, it is further possible to extract the near-wall velocity profile in the viscous sublayer, both time-averaged as well as instantaneous, which permits the estimation the wall shear rate γ˙\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\dot{\gamma }$$\end{document} and along with it the shear stress τw\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau _w$$\end{document} and friction velocity uτ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$u_\tau$$\end{document}. These data are then used for the calculation of space-time correlation maps of wall shear stress and velocity.