High-Speed Particle Tracking Probes Turbulent Flows
Measurements of pair dispersion offer insights into turbulent mixing and transport.
Daniel S. Burgess
Scientists in the US and Europe have used a high-speed optical particle tracking technique to monitor how particle pairs separate and diffuse in highly turbulent fluid media. The work promises to improve models of phenomena as varied as the spread of pollutants in the atmosphere, the use of odor signals by marine organisms and the fuel spray in a cylinder in a turbocharged engine.
“Most flows in the natural world, as well as in industry, are turbulent,” observed Eberhard Bodenschatz. “Turbulent pair dispersion is very closely tied both to turbulent mixing and transport, and so a deeper understanding of pair dispersion can give us a better handle on how substances are carried and mixed by turbulence.”
In the experimental setup, counterrotating propellers stirred a 100-l water tank seeded with 25-μm-diameter polystyrene spheres (background, surrounded by cameras). To enable the tracking of the movement of the particles in the turbulent flow with three high-speed cameras, two Q-switched frequency-doubled Nd:YAG lasers illuminated the tank. Courtesy of Eberhard Bodenschatz.
Bodenschatz, a professor of physics at Cornell University in Ithaca, N.Y., and a director at Max Planck Institut für Dynamik und Selbstorganisation in Göttingen, Germany, collaborated on the project with investigators from both institutions and from Laboratoire des Écoulements Géophysiques et Industriels in Grenoble, France, and Forskningscenter Risø in Roskilde, Denmark.
The dynamics of a fluid may be understood using an Eulerian or Lagrangian approach, he explained. The former takes the perspective of fixed points past which the fluid moves. The latter views the fluid as a system of corpuscular units whose individual movements are quantified.
“Pair dispersion is inherently a Lagrangian quantity,” Bodenschatz said. “You have to identify two fluid elements and watch them spread in time, just like following two snowflakes in a snowstorm.”
That posed a challenge to the experimental evaluation of the leading theoretical descriptions of the phenomena that had emerged over the past six decades or so. Although optical techniques such as digital particle image velocimetry offered the ability to track flows by the movement of tracers added to the fluid, the speed of the available imaging technologies used in these methods limited their utility to relatively low-velocity conditions and thus to relatively low levels of turbulence.
That has changed with the development of modern digital cameras. Using three Phantom v7.1 CMOS cameras from Vision Research Inc. of Wayne, N.J., the investigators can record 256 × 256-pixel images at a rate of 27,000 frames per second, with which they can deduce the trajectories of hundreds of particles through three dimensions simultaneously. In the current work, they resolved 25µm-diameter polystyrene particles in a water tank subjected to flows with a Taylor microscale Reynolds number — a gauge of turbulence — of up to 815. In contrast, previous approaches were limited to those with Reynolds numbers of less than 300.
The high speed of the imaging system requires intense illumination. The researchers thus used two Q-switched frequency-doubled Nd:YAG lasers from DDC Technologies Inc. of Oceanside, N.Y., Bodenschatz said. One laser is flashlamp-pumped and offers a repetition rate of 30 to 70 kHz, a pulse width of 300 ns and a peak power of 60 W. The other is diode-pumped and delivers a repetition rate of 10 to 120 kHz, a pulse width of 120 ns and a peak power of 90 W.
With this setup, they evaluated competing theoretical predictions involving the dispersion of two particles in a turbulent flow. One suggests that separation increases with the cube of time, the other, that separation scales with the square of time, provided that the time scale is shorter than the time it takes an eddy as large as the distance initially separating the particles to break up into smaller eddies. They found that the latter prediction proved true for their turbulent flows.
They note that the cube power law should govern pair dispersion for extremely fast and turbulent flows, but most real-world flows of interest to scientists and engineers do not approach such conditions.
Science, Feb. 10, 2006, pp. 835-838.
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