Measuring liquid turbulence

EVER WONDER why you don't see mosquitoes on a windy day? The answer to that question is important not only to campers but also to mathematicians who try to understand turbulence in gases and liquids, with applications in everything from weather forecasting to mixing industrial chemicals.

There are standard mathematical models that describe how a particle will move in a turbulent fluid, but up to now no one has been able to check the models against real measurements at high degrees of agitation because the particles sometimes move too fast to measure. Now, Cornell University researchers, using techniques developed to observe subatomic particles, have measured turbulent flow in liquids over a wide range of velocities and have come up with some surprising results: Particles often get an extra kick that accelerates them out of proportion to the general motion of the fluid.

Consider that poor mosquito. Compared to the atmosphere, she's just another tiny particle. In a 10 mph wind she will experience an acceleration of about 15 times that of gravity every 15 seconds; no wonder she lands and waits for calmer air.

The research has been reported in a paper, "Fluid Particle Accelerations In Fully Developed Turbulence," by Cornell research associate Arthur LaPorta, and published in the journal Nature. The particle-tracking group, led by Bodenschatz, is based in the Laboratory of Atomic and Solid State Physics and the Laboratory of Nuclear Studies At Cornell.

"It was something of an experimental surprise," says LaPorta. "There are computer simulations that show this at low Reynolds numbers, but no one has been able to check it experimentally." A Reynolds number expresses a relationship between the density and viscosity (stickiness) of a fluid and the velocity and length scale of its motion. Roughly it is a measure of how violently a fluid is stirred. The researchers made their measurements in a cylindrical tank of water about 20 inches (48 centimeters) in diameter by 24 inches (60 centimeters) tall, holding about 25 gallons (100 liters) of water, stirred by two propellers turning in opposite directions.

Measurements were made with the propellers turning at speeds ranging from one rotation every seven seconds up to seven rotations per second. Polystyrene spheres about one-twentieth of a millimeter in diameter were added to the water and illuminated with an argon laser. Their movements were measured by silicon strip detectors - somewhat like the charged coupled device (CCD) image sensors in a camcorder - placed in two positions to measure motion along two axes. For future experiments, LaPorta says, additional detectors will be added to measure motion in all three dimensions.

The detectors, developed to observe the scattering of subatomic particles produced by experiments in the Cornell Electron Storage Ring (CESR) are effectively taking moving pictures at up to 70,000 frames per second.

The resulting measurements showed some particles being accelerated up to 1,500 times the acceleration of gravity, or some 40 times what would be expected. A graph of the distribution of accelerations shows very long "tails," indicating that there are many high-acceleration events, as well as many moments when particles almost come to a stop. A more typical result would be a graph in which nearly all events cluster close to a central value in what is called a Gaussian distribution.

Mathematical models used to describe the mixing of fluids might need to be adjusted, LaPorta says. "Atmospheric scientists are interested in our results," he says. "It's of interest to anyone who studies how things mix." Other applications, he notes, would include the design of combustion chambers in automobile engines or the mixing of chemicals in industrial processes. In all these situations, chemical reactions occur only where the two reactants actually meet, so designers strive for the most thorough mixing possible.

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