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Discovery About Temperature in Convection
updated: Sep 17, 2012, 11:18 AM
Source: UCSB
An international team of physicists is working to ascertain more about the
fundamental physical laws that are at work in a process known as convection,
which occurs in a boiling pot of water as well as in the turbulent movement of
the liquid outer core of the Earth. The team's new finding specifies the way
that the temperature of a gas or liquid varies with the distance from a heat
source during convection. The research is expected to eventually help engineers
with applications such as the design of cooling systems, for instance, in
nuclear power plants.
Guenter Ahlers, professor of physics at UC Santa Barbara, worked with his team
at the Max Planck Institute for Dynamics and Self-Organization in Goettingen,
Germany, on this important discovery about turbulent convection. The results
will be published in the September 7 issue of Physical Review Letters, and are
available online now.
The experiments took place in a cylinder that was placed under the turret of a
large pressure container. The 8-foot tall cylinder was heated at the bottom and
cooled at the top. There were about 100 thermometers inside it, and it was
pressurized with sulfur hexafluoride, an inert gas. Convection occurred inside
the cylinder because, in the presence of gravity, the warmer gas at the bottom
tends to rise to the top, while the colder gas tends to sink.
"We like sulfur hexafluoride because it is harmless -- not poisonous, not
chemically reacting -- and because it is a heavy molecule," said Ahlers. "A
heavy molecule enables us to produce more vigorous convection with the same
temperature difference. The strength of the convection is measured by a
parameter called the Rayleigh number. We go to Rayleigh numbers as high as 10 to
the 15 -- a million billion -- which is very large by our standards."
Ahlers enjoys the ability to oversee and even run the continuing experiments
remotely on a computer in his office at UCSB (or anywhere else in the world),
even though the laboratory is 5,000 miles away.
He explained that convection occurs naturally in astrophysics and in Earth
systems. For example, the outer layer of the sun is composed of convection
cells. Convection occurs in the Earth's atmosphere and oceans. The liquid iron
in the outer core of the Earth undergoes vigorous convection and has Rayleigh
numbers well above 10 to the 20. That convection generates the magnetic field of
the Earth.
In their paper, the scientists present experimental and numerical data that show
that, except for a very thin layer in the immediate vicinity of the plates, the
temperature of this system varies linearly with the logarithm of the distance
from the confining plates. They discovered this profile and measured it in
detail.
The findings are especially intriguing because they echo an important discovery
from 1930 by Theodore von Kármán and Ludwig Prandtl, known as the "Law of the
Wall." This discovery involved the study of a gas or liquid flowing along a
wall, where its speed must be zero at the wall because of friction. The speed of
the fluid parallel to the wall increases as the distance from the wall
increases. Von Kármán and Prandtl showed more specifically that the speed
increases linearly with the logarithm of this distance when the flow is fast
enough so that the fluid becomes turbulent. This result is called the Law of the
Wall and is of great importance in many engineering applications.
Ahlers compared the new findings about the way temperature varies in convection
to the way speed varies with the Law of the Wall, noting that they are similar,
although the precise relationship has yet to be understood. "They behave in the
same way," said Ahlers. "But just because two things look the same doesn't mean
they are the same, so we still need to build the theoretical foundation that
connects them. That's what makes this a very active, very exciting field, with
theorists as far apart as Beijing (China), Marburg (Germany), and Twente (the
Netherlands) already trying to explain the experimental results. You make an
experimental discovery, and then theorists get excited. Then they start working
on it, and who knows what we will have six months down the road?"
He explained how the Law of the Wall is of importance in engineering
applications. "Pumping oil from Alaska down to the United States costs billions
of dollars," said Ahlers. "And if you can understand what causes the resistance
that you have to overcome, then maybe you can reduce that. Even if you only
reduce it by 2 or 3 percent, you've saved hundreds of millions. So it's very,
very important."
Ahlers went on to say that understanding the temperature in turbulent convection
is also very important because there are many applications where turbulent
convection is used to cool things. In nuclear reactors, for instance, cooling is
done by turbulent convection. "There are many applications of this turbulent
convection system in industry, where you would also like to understand what's
going on inside, what the temperature gradients are," he said. "So I can see
relevance for this in applications. Although I must say that is not our
motivation; our motivation is to understand the fundamental physics."
Eberhard Bodenschatz, one of the authors, was a postdoctoral fellow with Ahlers
at UCSB about 20 years ago and is now director of the Max Planck Institute for
Dynamics and Self-Organization in Goettingen. Co-author Xiaozhou He is a
postdoctoral fellow with Ahlers and is based in Goettingen. Scientists from The
Netherlands, Italy, and France are also involved.
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