杏吧原创

WHAT has a giant vacuum flask of supercold helium got to do with streamlining
nuclear submarines and jet aircraft so they travel faster and use less fuel? And
why are both astronomers and global warming experts so keen to keep an eye on
what happens in that flask?

Russell Donnelly, a low-temperature physicist at the University of Oregon in
Eugene, knows why. His dream is that supercold helium will be able to overcome a
major obstacle that is preventing engineers from carrying out realistic tests in
the laboratory. It could also shed some light on turbulence, one of last
unsolved problems of classical physics. The National Science Foundation has
faith: it has just awarded him a $5 million grant to build a prototype
helium flask and convince the world that he really can go where no engineer has
gone before.

Reflecting reality

The idea that low-temperature physics could contribute anything to the design
of submarines and aircraft seems bizarre. Nevertheless, supercold helium has the
potential to overcome a massive headache for engineers: when they test scale
models of new designs for jet aircraft, submarines and other large objects in
wind tunnels, they find it impossible to mimic accurately the flows that the
plane or submarine would experience in real life. That prevents them making the
object as streamlined and efficient as they could be. The difficulties arise
because the real-life objects are so large.

A flow is characterised by something called the Reynolds number. The Reynolds
number of a flow past a body is proportional to the body鈥檚 size鈥攖ypically
an average of its length, width and height. It is also proportional to the
density of the fluid and its velocity, and inversely proportional to the fluid鈥檚
dynamic viscosity, which is a measure of its stickiness.

When engineers want to study a new design for a light aircraft, for example,
they will build a scale model and see how it behaves in a wind tunnel. The test
will be realistic only if the flow over the model aircraft is the same as the
one the real plane will experience as it flies in the sky. But how is this going
to be possible when the real aircraft is so much bigger and the flow, measured
by the Reynolds number, is dependent on the size of the test object?

Scale modelling

Engineers have many tricks up their sleeves to boost the Reynolds number.
They can speed up the air passing over the model plane in the wind tunnel, or
increase its density by compressing it. They can build larger models but these
require larger test facilities and costs soon soar. At best, engineers can
create Reynolds numbers of up to about 10 million, which would be about what the
wing of a small aircraft experiences in flight.

However, if the real flow has a very high Reynolds number, it is difficult to
reproduce. Take the case of water flowing past a nuclear submarine, where the
huge size and speed of a nuclear sub can give a Reynolds number as high as a
thousand million. This flow cannot be mimicked in a water tunnel because you
can鈥檛 compress water and push it past a model much faster than about 100
kilometres per hour.

High Reynolds numbers mean that things are pretty turbulent (see 鈥淩eynolds
and Rayleigh numbers鈥�). And since turbulent flow causes the drag that impedes
the motion of aircraft, ships and cars, the inability to mimic high Reynolds
flows costs the world a fortune in wasted fuel. 鈥淓ven if you could cut energy
dissipation by 1 per cent, it would save a huge amount of money,鈥� says
Donnelly.

There is another way to increase the Reynolds number of a flow past a
model鈥攂y reducing the viscosity of the fluid. And this is where
low-temperature physics comes in. For what has far and away the lowest
viscosity? Helium. At its boiling point of 4.2 kelvin (鈭�269 掳C),
liquid helium鈥檚 viscosity is eight times less than that of water at room
temperature. Helium鈥檚 exceptional slipperiness is caused by quantum effects
which push helium atoms apart. The result is a liquid, only a seventh as dense
as water, where the atoms pass each other without the frequent collisions that
create viscosity.

Eternal flow

But normal liquid helium is like treacle compared with superfluid helium,
which comes into being when the temperature drops below 2.2 K. Superfluid helium
has no viscosity鈥攊t is infinitely slippery, and once set in motion, it
will flow forever. The discovery of such a wonder substance opened up the
possibility of creating a flow with an infinite Reynolds number. Unfortunately,
attempts to do this in the 1950s at the California Institute of Technology in
Pasadena ran aground. Donnelly says that before the flow could get to a Reynolds
number of 100, vortices appeared, wrecking the zero viscosity.

That result killed off interest in using helium to create superslippery flows
for more than three decades鈥攗ntil one afternoon in the summer of 1988,
when Donnelly was cycling along the Willamette river in Eugene.

鈥淪uddenly, I had a brainwave,鈥� he says. 鈥淚t might be impossible to achieve
infinite Reynolds numbers with superfluid helium. But why not use ordinary
helium to achieve Reynolds numbers that were merely ultra-large?鈥� A fan could
drive liquid helium with extremely low viscosity through a tunnel. This could
reveal realistic turbulence patterns around model submarines, ships and planes
in a vacuum flask.

Donnelly immediately realised that by replacing the liquid helium by chilled
helium gas, his flask could also shed light on another poorly understood aspect
of fluid motion鈥攃onvection. Like turbulence, convection is characterised
by a single quantity, this time known as the Rayleigh number (see 鈥淩eynolds and
Rayleigh numbers鈥�). The Rayleigh number is the ratio of the buoyancy force on a
body to the viscous force. When the buoyancy of a volume of fluid dominates the
viscous force, corresponding to a high Rayleigh number, convection will
occur.

Until recently, researchers usually studied convection in a B茅nard
cell. This is a hollow, fluid-filled container heated from below like a saucepan
of water. The highest Rayleigh number that a standard B茅nard cell filled
with an everyday fluid could muster was about a million. But once again, this
was much lower than many situations in the real world. The ocean flows, for
instance, have a Rayleigh number that is typically about 10²⁰.

Donnelly reckoned that by using supercold gaseous helium, which is most
slippery at its 鈥渃ritical point鈥� of 5.2 K, it would be possible to investigate
thermal convection in the oceans, or to study the role of convection in weather
patterns, and the transport of heat in the atmosphere. Even the evolution of the
Sun depends on how convection brings heat to its outer regions. All these
processes occur on scales that are too large to be scaled down to the lab.

But a brainwave on a cycle path is one thing鈥攁cting on it is something
else. Donnelly organised a conference in Eugene in 1988. And the participants at
the meeting were as bowled over by the possibilities as Donnelly.

In fact, other researchers had anticipated Donnelly鈥檚 idea to some extent.
The first to recognise the potential of cryogenic helium was Gunter Ahlers of
Bell Labs, who studied B茅nard convection in 1972. Three years later at
the University of Cambridge, David Threlfall used supercritical helium gas to
achieve an unprecedented range of Rayleigh numbers. And in 1991, a team led by
Albert Libchaber at the University of Chicago set up a much larger version of
Threlfall鈥檚 experiment. Libchaber鈥檚 B茅nard cell was 40 centimetres high
and filled with helium gas at close to 4.2 K. By increasing the density of the
gas, Libchaber reached a Rayleigh number of about 10¹⁵.

In 1988, however, Donnelly was unaware of the earlier work. He was used to
thinking small after a lifetime in low-temperature physics. Everything changed,
however, when he bumped into one of his old postgraduate students at a meeting
in Florida. 鈥淗e asked me whether I鈥檇 thought of using the giant refrigerators at
the Superconducting Supercollider,鈥� says Donnelly.

Tricky problem

The SSC was the biggest particle accelerator ever conceived. At its site in
Waxahachie, Texas, physicists had built an enormous plant to refrigerate helium
for 80 kilometres of bending magnets and giant vacuum flasks, at a cost of over
$40 million. What kind of Reynolds numbers might be possible with such
equipment? On the plane back to Oregon, Donnelly did some calculations. 鈥淭he
figures freaked me out,鈥� he says.

Donnelly contacted Michael McAshan, head of cryogenic research at the SSC,
and was given permission to use the refrigeration equipment. But in October
1994, before he could make a start, Congress canned the SSC. A team led by
Donnelly proposed using the unwanted cryogenic equipment for their helium work.
To his disappointment, all the equipment was distributed to other institutes in
the end. But Donnelly鈥檚 plan impressed the powers that be enough for his team to
win a National Science Foundation grant of $5 million to build a large
prototype helium flask from scratch.

Donnelly鈥檚 team, which includes McAshan and Katepalli Sreenivasan, a
physicist and mechanical engineer at Yale University, is now building a
prototype vacuum flask at the University of Oregon. The stainless-steel flask
will be a metre high and half a metre wide, and should be completed within a
year. It should notch up Reynolds numbers of 10⁸ with a flow speed of 4 metres
per second, and Rayleigh numbers of about 10¹⁶.

Finding a way to keep the helium cold has been one of the big challenges. The
helium inside the flask will be insulated from its hot surroundings by an outer
jacket of liquid nitrogen, the vacuum jacket itself and a layer of aluminised
plastic on the surface next to the vacuum to keep out radiation. 鈥淚t鈥檚 known as
superinsulation,鈥� says Donnelly. 鈥淚f your coffee was as well insulated as our
helium, it would take 75 years to cool.鈥� The vacuum flask will contain about 100
litres of liquid helium or cooled helium gas, depending on whether turbulence or
convection is under the spotlight.

Then there鈥檚 the problem of making the helium visible so you can see the
flow. Helium is transparent and there is no convenient dye to highlight it.
Instead, Donnelly and his colleagues intend to seed the flow with tiny particles
of frozen hydrogen-deuterium that will glow if carefully illuminated. Of course,
this requires having a window in the vacuum flask, which in turn means creating
a hole in the reflecting plastic layer. 鈥淚t鈥檒l damage the insulation, but we鈥檒l
just have to live with it,鈥� says Donnelly.

Getting the model in the flask is another tricky problem. For a start, it
involves inserting into the vacuum flask a flow tunnel鈥攁 hollow cylinder
through which a fan drives liquid helium. Then Donnelly鈥檚 team will have to find
a way to suspend a model such as a submarine without using bulky support cables.
鈥淭his is a terrible problem in normal wind tunnels because it completely screws
up the flow,鈥� says Donnelly. His team hopes to get round this by making
stainless-steel models that can be suspended by superconducting magnets outside
the flask.

Despite the problems, however, helium has tremendous advantages. For a start,
the power requirements are low. Large wind tunnels (such as the one at NASA鈥檚
Langley Research Center in Virginia) use 93 megawatt motors to generate the wind
and are the size of several city blocks. But a helium flow tunnel a metre across
would need only a 750 watt fan, according to Donnelly. 鈥淵ou only pay to
refrigerate the helium,鈥� he says. Also, the forces exerted by the helium on any
model are small: 鈥淚n a wind tunnel, they can often be enough to destroy it.鈥�

Another advantage of helium is that it is easy to change its slipperiness.
Changing the temperature can change the Reynolds number of liquid helium by a
factor of three. Even better, the Rayleigh number of supercritical helium gas in
the prototype helium cell at Oregon will vary by an astonishing factor of 10¹⁶
when the pressure changes.

If all goes well with the prototype, the plan is to create a giant version at
the National Cryogenics Turbulence Center in Brookhaven, New York (see
Diagram
). The scaled-up flask, which will be 10 metres high, 5 metres in
diameter and contain 60 000 litres of helium, is likely to cost tens of millions
of dollars. The flask will use the world鈥檚 largest helium liquefier, built for
particle physics at Brookhaven, which will liquefy 24 000 litres of helium each
hour.FIG-20734701.gif

The full-size flask, which should take three years to build, will achieve
Reynolds numbers of 10¹⁰ and Rayleigh numbers of 10²⁰. Plans to build other
experiments at the Brookhaven site include a dedicated liquid helium wind
tunnel. This could eventually result in huge savings by reducing turbulent drag
on ships, aircraft and cars.

There is also unprecedented potential for basic science. Donnelly believes
that the work with helium could provide insights into the nature of turbulence,
dubbed 鈥渢he last unsolved problem of classical physics鈥�. The leading turbulence
model was developed by the Russian Andrei Kolmogorov in the 1940s. 鈥淭he main
idea is that if the Reynolds number is high enough, all flows, whether turbulent
or convective, converge so that they look exactly the same,鈥� says Donnelly. 鈥淏ut
nobody has ever established that.鈥� In fact, says Sreenivasan, 鈥渆xperiments have
consistently deviated from Kolmogorov鈥檚 theory鈥�.

Stellar evolution

Libchaber says that these discrepancies may arise because convection
simulations have until now used unrealistically small cells. His experiments
with a 40-centimetre B茅nard cell have shown that the boundary
plates鈥攈ot and cold plates in the cell that drive the
convection鈥攈ave an important influence on the flow. They launch thermal
plumes into the flow that interfere with convection.

鈥淲hat you actually see is a combination of large-scale flow and thermal
excitations from the boundaries,鈥� says Libchaber. 鈥淚t鈥檚 possible this may
prevent the study of pure convection, although the confusing effect should
diminish with a bigger B茅nard cell.鈥�

Besides resolving this kind of issue, the research with helium could
transform a range of applied sciences. For instance, astrophysicists would like
to understand convection in the stars, where Rayleigh numbers are enormous.
Convection governs the transport of heat through stars鈥� outer layers and,
through this, their structure and evolution. Theoretically, the rate of heat
flow depends on the Rayleigh number raised to a power that Kolmogorov鈥檚 theory
says should be 1/3, but Libchaber鈥檚 experiments have shown to be 2/7. 鈥淚t is not
clear whether the difference is real or whether we are seeing the effect of the
boundary plates once again,鈥� says Libchaber.

Answering prayers

鈥淚t鈥檚 urgent that we settle the matter because it could have a bearing on the
age of the oldest stars, which currently seem to be older than the Universe,鈥�
says Ed Spiegel, an astronomer at Columbia University in New York. Using the
Brookhaven flask, researchers could set up convection at the Rayleigh number
typical of stellar atmospheres (about 10²¹), and measure exactly how much heat
the convection carries using a series of bolometers.

Meteorologists are also keen to see the helium flask in action. Convection
drives all sorts of weather patterns鈥攎ost dramatically,
hurricanes鈥攁nd understanding it could improve weather prediction. They
would also like to check their computer models of global warming because its
pace depends on exactly how fast convection carries heat through the
atmosphere.

鈥淲e need to give our computer codes a reality check, and the helium work
could do that,鈥� says Jackson Herring, a physicist who models convection at the
National Center for Atmospheric Research in Boulder, Colorado.

Herring adds that the flask won鈥檛 answer all their prayers immediately. 鈥淚t
will take a bit of work to extrapolate from a system as simple as Donnelly鈥檚 to
one as complex as the Earth鈥檚 atmosphere,鈥� he says. True, but at least the giant
helium flask will be a good place to start. 鈥淣ot bad for a brainwave on a bike
path,鈥� says Donnelly. 鈥淚t鈥檚 the only idea I鈥檝e had in my career that has such
enormous ramifications.鈥�

Mixed bag: with a fan driving liquid helium through a flow tunnel, the
Brookhaven vacuum flask could show realistic turbulence patterns around planes.
With chilled helium gas and a heat source, the same flask will reveal convection
patterns

* * *

Reynolds and Rayleigh numbers

THE Reynolds number is the ratio of the inertial force to the viscous force
on a body. For a submarine, the inertial force is the force the water exerts
when it gets in the way of the submarine, whereas the viscous force is the force
the water exerts because of its 鈥渟tickiness鈥�.

The connection between Reynolds number and turbulence is straightforward. A
sticky fluid is not prone to turbulence鈥攖ry stirring up a storm in a tin
of treacle鈥攂ut a slippery fluid is. So it is easy for the flow past a body
to become turbulent if the viscous force is tiny compared with the inertial
force. This is why turbulence occurs with high Reynolds numbers. In a pipe, the
flow of water becomes turbulent at a Reynolds number of a few thousand, and in a
wind tunnel, turbulence starts at a Reynolds number of a few million.

The Rayleigh number is the ratio of the buoyancy force on a body to the
viscous force. In the case of water in a heated saucepan, the buoyancy arises
because hot water is less dense than cold water and has a tendency to rise above
it. The continual rising of hot water and sinking of cold water to replace it
sets up a complex pattern of convection cells.

The connection between the Rayleigh number and convection is simple. If the
buoyancy force on a volume of fluid is large compared with the viscous force,
convection will occur. So convection goes hand-in-hand with high Rayleigh
numbers.