THERE is no escaping the vortex. It is there when you stir your cup of coffee, and when air and fuel mix in your car’s engine. It’s at work in the giant swirling storm that is Jupiter’s great red spot, and in the toilet bowl after you flush it.
There is a reason for the ubiquity of the vortex. Given the slightest excuse, any fluid will swirl into a vortex as it is moved.
“You can’t turn around without hitting a vortex – or creating one. They’re everywhere,” says Chuck Pell at Duke University in Durham, North Carolina, who studies the vortices that fish leave in their wake.
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Vortices are excellent at soaking up spare energy in a fluid, and engineers have long been keen to learn how to harness this energy and put it to good use. One way is in propulsion. A better understanding of vortices is already changing the way we build underwater vehicles, boosting propulsion power and manoeuvrability. And thanks to the power of the vortex, tiny medical robots that can move and turn around inside your body are closer than you think.
Ever since Leonardo da Vinci sketched the waves formed by water flowing in a fountain 500 years ago, people have struggled to understand how these ubiquitous yet complex structures form, and to work out how they can use them to their advantage. Yet even today, modelling the trajectory of zillions of fluid molecules is beyond the world’s largest supercomputers, and the equations that govern the formation of vortices are hard to apply to real situations.
This prompted an engineer at the University of Colorado at Boulder to look at vortices afresh. While earning his doctorate at the California Institute of Technology in Pasadena in the 1990s, Kamran Mohseni was struck by a mystery surrounding a kind of vortex called the “vortex ring”.
A vortex ring forms when a very quick burst of fluid shoots out of an opening. As the fluid moves forwards, it spreads out and its front edges curl back. If the speed of the burst is fast enough, the curling fluid eventually curls all the way round, until it is travelling forwards again in the direction of the original burst (see Diagram). The result is a ring-shaped vortex that pinches off the stream of fluid coming out of the opening and moves off, carrying with it a huge amount of momentum. And of course, that means there is a reaction in the opposite direction, pushing on whatever produced the vortex.
Smoke rings are one example. To blow a smoke ring, smokers form their lips into an O, then quickly clench the back of their throat to blow out a fast-moving puff of smoke. Squid and jellyfish use the same trick when they squirt pulses of water out of their mouths to push themselves along. As the jet pushes into the surrounding water, its outer edges curl back and form the classic doughnut-shaped ring. The bigger the ring, the faster the sea creature goes shooting off in the opposite direction.
It sounds simple, but the act of forming a vortex ring has proved very difficult to model mathematically. Yet if scientists could understand exactly how vortex rings form, they could use that insight to devise more efficient propulsion, just like jellyfish and squid. And that’s what got Mohseni hooked.
In 1998, he attended a talk by vortex dynamics expert Mory Gharib, also at Caltech. Experimenters generate vortex rings in the lab by using a piston to push a column of one fluid into another. Gharib had noticed that piston chambers that were four times longer than they were wide always produced the biggest rings. This was a widely accepted rule, but Mohseni couldn’t find an explanation that really satisfied him.
To try to understand the puzzle, Mohseni focused on how the energy of the piston is converted into the energy of the fast-moving vortex at the end. He realised that vortex growth depends on the fluid joining the vortex at the same speed as the fluid in the part of the vortex it joins. So he built a computer simulation based on this idea, and began to experiment with different piston chamber designs. The results produced two ways to beat the 4:1 limit, making “optimal” vortex rings that would be bigger than ever before.
“What I suggested was that there are only two ways to do this – accelerate the piston during the formation of the jet, or increase the exit diameter of the cylinder as a function of time,” he says. Both methods work by tuning the speed of the emerging fluid to exactly the speed of the growing vortex. Accelerating the piston allows water coming out later to match the speed of the growing vortex. Increasing the diameter of the opening also helps, because it allows slow water to join the vortex further from its fast-rotating centre.
This also helps to explain the 4:1 ratio. If the speed of the piston and the size of the aperture are constant, then the maximum ring size is achieved when the ring pinches off just as its formation is complete. If the piston chamber emitting the burst is much longer than four times its width, the vortex grows too fast, and fluid near the back of the burst will be travelling too slowly to join it. If it is much smaller than four times its width, the vortex will form, but it will be very small.
When Mohseni took a job as assistant professor of aerospace engineering sciences at the University of Colorado in 2001, he began trying to turn these insights into new kinds of propulsion systems. Because Mohseni’s optimal vortices pull in plenty of fluid and move off with lots of momentum, they should provide much more propulsion for the same volume of water compared to ordinary vortex ring thrusters.
Mohseni’s first step was to build a thruster that tested the theory. He designed a small thruster with very few moving parts. On its inside, a flexible plastic diaphragm 2.5 centimetres across pulls back to suck water into a chamber, and then plunges forward to quickly push the water back out again. The diaphragm accelerates as it plunges forward, which makes a much larger vortex ring, massively increasing the overall thrust for the same amount of water.
The next step is to incorporate these into a vehicle. Today’s underwater vehicles generally follow one of two different designs: torpedo-shaped submarines that use rudders to change direction, and bulkier craft that steer with thrusters and propellers. The torpedo design is faster, but doesn’t offer as much manoeuvrability when it moves at low speeds. Bulkier designs can hover and turn with precision, but move only very slowly. Mohseni realised that he could combine the best features of both designs by incorporating optimal vortex ring thrusters unobtrusively into the hull of a bulky craft.
His group is now working to incorporate four thrusters, each squirting out rings about 50 times a second, into an underwater craft. The thrusters make for an elegant and efficient system, says Pell, who designs underwater vehicles for Neckton Research in Durham, North Carolina. “They’ve gotten the mechanism down to a little oscillator that produces controlled force, and uses little water to do it. If you increased the size of this device, you’d have a jellyfish.”
“The thrusters make for an elegant and efficient system. If you increased the size of this device, you’d have a jellyfish.”
William Devenport, professor of aerospace and ocean engineering at Virginia Tech in Blacksburg, spends most of his time developing ways to prevent vortices from forming in aircraft engines. He says Mohseni’s thrusters could also work well in air. “It’s a neat idea,” he says. “By drawing air into a cavity and blowing it out again, you could essentially make a jet out of nothing.” But Devenport thinks the design might not work as well on larger scales, where the rapid-fire puffing of the actuators could vibrate a craft and create a lot of noise.
One possible problem with using the vortex thrusters underwater is noise. “You wouldn’t want to make a lot of noise if the object you were inspecting was an undersea mine,” Pell warns. Mohseni agrees. “While we have not measured noise level for the current design, I could imagine that it is noisy,” Mohseni says. “But nothing worse than a propeller.” Using many smaller nozzles rather than one large one might solve the problem.
With further development, his ultra-manoeuvrable craft could dive beneath polar ice into nooks where other craft cannot go, carrying a payload of scientific instruments for polar studies. Kitted out with a camera, it could also be used in search-and-rescue missions and underwater archaeology, he says.
It could even go into truly uncharted territory. Shrink an underwater vehicle down to the size of a vitamin capsule, and you’ve got a vehicle that could navigate a very different frontier: the human body. Mohseni has filed a patent for a device that would use mini vortex ring thrusters to travel through the digestive tract, diagnosing and treating disease. With the help of Yang Chen, a doctor at the University of Colorado Health Sciences Center, he wants to incorporate a camera, sensors, and reservoirs for dispensing medicine. Though doctors can image most of the intestines with a probe called an endoscope, a remote-controlled capsule could offer a better view, and be more comfortable for the patient.
There is already one camera-toting “smart pill”, made by Given Imaging in Yoqneam, Israel, which has FDA approval to carry out endoscopies. Pushed along by the peristaltic gut muscles, the 2.6-centimetre-long pill lacks propulsion and simply goes on a one-way trip through the body. The patient swallows the pill with water and then goes about their day as normal, while from inside the pill a tiny camera complete with flash bulbs snaps colour photos at a rate of two frames per second. A wireless transmitter sends the photos to a digital receiver worn by the patient. Eight hours later, the patient returns the receiver to the hospital, where software converts the still photos into a video for doctors. The capsule makes for much safer and cheaper endoscopies because there’s no need to anaesthetise the patient, says Chen.
If a pill like this were fitted with vortex ring thrusters, doctors could watch the video live, and even hit rewind. “The capability that a pill doesn’t have – and that we can offer – is that if doctors are watching the video and they see something pass by like a site of internal bleeding, they can back up and take a look at it again. Or do a biopsy or deliver a drug to a specific location,” Mohseni says.
For now, he and Chen still need to solve the problem of making the navigation precise enough. They also worry that the on-board power system will have to be able to support not only the vortex thrusters, but instruments for imaging and treatment.
So far, Mohseni has a working model of a vortex thruster about the size of a penny. Rather than being piston operated, the diaphragm is pushed by an actuator that moves in response to an electric field. Chen hopes to have a stripped-down capsule ready for clinical testing in two to three years. So it may not be long before the power of the vortex can be unleashed inside your body.
Tornado gyros
WHILE giant vortices swirl in hurricanes and tornadoes, a very small vortex may have big uses in monitoring the Earth, according to physicist Richard Packard and his colleagues at the University of California at Berkeley.
There they stir liquid helium-3 inside a small doughnut-shaped container chilled to near absolute zero. At that temperature, helium is a superfluid, which means it is perfectly frictionless and does not flow like a normal liquid. If you spun a bucket of superfluid, the liquid would remain still while the container spun around it. So to spin their helium, the Berkeley physicists put a partition inside the container that acted as a stirrer. They also made pinholes in the partition, so some of the fluid trickled back against the flow (żěè¶ĚĘÓƵ, 5 September 1998, p 24).
What happens next relies on some mind-bending physics. Because a superfluid does not “want” to spin, it does whatever it has to do to make its average velocity equal to 0. So, since the superfluid in most of the container is forced round one way, the superfluid in the pinhole must move much faster in the opposite direction, so that the two velocities cancel each other out.
Here’s where vortices come in: when the container spins fast enough, the helium squirting through the pinholes twists into a tornado. It is similar to the vortex that forms when you pull the plug out of your bath, except that the vortex in your bath spins in the same direction as the water in the bath, whereas the superfluid vortex spins in the opposite direction to the fluid in the doughnut.
The superfluid vortex only forms if the speed of the fluid in the doughnut is above a critical velocity. And this is incredibly sensitive. Changes in the Earth’s rotation due to ocean currents, weather patterns, even the flow of molten rock in the core will make the rotating superfluid adjust, and so affect the critical velocity at which the vortex forms.
Packard and his colleagues used the vortex-formation velocity to measure the rotation of the Earth over one hour achieving an accuracy of 0.1 per cent. Researchers in Saclay, France, demonstrated measurements in similar devices. Earlier this year, Emile Hoskinson, a graduate student at Berkeley, found the vortex effect in helium-4, which becomes superfluid at a far higher temperature than helium-3, and so could be of more practical use.
Packard hopes in future superfluid gyros could be made accurate enough to increase the accuracy of global positioning systems. Commercial GPS offers 15-metre resolution, but millimetre-level resolution might be possible in future if receivers knew the Earth’s rotation with greater precision. A superfluid gyroscope could make that possible.
The superfluid gyro could also improve earthquake detection. Presently seismometers detect side-to-side and to-and-fro motion of the Earth, but superfluid gyros might make it possible to detect rotational movements as well.