Turbulent flows feature swirling eddies over a range of sizes — the larger the size range, the higher the Reynolds number. In this satellite image, sediment highlights these eddies in shades of turquoise, showing off the complexity of the flows created where rivers, ocean, and tides meet. The eddies we see here stretch from kilometers in width down to a handful of meters, but the flow’s turbulence persists down to millimeter-scales before viscosity damps it out. (Image credit: L. Dauphin; via NASA Earth Observatory)
Tag: Reynolds number
An Introduction to the Reynolds Number
For those who’d like an overview of the mathematics involved in fluid dynamics, Numberphile has a lovely introduction, given by our friend Tom Crawford. The governing equations in fluid dynamics, the Navier-Stokes equations, are quite complicated, but that’s just been inspiration for scientists and mathematicians to come up with clever ways to simplify them. And, ultimately, that’s what the Reynolds number is — a way to help us judge which forces, and therefore which mathematical terms, are the most important in a given problem. (Video credit: Numberphile; submitted by COMPLETE)
Pouring a Liquid Mirror
In this video, the Slow Mo Guys play with liquid gallium, giving us a chance to see how molten metals behave (outside of, say, the Terminator movies). Near its melting point, gallium is about six times denser than water, with a viscosity three times higher, and a surface tension about ten times greater. So how do those properties affect its behavior?
You may be surprised that when watching the gallium vibrate on a speaker or get poured into a pan, it doesn’t look all that different from water. Yes, it’s highly reflective, but, on the whole it doesn’t look radically different from a distance. We can use the Reynolds number to quantify what’s going on here. It’s a dimensionless number that compares the fluid’s inertial force to the viscous force. Imagine we have two versions of an experiment, one where we pour gallium at a given speed and one pouring at the same volume and speed but with water. If we compared the Reynolds numbers of the water and the gallium, they only differ by a factor of two. Overall, that’s not very much. That’s why the two pours look similar.
The story is different, though, if we look at individual drops of gallium and water, like when the first few drops of our pour hit the surface. Check out the gallium drops below. They’re conical on either end! This looks very different from what we expect with water droplets. You might think that’s because the metal is more viscous, but if we compare a water drop with a gallium drop of the same characteristic size and impact speed, we find a different story. For this, we’ll use the Ohnesorge number, which compares the viscous forces to a combination of inertia and surface tension. In this case, we find that the gallium drop’s Ohnesorge number is almost an order of magnitude smaller than the water droplet’s. That means that viscosity isn’t a major factor for our gallium drop. Both surface tension and inertia are more important.
But if the surface tension is so high, then why aren’t the droplets spherical? Mostly because they don’t have time to form spheres before they hit. Their shape suggests that they’ve only just broken into droplets, which makes sense if the pour is fast and the surface tension is strong. (Video and image credit: The Slow Mo Guys)
Why Does This Kite Look So Real?
A recent viral video features mesmerizing footage of a giant octopus kite flown at a kite festival in Singapore earlier this month. The kite’s arms twist and wave lazily in the breeze. Watching the video, I was struck by how realistic the kite’s motion looks. It really looks like an octopus is just cruising there in mid-air. And that resemblance might not be accidental.
In fluid dynamics, scientists often use a concept called dynamic similitude to test the physics of a scale model instead of the full-size original. The simplest version of this uses the Reynolds number to compare the model and the original. The Reynolds number is a dimensionless number that depends on the object’s size, the flow’s speed, and the density and viscosity of the fluid. If you match the scale model’s Reynolds number to the original’s Reynolds number, then the physics will be the same – even if you changed the fluid or the size of the object.
Returning to our kite, one thing the footage doesn’t entirely convey is just how enormous this kite really is. The Straits Times reports the kite is about the length of five buses and requires six people to get aloft. But the kite’s size helps compensate for the fact that it’s flying in air instead of swimming through viscous water like a real octopus. Although I’m left estimating the kite’s size and the wind’s speed, my quick calculations put the Reynolds numbers for the kite and the octopus on the order of 10,000. So, strange as it seems, this giant kite really is acting like a swimming octopus!
The Challenges of Micro Air Vehicles
Interest in micro-aerial vehicles (MAVs) has proliferated in the last decade. But making these aircraft fly is more complicated than simply shrinking airplane designs. At smaller sizes and lower speeds, an airplane’s Reynolds number is smaller, too, and it behaves aerodynamically differently. The photo above shows the upper surface of a low Reynolds number airfoil that’s been treated with oil for flow visualization. The flow in the photo is from left to right. On the left side, the air has flowed in a smooth and laminar fashion over the first 35% of the wing, as seen from the long streaks of oil. In the middle, though, the oil is speckled, which indicates that air hasn’t been flowing over it–the flow has separated from the surface, leaving a bubble of slowly recirculating air next to the airfoil. Further to the right, about 65% of the way down the wing, the flow has reattached to the airfoil, driving the oil to either side and creating the dark line seen in the image. Such flow separation and reattachment is common for airfoils at these scales, and the loss of lift (and of control) this sudden change can cause is a major challenge for MAV designers. (Image credit: M. Selig et al.)
Cylinder Wakes
A simple cylinder in a steady flow creates a beautiful wake pattern known as a von Karman vortex street. The image above shows several examples of this pattern. Flow is from bottom to top, and the Reynolds number is increasing from left to right. In the experiment, this increasing Reynolds number corresponds to increasing the flow velocity because the cylinder size, fluid, and temperature were all fixed. As the Reynolds number first increases, the cylinder begins to shed vortices. The vortices alternate the side of the cylinder from which they are shed as well as alternating in their sense of rotation (clockwise or counterclockwise). Further increasing the Reynolds number increases the complexity of the wake, with more and more vortices being shed. The vortex street is a beautiful example of how fluid behavior is similar across a range of scales from the laboratory to our planet’s atmosphere. (Image credit: Z. Trávníček et. al)
The Reynolds Experiment
One of the most famous and enduring of all fluid dynamics experiments is Osborne Reynolds’ pipe flow experiment, first published in 1883 and recreated in the video above. At the time, it was understood that flows could be laminar or turbulent, though Reynolds’ terminology of direct or sinuous is somewhat more poetic:
Again, the internal motion of water assumes one or other of two broadly distinguishable forms-either the elements of the fluid follow one another along lines of motion which lead in the most direct manner to their destination, or they eddy about in sinuous paths the most indirect possible. #
There had, however, been no direct evidence of these eddies in a pipe. Reynolds built an apparatus that allowed him to control the velocity of flow through a clear pipe and simultaneously introduce a line of dye into the flow. He carefully varied the velocity and temperature (and thus viscosity) in his apparatus and not only documented both laminar and turbulent flow but found that the transition from one to another could be described by a dimensionless number he derived from the Navier-Stokes equation. This number was dependent on the fluid’s velocity and kinematic viscosity as well as the diameter of the pipe. This was the birth of the Reynolds number, one of the most important parameters in all of fluid dynamics. (Video credit: S. dos Santos; research credit: O. Reynolds)
The Reynolds Number Illustrated
The dimensionless Reynolds number is a key concept in fluid dynamics, allowing scientists to distinguish regimes of flow between differing geometries and even different fluids. This video gives a great primer on the subject by examining the physics of swimming for a sperm versus a sperm whale. The Reynolds number is essentially a ratio between inertial forces (driven by velocity and size) and viscous forces, and its value can indicate how important different effects are. Sperm and other microbes live at very small Reynolds numbers, meaning that viscosity dominates as the force they must overcome to move. For more on the low Reynolds number world, check out how brine shrimp swim and what happens if a microbe tries to flap its tail. (Hint: it goes nowhere, and this is why.) (Video credit: A. Bhatia/TED Ed; via Jennifer Ouellette)
Ig Nobel Fluids: Swimming in Syrup
Does a person swim faster in water or syrup? One expects the more viscous syrup would offer a swimmer greater resistance, but, at the same time, it could also provide more to push against. Gettelfinger and Cussler put this to a test experimentally with competitive and recreational swimmers in a pool of water and in one with a fluid measuring roughly twice the viscosity of water. Their results showed no significant change in swimming speed. When you consider that human swimming is highly turbulent, however, the result makes sense. In fluid dynamics, the dimensionless Reynolds number represents a ratio between inertial forces and viscous forces in a flow. The researchers estimate a Reynolds number of a typical human in water at 600,000, meaning that inertial effects far outweigh viscous effects. In this case, doubling the viscosity only reduces the Reynolds number by half, leaving it still well inside the turbulent range. Thus, swimming in syrup has little effect on humans. The Mythbusters also tackled this problem, with similar conclusions. This is a continuation of a series on fluids-related Ig Nobel Prizes. (Photo credit: Mythbusters/Discovery Channel; research credit: B. Gettelfinger and E. L. Cussler, winners of the 2005 Ig Nobel Prize in Chemistry)
Watching the Boundary Layer Go By
In experiments, it can be difficult to track individual fluid structures as they flow downstream. Here researchers capture this spatial development by towing a 5-meter flat plate past a stationary camera while visualizing the boundary layer – the area close to the plate. The result is that we see turbulent eddies evolving as they advect downstream. Despite the complicated and seemingly chaotic flow field, the eye is able to pick out patterns and structure, like the merging of vortices that lifts eddies up into turbulent bulges and the entrainment of freestream fluid into the boundary layer as the eddies turn over or collapse. It is also a great demonstration of how the Reynolds number relates to the separation of scales in a turbulent flow. Notice how much richer the variety of length-scale is for the higher Reynolds number case and how thoroughly this mixes the boundary layer. (Video credit: J. H. Lee et al.)
