Fuck Yeah Fluid Dynamics

Celebrating the physics of all that flows. Ask a question, submit a post idea or send an email. You can also follow FYFD on Twitter and Google+. FYFD is written by Nicole Sharp, PhD.

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Posts tagged "vortex shedding"

Von Karman vortex streets are a pattern of alternating vortices shed in the wake of a bluff body. They’re commonly associated with cylinders and can be demonstrated in simulation and in the lab. (They even show up in supersonic flows.) But they also show up in nature quite frequently, like in this cloud pattern off Central America. Such wakes often occur downstream of rocky, volcanic islands that rise above the smooth ocean surface and disrupt the atmosphere’s boundary layer. The same phenomenon is responsible for the “singing” of electrical lines on a windy day, and I’ve even heard it make the spokes on my bicycle wheel sing in a crosswind. (Photo credit: R. Mastracchio; via @BadAstronomer; submitted by jshoer)

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)

Vortex shedding frequently happens in the wakes of non-streamlined bodies as a result of flow around the obstacle. Newton’s third law states that forces come in equal and opposite pairs, meaning that the vortex shedding behind an obstacle is accompanied by a force on the obstacle. For a fixed cylinder, this is not always apparent, but for a pendulum, like the ones demonstrated in this video, this vortex-induced vibration causes significant motion. This same effect can make traffic lights and industrial chimneys sway. You’ve likely experienced it yourself as well, if while swimming you’ve ever spread your fingers underwater and spun in place. Try it sometime with your arm out and you’ll feel the vortices make your arm vibrate up and down as you spin.  (Video credit: Harvard Natural Sciences Lecture Demonstrations)

Today’s post is largely brought to you by the fact that I have been sick the past four days and my fiance and I have been bingeing on Star Trek Voyager. At some point, we began wondering about the sequence from 0:30-0:49 in which Voyager flies through a nebula and leaves a wake of von Karman vortices. Would a starship really leave that kind of wake in a nebula?

My first question was whether the nebula could be treated as a continuous fluid instead of a collection of particles. This is part of the continuum assumption that allows physicists to treat fluid properties like density, temperature, and velocity as well-defined quantities at all points. The continuum assumption is acceptable in flows where the Knudsen number is small. The Knudsen number is the ratio of the mean free path length to a characteristic flow length, in this case, Voyager's sizeThe mean free path length is the average distance a particle travels before colliding with another particle. Nebulae are much less dense than our atmosphere, so the mean free path length is larger  (~ 2 cm by my calculation) but still much smaller than Voyager's length of 344 m. So it is reasonable to treat the nebula as a fluid.

As long as the nebula is acting like a fluid, it’s not unreasonable to see alternating vortices shed from Voyager. But are the vortices we see realistic relative to Voyager's size and speed? Physicists use the dimensionless Strouhal number to describe oscillatory flows and vortex shedding. It’s a ratio of the vortex shedding frequency times the characteristic length to the flow’s velocity. We already know Voyager's size, so we just need an estimate of its velocity and the number of vortices shed per second. I visually estimated these as 500 m/s and 2.5 vortices/second, respectively. That gives a Strouhal number of 0.28, very close to the value of 0.2 typically measured in the wake of a cylinder, the classical case for a von Karman vortex street.

So far Voyager's wake is looking quite reasonable indeed. But what about its speed relative to the nebula's speed of sound? If Voyager is moving faster than the local speed of sound, we might still see vortex shedding in the wake, but there would also be a bow shock off the ship’s leading edge. To answer this question, we need to know Voyager's Mach number, its speed relative to the local speed of sound. After some digging through papers on nebulae, I found an equation to estimate speed of sound in a nebula (Eq 9 of Jin and Sui 2010) using the specific gas constant and temperature. Because nebulae are primarily composed of hydrogen, I approximated the nebula’s gas constant with hydrogen’s value and chose a representative temperature of 500 K (also based on Jin and Sui 2010). This gave a local speed of sound of 940 m/s, and set Voyager's Mach number at 0.53, inside the subsonic range and well away from any shock wave formation.

Of course, these are all rough estimates and back-of-the-envelope fluid dynamics calculations, but my end conclusion is that Voyager's vortex shedding wake through the nebula is realistic after all! (Video credit: Paramount; topic also requested by heuste11)

Flow over blunt bodies produces a series of alternating vortices that are shed behind an object. The image above shows the turbulent wake of a cylinder, with flow from right to left. Red and blue dyes are used to visualize the flow. This flow structure is known as a von Karman vortex street, named for aerodynamicist Theodore von Karman. The meander of the wake is caused by the shed vortices, each of which has a rotational sense opposite its predecessor. The rapid mixing of the two dyes is a result of the flow’s turbulence. In low Reynolds number laminar cases of this flow the structure of individual vortices is more visible. Similar flow structures are seen behind islands and in the wakes of flapping objects. (Photo credit: K. Manhart et al.)

Most objects are not particularly aerodynamic or streamlined. When air flows over such bluff bodies, they can shed regular vortices from one side and then the other. This periodic shedding creates a von Karman vortex street, like this one stretching out from Isla Socorro off western Mexico. From the wind’s perspective, the volcanic island forms a blunt disruption to the otherwise smooth ocean. This vortex shedding is seen at smaller scales, as well, in the wind tunnel, in soap films, and in water tunnels. If you’ve ever been outside on a windy day and heard the electrical lines “singing” in the wind, that’s the same phenomena, too. With the right crosswind, radial bicycle spokes will buzz for the same reason as well!  (Photo credit: MODIS/NASA Earth Observatory)

Originally posted: 14 Jan 2011 This gorgeous butterfly-like double spiral roll takes place on a horizontal soap film. The foil (seen top center) inserted in the film flaps back and forth. Each time the foil changes direction a vortex forms at the tip and gets advected away. The vortices stretch and distort in the roll, but if you look at the photograph closely, you’ll see the tiny shed vortices persisting throughout the roll structure. The bright colors that make this flow visible are due to interference patterns related to the local thickness of the film. (Photo credit: T. Schnipper et al.)

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Flow around an airfoil with a leading-edge slat is visualized above. At this Reynolds number, alternating periodic vortices are shed in its wake. Understanding how multi-element airfoils and control surfaces affect local flow is important in controlling aircraft aerodynamics. When multiple instabilities interact—like those in the wing’s boundary layer interacting with the wake’s—it can generate disturbances that are problematic in flight. Being able to predict and avoid such behavior is important for safe aircraft. (Photo credit: S. Makiya et al.)

This gorgeous visualization shows the flow behind a flapping foil. Flow in the water tunnel is from right to left, with dye introduced to show streamlines. A flapping foil is a good base model for most flapping flight as well as finned swimming - anything that oscillates to create thrust. As the foil flaps, vorticity is generated and shed along the trailing edge, creating a regularly patterned wake of trailing vortices. (Video credit: R. Godoy-Diana)

Soap films are a handy way to create nearly two-dimensional flow fields. Previously we’ve seen them used to show wake structures of pitching foils, flapping flags, and multiple bodies. In this video, we see the dynamics of a pendulum in a soap film. Initially its length is quite long, and the ring end of the pendulum bobs side-to-side in a figure-8 motion. There are two rotational effects here: one is the standard oscillation of a pendulum about its pivot, the other is the rotation of the pendulum’s ring about its attachment point. Interestingly, they have the same frequency. The major destabilizing force for the pendulum is the periodic shedding of vortices we see off the ring. By shortening the pendulum length, the pendulum’s behavior shifts; first it loses the stationary node in its string. Eventually, the string becomes so short that the pendulum no longer oscillates. (Video credit: M. Bandi et al.)