This high-speed video of a bullet fired into a water balloon shows how dramatically drag forces can affect an object. In general, drag is proportional to fluid density times an object’s velocity squared. This means that changes in velocity cause even larger changes in drag force. In this case, though, it’s not the bullet’s velocity that is its undoing. When the bullet penetrates the balloon, it transitions from moving through air to moving through water, which is 1000 times more dense. In an instant, the bullet’s drag increases by three orders of magnitude. The response is immediate: the bullet slows down so quickly that it lacks the energy to pierce the far side of the balloon. This is not the only neat fluid dynamics in the video, though. When the bullet enters the balloon, it drags air in its wake, creating an air-filled cavity in the balloon. The cavity seals near the entry point and quickly breaks up into smaller bubbles. Meanwhile, a unstablejet of water streams out of the balloon through the bullet hole, driven by hydrodynamic pressure and the constriction of the balloon. (Video credit: Keyence)
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 size. The 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)
Complicated shock wave patterns envelope vehicles traveling at supersonic and hypersonic speeds. A shock wave is essentially a very tiny region–only a few mean free path lengths wide–over which flow conditions, including density, pressure, velocity, and temperature, change drastically. The image above shows a model of the Space Shuttle at a re-entry-like, high angle of attack at around Mach 20 in one of NASA Langley’s historic helium tunnels. The eerie glow outlining the shock structures around the model is a result of electron-beam fluorescence. In this flow visualization technique, a beam of high-energy electrons is swept over the model, causing the gas molecules to fluoresce according to temperature. (Photo credit: NASA Langley)
Male emperor penguins have the unenviable task of incubating their eggs in temperatures as cold as -50 deg Celsius and winds of up to 200 km/h. To stay warm, the penguins form huddles of up to thousands of individuals. Observations in the wild show that these huddles move in a stop-and-go fashion, with changes propagating through the penguins like waves. Researchers adapted a model used for heavy traffic flow to describe the penguins’ motion. They found that motions like those found in observed penguin huddles could be initiated by slight movements of any penguin in the model huddle, regardless of its position; in other words, the huddle has no leader. They also found that the wave that travels through the penguins can align the huddle to uniform density or help two huddles merge. To learn more, check out the researchers’ video or their paper. (Video credit: D. Zitterbart et al./New Scientist; via J. Ouellette)
A bullet passes through a soap bubble in the schlieren photo above. The schlieren optical technique is sensitive to changes in the refractive index and, since a fluid’s refractive index changes with density, permits the visualization of shock waves. A strong curved bow shock is visible in front of the bullet as well as weaker lines marking additional shocks waves around the bullet. Impressively, the bullet’s passage is so fast (and the photo’s timing so perfect) that there are no imperfections or signs of bursting in the soap bubble. The photo’s caption suggests that the bubble may be filled with multiple gases. If they are unmixed and of differing densities, this may be the source of the speckling and plume-like structures inside the bubble. Incidentally, if anyone out there has high-speed schlieren video of a bullet passing through a soap bubble, I would love to see it. (Photo credit: H. Edgerton and K. Vandiver)
Fluid dynamics appear at all kinds of scales. The animation above shows two comets, Encke and ISON, on their recent approach toward the sun. The darker wisps emanating from the right side of the image are part of the solar wind, a plasma stream continuously emitted by the sun’s upper atmosphere. Although the solar wind is very rarefied by terrestrial standards, its density is sufficient to whip the comets’ tails of gas and dust from side-to-side. Scientists use images like these to learn more about the structure of the solar wind based on its interaction with the comets. For more great images of ISON’s journey around the sun, check out NASA Goddard. (Image credit: K. Battams/NASA/STEREO/CIOC; submitted by John C)
The Richtmyer-Meshkov instability occurs when two fluids of differing density are hit by a shock wave. The animation above shows a cylinder of denser gas (white) in still air (black) before being hit with a Mach 1.2 shock wave. The cylinder is quickly accelerated and flattened, with either end spinning up to form the counter-rotating vortices that dominate the instability. As the vortices spin, the fluids along the interface shear against one another, and new, secondary instabilities, like the wave-like Kelvin-Helmholtz instability, form along the edges. The two gases mix quickly. This instability is of especial interest for the application of inertial confinement fusion. During implosion, the shell material surrounding the fuel layer is shock-accelerated; since mixing of the shell and fuel is undesirable, researchers are interested in understanding how to control and prevent the instability. (Image credit: S. Shankar et al.)
The APS Division of Fluid Dynamics conference begins this Sunday in Pittsburgh. I’ll be giving a talk about FYFDSunday evening at 5:37pm in Rm 306/307. I hope to see some of you there!
Differences in surface tension cause fluid motion through the Marangoni effect. Because an area with higher surface tension pulls more strongly on nearby liquid than an area of low surface tension, fluid will flow toward areas of higher surface tension. Here surfactants, shown in white, are constantly injected onto a layer of water dyed blue. You can also see the flow in motion in this video. Outside of the central source flow, the pattern features lots of 2D mushroom-like shapes reminiscent of Rayleigh-Taylor instabilities. But these shapes are driven by variations in surface tension rather than unstable density variations. For more, check out the original paper or learn about other examples of Marangoni effect. (Photo credit: M. Roché et al.)
When droplets collide, there are three basic outcomes: they bounce off one another; they coalesce into one big drop; or they coalesce and then separate. Which outcome we observe depends on the relative importance of the droplets’ inertia compared to their surface tension. This is expressed through the dimensionless Weber number, made up of density, velocity, droplet diameter, and surface tension. For a low Weber number droplet, surface tension is still significant, so colliding droplets bounce off one another. At a moderate Weber number, the droplets coalesce. But when the fluid inertia is too high, as in the high Weber number example, the drops will coalesce but still have too much momentum and ultimately separate. (Video credit: G. Oldenziel)
