In a recent video, Warped Perception filmed a model rocket engine firing underwater. Firstly, it’s no surprise that the engine would still operate underwater (after its wax waterproofing). The solid propellant inside the engine is a mixture of fuel and oxidizer, so it has all the oxygen it needs. Fluid dynamically speaking, though, this high-speed footage is just gorgeous.
Ignition starts at about 3:22 with some cavitation as the exhaust gases start flowing. Notice how that initial bubble dimples the surface when it rises (3:48). At the same time, the expanding exhaust on the right side of the tank is forcing the water level higher on that side, triggering an overflow starting at about 3:55. At this point, the splashes start to obscure the engine somewhat, but that’s okay. Watch that sheet of liquid; it develops a thicker rim edge and starts forming ligaments around 4:10. Thanks to surface tension and the Plateau-Rayleigh instability, those ligaments start breaking into droplets (4:20). A couple seconds later, holes form in the liquid sheet, triggering a larger breakdown. By 4:45, you can see smoke-filled bubbles getting swept along by the splash, and larger holes are nucleating in that sheet.
The second set of fireworks comes around 5:42, when the parachute ejection charge triggers. That second explosive triggers a big cavitation bubble and shock wave that utterly destroys the tank. If you look closely, you can see the cavitation bubble collapse and rebound as the pressure tries to adjust, but by that point, the tank is already falling. Really spectacular stuff! (Video and image credit: Warped Perception)
In 2013, a meteor about 20-meters in diameter broke up over Chelyabinsk, Russia in a dramatic display that damaged buildings within 100 km and injured more than 1200 people. To better understand the threat presented by such objects, NASA has been conducting 3D, hypersonicsimulations like the one shown here. The meteor material is shown in gray and black. Brighter colors like red and yellow indicate the hot, high-pressure shock wave caused when the meteor slams into the atmosphere. Aerodynamic effects quickly erode the meteor, ripping it into pieces that disperse energy explosively in the atmosphere. While you might think the meteor breaking up is good for us, it’s actually the blast waves from its break-up that cause the most damage. (Image and video credit: NASA, source; via Gizmodo)
Cavitation happens when the local pressure in a liquid drops below its vapor pressure. A low-pressure bubble forms, typically very briefly, when this occurs. These bubbles are spherical unless they form near a surface. In that case, the bubbles take on a flatter, oblong shape. As they collapse, the bubbles form a jet, like the one seen inside the bubble above. The jet extends through the bubble and stretches into a funnel shaped protrusion on the bubble’s far side. Eventually, the whole shape becomes unstable and breaks into many smaller bubbles. Shock waves can be generated in the collapse, too; often the jet generates at least two in addition to the ones created when the bubble reaches its minimum size. This is part of why cavitation can be so destructive near a surface. (Image credit: L. Crum)
In the latest Veritasium video, Derek demonstrates how to see gas motions that are normally invisible using a schlieren photography set-up. Schlieren techniques have been important in fluid dynamics for well over a century, and Derek’s set-up is one of the two most common ways to set up the technique. (The other method uses two collimating mirrors instead of a single spherical or parabolic one.) As explained in the video, the schlieren optical set-up is sensitive to small changes in the refractive index, making density changes or differences in a gas visible. This makes it possible to distinguish gases of different temperatures or compositions and even lets you see shock waves in supersonic flows. (Video and image credit: Veritasium; submitted by Paul)
Dropping a partially-filled test tube of water against a table makes the meniscus at the air-water interface invert into a jet of liquid. In some cases, the impact is strong enough to generate splashing crowns of water around the base of the jet. These crowns come in two forms – one with many splashes layered upon one another and the other with only a few splashes and a faster jet.
The many-layered splash crowns come from the pressure wave that reflects back and forth from the bottom of the tube to the surface and back. This pressure wave moves at the speed of sound and vibrates the water surface, creating the many splashes. The same reflected pressure wave occurs in the second type of splash crown, but it gets disrupted by cavitation bubbles that form in the water (visible in the lower left image). Instead the splash crowns form from the shock waves generated when the cavitation bubbles collapse. (Image credits: A. Kiyama et al.)
The pop of an overfilled balloon is enough to make anyone jump, but you’ve probably never seen it like this. The photo above uses an optical technique known as schlieren photography that reveals changes in density of a transparent gas like air. The shredded rubber of the balloon is still visible in black, and around the balloon there’s an expanding spherical shock wave. It’s the sudden release of energy when the balloon ruptures and the gas inside begins to expand that causes the shock wave. Notice, though, that the gas from the balloon is still clearly visible and balloon-shaped–much like a water balloon that’s just popped. From that clear delineation, I would say that this balloon was filled with a different gas than air–otherwise the density shouldn’t be different enough to make the interior gas distinguishable. (Image credit: G. Settles)
Cavitation bubbles live a short and violent life. It begins when a low-pressure void forms in a fluid–for example, when a liquid is accelerated so that the pressure drops below the vapor pressure, which can happen at the tips of a boat’s propeller or when striking a bottle. The bubbles that form expand and then collapse rapidly as the higher pressure of the liquid surrounding them squeezes them down. That collapse of the bubble is so violent that it heats the fluid inside the bubble to temperatures hotter than the surface of the sun, generating both a flash of light and a shock wave. It’s these shock waves that cause much of the damage associated with cavitation in engineering, but they can be used for good as well. Shock wave lithotripsy uses cavitation-induced shock waves to break down kidney stones. (Image credit: O. Supponen et al., source)
During a supernova, shock waves moving outward push denser material into less dense plasma and gas. This causes what is known as a Richtmyer–Meshkovinstability, where the interface between the two fluids first becomes wavy and then develops finger-like intrusions. Those too break down, as seen in the simulation above, causing large-scale mixing between the different fluids.
Here on Earth this instability shows up in the process of inertial confinement fusion. In that case, the outer shell material is denser than the fuel core and the instability is triggered during the implosion process. As the fusion material is suddenly compressed, waviness and mixing occurs along the interface between the shell and the fuel. That’s undesirable because it reduces the efficiency of the fusion reaction. (Image credit: E. Evangelista et al.)
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)
Happy 50th anniversary, Star Trek! Some of my earliest memories of TV are of watching TNG with my parents. Star Trek taught me that curiosity and scientific inquiry were vital and valuable, and that anyone could grow up to be a scientist, engineer, and leader. Thank you for such an inspiring and hopeful vision for humanity’s future!
And, seriously, those von Karman vortices are awesome.
In some countries, there are still people using dynamite to catch fish. This practice is incredibly destructive, not just to adult fish but to the entire marine ecosystem. A blast wave traveling through air loses some its energy to the compression of the gas. Water, on the other hand, is incompressible, so the blast wave’s energy just keeps going, expanding its destructive radius. Many fish contain swim bladders, gas-filled organs the fish use to regulate their depth. When a shock wave passes through the fish, the gas in the swim bladder will expand and contract violently, much like the balloons shown underwater in the animation below. This typically ruptures the swim bladder and surrounding tissues.
Fish without swim bladders will often hemorrhage after being struck by a blast wave. The sudden changes in pressure create bubbles in the dissolved gases collected in their gills. Those bubbles tear apart the fish’s blood vessels.
Blasting is effective but entirely indiscriminate. It kills adults and juveniles of all species, not just the ones a fisherman can sell. Simultaneously, it destroys the slow-growing coral reefs that are key habitats for these populations. It’s an incredibly short-sighted practice that guarantees there will be no fish to catch in years to come. (Video credit: National Geographic; image credit: M. Rober, source; research credit: K. Dunlap, pdf)
