The forces on an object in flight come from the distribution of pressure on the surface. To alter an object’s trajectory, one has to shift the pressure distribution. On subsonic and transonic aircraft, this is usually done with control surfaces like an aileron, but at supersonic speeds this can require a lot of force. The schlieren images above show an alternative approach in which a plasma actuator near the nosetip generates asymmetric forces on the cone. The actuator discharges plasma at t=0, and flow is from left to right. In the first image, the bubble of plasma is expanding on the upper side of the cone, disrupting the nearby shock wave. Over time, it moves downstream, carrying its disruption with it. The asymmetric effect of the plasma causes uneven pressures on either side of the cone that can be triggered in order to turn it in flight. (Photo credit: P. Gnemmi and C. Rey)
Category: Research
Measuring Wind Turbines with Snowfall
One of the challenges in large-scale wind energy is that operating wind turbines do not behave exactly as predicted by simulation or wind tunnel experiments. To determine where our models and small-scale experiments are lacking, it’s useful to make measurements using a full-scale working turbine, but making quantitative measurements in such a large-scale, uncontrolled environment is very difficult. Here researchers have used natural snowfall as seeding particles for flow visualization. The regular gaps in the flow are vortices shed from the tip of the passing turbine blades. With a searchlight illuminating a 36 m x 36 m slice of the flow behind a wind turbine, the engineers performed particle image velocimetry, obtaining velocity measurements in that region that could then be correlated to the wind turbine’s power output. Such in situ measurements will help researchers improve wind turbine performance. (Video credit: J. Hong et al.)
Air Pressure Affects Splashes
When a drop falls on a dry surface, our intuition tells us it will splash, breaking up into many smaller droplets. Yet this is not always the case. The splashing of a droplet depends on many factors, including surface roughness, viscosity, drop size, and–strangely enough–air pressure. It turns out there is a threshold air pressure below which splashing is suppressed. Instead, a drop will spread and flatten without breaking up, as shown in the video above. For contrast, here is the same fluid splashing at atmospheric pressure. This splash suppression at low pressures is observed for both low and high viscosity fluids. Although the mechanism by which gases affect splashing is still under investigation, measurements show that no significant air layer exists under the spreading droplet except near the very edges. This suggests that the splash mechanism depends on how the spreading liquid encroaches on the surrounding gas. (Video credit: S. Nagel et al.; research credit: M. Driscoll et al.)
Hydrodynamic Quantum Analogs
Over the past few years, researchers have been exploring the dynamics of droplets bouncing on a vibrating fluid. These systems display many behaviors associated with quantum mechanics, including wave-particle duality, single-slit and double-slit diffraction, and tunneling. A new paper examines the system mathematically, showing that the droplets obey many of the same mathematics as quantum systems. In fact, the droplet-wave system behaves as a macroscopic analog of 2D quantum behaviors. The implications are intriguing, especially for teaching. Now students of quantum mechanics can experiment with a simple apparatus to understand some of the non-intuitive aspects of quantum behavior. For more, see the paper on arxiv. (Image credit: D. Harris and J. Bush; research credit: R. Brady and R. Anderson)
Simulating Early Planetary Impacts
Early in our geological history, Earth was a hellish landscape of molten oceans into which metallic impactors would sometimes collide. Geophysicists have been curious how the impactors behaved after collision: did they maintain their cohesion, or did they break up into a cloud of droplets? Here the UCLA Spinlab simulates this early planetary formation by dropping liquid gallium through a tank of viscous fluid. As the video shows, the impactor’s behavior varies strongly with size. Smaller impactors stick together as a single diapir, but, as the initial size increases, the diapir becomes unstable, eventually breaking down into a cascade of droplets – a metallic rain through an ocean of magma. (Video credit: J. Wacheul et al./UCLA Spinlab; submitted by J. Aurnou)
The Physics of a Flying-V
New research using free-flying northern bald ibises shows that during group flights the birds’ positioning and flapping maximize aerodynamic efficiency. In flight, a bird’s wings generate wingtip vortices, just as a fixed-wing aircraft does. These vortices stretch in the bird’s wake, creating upwash in some regions and downwash in others as the bird flaps. According to theory, to maximize efficiency a trailing bird should exploit upwash and avoid downwash by flying at a 45-degree angle to its leading neighbor and matching its flapping frequency. The researchers found that, on average, this was the formation and timing the flock assumed. In situations where the birds were flying one behind the next in a straight line, the birds tended to offset their flapping by half a cycle relative to the bird ahead of them–another efficient configuration according to theory. Researchers don’t yet know how the birds track and match their neighbors; perhaps, like cyclists in a peloton, they learn by experience how to position themselves for efficiency. For more information, see the researchers’ video and paper. (Photo credit: M. Unsold; research credit: S. Portugal; via Ars Technica; submitted by M. Piedallu van Wyk)
Solution to a Millennium Prize Problem?
Reports emerged this weekend that Kazakh mathematician Mukhtarbay Otelbaev has published a proposed solution to the Navier-Stokes existence and smoothness problem, one of the seven Millennium Prize problems offered by the Clay Mathematics Institute. Today I want to explain some of the background of this problem, what is known about Otelbaev’s proposed solution, and what a solution would mean for fluid dynamics.
The Navier Stokes Equation
The Navier-Stokes equation is one of the governing equations of fluid dynamics and is an expression of conservation of momentum in a fluid. With the exception of a few very specific and simplified cases, there is no known general solution to equation. Instead, the equation, or a simplified model, is solved numerically using supercomputers as part of direct numerical simulation (DNS) or other forms of computational fluid dynamics (CFD). These methods allow scientists and engineers to solve the equations of fluid motion for practical problems from flow through a pipe to flow around a re-entering spacecraft.
Existence and Smoothness
Although the Navier-Stokes equation has been known for more than 150 years and can be solved numerically for many situations, some basic mathematical aspects of the equation have not yet been proven. For example, no one has proven that a general solution always exists in three-dimensions and that the energy of such a solution is bounded at all points. Colloquially, this is known as the Navier-Stokes existence and smoothness problem. The Clay Mathematics Institute has a very specific problem statement (PDF) asking for a proof (or counter-proof) of the existence and smoothness of the Navier-Stokes equation for an incompressible fluid in three-dimensions. Otelbaev contends that he has provided such a proof.
Otelbaev’s Proposed Solution
Mukhtarbay Otelbaev is an experienced mathematician with numerous papers addressing related mathematical problems. His latest paper, entitled “Existence of a strong solution to the Navier-Stokes equation,” is freely available online (PDF, in Russian, with an English abstract at the end). There is an ongoing project to translate the paper into English, and mathematicians are already evaluating the validity of this proposed solution. From what I can gather of the paper, it specifically address the Millennium Prize problem and presents Otelbaev’s proposed solution for the existence and smoothness of an incompressible fluid in three dimensions with periodic boundary conditions.
What It Means
As with any announcement of a major technical breakthrough, skepticism is warranted while experts evaluate the proposal. If the mathematical community upholds the validity of Otelbaev’s proof, he may be offered the Millennium Prize and other honors. More importantly, his solution could lead to a better understanding of the nature of the equation and the flows it describes. It is not, in itself, a general solution to the Navier-Stokes equation, but it may be a stepping stone in the path toward one. In the meantime, scientists and engineers will continue to rely on a combination of theory, experiment, and computation to progress our understanding of fluid dynamics.
For More
The story of Otelbaev’s proof and the community’s evaluation of its validity is on-going. You can follow @fyfluiddynamics and the #NavierStokes hashtag on Twitter for updates and commentary. I’d like to specially thank Catriona Stokes, Praveen C, David Sarma, and Glenn Carlson for their helpful links and observations as this story develops.
Acoustic Levitation in Three Dimensions
Acoustic sound is a form of pressure wave propagating through air or another fluid. Place a speaker opposite a plate, and its sound will reflect off the surface. The original pressure wave and its reflection form a standing wave. With intense enough sound waves, the acoustic radiation pressure can be large enough to counter the force of gravity on an object, causing it to levitate. We’ve shown you several examples of acoustic levitation before, including squished and vibrating droplets and applications for container-free mixing. Today’s video, however, shows the first acoustic levitation system capable of manipulating objects in three dimensions, an important step in developing the technology for application. (Video credit: Y. Ochiai et al.; via NatGeo)
Impacting a Viscous Pool
Whenever a hollow cavity forms at the surface of a liquid, the cavity’s collapse generates a jet–a rising, high-speed column of liquid. The composite images above show snapshots of the process, from the moment of the cavity’s greatest depth to the peak of the jet. The top row of images shows water, and the bottom row contains a fluid 800 times more viscous than water. The added viscosity both smooths the geometry of the process and slows the jet down, yet strong similarities clearly remain. Focusing on similarities in fluid flows across a range of variables, like viscosity, is key to building mathematical models of fluid behavior. Once developed, these models can help predict behaviors for a wide range of flows without requiring extensive calculation or experimentation. (Image credit: E. Ghabache et al.)
What Makes Squids Fast
Cephalopods like the octopus or squid are some of the fastest marine creatures, able to accelerate to many body lengths per second by jetting water behind them. Part of what makes its high speed achievable, though, is the way the animal changes its shape. In general, drag forces are proportional to the square of velocity, meaning that doubling the velocity increases the drag by a factor of four. The energy necessary to overcome such large drag increases generally prevents marine animals from going very fast (compared to those of us used to moving through air!) But drag is also proportional to frontal area. Like the bio-inspired rocket in the video above, jetting cephalopods begin their acceleration from a bulbous shape and then shrink their exposed area as they accelerate. Not only does this shape change help mitigate increases in drag due to velocity, it prevents flow from separating around the animal, shielding it from more drag. The result is incredible acceleration using only a simple jet for thrust. For example, the octopus-like rocket in the video above reaches velocities of more than ten body lengths per second in less than a second. (Video credit: G. Weymouth et al.)
