Colorful streaks of dye wrap like ribbons along the leading edge of a delta wing. At an angle of attack, this triangular wing forms a set of vortices that run along its edge, providing much of the low pressure–and therefore lift–on the upper surface of the wing. In contrast, the red streaks of dye in the middle of the wing demonstrate clean, laminar flow. Highly swept delta wings are popular for aircraft traveling at supersonic speeds, but they can also work well subsonically, as shown here. For more incredible and beautiful examples of flow visualizations by Henri Werlé, check out his 1974 film Courants et couleurs. (Photo credit: H. Werlé; via eFluids)
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Reader Question: Lift
everyonelikespotatissallad asks:
so, how is lift actually generated? i’ve been going through Anderson’s Introduction to Flight (6th Ed.) and while it offers the derivation of various equations very thoroughly, it barely touches on why lift is generated, or how camber contributes to the increase of C(L)
This is a really good question to ask. There are a lot of different explanations for lift out there (and some of the common ones are incorrect). The main thing to know is that a difference in pressure across the wing–low pressure over the top and higher pressure below–creates the net upward force we call lift. It’s when you ask why there’s a pressure difference across the wing that explanations tend to start diverging. To be clear, aerodynamicists don’t disagree about what produces lift – we just tend to argue about which physical explanation (as opposed to just doing the math) makes the most sense. So here are a couple of options:
Newton’s third law states that for every action there is an equal and opposite reaction. If you look at flow over an airfoil, air approaching the airfoil is angled upward, and the air leaving the aifoil is angled downward. In order to change the direction of the air’s flow, the airfoil must have exerted a downward force on the air. By Newton’s third law, this means the air also exerted an upward force–lift–on the airfoil.
The downward force a wing exerts on the air becomes especially obvious when you actually watch the air after a plane passes:
This one can be harder to understand. Circulation is a quantity related to vorticity, and it has to do with how the direction of velocity changes around a closed curve. Circulation creates lift (which I discuss in some more detail here.) How does an airfoil create circulation, though? When an airfoil starts at rest, there is no vorticity and no circulation. As you see in the video above, as soon as the airfoil moves, it generates a starting vortex. In order for the total circulation to remain zero, this means that the airfoil must carry with it a second, oppositely rotating vortex. For an airfoil moving right to left, that carried vortex will spin clockwise, imparting a larger velocity to air flowing over the top of the wing and slowing down the air that moves under the wing. From Bernoulli’s principle, we know that faster moving air has a lower pressure, so this explains why the air pressure is lower over the top of the wing.
Asymmetric Flow and Bernoulli’s Principle
There are two basic types of airfoils – symmetric ones (like the one in the first picture above) and asymmetric, or cambered, airfoils (like the one in the image immediately above this). Symmetric airfoils only generate lift when at an angle of attack. Otherwise, the flow around them is symmetric and there’s no pressure difference and no lift. Cambered airfoils, by virtue of their asymmetry, can generate lift at zero angle of attack. Their variations in curvature cause air flowing around them to experience different forces, which in turn causes differing pressures along the top and the bottom of the airfoil surface. A fluid particle that travels over the upper surface encounters a large radius of curvature, which strongly accelerates the fluid and creates fast, low-pressure flow. Air moving across the bottom surface experiences a lesser curvature, does not accelerate as much, and, therefore, remains slower and at a higher pressure compared to the upper surface.
(Image credit: M. Belisle/Wikimedia; National Geographic/BBC2; O. Cleynen/Wikimedia; video credit: J. Capecelatro et al.)
Soap Film Visualization
Soap films provide a simple and convenient method for flow visualization. Here an allen wrench swept upward through a soap film leaves a distinctive wake. This trail of counter-rotating vortices is known as a von Karman vortex street. Their spacing depends on the wrench’s size and speed. Although the von Karman vortex street is usually associated with the wake of cylinders, it shows up often in nature as well, especially in the clouds trailing rocky islands. (Photo credit: P. Nathan)
The Free Surface of a Typhoon
Gazing across the top of of Typhoon Maysak highlights the three-dimensionality of the storm. Like a swirling vortex seen in a bathtub, hurricanes are a kind of free surface vortex with a surface indentation near their eye. To understand this shape, imagine spinning a container of water on a rotating plate. Like the vortex, the water’s surface would take on a parabolic shape. The two forces acting on the rotating water are gravity in the downward direction and centrifugal force in the radial direction. By taking on a parabolic shape, the fluid remains perpendicular to the combination of these two forces at every point along the surface, thereby ensuring that pressure is a constant across the free surface of the fluid. (Image credits: S. Cristoferreti/ESA/NASA; T. Virts/NASA)
Newtonian and Non-Newtonian Vortices
Not all vortex rings are created equal. Despite identical generation mechanisms and Reynolds numbers, the two vortex rings shown above behave very differently. The donut-shaped one, on the top left in green and in the middle row in blue, was formed in a Newtonian fluid, where viscous stress is linearly proportional to deformation. As one would expect, the vortex travels downward and diffuses some as time passes. The mushroom-like vortex ring, on the other hand, is in a viscoelastic fluid, which reacts nonlinearly to deformation. This vortex ring first furls and expands as it travels downward, then stops, contracts, and travels backward! (Image credit: J. Albagnac et al.; via Gallery of Fluid Motion)
Martian Dust Devil
This photo from the Mars Reconnaissance Orbiter stares almost straight down a dust devil on Mars. Like their earthbound brethren, Martian dust devils form when the surface is heated by the sun, causing warm air to rise. The rising air causes a low pressure area that the surrounding air flows into. Any rotational motion of the air intensifies as it is entrained. This is a consequence of conservation of angular momentum. Just as a spinning ice skater spins faster when he pulls his arms in, the vorticity of the inward-flowing air increases, forming a vortex. In addition to dust devils, this same physical mechanism applies to waterspouts and fire tornadoes, although the heating source for those is different. (Photo credit: NASA; via APOD)
Below a Surfer’s Wave
From below a plunging breaking wave–the classic surfer’s wave–looks like a giant vortex tube. Smaller rib vortices, the rings around the main vortex in the photo above, can form where there are variations along the breaking wave. As the wave rolls on, it stretches the vorticity variations along the wave’s span. When stretched, vortices spin up and intensify; this is a result of conservation of angular momentum. Check out more amazing photos of waves in Ray Collins’ portfolio. (Photo credit: R. Collins; via The Inertia)
Vertical-Axis Wind Turbines
Vertical-axis wind turbines (VAWT) are an alternative to traditional wind turbine designs. Unlike their more common cousins, VAWTs rotate about a vertical axis and are omni-directional, meaning that they do not have to be pointed into the wind to produce power. While their size allows VAWTs to be packed much closer to one another than traditional turbines, a clear understanding of the flow around the turbines is needed in order to place the turbines for effective and efficient operation. The images above show the complicated and turbulent wake of a three-bladed VAWT when stationary (top) or rotating (bottom). The flow is visualized using a gravity-driven soap film (flowing left to right in the images) pierced by a model VAWT (seen at the left). The wakes contain many scales from simple, periodically-shed vortices off a blade to very large-scale vortical structures forming downstream of the turbine. This work originally appeared as a poster in the Gallery of Fluid Motion at the 2014 APS DFD Annual Meeting. (Image credit: D. Araya and J. Dabiri)
Turbine Blade Separation
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Maintaining consistent air flow along the contours of an object is key to aerodynamic efficiency. When air flow separates or forms a recirculation zone, the drag increases and efficiency drops. On wind turbine blades, flow often separates on the root end of the blade near its attachment point. This behavior is apparent in the video above at 0:34. The tufts in the foreground on the turning blade flap and flutter with no clear pattern because the air flow has separated from the surface. In the subsequent clip, a line of vortex generators has been attached near the leading edge of the blade. These structures–also commonly seen on airplanes–trail vortices behind them, mixing the flow and generating a turbulent boundary layer which is better able to resist flow separation. The effect on the flow is clear from the tufts, most of which now point in a consistent direction with little to no fluttering, indicating that the air flow has remained attached. (Video credit: Smart Blade Gmbh/Technische Universität Berlin)
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Crow Instability
Behind airplanes in flight, water vapor from the engine exhaust will sometimes condense in the wingtip vortices, thereby forming visible contrails. The two initially parallel vortex lines are unstable and any small perturbation to them–a slight crosswind, for example–will cause an instability known as the Crow instability. The contrails become wavy, with the amplitude of the wave growing exponentially in time due to interactions between the two vortices. Eventually, the vortex lines can touch and pinch off into vortex rings. The effect is also quite noticeable when smoke generators are used on a plane, and there are some great examples in this air show video between 3:41:00 and 3:44:00. (Video credit: M. Landy-Gyebnar; h/t to Urs)
