Fuck Yeah Fluid Dynamics

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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.)

At high angles of attack, the flow around the leading edge of an airfoil can separate from the airfoil, leading to a drastic loss of lift also known as stall. Separation of the flow from the surface occurs because the pressure is increasing past the initial curve of the leading edge and positive pressure gradients reduce fluid velocity; such a pressure gradient is referred to as adverse. One way to prevent this separation from occurring at high angle of attack is to apply suction at the leading edge. The suction creates an artificial negative (or favorable) pressure gradient to counteract the adverse pressure gradient and allows flow to remain attached around the shoulder of the airfoil. Suction is sometimes also used to control the transition of a boundary layer from laminar to turbulent flow.

In recent years unmanned aerial vehicles (UAVs) have grown in popularity for both military and civilian application and are shifting from a remotely controlled platform to autonomous control. Since no pilot flies onboard an UAV, these craft are much smaller than other fixed-wing aircraft, with wingspans that may range from a few meters to only centimeters. At these sizes, most fixed-wing airfoil theory does not apply because no part of the wing is isolated from end effects. This complicates the prediction of lift and drag on the aircraft, particularly during maneuvering and necessitates the development of new predictive methods and control schemes. Shown above are flow visualizations of a small UAV executing a perching maneuver, intended to allow the craft to land as a bird does by scrubbing speed with a high-angle-of-attack, high-drag motion. (Photo credit: Jason Dorfman; via Hizook; requested by mindscrib)

At small angles of attack, air flows smoothly around an airfoil, providing lifting force through the difference in pressure across the top and bottom of the airfoil. As the angle of attack increases, the lift produced by the airfoil increases as well but only to a point. Increasing the angle of attack also increases the adverse pressure gradient on the latter half of the top surface, visible here as an increasingly thick bright area. Over this part of the surface, the pressure is increasing from low to high—the opposite of the direction a fluid prefers to flow. Eventually, this pressure gradient grows strong enough that the flow separates from the airfoil, creating a recirculating bubble of air along much of the top surface. When this happens, the lift produced by the airfoil drops dramatically; this is known as stall.

As a followup to yesterday’s question about ways to explain lift on an airfoil, here’s a video that explains where the circulation around the airfoil comes from and why the velocity over the top of the wing is greater than the velocity around the bottom. Kelvin’s theorem says that the circulation within a material contour remains constant for all time for an inviscid fluid. Before the airplane moves, the circulation around the wing is zero because nothing is moving. As shown in the video, as soon as the plane moves forward, a starting vortex is shed off the airfoil. As the plane flies, our material contour must still contain the starting position and thus the starting vortex. However, in order to keep the overall circulation in the contour zero, the airfoil carries a vortex that rotates counter to the starting vortex. This is the mechanism that accelerates the air over the top of the wing and slows the air around the bottom. Now we can apply Bernoulli’s principle and say that the faster moving air over the top of the airfoil has a lower pressure than the slower moving air along the bottom, thus generating an upward force on the airfoil. (submitted by jessecaps)

I'm a Undergrad Aeronautical Engineering student. I'm curious as to your opinion as to how airfoils produce lift. I know the usual theory told in this situation. However my aerodynamics professor says that there are many things going on during the flow around an airfoil. I'm hoping to get a better idea of the different mechanisms responsible for lift.
fuckyeahfluiddynamics fuckyeahfluiddynamics Said:

There’s a common misconception of Bernoulli’s principle that’s often used to explain how an airfoil creates lift (which I assume is the “usual theory” to which you refer), and while there are many correct (or, perhaps, more correct) ways of explaining lift on an airfoil, I think the only opinions involved are as to which explanation is best. After all, opinions don’t keep a plane in the air, physics does!

I tackled the air-travels-farther-over-the-top misconception and presented one of my preferred ways of looking at the situation in a previous post; in short, the airfoil’s shape causes a downward deflection of the flow, which, by Newton’s 3rd law, indicates that the air has exerted an upward force on the airfoil. There’s a similar useful video from Cambridge on the topic here.

Another explanation I have heard used concerns circulation and its ability to produce lift (see the Kutta-Joukowski theorem for the math). In this case, it’s almost easier to think about lift on a cylinder instead of lift on a more complicated shape like an airfoil.  If you spin a cylinder, you’ll find that the circulation around that object results in a force perpendicular to the flow direction. This is called the Magnus effect and, in addition to explaining why soccer balls sometimes curve strangely when kicked, has been used to steer rotor ships. One of my undergrad aero professors used to do a demonstration where he’d wrap a string around a long cardboard cylinder and demonstrate how, by pulling the string, the cylinder’s spinning produced lift, making the cylinder fly up off the lectern and attack the unsuspecting students.

An airfoil doesn’t spin, but its shape produces the same type of circulation in the flow field.  Without delving into the mathematics, it’s actually possible through conformal mapping and the Joukowski transform to show that the potential flow field around a spinning cylinder is identical to that around a simple airfoil shape! Although that mathematical technique is not all that useful in a world where we can calculate the inviscid flow around complicated airfoils exactly, it’s still pretty stunning that we can analytically solve potential flow around (and thus estimate lift for) a host of airfoil shapes on the back of an envelope.

In short, your aerodynamics professor is right in saying that there are many things going on during the flow around an airfoil. If you get a roomful of aerodynamicists together and ask them to explain how airfoils generate lift, you would be faced with a lively discussion with about as many competing explanations as there are participants. As you learn more in your classes, you’ll gain a better intuitive feel for how it works and you’ll learn more of the nuances, which will help you understand why there is no one simple-to-understand explanation that we use!**

** Lest I confuse someone into thinking that aerodynamicists don’t know how airfoils produce lift, let me add that the argument here is over how best to explain the production of lift, not over how the lift is produced. We have the equations to describe the flow and we can solve them. We know that lift is there and why. We simply like to argue over how to explain it to people without all the math.

This flow visualization of a pitching wind turbine blade demonstrates why lift and drag can change so drastically with angle of attack. When the angle the blade makes with the freestream is small, flow stays attached around the top and bottom surfaces of the blade. At large (positive or negative) angles of attack, the flow separates from the turbine blade, beginning at the trailing edge and moving forward as the angle of attack increases. The separated flow appears as a region of recirculation and turbulence. This is the same mechanism responsible for stall in aircraft. (Submitted by Bobby E)

A flapping airfoil in a vertically flowing soap film produces six vortices per cycle. The vortices form a pattern of two vortex pairs separated by vortex singlets. In the wake of the foil, they advect relative to one another due to their mutual influence, as if dancing. #

This video shows the turbulent boundary layer on a NACA 0010 airfoil at high angle of attack (15 degrees). Notice how substantial the variations are in the boundary layer over time. At one instant the boundary layer is thick and smoke-filled and in another we see freestream fluid (non-smoke) reaching nearly to the surface. This variability, known as intermittency, is characteristic of turbulent flows, and is part of what makes them difficult to model.

I discovered this interesting bit of icing a couple years ago near the foot of a waterfall in Ithaca, NY. The predominant wind was always heading toward the falls (left to right in these pictures), while the falls were always throwing spray up into the wind. The result was that ice airfoils (center) formed in the wake of each tree branch throughout most of the gorge (top).