In the previous section I discussed why air tends to curve instead of going in a smooth uninterrupted line. This section I'll talk about the properties of swirling air. Lewis Fry Richardson has/had a famous saying: "Big whirls have little whirls, that feed on their velocity, little whirls have lesser whirls, and so on to viscosity."
What does this mean? It means that turbulence is really just small vortices, and that large vortices, have small vortices, which have still smaller vortices, which terminate due to viscous forces. When a mass displaces air, the fastest most efficient way for that air to be replaced is by turbulence. Turbulence is the most efficient way to mix and fill a volume with air. Take an internal combustion engine, in order to get the most homogenous mixture of air and fuel, turbulence is actually a good thing. After all, turbulence are small vortices, these minimum volume swirls transport the fuel droplets and distribute them in a given volume faster than smooth laminar flow can.
Internal combustion engines are less efficient at burning fuel at idle, than they are at higher engine speeds. This is because the increased piston velocity creates more turbulence in the cylinder, creating a more homogenous mixture of air and fuel.
In order to generate a vortex in an aerodynamic sense, energy must be introduced. The force of a wing slicing through the air requires energy to propel the wing through the air. Energy must be expended to force the wing through the air fast enough to create the pressure difference between the two surfaces of the wing. The vortex that results as the air migrates to fill the low pressure created by the wing, is itself a form of drag. The energy used to move the wing through the air is dissipated as a vortex. This vortex becomes dissipated as it interacts with the air surrounding it, because the large vortex begins to swirl the surrounding air, that surrounding air produces vortices of its own, further dissipating the energy. The swirls and eddies caused by the primary vortex take the energy from the main vortex, and mix it turbulently until the air is completely still, and "static pressure" is recovered.
Even though vortices are a source of drag, they can be used in order to improve the aerodynamic characteristics of wings and a vehicle's aerodynamics. This is because the cyclical momentum of a vortex can help airflow stay attached to a surface.
https://i.stack.imgur.com/O0h2f.jpgHere the leading edge slats near the cockpit of this F18, generate vortices which help the airflow to stay attached to the wings, and over the fuselage. This is the same principle behind the so called NACA duct. The sides of the NACA duct generate a pair of vortices, which entrain air upstream into the duct.
https://tianyizf1.files.wordpress.com/2013/12/delta-wing-vortex.pngPaper airplanes and other delta wing shaped craft exploit the same principle.
The main vortex rotates away from the center of the delta wing pulling air along with it, lowering the pressure at the center, air upstream then follows that low pressure zone as the path of least resistance. The air won't impede on the vortex, because the walls of the vortex are at or very near atmospheric pressure. This means the air has no need or reason to pass across the vortex.
https://www.centennialofflight.net/essay/Theories_of_Flight/Vortex/TH15G5.jpgVortices are partly why wings on aircraft tend to have an elliptical lift distribution.
Next section we'll discuss wing design, and the theory behind the distribution of lift on a wing.
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