Prandtl-Glauert singularity

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FA-18_Hornet_breaking_sound_barrier_(7_July_1999).jpg
F/A-18 demonstrating singularity effect

The Prandtl-Glauert singularity, at which point a sudden drop in air pressure occurs, is generally accepted as the cause of the visible condensation cloud when an airplane breaks the sound barrier, though there remains some debate. It is an example of a mathematical singularity in aerodynamics.

One view of this phenomenon is that it exhibits the effect of compressibility and the so-called N-wave. The N-wave is the time variant pressure profile seen by a static observer as a sonic compression wave passes. The overall three-dimensional shock wave is in the form of a cone with its apex at the supersonic aircraft. This wave follows the aircraft. The pressure profile of the wave is composed of a leading compression component (the initial upward stroke of the "N"), followed by a pressure descent forming a rarification of the air (the downward diagnonal of the "N"), followed by a return to the normal ambient pressure (the final upward stroke of the "N"). The rarefaction may be thought of as the "rebounding" of the compression due to inertial effects.

Since heat does not leave the affected air mass, this is an adiabatic change of pressure, with an associated change of temperature. Under humid air conditions, the drop in temperature in the most rarified portion of the shock wave (close to the aircraft) can bring the air temperature below its dew point. At this temperature, moisture condenses to form visible microscopic water droplets. As the pressure effect of the wave is reduced by its expansion (the same pressure effect is spread over a larger radius), the vapor effect also has a limited radius.

See also

External links

fr:Singularité de Prandtl-Glauert ja:Prandtl-Glauert Singularity

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