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Shock diamonds (also known as Mach diamonds, Mach disks, Mach rings, doughnut tails or thrust diamonds) are a formation of standing wave patterns that appears in the supersonic exhaust plume of an aerospace propulsion system, such as a supersonic jet engine, rocket, ramjet, or scramjet, when it is operated in an atmosphere. The diamonds are formed from a complex flow field and are visible due to the abrupt changes in local density and pressure caused by standing shock waves. Mach diamonds (or disks) are named after Ernst Mach, the physicist who first described them.[1]

Mechanism

Shock diamonds behind a Lockheed SR-71 Blackbird in flight.
Mach diamonds from an F-16 taking off with afterburner.
An F-22 Raptor with shock diamonds behind it.

Shock diamonds form when the supersonic exhaust from a propelling nozzle is slightly over-expanded, meaning that the static pressure of the gases exiting the nozzle is less than the ambient air pressure. This pressure increase in the exhaust gas stream is isothermal, and therefore, by the second-law of thermodynamics, its static temperature is substantially increased; thus reigniting the unburned combustion products in the engine’s exhaust.[2] The exhaust is generally over-expanded at low altitudes where air pressure is higher.

As the flow exits the nozzle, ambient air pressure will compress the flow.[2] The external compression is caused by oblique shock waves inclined at an angle to the flow. The compressed flow is alternately expanded by Prandtl-Meyer expansion fans, and each "diamond" is formed by the pairing of an oblique shock with an expansion fan. When the compressed flow becomes parallel to the center line, a shock wave perpendicular to the flow forms, called a normal shock wave. The first shock diamond is located here and the space between it and the nozzle is called the "zone of silence".[3] The distance from the nozzle to the first shock diamond can be approximated by:

$$x = 0.67 D_0\sqrt{\frac{P_0}{P_1}}$$

where x is the distance, D0 is the nozzle diameter, P0 is flow pressure and P1 is atmospheric pressure.[3]

As the exhaust passes through the normal shock wave, its temperature increases, igniting excess fuel and causing the glow that makes the shock diamonds visible.[2] The illuminated regions either appear as disks or diamonds, giving them their name.

Eventually the flow expands enough so that its pressure is again below ambient, at which point the expansion fan reflects off the contact discontinuity (the outer edge of the flow). The reflected waves, called the compression fan, cause the flow to compress.[2] If the compression fan is strong enough, another oblique shock wave will form, creating a second shock diamond. The pattern of disks would repeat indefinitely if the gases were ideal and frictionless,[2] however, turbulent shear at the contact discontinuity causes the wave pattern to dissipate with distance.[4]

Diamond patterns can similarly form when a nozzle is under-expanded (exit pressure higher than ambient), in lower atmospheric pressure at higher altitudes. In this case, the expansion fan is first to form, followed by the oblique shock.

Alternative sources
Shock diamonds beneath Masten Space Systems Xoie rocket during the Lunar Lander Challenge competition-winning landing.

Shock diamonds are most commonly associated with jet and rocket propulsion, but they can form in other systems.

Artillery

When artillery pieces are fired, gas exits the cannon muzzle at supersonic speeds and produces a series of shock diamonds. The diamonds cause a bright muzzle flash which can expose the location of gun emplacements to the enemy. It was found that when the ratio between the flow pressure and atmospheric pressure is close to one, the shock diamonds were greatly minimized. Adding a muzzle brake to the end of the muzzle balances the pressures and prevents shock diamonds.[5]

Volcanism

Some volcanoes have been shown to produce jets containing shock diamonds. These highly destructive jets have occurred in gas-rich volcanoes such as Mount St. Helens and Krakatoa.[6]

Some radio jets, powerful jets of plasma that emanate from quasars and radio galaxies, are observed to have regularly spaced knots of enhanced radio emissions.[7] The jets travel at supersonic speed through a thin "atmosphere" of gas in space,[8] so it is hypothesized that these knots are shock diamonds.

Afterburner
Exhaust gas
Plume (hydrodynamics)
Rocket engine nozzle
Shock wave

Notes

Norman, p. 48
Scott, Jeff (17 April 2005). "Shock Diamonds and Mach Disks". Aerospaceweb.org. Retrieved 6 November 2011.
Niessen, Wilfried M. A. (1999). Liquid chromatography-mass spectrometry 79. CRC Press. p. 84. ISBN 978-0-8247-1936-4.
"Exhaust Gases' Diamond Pattern". Florida International University. 12 March 2004. Retrieved 6 November 2011.
Norman, p. 41
Norman, p. 45
Norman, p. 68

Norman, p. 51

References

Norman, Michael L.; Winkler, Karl-Heinz A. (Spring–Summer 1985). "Supersonic Jets" (PDF). LOS ALAMOS SCIENCE. Los Alamos National Lab. Retrieved 6 November 2011.

Physics Encyclopedia