Shock diamond

Shock diamonds (also known as Mach diamonds, Mach disks, Mach rings, donut tails or thrust diamonds) are a formation of standing wave patterns that appear 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 actually a complex flow field made visible by abrupt changes in local density and pressure as the exhaust passes through a series of standing shock waves and expansion fans. Mach diamonds (or disks) are named after Ernst Mach, the physicist who first described them.:48 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. The higher ambient pressure compresses the flow, and since the resulting pressure increase in the exhaust gas stream is adiabatic, and reduction in velocity causes its static temperature to be substantially increased. This causes reignition of the unburned combustion products in the engine’s exhaust. 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. 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'. The distance from the nozzle to the first shock diamond can be approximated by where x is the distance, D0 is the nozzle diameter, P0 is flow pressure, and P1 is atmospheric pressure. 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. 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 from the contact discontinuity (the outer edge of the flow). The reflected waves, called the compression fan, cause the flow to compress. 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. However, turbulent shear at the contact discontinuity causes the wave pattern to dissipate with distance. 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.