Shock Diamond - distance from the nozzle

Description

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 density changes caused by standing shock waves. Mach diamonds (or disks) are named after Ernst Mach, the physicist who first described them.

Shock diamonds form when the supersonic exhaust from a nozzle is slightly over- or under-expanded, meaning that the pressure of the gases exiting the nozzle is different from the ambient air pressure. The exhaust is generally over-expanded at low altitudes where air pressure is higher, and under-expanded at higher altitudes.

As the flow exits the nozzle, ambient air pressure will either expand or compress the flow; over-expanded flow is compressed while under-expanded flow expands. The compression or expansion is caused by oblique shock waves inclined at an angle to the flow. 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 the formula shown here.

Related formulas

Variables

xdistance (m)
D0nozzle diameter (m)
P0flow pressure (N/m2)
P1atmospheric pressure (N/m2)