when the gas is over-expanded, compared with the external atmosphere, the gas pressure in the exhaust gas is lower, which causes the exhaust gas to be compressed or squeezed inward. This compression will increase the exhaust pressure. However, the flow may be compressed so much that its pressure exceeds the atmospheric pressure. At this time, the air flow expands outward again to reduce the pressure.

this process may also last for a long time, causing the pressure inside the plume to be lower than the ambient pressure again. With the passage of time, the compression and expansion processes are repeated, and the difference between the gas pressure in the exhaust and the external atmospheric pressure gradually decreases until the exhaust pressure is the same as the ambient atmospheric pressure.

Mach rings are named after Ernst Mach, who was the first physicist to describe them.

formation process

when the engine nozzle discharges the over-expanded airflow, the airflow near the center line will flow parallel to the center line of the nozzle longitudinal axis. However, the ambient atmospheric pressure outside the free jet boundary is higher than the exhaust pressure, forcing the exhaust flow direction to change inward toward the center line. This change is achieved by a wave called an oblique shock wave.

the direction of oblique shock wave forms a certain angle with the direction of airflow passing through it, and increases the pressure of airflow passing through it. In particular, the shock wave perpendicular to the air flow direction is called normal shock wave. When the airflow rotates parallel to the center line again, a normal shock wave appears and produces a mach disk in the exhaust flow.

The temperature of the airflow passing through this normal shock wave will increase, which will cause the excess fuel in the exhaust gas to be ignited, thus making the fuel burn, making the mach disk glow and forming a visible annular pattern. Like oblique shock wave, normal shock wave will also increase the exhaust pressure. When the exhaust pressure is greater than the pressure of the surrounding atmosphere, the airflow begins to flow outward and expand.

this change is realized by a series of expansion wave, which are reflected from the boundary of the free jet to the center line. These waves make the air flow outward and reduce the pressure of the air flow. Then, the expansion wave meets the expansion wave formed on the other side of the nozzle at the center line and begins to reflect outward.

when the airflow passes through these reflected expansion waves, it will flow parallel to the center line and reduce the pressure again. These two groups of expansion waves are collectively called expansion fan. When the expansion wave reaches the boundary of the free jet, it will be reflected inward again, resulting in compression wave and compression fan.

these compression waves force the airflow to flow inward and increase the pressure. If the compression waves are strong enough, they will merge into an oblique shock wave to form a new mach disk, similar to the mach disk near the nozzle outlet. This series of compression and oblique shock waves will increase the pressure of exhaust flow and lead to the formation of new expansion fans. This process is repeated again and again, creating a series of mach disk.

a similar process occurs in the underexpanded airflow from the high-altitude nozzle. The sequence of compression and expansion is the same as that described by the over-expansion nozzle, except that it starts from the generation of the expansion fan, which causes the airflow to flow outward at first, instead of compressing inward. In any case, the subsequent series of expansion and compression will lead to the formation of the same mach disk downstream.

In an ideal gas, this process of expansion and contraction will continue, creating an infinite number of mach disk. However, the actual gas is not ideal, and the friction caused by the free jet boundary between the ambient atmosphere and the exhaust gas leads to the formation of turbulent shear layer. This layer produces viscous damping and gradually dissipates the wave structure. This viscous friction finally balances the pressure difference between the exhaust gas and the surrounding atmosphere, so that mach disk is no longer formed.

alternative sources

impact diamonds are most often associated with jet and rocket propulsion, but they can be formed in other systems.

1. Natural gas pipeline blowdown

During the blowdown of natural gas pipeline, impact diamonds can be seen because the gas is under high pressure and leaves the blowdown valve at a very high speed.

2. Artillery

When a cannon is fired, the gas leaves the big muzzle at supersonic speed and produces a series of impact diamonds. Diamonds will cause bright muzzle flashes, thus exposing the position of guns to the enemy. It is found that when the ratio between flow pressure and atmospheric pressure is close, the impact on diamond is greatly minimized. Adding a muzzle brake at the end of the muzzle can balance the pressure and prevent the impact.

3. Radio Jets

Some radios emitted from quasars and radio galaxies, that is, powerful plasma jets, were observed to have increased radio emission junctions at regular intervals. The jet travels through the thin "atmosphere" in space at supersonic speed, so it can be inferred that these knots are impact diamonds.

what are the above references? Baidu Encyclopedia-mach disk