喷嘴分析：收敛喷嘴与收敛-扩散喷嘴中马赫数和压力的变化

As the nozzle area decreases from entry to throat, flow velocity increases, reaching its maximum at the throat. This acceleration occurs because the same mass flow rate must pass through progressively smaller cross-sectional areas. The flow remains subsonic in a converging nozzle, with velocity increasing until it reaches Mach 1 at the throat under choked flow conditions.

Choked flow occurs when the Mach number at the nozzle throat reaches 1, meaning the flow velocity equals the speed of sound. This happens at a back-pressure ratio of 0.5283. Once choked, further increases in inlet pressure do not increase throat velocity, limiting converging nozzles to subsonic flow acceleration applications.

Back-pressure ratio is the ratio between exit pressure and stagnation pressure at the nozzle entry. When these pressures are equal, no flow occurs. As back-pressure decreases, the pressure difference increases, accelerating flow velocity throughout the nozzle. This ratio directly controls flow conditions and determines whether the flow becomes choked.

At low back-pressure ratios, three patterns emerge: first, choked subsonic deceleration in the diverging section; second, supersonic acceleration followed by deceleration to subsonic velocities; third, continuous supersonic acceleration throughout the diverging section. These patterns depend on how much the back-pressure is reduced below the choked flow condition of 0.5283.

Over-expanded flow occurs when nozzle exit pressure is lower than ambient pressure, creating unstable flow with pressure and velocity variations. Under-expanded flow occurs when exit pressure exceeds ambient pressure, producing similar instability. Both conditions result from mismatches between internal nozzle conditions and external atmospheric pressure.

The mass flow parameter (MFP) increases as back-pressure ratio decreases until reaching the choked flow condition at 0.5283. At this point, MFP should remain constant because mass flow cannot increase further. Measuring MFP across varying back-pressure ratios helps experimentally verify theoretical choked flow predictions and flow regime transitions.

A converging-diverging nozzle accelerates subsonic flow to Mach 1 at the throat, then the diverging section allows continued acceleration to supersonic speeds. In contrast, a converging nozzle alone cannot exceed Mach 1 because the throat is the exit point. The diverging section provides the expanding area needed for supersonic flow expansion using schlieren imaging technique visualize supersonic flow features to observe these phenomena.