Underexpanding nozzle

The type of flow encountered when a highly underexpanded nozzle exhausts into a vacuum differs significantly from the random free-molecule flow characterized by the Max-well-Boltzmann distribution function, which is normally encountered in vacuum practice. The difference is illustrated in Fig. 1 and is primarily due to the large directional velocity component given to the gas molecules while still in a dense continuum flow condition in the nozzle. The velocity distribution function for the exhaust gas thus differs from that of the random flow in that it contains both the random thermal velocity components and the large directional velocity component. 

If the pressure at the end of the nozzle is smaller than the pressure of the surroundings (which occurs in the case of a so-called overexpanding nozzle), the pressure term then has a negative value and reduces the total thrust. Therefore, a pressure Pe which is the same or higher (underexpanding nozzle) than the air pressure is desirable. 

When the initial pressure is lower than the vapour pressure at the initial temperature only vapour flows through the nozzle and one obtains a well-known underexpanded supersonic gas jet (Figure 3f). 

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