Lower critical discharge pressure ratio

We may assume that the nozzle will be designed to produce a supersonic discharge velocity, and that the design pressure ratio will coincide with the lower critical discharge pressure ratio for the design inlet conditions, i.e. (pi/por)lo = (Pimi2/Por)lo-The nozzle will be choked at this point, and this implies that the pressure at the throat will be at its critical value. The associated throat critical pressure ratio is given by equation (14.55) ... 

Since the design pressure ratio coincides with the lower critical discharge pressure ratio, it must satisfy equation (14.75), namely... 

Nozzle efficiency at discharge pressure ratios substantially below the lower critical ratio for a convergent-divergent nozzle... 

We have already calculated the design pressure ratio, which can be assumed to be the same as lower critical discharge ratio (p cnn)/poT =0.1845. 

Critical Flow Nozzle For a given set of upstream conditions, the rate of discharge of a gas from a nozzle will increase for a decrease in the absolute pressure ratio po/pi until the linear velocity in the throat reaches that of sound in the gas at that location. The value of po/pi for which the acoustic velocity is just attained is called the critical pressure ratio r. The actual pressure in the throat will not fall below even if a much lower pressure exists downstream. 

The lower velocity in the throat does not affect the jet s performance, as long as the velocity remains above the speed of sound. If the velocity in the throat falls below the speed of sound, we say that the jet has been forced out of critical flow. The sonic pressure boost is lost. As soon as the sonic boost is lost, the pressure in the vacuum tower suddenly increases. This partly suppresses vapor flow from the vacuum tower. The reduced vapor flow slightly unloads condenser 1 and jet 2 shown in Fig. 16.2. This briefly draws down the discharge pressure from jet 1. The pressure in the diffuser throat declines. The diffuser throat velocity increases back to, or above, sonic velocity. Critical flow is restored, and so is the sonic boost. The compression ratio of the jet is restored, and the vacuum tower pressure is pulled down. This sucks more vapor out of the vacuum tower, and increases the loads on condenser 1 and... 

---