Choking during liquid flow

Eliminating the throat pressure, p and rearranging produces the following relationship between the valve upstream and downstream pressures  

Substituting from equation (8.9) into equation (8.10) allows the elimination of valve downstream pressure, p,2  

This may be rearranged to yield an expression for the valve upstream pressure, p i  

As a result, if there is a possibility of the valve throat pressure falling to or near the vapour pressure of the liquid, equation (8.4) calculating mass flow should be 

The onset of cavitation for a globe valve occurs with the onset of choking, as was noted in Section 7.5.2. Hence it will be predicted when W = Wchokr-Cavitation in a rotary valve occurs before choking, when the throat pressure equals the vapour pressure at valve inlet temperature, and equation (7.11) applies. This is of precisely the same form as equation (7.19), but with K replaced by and set to unity. This similarity of form enables us to repeat the development set out in Section 8.3 to determine the flow at choking. Thus we reach the following equation for cavitating flow, IV,.,  

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During the quasi-steady phase (about 100 ms) the base and exit pressures are nearly constant (Fig. 3). Indeed, the pressure in these experiments is much more constant than in many so-called blowdown experiments, in which nucleation and bubble growth typically occur in the bulk of the liquid (see, e,g.. Winters and Merte [8]). The difference between p ase PexU is the wave amplitude , in this case 0.53 bar. In the steady state the upstream pressure is approximately maintained by the thrust of rapid vaporization. The fact that the exit pressure is greater than the reservoir pressure (namely, 0) indicates that the flow is choked. The instantaneous pressure fluctuates with frequency components between 0 and about 2 kHz the strongest peaks are below 250 Hz. The rms pressure fluctuations are approximately 3% of the mean pressure for both and... 

In order to check our understanding of the process, the temperature profiles shown in Fig. 5 were used to calculate the pressure decay in the venting operation of the flight tank. The decay in tank pressure was found to be a function of liquid temperature, vapor temperature, vaporization rate, ullage, and line and valve size. The calculated values, as well as the experimentally measured values, are shown in Fig. 6. The pressure dropped rapidly during the initial few seconds and then decreased at a much lower rate until the vent valve was closed. The pressure conditions in the tank with respect to the ambient pressure of about 3 psia (altitude 40,000 ft) caused the flow out of the tank to be choked (sonic velocity in the vent valve) during the entire venting process. 

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