Unchoked flow

Choked and unchoked flow situations arise in pipes and nozzles in the same fashion for homogeneous equihbrium flashing flow as for gas flow. For nozzle flow from stagnation pressure po to exit pressure pi, the mass flux is given by... 

This is below atmospheric pressure and therefore the flow is not choked. A further correction factor for unchoked flow is therefore required. 

If Peril < P2 there is no limitation of flow ( unchoked flow )- The flow is subcritical and the mass flow rate is obtained from... 

Thompson et al [3] have suggested on the basis of their evaporation wave experiments that the Chapman-Jouget (Ch-J) condition (sonic outflow in the reference frame of the wavefront) which applies to classical detonation also applies to evaporation waves. In our experiments, a choked exit is essentially the same as the Ch-J condition, since the wave motion relative to the exit is negligible compared to the two-phase flow velocity. We observe waves both with choked and unchoked flows (see Table 1) hence, subsonic outflow is also possible, and the Ch-J condition is not necessary for the propagation of evaporation waves. 

When it is desired to determine the discharge rate through a nozzle from upstream pressure p0 to external pressure p2, Equations (6-115) through (6-122) are best used as follows. The critical pressure is first determined from Eq. (6-119). If p2 > p , then the flow is subsonic (subcritical, unchoked). Then p, = p2 and M, may be obtained from Eq. (6-115). Substitution of Mx into Eq. (6-118) then gives the desired mass velocity G. Equations (6-116) and (6-117) may be used to find the exit temperature and density. On the other hand, if p2< p , then the flow is choked and M = 1. Then j> = p , and the mass velocity is G obtained from Eq. (6-122). The exit temperature and density may be obtained from Eqs. (6-120) and (6-121). 

The following simplified equation can be used to estimate the rate of gas or vapor flow from the open end of a pipe, for unchoked (sub-sonic) conditions [10] ... 

The convergent-only nozzle will usually be designed to work in the unchoked region, where the flow is always less than sonic. Provided the flow is not choked. 

Example 7.5 Dimensioning of a safety valve for a pressure reUef with two-phase flow—subcritical (unchoked) discharge... 

Since now pent < p2. tbe flow is unchoked. Hence, the necessary minimum cross sectional area is obtained from Eq. (7.31) as... 

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