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4.6. The Physical Basis of Choked Two Phase Flow

For a single phase flow choking occurs where the velocity of the gas is equal to the sonic velocity. This occurs at a particular section in any given apparatus and, as far as all the experiments show, a true choke occurs. The flow rate is absolutely independent of the discharge pressure as long as this pressure is below the choked pressure. We have no such foundation for predicting a "choking" condition in a two phase flow [17].

Experiments reported in Reference [14] show that the velocity of sound in a two-phase mixture is a function of flow regime, frequency and whether the pressure wave is a rarefaction or condensation wave. The sound velocity in a two phase mixture is, by no means, a thermodynamic property. For a two phase flow then the choking velocity and the sound velocity are not equal as they are for a single phase system.

If we now confine our attention to critical two-phase flows alone the problem is still not simple. None of the models mentioned in the References show the existence of a choking condition without making assumptions beyond those which can be justified experimentally. In this section we would like to examine the characteristics of the critical flow model. These characteristics are as follows:

1. When a choke occurs, downstream pressure no longer matters,
2. Downstream geometry no longer matters,
3. Upstream geometry does not matter so long as the enthalpy and pressure at the choked plane is unaltered,
4. The velocity ratio is as given by Equation 4.26, and
5. Thermodynamic equilibrium exists.

It becomes evident by examining the details of test data closely that assumption (1) is not valid and the downstream pressure does, in some small way, affect the flow rate. There are no experiments that show conclusively this is not true. As far as using this concept for engineering design is concerned, these departures from a true choked flow are of no consequence but they do cast doubt on the idea of the "choking" condition as a real physical occurrence for two-phase flow.

Experiments reported in Reference 16 show that downstream geometry does matter. Figure 4.6 shows several test section geometries while Figure 4.7 shows the corresponding critical mass velocity data. What this data shows is there is no plane at which choking occurs. Apparently there is only a very small increase in flow with a decrease in discharge pressure but this changes the fluid mechanics of the flow occurring over the entire tube. Upstream geometry clearly matters or it would not have been necessary to use Figure 4.10 to predict choked flow. For the same choke plane pressure and enthalpy, the choked flow mass velocity clearly depends on the upstream geometry. This is never true of a single phase flow.

Measurements of void made by Fauske and reported in Reference 8 show that the velocity ratio is very different from that calculated from Equation 4.26. If comparison is made with other models, they still do not show the behavior indicated by the data of Figure 4.17. Clearly, no simple velocity ratio expression has the needed properties to fit the range of data.

Thermodynamic equilibrium cannot exist for the data of Figure 4.17, for, if it did, the pressure drop would not be large enough to pass the flow. Thermodynamic equilibrium does not exist for L/D's less than (12) either, as it would not be necessary to distinguish between the L/D's and the longer ones. Therefore, one can say that none of the assumptions listed earlier are really true under all the conditions of interest.

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Next: Advanced Computational Models Up: Fluids Other Than Water Previous: Fluids Other Than Water

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Last Modified: Tue Sep 2 15:06:55 CDT 1997