Physics of Choking
Choking can happen when a fluid is discharged through a passage from a pressurized chamber into a chamber that is at a significantly lower pressure.When a flow passage is choked, it supports the maximum possible fluid discharge rate for the given system conditions.
Choking can be better understood by the simple experiment shown in Fig. 17.1, where a chamber containing a fluid at an elevated pressure P
0 is connected to another chamber that is at a lower pressure P
out by a flow passage. Suppose that the upstream conditions are maintained unchanged in the experiment, while the pressure in the downstream chamber, P
out, is gradually reduced, and the mass flow rate is continuously measured. It will be observed that the mass flux increases as P
out is reduced, until P
out reaches a critical value P
ch. Further reduction of P
out will have no impact on mass flux or anything else associated with the channel interior.
The physical explanation of critical flow is as follows. A flow is critical (choked) when disturbances (or hydrodynamic signals) initiated downstream of some critical cross section cannot propagate upstream of the critical cross section. In single-phase flow, infinitesimally small disturbances (hydrodynamic signals) travel with the speed of sound. In a straight channel often the critical cross section occurs at the exit. In nozzles and other converging–diverging channels, the throat acts as the critical cross section.
Critical flow is an important process. Predictive methods for critical flow are needed since drainage of high-pressure fluids through passages, breaks, cracks, etc., is important in many applications. Two-phase critical flow is particularly important for the modeling of a number of nuclear reactor accident scenarios.
In choking problems we often know the conditions upstream of the entrance and downstream from the outlet of the flow passage. Using the fluid properties in the chamber with higher pressure as well as the characteristics of the channel itself, we must be able to calculate P
ch. For P
ch, the fluid momentum conservation equation must be solved for the channel using P
0 and P
out as the boundary conditions, to determine the flow rate. However, for P
ch, the flow rate through the channel will no longer depend on the conditions downstream from the channel exit.