Choked flow
When a flowing fluid at a given pressure and temperature passes through a constriction (such as the throat of a convergent-divergent nozzle or a valve in a pipe) into a lower pressure environment the fluid velocity increases.
At initially subsonic upstream conditions, the conservation of energy principle requires the fluid velocity to increase as it flows through the smaller cross-sectional area of the constriction.
At the same time, the venturi effect causes the static pressure, and therefore the density, to decrease at the constriction.
The choked flow of gases is useful in many engineering applications because the mass flow rate is independent of the downstream pressure, and depends only on the temperature and pressure and hence the density of the gas on the upstream side of the restriction.
Under choked conditions, valves and calibrated orifice plates can be used to produce a desired mass flow rate.
Cavitation is quite noisy and can be sufficiently violent to physically damage valves, pipes and associated equipment.
In effect, the vapor bubble formation in the restriction prevents the flow from increasing any further.
Choked flow can occur at the change of the cross section in a de Laval nozzle or through an orifice plate.
Assuming ideal gas behavior, steady-state choked flow occurs when the downstream pressure falls below a critical value
When the gas velocity is choked, one can obtain the mass flowrate as a function of the upstream pressure.
If the gas is being released from a closed high-pressure vessel, the above steady state equations may be used to approximate the initial mass flow rate.
Calculating the flow rate versus time since the initiation of the discharge is much more complicated, but more accurate.
If the upstream conditions are such that the gas cannot be treated as ideal, there is no closed form equation for evaluating the choked mass flow.
[citation needed] The minimum pressure ratios required for choked conditions to occur (when some typical industrial gases are flowing) are presented in Table 1.
Therefore, flow through a venturi can reach Mach 1 with a much lower upstream to downstream ratio.
[9] The flow of real gases through thin-plate orifices never becomes fully choked.
[10] Cunningham (1951) first drew attention to the fact that choked flow does not occur across a standard, thin, square-edged orifice.
[11][12] In the case of upstream air pressure at atmospheric pressure and vacuum conditions downstream of an orifice, both the air velocity and the mass flow rate become choked or limited when sonic velocity is reached through the orifice.
The flow then decelerates through the diverging section and exhausts into the ambient as a subsonic jet.
In this state, lowering the back pressure increases the flow speed everywhere in the nozzle.
[13] When the back pressure, pb, is lowered enough, the flow speed is Mach 1 at the throat, as in figure 1b.
Flow through the nozzle is now choked since further reductions in the back pressure can't move the point of M=1 away from the throat.
However, the flow pattern in the diverging section does change as you lower the back pressure further.
The shock wave produces a near-instantaneous deceleration of the flow to subsonic speed.
In this regime if you lower or raise the back pressure you move the shock wave away from (increase the length of supersonic flow in the diverging section before the shock wave) the throat.
[13] If the pb is lowered enough, the shock wave sits at the nozzle exit (figure 1d).
Due to the long region of acceleration (the entire nozzle length) the flow speed reaches its maximum just before the shock front.
[13] Lowering the back pressure further causes the shock to bend out into the jet (figure 1e), and a complex pattern of shocks and reflections is set up in the jet that create a mixture of subsonic and supersonic flow, or (if the back pressure is low enough) just supersonic flow.
[13] A further lowering of the back pressure changes and weakens the wave pattern in the jet.
In this situation (called 'underexpanded') expansion waves (that produce gradual turning perpendicular to the axial flow and acceleration in the jet) form at the nozzle exit, initially turning the flow at the jet edges outward in a plume and setting up a different type of complex wave pattern.
