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According to compressible flow theory, a downstream pressure of 0.528 times upstream pressure is sufficient to choke a flow device.

So, how do industrial grade pressure regulators throttle a wide range of pressures (say 150 bar to 20 bar)?

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The short answer is that they don't. Choking is not a bad thing. For a gas flow regulator, it's actually a good thing, because under choking conditions, the mass-flow rate is no longer dependent on the downstream pressure. The mass-flow rate is still dependent on the upstream pressure and the size of the aperture connecting the high and low-pressure sides.

In a reduction valve that is designed to keep the downstream pressure constant, rather than the mass flow rate, a mechanism is needed to open and close the aperture depending on whether the downstream pressure is below or above the pressure set point.

Update: if you're worried about energy losses in the gas stream, due to viscous dissipation: don't. If a perfect gas (that's an ideal gas with an additional condition for the specific heat) enters a thermally insulated throttle device at low speed and exits it at low speed (through a pipe with a large diameter), then its temperature will be the same as when it entered. One way is to look at the enthalpy of the gas, $H=m C_V T+ pV$, which must be conserved if no energy is added or removed along the way. Because $pV=nRT$, this condition can only be met if the gas has the same temperature before and after. Note that I mentioned "low speed", which is what you typically want in a pressure regulator. In the nozzle, where the speeds are sonic, the energy balance will also include kinetic energy of the gas jet.

Its may take a few moments for you to wrap your head around this (at least, for me it did, years ago).

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  • $\begingroup$ But sonic flow would induce losses because of the formation of expansion waves and shocks right? That wouldn't be a desirable effect. $\endgroup$ – DBTKNL Jun 5 '16 at 6:20
  • $\begingroup$ @DBTKNL Counterquestion: why would that be an undesirable effect? $\endgroup$ – Han-Kwang Nienhuys Jun 5 '16 at 6:38
  • $\begingroup$ Basically, wouldn't loss in energy of the flowing fluid be reduced if operated at non-choking conditions? Choked condition would mean severe gradients, high shear losses, etc. $\endgroup$ – DBTKNL Jun 5 '16 at 6:49

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