behavior of a critical flow venturi operated with excessive pressure drop?

[JoeFrickinFriday]

AIUI, when operating a critical flow venturi (CFV) the goal is to maintain an outlet/inlet pressure ratio sufficiently low to achieve sonic flow at the throat and a normal shock wave somewhere in the downstream section. The pressure ratio should be low enough to keep that normal shock some distance downstream of the throat; if the pressure ratio increases enough for the shock wave to migrate all the way back upstream to the throat, then any further increase in pressure ratio results in loss of the sonic condition at the throat (and thus a flow measurement error).

But what happens if we go in the opposite direction, i.e. decrease the pressure ratio until the shock wave moves downstream all the way to the large end of the diverging section? Nothing much - you've just got a very strong shock wave at the end of the CFV. But what happens if we decrease the pressure ratio a little further from that condition? Now we're starting to move into rocket-engine territory - except rocket exhaust plumes exist in an environment where they're free to expand/contract laterally as necessary (via oblique shock waves and expansion fans) to match up with ambient pressure. For a CFV with a constant-area duct downstream of the diverging section, the "exhaust plume" doesn't have that freedom; it's constrained by the duct walls. So what happens? Flow is supersonic all the way from the throat to the end of the diverging section, and then...? Some pattern of shocks/fans in the constant-diameter section? Fixed-velocity supersonic flow all along the length of the constant-diameter duct? Enquiring minds want to know.

 

[casflo]

I think that the scenario of your post is similar,for example, to the discharge of a steam/gas safety valve through a vent piping to the atmosphere, a condenser, etc.
It´s necessary to size the vent piping in order to let the valve discharging free with its capacity as if there were not vent piping. To do this, calculate the diameter and length of the vent piping for the critical pressure (sonic condition) at the valve and the pressure at the end of the vent piping, where also critical conditions may exist. The length and diameter selected for the piping, must let to discharge a flow rate equal or greater than the valve capacity.
In your case, if the duct downstream the CFV has a discharge capacity greater than the CFV, the discharge is free, but if it is lower, the CFV will not have critical conditions.

 

[davefitz]

I am sure that NASA has thoroughly researched this configuration in the 1960's, and it is probably dealt with in compressible flow textbooks, eg "compressible fluid dynamics" by Philip Thompson.

"...when logic, and proportion, have fallen, sloppy dead..." Grace Slick