Choked Flow?
When dealing with liquid sizing for a control valve, what is really meant by choked flow? Sorry if this sounds like a dumb question...but here is where I am coming from:
I have a case where I am trying to size a new control arrangement (control valve and orifice plates, etc) for the problem valve I talked about in:
http://www.eng-tips.com/viewthread.cfm?qid=180443&page=1
This fluid is at 333 psig upstream of the valve and needs to drop to ~80 psig downstream. The vapour pressure is 0.57 psiA. So that tells me that if I drop roughly 348 psi from my inlet pressure, I will flash and the system will recover to 80 psig and I will cavitate. Okay...
So why is the max pressure drop (for choked flow) only about 93.5 psi using the ISA sizing equations? Doesn't choked mean the formation of vapour bubbles?
Ff=0.96-0.28(Pv/Pc)^0.5 = ~0.943 (Pc=152.2 psia)
DPmax=Fl^2*(P1-Ff*Pv) Fl=0.519
Therefore, DPmax = ~93.5 psi drop.
This is substantially less than 348 psi. Is this strictly based on turbulence velocities that are higher than bulk flow velocities such that local low pressure areas can form?
I wish choked flow was easier to 'splain. A lot of specifying engineers
seem to think it is one manifestation of the end of the earth, but it's
really just a point where the basic Cv equation breaks down.
Basic Cv equation Cv=Q Sqrt ( Gf/DP)
First
imagine that you set up a test stand with an infinite capacity
constant-pressure source, lossless pipe, and you open the test valve
valve to a fixed position. The downstream pressure starts out (with no
flow) at the same pressure at the inlet. Then, start dropping the
downstream pressure. As the downstream pressure decreases, flow through
the fixed valve orifice will increase as the square root of the DP.
At
some point, the flow stops increasing as the downstream pressure
decreases. "Choked" implies that the flow experienced is less than the
flow predicted by the Cv equation. When the flow measured is 2% less
than predicted by the Cv equation, it is said to be "choked". Further
reducing the downstream pressure with constant upstream pressure and
constant valve position will cause little if any increase in the
flowrate through the valve.
Here's where a lot of engineers get confused:
If you open the test valve(gate valve) more, you will still get more flow.
If you INCREASE the upstream pressure, you will get more flow. AND the DP will be greater before choked flow happens again.
The
reference to crowding in the vena contracta was good. The flow cannot
feel any more differential than the differential between P1 and where
the bubbles begin to form. Similarly with a gas, when sonic flow
occurs, a standing shock wave forms. The gas molecules downstream cannot
communicate back upstream that there is more room to expand downstram
of the shockwave, so the effective differential is between the inlet
pressure and the pressure at which the shockwave forms.
Bad
things happen when there is choked flow, but Choked flow itself does not
mean that does not mean that bad things MUST happen.
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