Choked Flow? 1

[jrjones]

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?

TIA
jrjones

 

[MortenA]

For a valve in liquid service choked flow refers to the situation where the pressure at vena contrator drops below the vapour pressure of the liquid.

Best regards

Morten

 

[Oldliar]

Chocked flow (or critical flow) for a liquid is when the mass flux through a restricted area (=critical area) is at its maximum (velocity is sonic). So, if you decrease the downstream pressure, the mass flow will not increase. It does not mean that flashing / cavitation occurs, only if the pressure at minimum area (=critical area) is reduced below the liquid's vapour pressure this will be the case.
So, you can have chocked flow w/o flashing.

This is why you have a critical pressure higher than the vapour pressure.

Did it make any sense?

 

[BigInch]

tiny correction. increasing the "differential" pressure will not increase mass flow.

BigInch-born in the trenches.

http://virtualpipeline.spaces.msn.com

 

[sailoday28]

BigInch (Petroleum) 17 Apr 07 15:00
tiny correction.
The mass flow will increase if the differential pressure is increased by increasing the upstream pressure with all other conditions remaining fixed

 

[MortenA]

This is a quote from Fishers web page:

"Aside from the possibility of physical equipment damage due to flashing or cavitation, formation of vapor bubbles in the liquid flowstream causes a crowding condition at the vena contracta which tends to limit flow through the valve. So, while the basic liquid sizing equation implies that there is no limit to the amount of flow through a valve as long as the differential pressure across the valve increases, the realities of flashing and cavitation prove otherwise. If valve pressure drop is increased slightly beyond the point where bubbles begin to form, a choked flow condition is reached. With constant upstream pressure, further increases in pressure drop (by reducing downstream pressure) will not produce increased flow. The limiting pressure differential is designated DP allow and the valve recovery coefficient (Km) is experimentally determined for each valve, in order to relate choked flow for that particular valve to the basic liquid sizing equation. Km is normally published with other valve capacity coefficients. Figures 4 and 5 show these flow vs. pressure drop relationships."

Check:

http://www.fisherregulators.com/technical/sizingcalculations/#ChokedFlow

The way I read it its the same as what i posted. Sonic velocity in a liquid is usually quite jigh (due to the high density compared to most gasses.

Are Fisher wrong or dont they say the same as I?

Best regards

Morten

 

[MortenA]

Oldilar

To elaborate a little - while you theoretically COULD have choking without formation of bobbles this would require so high a velocity that you would be very hard pressed to find a a liquid that indeed IS a liquid while still having SO high a vapor pressure that formation of bobbles dose not occur. I would be interested to see a reference. For all practical application my statement will stand.

Best regards

Morten

 

[sailoday28]

MortenA (Petroleum)-I was just responding to the definition for homogeneous flow.
And yes, a valve in liquid service can choke by flashing downstream within the valve.
Please also note that fluids may choke by going two phase in other forms, such as layered flow, annular flow and so on. For those cases, it is difficult to define sound speed.
Regards

 

[BigInch]

Right Morton, and thanks Sailoday. Absolute pressures prevail.

BigInch-born in the trenches.

http://virtualpipeline.spaces.msn.com

 

[JimCasey]

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 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.

 

[sailoday28]

JimCasey (Mechanical
A flow does not have to exactly follow the Cv equation.
Choking occurs when with any further decrease in dowstream pressure(whether absolute or gage-to satisfy BigInch)the flow will not increase.-- Upstream conditions, remaining fixed.---
Sonic velocity does not have to occur with choking. For isothermal flow of a gas, choking occurs when the Mach No.=1/sqrt(gamma).

 

[davefitz]

There may be formed vapor bubles even though the outlet pressure is more than 80 psid above vapor pressure.

The pressure of interest is the static pressure at the "vena contracta" . The vena contracta is the minimum flow area formed by fluid streamlines as it necks down at the point of throttling. Typically this flow area may be only 60% of the apparent flow area calculated by the physical clearance between throttling surfaces.

You can estimate if such a low pressure as 0.57 psia is transiently occuring at the vena contracta by calculating what the fluid velocity must be for a 1/2 rho V^2 to equal
the missing 80 psid. Once this vena contracta critical velocity is calulated, you can work back to the apparent vena contracta flow area - if it is on the order of magnitude of 60% of the geometric area available between seat and plug, then the choked flow prediction may begin to make sense.

 

[jrjones]

Thanks everyone, I appreciate all the help. I think I have the concept now. I was very surprised that between the main control valve and the bypass that one cavitates and the other doesn't. But now looking at the definition of FL it makes a lot of sense. In my case the control valve has FL=0.519 and the bypass FL=0.88.

I assume that a lot of the same theory can be used for sizing restriction orifices as they are assumed to be at choked flow?

jrjones

 

[MortenA]

For gas service yes but A RO may not have a so low a pressure at vena contractor as a control valve would have.

But the procedure would be the same.

Best regards

Morten