Choked Flow Question 1

[Krausen]

All,
Apologize if this same question has been asked on another thread, but I could not find.

I've been racking my brain on what happens in a liquid pipeline immediately downstream of throttling valve (e.g. control valve, surge relief valve, etc.) at choked flow. For example, say:

Upstream pressure (P1) = 605 psig (620 psia)
Downstream pressure (P2) = 50 psig
Required DP = 555 psid
DPmax = 260 psid [based on ISA choked flow equation - Fl^2*(P1-Ff*Pv), where Fl=0.65, Ff =0.92, Pv=11.0 psia, Pc = 667 psia]

Being that I can only drop 260 psid max across this valve, how is the system balancing/restoring itself down to the 50 psig downstream pressure? What happened with to the other 295 psi (555 - 260) of energy?

 

[zdas04]

"Choked flow" is not a concept in liquid flow, only gas flow. There is a special case where in a converging nozzle pressure in a liquid drops low enough to flash the liquid to vapor, and then the gas choked flow condition controls (but that condition is more often associated with cavitation than with choked flow).

David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist

 

[LittleInch]

I think you've misunderstood whichever equation it is you're using. You can't divorce flow from this equation.

To state that " I can only drop 260 psid max across this valve" means you're artificially restricting something or just using the wrong equation.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[Latexman]

It's unfortunate, but IMHO vocabulary is getting in the way here. Krausen, I believe you are on the right track. Take a look at Graphs 5 and 6 on page 629 of Valve Sizing Calculations to answer your questions. Be sure to read the entire section on Sizing for Liquid Service.

Good luck,
Latexman

To a ChE, the glass is always full - 1/2 air and 1/2 water.

 

[Krausen]

zdas - What you are calling a "special case" of choked flow happens regularly in liquid pipelines at control valves required to throttle higher pressures (or surge relief valves operating in abnormal events). While not an ideal operation, it oftentimes cannot be avoided.

Here is what I understand:
In the surge relief example above the fluid upstream of the valve is in liquid state. The flow is choked (at this instant). Through the valve (and immediately downstream) is a two-phase localized process where the liquid flashes to vapor, as you stated, and is then restored back a liquid in the relief line downstream by system backpressure. By definition, cavitation is occurring in this process (simultaneous with choked flow ... the two are not mutually exclusive).

Here is what I do not understand:
After dropping the DPmax (260 psid) across the valve, how do you account for the additional 295 psid supposedly lost in the relief process with only 50 psig of backpressure?

 

[Krausen]

Littleinch - I think you've misunderstood. If you look at the standardized ISA DPmax equation for choked flow, it has nothing to do with flow rate. Only the valve characteristics (Fl -Liquid Pressure Recovery Factor) & fluid properties (Ff - Critical Pressure Ratio Factor, Pv - Vapor Pressure, Pc - Critical Vapor Pressure)

 

[zdas04]

Krausen,
While cavitation is a major problem downstream of control valves, I don't believe that choked flow of a full vapor stream is actually controlling flow. Cavitation is by definition a multi-phase flow condition, not the single-phase vapor required for choked flow.

David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist

 

[Krausen]

Zdas - I'm not claiming the flow rate is being controlled by choked flow here (although there is another separate ISA equation that defines the max flow rate at choked flow based on the valve's rated Cv & inlet pressure). Instead I'm claiming the pressure drop across the valve (DPmax) is being controlled by choked flow.

Agreed that cavitation is a two-phase flow condition. In this case cavitation is occurring because vapor bubbles (that were created by choked flow) are imploding downstream of the valve once system backpressure is restored.

 

[LittleInch]

Krausen,

On the contrary, it has everything to do with flow. see page 3 of this nice document

http://www.documentation.emersonprocess.com/groups/public/documents/brochures/d351912x012.pdf

The graph shows that the DP can increase once you hit critical flow, but the flow doesn't

What your DP max is telling you is that when you reach that differential pressure, the flow rate has reached the maximum it can without changing something ( e.g. opening the valve more) or changing the valve Cv. Further reduction in downstream pressure will not increase the flow rate as it normally would.

The extra pressure drop you're talking about is simply the pressure drop of the vapour /two phase fluid within the control valve As the two phase fluid exits the valve and recovers back to your downstream pressure (50 psig) the vapour bubbles collapse, destroying your valve and pipe downstream but it is now a single phase fluid again.

DP max is simply a guide point for control valve designers to tell them when their valve won't work properly anymore and they are in danger of destroying the internals. It's not some magic maximum DP that can't be changed by screwing the valve even closer down.

All pressure drops through a control valve only work with flow. No flow, no Pressure drop.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[Krausen]

Littleinch - Maybe I have not been clear in my intentions & questions. I appreciate the response and it is all well & good in theory. In reality, this has to be applied. ISA has set forth standardized equations for all of this. Let us talk reality:

On the contrary, it has everything to do with flow. see page 3 of this nice document

http://www.documentation.emersonprocess.com/groups...

The graph shows that the DP can increase once you hit critical flow, but the flow doesn't.

Understand that this a full flow surge relief valve sizing case for a liquid pipeline. My flow rate is fixed based on the highest flow rate (worst case). Understand that my inlet pressure (P1) is the set point of this valve & cannot be increased since I'm trying to protect the upstream piping from a surge event (limited to 110% MOP of the piping). Therefore, given that the flow rate (Q) & inlet pressure (P1) cannot increase, the DPmax is set to 260 psid & the flow is choked as defined by ISA. These are not "artificial restrictions", but instead real-world practical limits to the sizing calculation.

The extra pressure drop you're talking about is simply the pressure drop of the vapour /two phase fluid within the control valve

Can you please explain in these fixed conditions how this valve would be dropping the additional 295 psid of pressure after already dropping the initial 260 psig (DPmax) through it, for a grand total of 555 psid? I realize I left out a critical piece of the backpressure ealier when I forgot to account for the required acceleration head needed at the outlet of this relief valve to accelerate all the liquid in the relief line to a steady state velocity. I'm in the process of working on this now...

DP max is simply a guide point for control valve designers to tell them when their valve won't work properly anymore and they are in danger of destroying the internals. It's not some magic maximum DP that can't be changed by screwing the valve even closer down.

Again, please understand that at a fixed flow rate & fixed inlet pressure you will not be increasing DP "by screwing the valve even closer down". This is the reason why understanding DPmax is so important. It is reality.

All pressure drops through a control valve only work with flow. No flow, no Pressure drop.

Or is it no flow, infinite pressure drop??? (for tight shutoff (TSO) control valves)

 

[Latexman]

Can you please explain in these fixed conditions how this valve would be dropping the additional 295 psid of pressure after already dropping the initial 260 psig (DPmax) through it, for a grand total of 555 psid?

Shock waves, similar to traditional vapor/gas only choked flow, but this is two phase choked flow, which is not understood as well, yet.

Good luck,
Latexman

To a ChE, the glass is always full - 1/2 air and 1/2 water.

 

[LittleInch]

"Can you please explain in these fixed conditions how this valve would be dropping the additional 295 psid of pressure after already dropping the initial 260 psig (DPmax) "

I'll try. Like I said previously, you seem to be thinking that this 260 psig is some sort of magic limit that the valve can physically not be able to reduce the pressure any more. This is your fundamental problem in understanding this issue. The 260 pis drop is simply the maximum pressure drop possible before the liquid starts to cavitate within the valve to the extent that you have choked flow. Assuming your inlet pressure is fixed (it is) then after this pressure drop is reached, lowering the pressure downstream of the valve has NO EFFECT on flow. That's it. So providing your flow is accommodated at this pressure drop then you don't really care, other than your valve may not survive a long time because you're busy cavitating. For a surge relief valve, it's probably OK. The extra 295 psig is simply lost in the turbulence of the two phase flow, but lowering the discharge pressure won't increase the inlet flow rate.

Does that make better sense?

"This is the reason why understanding DPmax is so important. ". No it isn't. All DPmax is giving you is telling you your valve is undersized and that cavitation and two phase flow will occur during operation. That's all it's telling you.

"Or is it no flow, infinite pressure drop??? " Ok - No flow, no pressure drop through the valve. I think you got the point earlier though.


Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[Krausen]

Latexman/Littleinch - Appreciate the feedback. There are some fundamental issues remaining that I'll try to summarize for the time being:

-At choked flow with a fixed inlet pressure (P1), the ISA DPmax (260 psid) is all I can drop across the valve. I'm struggling with visualizing how the additional 295 psig "is simply lost in two phase flow". It would seem that cavitation would be occurring at very far distances downstream of the valve if this is the case.

-Increasing the valve size (higher Cv rating) in these conditions will only make matters worse (higher valve Cv at same flow rate would result in a lower DP). The valve needs to throttle as much surge pressure as possible.

-Cavitation is not a direct result of choked flow. Cavitation only results from the downstream pressure (backpressure) restoring the fluid from vapor bubbles to liquid. The choked flow only caused the liquid stream to flash to a vapor originally.

-The ISA equation for choked flow DP plainly shows your governing parameters [DPmax = Fl^2*(P1-Ff*Pv)]. Max pressure drop at this point is only a function of valve characteristics & the difference between inlet pressure & the fluid's vapor pressure (not flow, not valve size).

-The only way DP (across the valve) can increase in this choked flow case is by increasing the inlet pressure (which I'm trying to avoid). My required DP and flow rate are not accommodated in this example, unless I consider Littleinch's two-phase flow pressure drop of 295 psi within the relief line downstream of the valve. If so, I'll need to increase the rating of the relief piping from Class 150 to Class 300.

 

[LittleInch]

Ok, One last time.

"At choked flow with a fixed inlet pressure (P1), the ISA DPmax (260 psid) is all I can drop across the valve. " NO IT ISN'T

What it is is the differential pressure based on a fixed inlet pressureat which you have MAXIMUM FLOW. Of course it can drop more pressure. As you say, this is reality. If you have a relief valve going into an open tank, what is going to stop it - Answer Nothing. This happens in htousands of relief valves all over the world. If this max DP was a real issue, I think it would be taught a lot more. The reason you can't find anything about it is that it doesn't exist.

The ISA calculation simply gives designers a maximum pressure at which choked flow occurs. Your question heading actually states this - Choked FLOW, not choked pressure.

A surge relief valve works on pressure. Go above the pressure, you get flow - quite a lot of flow for a short period. As soon as the pressure drops below your set point by 10%, the valve closes.

I really don't understand why you're having so much trouble accepting this.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[Latexman]

Do you understand choked flow of a gas? Do you understand about shock waves? Do you understand that shock waves = a pressure discontinuity? If so and for simplicity, think of similar phenomenon occurring in two phase choked flow. I know a pressure discontinuity is a little abstract and hard to get your mind around, it was for me many years ago, but . . . it happens.

In reality, it isn't that neat and clean for two phase choked flow. For example, see The Physical Basis of Choked Two Phase Flow. I'll leave it to you to study further. Enjoy!

Good luck,
Latexman

To a ChE, the glass is always full - 1/2 air and 1/2 water.

 

[Krausen]

All (especially Littleinch) - Thank you for the help. Evidently, I'm not too bright on this subject. I misread a line in one of the early posts that really threw me off course. I was irrationally concerned about the pressure rise above set point at the valve inlet during surge relief. I think I got it now. It helped to talk/write through it all.

 

[LittleInch]

Good. Glad you understand the process a little more.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.