Choked Flow For Vapor PSV Relief 3

[RJB32482]

Here are the conditions of the relief scenario I am looking at:

Case: Fire
Set Pressure: 120 psig
Relief Flow: 350 SCFM
Relief Material: Air

Now there is about 8 feet of piping in between the outlet of the relief and its discharge into atmosphere. To find if the flow is choked, how would I calculate the pressure at the outlet of the relief device? Would it just be atmospheric pressure or atmospheric pressure+(pressure drop through piping at relief conditions). Then using inlet pressure and specific heatt ratios, I could find if the outlet of the relief device is choked or not.


Thanks.

 

[sethoflagos]

You need a better textbook!

Coulson and Richardson (vol 3?) used to have a very good section on the fundamentals.

 

[EGT01]

Sethoflagos,

I may have spoken too quickly saying the differences between the equations in API 521 3rd and 4th editions were not significant. I said that remembering a comment that a colleague had made when we were discussing the differences and I never bothered to look at it closely till now.

As I said before, the only difference I see between the two editions is the 3rd edition uses the isothermal Mach number where the 4th edition uses the adiabatic Mach number, the difference being the inclusion of k = Cp/Cv in the 4th edition.
Following the method in API 4th edition the Mach number (M) is proportional to k^ -0.5 and fL/D is proportional to M^ -2.

When you combine the effects of the proportionalities, I believe this means the 4th edition will calculate a fL/D by a factor of k greater than what the 3rd edition calculates. As I interpret this, for a given allowable pressure drop in the outlet piping, the 4th edition says the line can be longer than what the 3rd edition will allow. Conversely, for an outlet line of given diameter and length, the 4th edition will calculate a lower pressure drop than the 3rd edition.

With the difference between the two editions being the value of k = Cp/Cv, I suspect that is what you had also found when comparing the other methods using k = 1.3 and finding a difference of about 25% in the results.

For as much difference the calculations in the two editions would indicate, I can't say I'm aware of any errata or techinal inquiry that API has issued that addresses this. I don't own a copy of the 4th edition but have access to it at work and I'm aware of only one errata published in 1999 that was not related to the isothermal method. API had been supporting a Technical Inquiries web page for their publications, but I've had trouble getting to it to check the latest for RP-521.

http://api-ep.api.org/committees/index.cfm?bitmask=002009002000000000

As far as how conservative the isothermal assumption might be, I would say the comparison should be against an adiabatic assumption but it may be somewhat dependent on what method of calculation you choose. The following gives you an idea of what I've seen but I would encourage you to conduct your own comparison so you don't end up making the mistake I made at the beginning of this post.

Using these conditions which would give a Mach number ~0.5 at the end of the pipe....
3000 lb/hr, MW=29, 100F, Z=0.95, k=1.4,
pipe id=1.939 in, total equivalent length of 15 ft,
14.7 psia at the outlet of the pipe

I find
The API 3rd edition isothermal method gives
Total backpressure = 19.7 psia, dP = 5 psi

Using the method Rbcoulter suggests, Cranes TP410 using the "Y" expansion factor gives
Total backpressure = 19.4 psia, dP = 4.7

The API 4th edition isothermal method gives
Total backpressure = 18.1 psia, dP = 3.4 psi

As additional comparison, I have the AIChE CCPS publication "Guidelines for Pressure Relief and Effluent Handling Systems" which came with a CDROM and a great set of relief valve calculation programs including one for compressible flow. Their program patterned after the analyses of Lapple and Shapiro, assumes adiabatic flow -- an assumption that is generally more realistic than the isothermal approximation. Their method gives basically the same result as Cranes TP410 using the "Y" expansion factor...
Total backpressure = 19.4 psia, dP = 4.7

In regards to the discussion of supersonic flow, I can't say I've ever heard anyone talk about that for relief valves before but I'm sure there are many other things that I haven't heard as well.

In reference to what Rbcoulter was remembering, he was probably referring to the typical converging/diverging nozzle arrangement that is used to purposely achieve supersonic flow...

http://www.engapplets.vt.edu/fluids/CDnozzle/cdinfo.html

As you mention, a free jet expansion is also likely to cause supersonic velocities...

http://members.aol.com/RudyHeld/dossier/dos1312.htm

But keep in mind that a relief valve is not arranged in such a way to give an unobstructed free jet. The nozzle of the relief valve discharges (impinges) directly against the disc, so I would expect that to dissipate some of the energy so that supersonic velocities are not actually achieveable in a relief valve.

 

[sethoflagos]

Thankyou again, EGT01, you confirm that API 4th ed is significantly NON-conservative for estimating dP. (From my own work I've found that back calculating allowable equivalent length from a given dP is even worse due its dependence on the square of upstream pressure).

I was sort of wishing I hadn't mentioned the 'free jet expansion' stuff! However, if you guys are going to gang up on me, here's a couple of questions for you.

We know that at rated discharge, the valve disk is held open by the stagnation pressure of the relieving gas (1.1 x Pset minus say 3% inlet line loss). For critical conditions, the flow in the throat is sonic at a flowing pressure equal to stagnation pressure (abs) x critical flow pressure ratio (0.53 for air). In our original case, conditions in the throat are therefore sonic at around 56 psig.

Between us, we have established that the flow close to the relief valve discharge is no more than 5 psig at ~30% sonic.

What has happened to the missing 50 psi and 90% of a Mach's worth of kinetic energy?

Surely, Bernoulli, or any other form of energy balance tells us that if pressure falls, then velocity increases. And if is to lose 90% of its pressure, isn't that a lot of velocity increase?

Well, you can put it all down to line losses, but then what if the PRV orifice was half the size? - Do you still get 56 psi line loss?

If this is the case then aren't you saying that critical relief is merely the extreme case of subcritical relief and there is nothing beyond that?

No argument at all if the downstream piping were the same cross-section as the throat. But it isn't is it? It's heading for an order of magnitude larger cross-section. Room for a bit of free expansion?

 

[Latexman]

What has happened to the missing 50 psi and 90% of a Mach's worth of kinetic energy?

The flow pressure decreases to the back pressure outside the nozzle by means of expansion waves. The fluid over which an expansion wave passes undergoes a reduction in pressure.

Good luck,
Latexman

 

[EGT01]

Sethoflagos,

I see that you are somewhat of a new-comer to the forums, and if you think "that" is ganging up on you, well.... give it a little more time. ;-)
Just joking, of course!

I can't say I know completely what goes on inside a relief valve. I know that the nozzle discharges against a disc that has a greater area than the nozzle seat. As the disc lifts, it creates a secondary pressure chamber referred to as the "huddling chamber" and that there is a secondary "orifice" created by the annular space (curtain area) between the disc and nozzle. I guess I never really thought about what the flow conditions might be through these passages but I've always heard that the rapid expansion of vapor within the huddling chamber is one thing that helps to make safety valves open with a pop action. I suppose you could consider that to be a type of free jet expansion.

With that said, I was able to find some info from the

http://WWW relating

to a search for
"relief valve supersonic".
There were a number of hits but I found this one especially intersesting...
"Cartridge-type direct loaded safety and pressure-relief valve having flow path for preventing supersonic flow and minimizing valve hysteresis
Document: United States Patent 4979540"

http://freepatentsonline.com/4979540.html

The jury may still be out on this topic but supersonic flow in a relief valve is something that can occur but at least one valve manufacturer seems to be designing to prevent it.

Don't know if this counts as a MythBuster

http://dsc.discovery.com/fansites/mythbusters/mythbusters.html

but I give you a star for making me think!

 

[sethoflagos]

Hmmm, interesting. So it takes a special design of relief valve to prevent supersonic flow? ;-)

 

[Latexman]

In many compressible flow applications there are regions of subsonic, sonic, and supersonic flow. It's called "mixed flow". The trick is to be able to determine which one predominates.

Good luck,
Latexman

 

[sethoflagos]

What actually got me thinking hard about this is EGT01's comments on the API 521 'anomaly' and whether that compromises the conservatism of the isothermal assumption.

If the rev 4 version underestimates pressure drops by 25+%, is there always at least 25% conservatism in the rev 3 version and others in the same vein (Crane, GPSA etc).

The very high pressure reliefs don't give me much concern, because the near adiabatic expansion combined with J-T effect depress (actual) temperatures quite substantially, and I can see a lot of conservatism there.

But what about the lower pressure relief cases when isothermal and adiabatic flow extremes are very close? Does rev 4 (which I am contractually obliged to use) lead to inadequately designed low pressure relief systems?

I hope this equation is never applied to noble gas reliefs!!!

Any thoughts, tipsters?