×
INTELLIGENT WORK FORUMS
FOR ENGINEERING PROFESSIONALS

Log In

Come Join Us!

Are you an
Engineering professional?
Join Eng-Tips Forums!
  • Talk With Other Members
  • Be Notified Of Responses
    To Your Posts
  • Keyword Search
  • One-Click Access To Your
    Favorite Forums
  • Automated Signatures
    On Your Posts
  • Best Of All, It's Free!
  • Students Click Here

*Eng-Tips's functionality depends on members receiving e-mail. By joining you are opting in to receive e-mail.

Posting Guidelines

Promoting, selling, recruiting, coursework and thesis posting is forbidden.

Students Click Here

Jobs

Choked Flow For Vapor PSV Relief
3

Choked Flow For Vapor PSV Relief

Choked Flow For Vapor PSV Relief

(OP)
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.

RE: Choked Flow For Vapor PSV Relief

Find the resistance coefficient (Keq) of your discharge system.   Using this value and the ratio of specific heats of air to deterime the  pressure ratio.  Crane technical paper No. 410 has charts on this.  If your pressure ratio is greater than the critical pressure ratio (delta P)/(inlet P) then your flow is choked.

RE: Choked Flow For Vapor PSV Relief

(OP)
Thanks for the response.  When doing this calc, do I have to take account any pressure drop in the valve itself?  If so, how would I calculate the pressure drop in a PSV?

Thanks.

RE: Choked Flow For Vapor PSV Relief

Yes.  You must account for the pressure drop in the relief valve.  You can probably get a Cv value for the valve from the manufacturer.  Convert this to a K Value per the relationships in the Crane paper. Add to this the K values for the pipe lengths, fittings, entrances, exits, etc.   Determine the pressure ratio as mentioned above.  Use the pressure ratio to determine the flow rate through the system.   Use the flow rate to determine the pressure drop across the relief valve.

RE: Choked Flow For Vapor PSV Relief

Are you are referring to the charts for Net Expansion Factor Y for Compressible Flow Through Pipe to a Larger Flow Area?  These charts were derived for a single diameter pipe.  Combining a K for a PSV (the flow nozzle ~ 0.2") and a K for an outlet pipe (d ~ 2"), even if both K's are based on the smaller diameter, is not practical.  The PSV K will overwhelm the numbers and make it difficult to get good numbers for the tailpipe.

Good luck,
Latexman

RE: Choked Flow For Vapor PSV Relief

RJB32482,

Let's backup to your original post.  The flow through a relief system can "choke" at several different points.  Choked flow is also referred to as critical flow or sonic flow when the velocity of the fluid reaches its limiting velocity which is the velocity of sound in the flowing fluid at that location.

Typically, flow through a relief valve nozzle will experience critical flow unless the relief valve set pressure is very low (say about 15 psig) or you have substantial backpressure.  You can use the methods in API RP-520 Part I to determine when you have critical or subcritical flow through your relief valve nozzle.  When discharging to atmosphere, the backpressure (absolute) will be the sum of the pressure drop through the piping + atmospheric pressure.  Compare your backpressure (absolute) to the critical flow pressure as determined in API to determine if you have critical or subcritical flow through your relief valve in order to select the proper relief valve sizing equations.

You can also experience critical (choked) flow in the relief valve outlet piping and typically this can occur at the end of the pipe where the fluid exits to atmosphere or at a point where the piping diameter changes such as at an expansion fitting.  You can refer to the methods in API RP-521 to determine whether you experience critical flow in your outlet piping.  Critical flow at points in the outlet piping will produce a pressure discontinuity and you can have a substantial pressure drop over small distances of travel and again it is related to the limiting velocity at that location.  Any pressure discontinuities also need to be included as being part of the pressure drop through your piping.

I would add that there is some difference in the equations presented in 3rd (1990) and 4th (1997) editions of API RP-521.  The method API RP-521 presents is based on an isothermal flow assumption.  In the 3rd edition the equation for mach number is the isothermal mach number which I believe is the correct one to use for the isothermal assumption.  The 4th edition gives the equation for mach number as the adiabatic mach number which differs only by inclusion of the specific heat ratio.  I don't think the difference is great enough to be of significant concern but I think the next edition (5th) of API 521 is going back to showing the isothermal mach number equation.

RE: Choked Flow For Vapor PSV Relief

Yes.  Even with the limitations it is the best method that I am aware.  The method would be to find the Keq of the valve best on the inside diameter of the 2" pipe and add that to the pipe lengths specified.  See page 2-8 of Crane.


Seems like a very low beta for a relief nozzle.  If this is this case, then the method simply indicates that the tail pipe has very little contribution to the back pressure.

RE: Choked Flow For Vapor PSV Relief

Not only do I disagree with treating a PSV, which I treat as an isentropic nozzle, like a piece of pipe, but this straightforward PSV can be sized without combining the PSV with the outlet (or the inlet) into a K value.  In fact, compressible flow methods do not have to be used on the inlet or outlet dP.

With a set pressure of 120 psi, we know the flow will be sonic at the flow nozzle exit in the PSV.  350 scfm sets the mass flow rate of the sizing basis (1604 lb/hr).  If you pick a make, model, and flow nozzle size of PSV, this plus knowing Cp/Cv = 1.4 determines rc.  With the PSV fixed now, the actual peak flow rate through the PSV alone can be calculated and compared to the sizing basis.  Ignore the inlet and outlet.  Just calculate the flow through a wide open PSV with air at 120 x 1.21 psig.

Knowing the lengths and fittings, calculate the pipe  diameter for the inlet (dP < 3% x 120 psig) and the outlet (dP < 10% x 120 psig) at the actual peak flow rate.  Incompressible methods can be used here since dP < 10% of P1.  

At this point, I believe Code has been satisfied and good engineering practice has been used.  The PSV is big enough.  Inlet dP < 3% of set pressure.  Outlet dP < 10% of set pressure.

Good luck,
Latexman

RE: Choked Flow For Vapor PSV Relief

By "Incompressible methods can be used here since dP < 10% of P1" I meant to say incompressible methods can be used here if we choose a diameter so dP < 10% of P1 (or P2),

Good luck,
Latexman

RE: Choked Flow For Vapor PSV Relief

You are correct if the discharge pipe offers little resistance compared to the relief valve, but can you always assume that to be the case? I don't think so. You also cannot always assume the flow is incomopressible in the tail pipe.  What if the relief valve had a high beta (like 0.8) and the discharge pipe long enough to have comparable resistance to the relief valve?

RE: Choked Flow For Vapor PSV Relief

I agree you cannot always assume the flow is incompressible in the tail pipe.  Good engineering practice suggests that when dP/P1 is greater than or equal to 40%, compressible flow methods must be used.

In a case where the tailpipe offers more resistance than this particular case, you can still keep the PSV and tailpipe flow calculation separate, but as the built-up backpressure increases you have to select a bellows PSV or pilot operated PSV that can handle the increased back-pressure.  As mentioned above, the correct dP method for the tailpipe must be used.

Good luck,
Latexman

RE: Choked Flow For Vapor PSV Relief

Fellow Tippers,

I strongly suggest you review the references in API RP-521 when comes to the design of relief valve discharge piping.  I believe it offers a very reasonable and practical approach and I see no reason to re-invent the wheel on this subject.  

As quoted from API RP-521
"Vapor flow in relief discharge piping is characterized by rapid changes in density and velocity; consequently, the flow should be rated as compressible."

Latexman, I believe you have mistakenly associated P1 with Pset in your evaluation of the use of an incompressible calculation for the outlet piping.  

For Pset = 120 psig, and in the case of a conventional type relief valve, the allowable backpressure is 10% of Pset then Pb = 12 psig.  If that backpressure is a result of builtup backpressure then dP = 12 psi.  

For Pb = 12 psig or 26.7 psia this is in effect P1 of the outlet piping.  In that case,
12 psi/26.7 psia = 0.45
which is well outside the limit of 0.1 in order to use the incompressible calculation approach with either the upstream or downstream denisty.  

This is also beyond the limit of 0.4 where the incompressible approach is used with the average density between upstream and downstream conditions.

RE: Choked Flow For Vapor PSV Relief

EGT01,

I can see how you interpreted it that way.  I should have explained the nomenclature to avert this, instead of writing in "Crane TP410-ese", or separated the sentence they are in with more explanantion.

It was clear in my mind that I was talking about two separate conditions that each have a different 10% guideline.  I put the Code requirement for the tailpipe in parentheses, like (dP < 10% x 120 psig), and said "incompressible methods can be used here if we choose a diameter so dP < 10% of P1".  120 psig is Pset, P1 is the beginning of the tailpipe, and P2 is the end of the tailpipe.  Nowhere did I say P1 = 120 psig, but the two similar looking guidelines are confusing in this case.

Good luck,
Latexman

RE: Choked Flow For Vapor PSV Relief

Latexman,

Actually, I did not see your post at 12:09 before my post at 12:29 so your previous post helped to clear up that confusion.  

Also, I definitely agree with you about keeping the relief valve calculation separate from the piping calculations.

RE: Choked Flow For Vapor PSV Relief

EGT01,

Your earlier comment on API RP 521 Rev 4 isothermal flow equation is very interesting. I did a check of equation 21 in the course of some recent (subsea) flare header work, against Crane (eq 1-6) and GPSA (Eqn 17-15); after some algebra shuffling API seems to be short by Z/k on the right hand side. This isn't a trivial difference. I found it underestimating the header equivalent length by about 25% (Z~1, k~1.3) compared to the other two methods. Have you any feel for how conservative the isothermal assumption is for low pressure relief systems operating, say ~ Mach 0.5?      

RE: Choked Flow For Vapor PSV Relief

rbcoulter,

It's probably a bit late in the day, but for the record the choked flow check for the short tailpipe you discribed is very straightforward. We assume the exit loss at the end of the tailpipe equals 1 velocity head which conveniently makes the flare tip (flowing) pressure atmospheric. Assuming the boiling liquid in your fire case is water, the relieving temperature is around 357F (b.p. @ 1.1 x Pset). This gives a tip velocity of 446 fps or Mach 0.32 for AIR (steam gives lower Mach No.). In pipes of constant cross section (subsonic) Mach No.s increase with distance, therefore upstream Mach numbers are less than 0.32 and there is no choked condition.

Finally, providing the line loss calcs described by latexman and EGT01 pass code requirement of dP<0.1 x Pset, everything has checked out ok.

Hope this helps      

RE: Choked Flow For Vapor PSV Relief

sethoflagos,

I am not certain which case you are referencing.   This thread refers back to RJB32482's scenario.  I am not certain how you arrived at subsonic flow for the case you proposed.  Maybe you can elaborate.
 

RE: Choked Flow For Vapor PSV Relief

Oops, You're right of course, it was RJB32482's posting.

Anyway for the original case, of 350 scfm exiting the tailpipe tip at atmospheric from (I guessed Sch 80) 2" pipe, the velocity is subsonic (446 fps vs sonic velocity of ~1400 fps @ 357 deg F). Upstream, so long as there's no change in cross-section, the density is higher so the velocity is less. ie the exit velocity of 0.32 Mach at the tailpipe tip is the maximum Mach value.

Note that the only parameters here are exit pressure, mass flow and pipe geometry - the tailpipe hydraulics are independent of PRV set pressure.


However, providing downstream pressures are less than about half Pset, the PRV discharge nozzle is running in an altogether different regime that is dependent only on PRV set pressure and throat size - the PRV throat hydraulics are independent of exit pressure.  

In this regime, flow through the PRV throat is sonic at a little below Pset. Exiting the throat, the gas accelerates and depressurises extremely rapidly in a free expansion jet that may achieve Mach 3 or so. Being supersonic, no downstream pressure information can travel against the flow which is why this zone is independent of exit pressure.

Eventually the two competing regimes must join but this requires the jet being able to match both the downstream pressure and velocity. It can only do this by converting a velocity drop to a pressure increase (conservation of momentum) in an adiabatic recompression. Because there is so much velocity to lose it has to first expand to substially below atmospheric pressure to make room for the positive step in pressure. When it reaches a point where everything balances the jet can jump instantaneously to the downstream subsonic regime creating a pressure discontinuity and a front of pressure shockwaves. Typically, this all happens within the PRV discharge nozzle or immediately downstream, so for all the noise it makes, it actually has little impact on tailpipe hydraulics.



 

  

RE: Choked Flow For Vapor PSV Relief

I understand your point now.  Of course, the choice of the 2" discharge pipe is arbitrary since it wasn't mentioned in the original post.  Assuming that that is indeed the case then you are correct that the flow will most likely be choked at the relief valve orifice or nozzle because the delta p to upstream pressure ratio is quite high.   You seem to be speculating about what occurs downstream of the nozzle.   I don't really know.   I have read that supersonic velocity can occur but my understanding is that you need a certain shape expansion nozzle to do this.  Most likely, the energy is lost to shock waves, turbulence, etc. without achieving sonic velocity.  I am basically paraphrasing what I have read in my Thermodynamics textbook from college which I keep on my computer desk.

RE: Choked Flow For Vapor PSV Relief

I meant to say "supersonic" velocity in line 6.

RE: Choked Flow For Vapor PSV Relief

You need a better textbook!

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

RE: Choked Flow For Vapor PSV Relief

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.

RE: Choked Flow For Vapor PSV Relief

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?

RE: Choked Flow For Vapor PSV Relief

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

RE: Choked Flow For Vapor PSV Relief

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.  winky smile
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 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!  thumbsup2

RE: Choked Flow For Vapor PSV Relief

Hmmm, interesting. So it takes a special design of relief valve to prevent supersonic flow? winky smile

RE: Choked Flow For Vapor PSV Relief

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

RE: Choked Flow For Vapor PSV Relief

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?    

Red Flag This Post

Please let us know here why this post is inappropriate. Reasons such as off-topic, duplicates, flames, illegal, vulgar, or students posting their homework.

Red Flag Submitted

Thank you for helping keep Eng-Tips Forums free from inappropriate posts.
The Eng-Tips staff will check this out and take appropriate action.

Reply To This Thread

Posting in the Eng-Tips forums is a member-only feature.

Click Here to join Eng-Tips and talk with other members!


Resources