PSV discharge piping sizing calculation for compressible flow 1

[niallPOC]

I have an application where I am installing a pressure safety valve on the discharge pipework of an air compressor to protect the piping from overpressure. The PSV is located close to the compressor in the plant room but it is necessary to pipe the discharge of the PSV to outside the room to reduce noise in the plant room. The PSV will be an L orifice valve with a DN80 inlet and DN100 outlet. In order to keep cost down, I want to use a convential spring operated valve, not a bellows type and therefore am calculating the built-up back pressure in the discharge piping during venting to ensure it is not greater than 10% of the valve set pressure.
The difficulty I am having is calculating this built up back pressure. If I use a DN100 pipe for the discharge piping, with the flow rate at 14190kg/hr, which the valve is rated for, as the air expands down to atmospheric pressure through the discharge pipe it will easily reach sonic velocity and flow will be choked. Therefore I have looked at using DN150 pipe for the discharge piping with a DN100 to DN150 enlarger immediately downstream of the valve. To calculate the back pressure with this arrangement I have tried setting the exit pressure of the discharge pipe to atmospheric. However with the minimal pressure drop through the DN150 section of piping and a increase in pressure which occurs through the enlarger, the calculation is telling me choked flow will occur at the inlet of the enlarger.
I have been referring to API521/ISO23251 to help understand the sizing methodology and using FFDS 2.5C and standard isothrmal calculation sheets to calculate pressure drop.
I am stuck on the following basic points;
1 - For flow which is sub-sonic, i.e. not choked and capable of achieving full flow rate required, is setting the exit pressure from the discharge pipe at atmospheric pressure and working back to calculate back pressure at the valve the right approach?
2 - To calculate this is using Isothermal flow equation a suitable approach? The problem it generates is that the static pressure increases significantly through the enlarger. Is this realistic?
3 - If a PSV is rated for 14190kg/hr and greater, but has a DN100 outlet, will flow not choke in the outlet of this valve without any discharge piping, assuming that the air will be at atmospheric pressure right at the exit of the valve?

 

[sailoday28]

Assuming steady state conditions.
Item 1 Make sure that with exit to atmosphere at atmospheric pressure, the flow is not choked at the pipe exit. For perfect gas, constant specific heats
adiabatic flow, choke will occur at Mexti =1.
isothermal flow choke will occur at Mexit =1/sqrt(gamma)
Item 2- If pipe is well insulated, I would assume adiabatic flow in discharge piping--FANNO LINE
Is there enough heat transfer in the reducer (your enlarger) to justify isothermal conditions?
Item 3- You have to do the calculation for dischare piping and work back to the reducer to see if choking occurs in both valve AND reducer.

 

[niallPOC]

Thanks Sailoday28 for your post, though I am still stuggling a bit.
1 - I am confident that with a DN150 pipe at exit to atmosphere, flow will not be choked at pipe exit.
2 - I thought isothermal meant no heat transfer (constant temperature). I don't really see why there would be heat transfer in the enlarger. Pipe is not insulated at all. What do you mena by FANNO LINE?
3 - When you say 'do the calculation for the discharge piping and work back', that is what I have tried and and got stuck on. Starting at the end and assuming pressure at exit is atmospheric, calculates pressure at upstream end of DN150 section to be about 30kpag. But to have 30kpag at end of enlarger would require pressure to be significantly below atmospheric at inlet of reducer as pressure increases significantly as velocity slows down through the enlarger. If this where the case, with very low pressure at inlet of enlarger, flow would be choked at that point. This is where i get stuck doing a calculation from discharge piping back to valve.

 

[sailoday28]

For your comment
2-A FANNO line or process is where the flow is adiabatic (well insulated) steady state process with friction.
1- How have you determined flow will not be choked at exit.

For the DN150 what is the fL/d or 4fL/d ?
What is flow area of DN150?

 

[Latexman]

Forget about the inlet of the expander. The built-up backpressure calculation assumes the flow upstream of the expander (i.e. in the outlet flange of the PSV) is "well-developed flow" that can be represented by continuous mathmatical relationships to the flow in the expander and further downstream. In your case, it isn't! The flow upstream of the expander (i.e. in the outlet flange of the PSV) is determined mainly by the flow in the PSV, which will be sonic at the outlet of the nozzle, and have discontinuities (shock waves, expanding jets, etc.) as it goes through the rest of the PSV to the outlet flange. You have a discontinuity between the PSV outlet flange and the inlet to the expander. I envision a high speed jet of flow that only partially fills the downstream end of the expander blasting into the larger pipe with backmixing going on in the annular space until the jet expands to completely fill the pipe.

The folks that wrote the Code knew this. That's why they broke the calculation into discontinuous parts.

Good luck,
Latexman

 

[4Pipes]

Latexman,

I would sagree on 1 points and completely disagree on the other.
Yes. Back pressure is the static pressure at the face of the PSV outlet flange.
Definitely disagree on ignoring the expander. How do you know what shape it is? Secondly, and more importantly, even if it was actually a step change as you suggest, it could have a shock wave across it if it was choked hence back pressure at the flange. If it was a gradual expansion it would act as a nozzle.
I fully agree with Sailoday28. The calc should be fanno line from the pipe exit back to the downstream end of the reducer (Expander) if the flow can be reasonably assumed to be adiabatic. i.e. relatively short line). Then a separate calc for the expander using the results of the fanno line.

After saying all that, for an air system at normal pressure, I would suspect the expander will not be choked in which case you could treat it as a pipe fitting rather than a nozzle. For an air system, it would be simpler to use an isothermal calc which is less favourable than a fanno line. (still in 2 parts). If this shows the back pressure is ok then job done. If not, fanno line is another option if the line is short enough to be considered adiabatic. For a long line (I don't know how long is long) fanno and isothermal are the 2 extreme ends of calc. The real situaion is somewhere between.

 

[sailoday28]

niallPOC (Mechanical)
Can you supply the orifice area of the safety valve and areas of the 100 and 150 DN piping. Also the fl/d of the 150DN piping?
In addition, source pressure and temperature.

What is your basis for subsonic flow from the exit of the 150DN piping?

Regards

 

[Latexman]

4Pipes,

I said ignore “the inlet of the expander”. What I should have said was, ignore the fact that your 1D calc said the flow at the inlet of the expander is at mach 1, because there will be strong 3D effects going on there from the PSV immediately upstream. At least that’s what CFD has told me in the past. I really was not intending to suggest that “ignoring the (whole) expander” in the backpressure calculation was correct. I should have worded it more carefully. The expander should be included, in a 1D flow calc. For air, I subconsciously assumed the expander was a normal, commercial, concentric 6” x 4” pipe reducer, as did you, I believe. And, I agree wholeheartedly that “the (1D, backpressure) calc should be fanno line from the pipe exit back to the downstream end of the reducer”, followed by a separate calc for the expander.

I, like you, strongly suspect the expander inlet will not be chocked and can be treated like a pipe fitting.

Good luck,
Latexman

 

[4Pipes]

Latexman,

Apologies for not misinterpreting your post.

There are sizes of valve where choking at the reducer (expander) could be a consideration. However, I don't think this is one of them. What I have never figured out and would like to know, is how effective a commerical reducer is as a nozzle. I suspect not very, but possbily slightly with separation and shock waves somewhere in its length. Being simple, I would avoid that situation but not always possible when specified by others.

 

[4Pipes]

Doh. Should be "Apologies for misinterpreting".

 

[Latexman]

No worries. I don't think you have to worry about "body choke" in a PSV with air until you get up to a T orifice, which is about 8" inlet by 10" outlet IIRC.

Good luck,
Latexman

 

[CJKruger]

Latexman, calculations sometimes show choke flow at the PSV outlet flange/inlet to expander. If I understand correctly, you say this will not actually occur.

Do you have any references that discuss this issue, maybe with some measurements to back it up ?

CKruger

 

[niallPOC]

Thanks all for your valued comments on this. I believe I am now beginning to "see the light", though still a little confused by the concept of the "discontinuity" at the PSV outlet/expander inlet and how to actually do separate calculations for the DN150 line and expander. Does that mean that, starting with atmospheric pressure at outlet of DN150 pipe(P exit) and working back to determine pressure at start of DN150 section (P1), using either an adiabatic, fanno line or isothermal calculation, the pressure determined for p1 from this calculation is not the pressure at the outlet of the expander?

Maybe if I throw up some actual number on the problem, as suggested by sailoday, some of you guys can have a go!
-PSV is an L orifice valve (1840mm^2 area)
-Set pressure is 960kPag @50degC
-flowing pressure 1166kPa(a)
-Rated flow through PSV which I am using as basis for discharge piping calc = 16700kg/hr
-fluid is dry air
-Discharge piping consists of the following, working from DN100 (4") PSV outlet flange to exit point to atmosphere
-standard DN100(4")cl150 weldneck flange - standard ANSI B16.9 140mm long DN100(4") to DN150(6") eccentric enlarger (reducer) - Standard B16.9 ANSI DN150 (6") Long radius 90 degree elbow - 2m of DN150 (6") sch 40 commercial carbon steel pipe vertical - Standard B16.9 ANSI DN150 (6") Long radius 90 degree elbow - 4m of DN150 (6") sch 40 commercial carbon steel pipe horizontal with end venting to atmosphere ( 98kPa (a) site atmospheric pressure)

I have calculated that this flowrate exiting a DN150 (6") pipe at atmospheric pressure will have a mach number of 0.77 using API521 equation (27) or lower if I calulate it using adiabatic or isothermal flow calc in my FFDS software.
Therefore not choked flow at exit
Also calculate, setting Pexit at 98kPa(a) that pressure at start of DN150 section (outlet of enlarger) will be 129kPa (a), using adiabatic flow calulation.
But what will buit up back pressure on valve be when flowing???????????????

Apologies for dragging this out. I am not an engineer who regularly gets into this type of theory.
Any attempts at a calc would be appreciated. Make any assumptions necessary if info not included above and state assumptions made.

 

[CJKruger]

niallPOC, another hydraulic program (Korf) gives the following results (isothermal flow):

- Pres at tail pipe outlet = 0 kPag
- Pres at enlarger outlet = 36 kPag
- Pres at enlarger inlet = choked, pres approx 70 kPag (iterative calc)
- Pres at PSV outlet = approx 80 kPag

Thus, even if you have choke flow at the expander inlet, the PSV back pressure will be fine. This is still a big "if", as Latexman recommend that we do not actually get choke flow.

CKruger

 

[sailoday28]

For the exit to the atmosphere to have M = or <1
and adiabatic flow, the following must be met


(PA)/(PoAt) > or = 0.528
Po is source pressure P= pexit A= Aexit.
At = 0.9 *Athroat
My numbers Using where Athroat is "L" orifice area
0.9 for a coefficient of discharge.

(PA)/(PoAt)=0.183

Thus, exit under Fanno conditions will not be subsonic.
Please check my numbers in obtaining the 0.183 ratio.

Regards

Please check my input

 

[sailoday28]

I caught my error on discharge flow area.
Checking my input (PA)/(PoAt)=.95 which yields Mexit to atmosphere at M=0.59


If Cd=1 Mexit=0.6

Therefore original basis of subsonic exit flow is correct, with adiabatic flow.

Next the FANNO process should be checked with fl/d

 

[Latexman]

P_{tailpipe outlet} = -3.325 kPag
P_{enlarger outlet} = 38.6 kPag
P_{enlarger inlet} = P_{PSV outlet} = 76.5 kPag

BP = 8.3% (corrected to 0 kPag atmospheric pressure) and a conventional PSV is fine.

From the practical view and in this case, you can ignore the fact that a one dimensional (1D) analysis says the velocity is Mach 1 at the enlarger inlet. Why? BP < 10% and one cannot reduce atmospheric pressure (to increase flow if there was no choke) anyway. In short, it's not hindering the flow and no one (in their right mind) would do anything about it anyway.

From a purely academic view, I question if a 1D analysis from the outlet of the PSV's flow nozzle to about 10 pipe diameters downstream is the best method for this analysis. Yes, it is adequate for the task at hand, based on decades of evidence. But, I suspect there are strong three dimensional effects going on that may impact whether it is truly choked or not. I have not seen a CFD for niallPOC's application, but I have seen some done during root cause investigations of PSVs that failed. One failed from erosion and one in oxygen service exploded. Both were higher pressure applications and the CFDs said velocities approached sonic speed, but fell a little short of Mach 1.

Good luck,
Latexman

 

[Latexman]

Here is a similar analysis I found on NTRS:

http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19950024441_1995124441.pdf

Good luck,
Latexman

 

[sailoday28]

Based upon Mexit to atm at ).6
For FANNO line.----adiabatic flow or no heat transfer.
Note, elevation effects are negligible.

For fL/d= 1 Penlarger outlet/Patm= 1.33
Penlarger outlet =98kPa(a)*1.33= 130.6 kPa(a) =32.6 kPa(g)

For fL/d=1.5 Penlarger outlet/Patm= 1.477
Penlarger outlet =98kPa(a)*1.477= 144.8 kPa(a) =46.8 kPa(g)

What is Temperature at valve inlet under relieving conditions?

 

[sailoday28]

Conditions at valve outlet
For adiabatic flow
(PA)/(PoAt)= 0.528 M=1
neglecting KE and assuming Cd=0.9 At=.9*A"lorifice"
Aoutlet= 12.73 sq in Poutlet= Penlarger inlet= 124.1 kPa(a)
26.2kPa(g)
Poutlet Stagnation= 235.2 kPa(a)

A=11.5 sq in Poutlet= Penlarger inlet= 137.5 kPa(a)
39.5kPa(g)
Poutlet Stagnation= 260.3 kPa(a)