We have open discharge and closed discharge PSVs in plants.

For open discharge piping the PSV outlet first leg is of very short length and then piping is vertical at the end of which we put downward PSV relieving force multiplied with DLF in static analysis.

For closed discharge piping the PSV outlet first leg is of short length; here we put full PSV relieving force multiplied with DLF in static analysis in direction opposite to fluid flow.

Why in larger legs in PSV inlet and outlet the PSV relieving force multiplied with DLF in static analysis will not be applied is not understood!

It is as if of steam hammer load discussed in article in Coade MEN Jun 94, the first leg from TTV valve is considered for steam hammer load, not other legs! In page 401 of Peng book on piping stress analysis, it is written that the longer the leg, the greater the net force with maximum for Length sonic velocity*closing time figure.

Relatively, for 660-800MW STG unit TTV of closing time of 10mSec is rare, but PSV with 10mSec in process plants are commonnplace.

Are we underdesigning our PSV piping currently by ignoring occasional loads on other legs ?
reg,
sam

Perhaps part of the problem here is the type of CAESAR II dynamic analysis used to evaluate this situation. Both force response spectrum analysis and time history analysis can be used. The force spectrum method can be used for individual runs of pipe while the time history method allows you to schedule events on one straight run after another to evaluate the interaction of many sequential elbow "hits" through the system.
Whether it's force response spectrum or time history analysis, the dynamic analysis will develop the amplification (your DLF) associated with each mode of system vibration included in the analysis. There is no DLF to define in dynamic analysis. You would set a general DLF (=2?) for the static analysis, not for the dynamic analysis.
It is up to the engineer to determine if analyzing additional legs down the run is significant. A time history analysis would be indicated if you wish to examine the interaction with pressure imbalances developed elsewhere in the system.

As you say, it is common practice for many stressers to only analyze the first load at the PSV in closed systems, often calculating the load via API-520 or similar.

It is typically simultaneously over-conservative and under-conservative. The first run off PSVs is often short. Actual load seen for short runs will be much lower. However, they forgo loads within the rest of the closed system.

I tend to stick with the DLF of 2 throughout a static analysis as this methodology remains both conservative and results in stresses well below allowable in my line of work.

Hello Stressers,

Just want to share my thoughts on this topic.

One of our client have added a requirement in PSV systems just recently. The old spec doesn't show this.

"Relief in closed systems shall consider the force due to change of momentum at every elbow up to the main header. Static analysis shall consider the force in just one elbow at a time. In lieu of static analysis, a time history analysis may be considered."

𝐹=𝜌(𝑉^2)(𝐴)

If I'm not mistaken, the formula above is due to drag force created during the high velocity flow (in a turbulent regime).

But I think, this one is still subject for discussion as most of procedure established in the majority of EPC company's is considering that in the steady state condition the forces are balanced in a closed system. In my previous experience, we can consider (pop-up condition and steady state condition).For closed system, we put the force at the elbow nearest to the header (with the assumption that the header is a large volume and can be considered an open boundary). So basically, in this manner the treatment is almost the same for both open and closed system.

Anyway, just sharing what I have experienced so far. This requirement becomes additional man-hour in our part because it was not included in the old spec. Even in my 1st EPC company I have read this in the procedure: "Only the reaction force of a relief system with the tail pipe open to the atmosphere needs
to be considered. The reaction of a closed system can be ignored."

What I can see in this case is during those days the procedure are simplified as long as good design practice is followed. But nowadays with the availability of powerful computer software in fluid simulation, the physics behind all this can now be coded in these software. Integrating the mechanical and fluid simulation software is even possible now. But in a typical EPC set-up it is the process engineer who do the fluid simulation and the stress engineer who do the mechanical simulation. So as a stress engineer it would be best for us also to know some basic physics in fluid mechanics/dynamics related to fluid flows so we can effectively communicate with the process engineer what we need from them.

Any other opinion is greatly appreciated.

Cheers!!!

It seems like this is what you get if you imagine a relieving event as a ball thrown into a pipe.

It ignores the effects of sudden pressurization (non-conservative) (this is outlined by the Peng method), and it ignores load cancellation in fluid flow in consecutive elbows (conservative).

With regards to pipe stress evolution, it does make sense as analysis becomes cheaper and more reliable to veer towards thinner and lighter pipe, but until piping codes (and laws mandating their use) also evolve, I suspect that it'll be a long time before it becomes standard. This isn't terrible, as tried and true results in greater public and end-user safety, and longer life of their systems.

I also suspect that within the next decade or so that we'll see more in the way energy conservation within piping systems (e.g. looking for ways to pipe systems to eliminate pressure losses to save operating costs).

Hi Michael,

Thanks for that opinion. This requirement was added to the normal (pop-up & steady state condition) that most of the EPC company use which makes the system more robust.

Any other opinion is highly appreciated.

Cheers!!!

Hello Stressers!!!

I would like to share ASME B31.1 regarding possible excitation of standing wave (air in a closed psv discharge system) by the release of steam (high velocity flow) during psv pop-up condition.

"The pressures in a closed discharge pipe during steady state flow may be determined by the methods described
in para. II-2.2.1. However, when a safety valve discharge
is connected to a relatively long run of pipe and is
suddenly opened, there is a period of transient flow
until the steady state discharge condition is reached.
During this transient period, the pressure and flow will
not be uniform. When the safety valve is initially opened,
the discharge pipe may be filled with air. If the safety
valve is on a steam system, the steam discharge from
the valve must purge the air from the pipe before steady
state steam flow is established and, as the pressure
builds up at the valve outlet flange and waves start
to travel down the discharge pipe, the pressure wave
initially emanating from the valve will steepen as it
propagates, and it may steepen into a shock wave before
it reaches the exit. Because of this, it is recommended
that the design pressure of the closed discharge pipe be
greater than the steady state operating pressure by a
factor of at least 2."

As we know from physics of waves that in a closed boundary condition waves maybe reflected and can be amplified if there will be an in-phase depending on the geometry and frequency of the system, but will eventually go to steady state due to damping effects, e.g. friction.

Any other opinion is highly appreciated.

Cheers!!!

Dear Borzki,

The usual design procedures presume (and assure in practice) sonic flow in the throat of the PSV nozzle.

We know that when a flowing gas at some location in the pipe/ tube experiences a local velocity equal to the sonic velocity of the gas at that temperature, sonic choking occurs and a shock wave forms and we have the math to describe the wave. The problem is that a PSV has a complex 3D geometry which certainly cannot be compared with a pipe/ tube/ pipeline/ duct. A supplementary complication is that we have to consider (but usually we neglect to do it) the wave propagation together with the unsteady flow and built-up back-pressure. Simply said, we haven't the math to describe the wave but we try to say something. The assumption of a wave described by chocked flow rate/ thrust force correlated with PSV opening time is a tentative to say something about the subject and anyway it is better than considering nothing. In brackets, I still think that I have no problems of engineering ethics saying that this approach is just an engineering one that seems to be naive for a scientist. For sure I have no problem that for some of us, this scenario is the ultimate knowledge in this field.

Returning to the subject, I think that what B31.1 wrote there is another tentative to re-conciliate the fluid flow and the wave.
They say "as the pressure builds up at the valve outlet flange and waves start to travel down the discharge pipe, the pressure wave initially emanating from the valve will steepen as it propagates, and it may steepen into a shock wave before
it reaches the exit.". I comment because I do not understand to which kind of shock waves they refer to. It seems that this category of shock waves is correlated with a pressure increase ("as the pressure builds up at the valve outlet flange") that is able to accelerate the initial subsonic wave?
I think my miss-understanding issue is also because the shock waves generated by sonic choking are associated with pressure and density decrease, not increase. Basically, in expansion choking, end-point choking or restriction choking the fluid flow generates the wave because the gas pressure cannot drop to match local conditions without the gas accelerating to sonic velocity.
As my conclusion, it appears for me as an rough tentative to explain shock- waves traveling through discharge piping.

Hi Mariog,

Thanks for the very detailed explanation. Honestly speaking, I find it hard to fully understand and simulate in CFD the complex physics of PSV system. It takes a lot of patience to study this deeper. And sometimes problem of this nature is being solved reactively, as it happens in the field as there are so many uncertainties being faced during the design phase.

What maybe I can do in the design phase is to have well-restrained piping system to cover this uncertainties.

Here is another section in ASME B31.1:

"Reaction Forces With Closed Discharge
Systems. When safety valves discharge a closed piping
system, the forces acting on the piping system under
steady state flow will be self-equilibrated, and do not
create significant bending moments on the piping system.
The large steady state force will act only at the
point of discharge, and the magnitude of this force may
be determined as described for open discharge systems.
Relief valves discharging into an enclosed piping system
create momentary unbalanced forces which act on
the piping system during the first few milliseconds following
relief valve lift. The pressure waves traveling
through the piping system following the rapid opening
of the safety valve will cause bending moments in the
safety valve discharge piping and throughout the
remainder of the piping system. In such a case, the
designer must compute the magnitude of the loads, and
perform appropriate evaluation of their effects."

Any other opinion is greatly appreciated.

Cheers!!!

Hi Mariog,

I like this statement you have mentioned in the post.

"Basically, in expansion choking, end-point choking or restriction choking the fluid flow generates the wave because the gas pressure cannot drop to match local conditions without the gas accelerating to sonic velocity."

Any other opinion is highly appreciated.

Cheers!!!

Related to the statement I've made, I'm afraid is not an original one. I attach again an article about compressible flow written by Trey Walters, creator of AFT package. The article has a nice title- Gas-flow Calculations: Don't Choke- and includes more valuable information than many books dedicated to this subject. And it is accessible to engineers.

In fact that statement explains also what is happening in your PSV system delivering steam to atmosphere (you've mentioned it in a recent post); the steam pressure cannot drop to atmospheric conditions without the steam accelerating to sonic velocity. Of course the steam pressure drops but to a pressure correlated with sonic velocity. That pressure participates to the reaction force.

Returning now to the waves generated by PSV chocked conditions, one may consider that the chocked pressure is responsible for the wave generated; this assumption remains in the same "innocent" engineering approach as many others... And next question, accepting this assumption, it is more likely to be a plane wave- outlet flange orientated or a cylindrical one, around the disk?

Thanks Mariog for that further explanation. It's a bit clearer now to me in a nutshell. Especially my dilemma in another post regarding two enlarging reducer after the PSV towards the outlet (10"x18x26") where 26" is the outlet discharge pipe to atmosphere. I've found out in one of the youtube videos that the effect on the back pressure on the sub-sonic flow (M<1) and supersonic flow (M>1) on a diverging nozzle is different where the pressure will increase in a sub-sonic and pressure will decrease in a supersonic flow.

https://www.youtube.com/watch?v=3lkO12Fz-Q8

This clears my mind of thinking that the pressure will increase after reducer, but of course I need to check my mach number based on mass flow rate, density and outlet PSV pipe size. In my case the Mach number is 1.3.

Any other opinion is greatly appreciated & please correct some of my statements just in case.

Cheers!!

Here I remain rather in line with Mr. Trey Walters/ AFT opinion- please see the article. It is more likely to have a chocked flow in the reducer than to have Mach>1 there.

Hi Mariog. That was a quick reply. Anyway, I'll read first the article and digest it more. Can this phenomena be proven by say physical testing.

Also, I'll try to study if the flow is choked and M is less than 1 at the nozzle.

This was indeed a very fruitful discussion.

Any other opinion is greatly appreciated.

Please correct some of my statements.

Cheers!!!

Hi Mariog,

Thanks for sharing this article. I like this part of the article:

"Sonic choking
In almost all instances of gas flow in pipes, the gas accelerates along the length of the pipe. This behavior can be understood from Equations (2), (3) and (5). In Equation (3), the pressure falls off, due to friction. As the pressure drops, the gas density will also drop (Equation [5]). According to Equation (2), the dropping density must be balanced by an increase in velocity to maintain mass balance.
It is not surprising, then, that gas flow in pipelines commonly takes place at velocities far greater than those for liquid flow — indeed, gases often approach sonic velocity, the local speed of sound. A typical sonic velocity for air is 1,000 ft/s (305 m/s).
When a flowing gas at some location in the pipeline experiences a local velocity equal to the sonic velocity of the gas at that temperature, sonic choking occurs and a shock wave forms. Such choking can occur in various pipe configurations (Figure 1)."

Sorry my bad if I directly converted the calculated entrance velocity to mach number of 1.3. From this article, what I can see is the flow after the three types of discontinuities described can only reach sonic state and not supersonic state due to choking (please correct me if this is a wrong statement), and the pressure will correspond to this sonic state.

Anyway, it still clear my thought process before that the pressure in an enlarging reducer will increase but in this article it will drop (the K values I'm referring to previously is I think developed for turbulent incompressible flow).

Please correct any misleading statements I've made above.

But in a nutshell it's a bit clear to me now.

Any other opinion is greatly appreciated.

Cheers!!!

Dear Borzki,

I think you understood well what Mr. Trey Walters wrote. Many engineers may not agree with his approach, however AFT package, particularly AFT Arrow for compressible flow is a success, being a software validated by experiences- and is based on the ideas exposed in the article.

In fact the steady-state compressible flow is not so complicated, the way the academics present it is complicated and probably more than 90% of engineers are confused on this subject after graduating. That's why I recommend all to read the article. I agree the unsteady compressible flow seems to be "terrible" and a little progress was made as to be really understood by engineers; here I cannot recommend a similar article.

Best regards.

Hi Mariog,

Thanks for that. I think now I'm getting your point. I also like this part of the article:

"Other simplified compressible-flow methods: A variety of simplified gas flow equations, often based on assuming isothermal flow, crop up in the practical engineering literature. These typically have several drawbacks that are not always acknowledged or recognized:
• Most gas flows are not isothermal. In such cases, one cannot know how much error is introduced by the assumption of constant temperature. Related to this is the general issue of the importance of heat transfer on the gas flow, already mentioned
• Simplified equations typically do not address sonic-choking issues
• These equations are of no help when the delivery temperature is important
• The simplified equations break down at high Mach numbers
• Unrealistically, the entire pipe is solved in one lumped calculation, rather than using a marching solution
• It is difficult to extend the equations to pipe networks
In summary, simplified compressible flow equations can be an improvement over assuming incompressible flow, but numerous drawbacks limit their usefulness."

What I can see is due to the simplifying assumptions made as mentioned above, results in high mach numbers ("The simplified equations break down at high Mach numbers."). I think most of the CFD software packages are based on this simplified equations for compressible flows (density based solvers), so the software have the results based on this assumption.

Maybe that's why most of the youtube videos (CFD simulation) I've watched have this kind of solution (M>1) at the diverging outlet.

Please correct me if I have made any wrong statement above.

Anyway, thanks for this fruitful discussion.

Any other opinion is highly appreciated.

Cheers!!!

Hi Mariog and fellow stressers,

Just to clear my doubt, I have run an example case with the data given below.

1) Back pressure at the outlet flange of PSV = 45 Kpag (shown in datasheet)
2) Mass flow rate during relieving of PSV (12.165 kg/sec)
3) Fluid is steam at 371 deg C
4) Pipe ID after outlet flange is 254.51mm (for 10" pipe).
5) After 10" flange outlet two enlarging reducers is directly welded to flange (18"x10" and 24"x18"). Pipe ID for 18" and 24" are 438.15 mm and 590.5mm respectively.
6) After the two enlarging reduces there is a 12m 24" diameter long run pipe going to open atmosphere.

Based on this data I modeled it in a steady state compressible fluid simulation software with the following boundary condition.

1) At the inlet of 10" pipe I assigned the 45KPAg and 371 deg C as the inlet boundary.
2) At the outlet of 24" pipe I assigned the 12.165 kg/sec mass flow rate as the outlet boundary.
3) For the two reducers I modeled it simply by using a enlarger fitting with an angle of 45 deg for example purposes.

The results I've got are the following:

1) Velocity at inlet (10" flange) = 488 m/sec (Mach number = 0.79)
2) Velocity at outlet (24" pipe) = 83 m/sec (Mach number = 0.129)
3) Pressure at inlet (10" flange) = 45 KPag
4) Pressure at outlet (24" pipe) = 71 KPag.

Basically this case is an example of sub-sonic diffuser where the Mach number is less than 1 and therefore the velocity will decrease and pressure will increase.

Is my approach correct?

I just doubt that I think for PSV system we always approach M=1 at the outlet but maybe the PSV design criteria must be less than 1 Mach no.

Your help is greatly appreciated.

Cheers!!!

The software I've used above is 1D type of solver.

I've also tried it in a 2D CFD density based solver software using transient analysis with energy equation on and k-epsilon turbulent on, and result of the pressure at outlet is approx. 13 KPa.

I'm confused which one is correct. Will the pressure decrease or increase at the outlet of 24" pipe to atmosphere from 45 KPa at the 10" flange.

I'm guessing the 2D CFD I've run is more accurate where the pressure decrease to 13 KPa at outlet.

Any other opinion is greatly appreciated.

Cheers!!

Dear Borzki,

Hard to say what your software gave you, but I have some remarks.

1. As a stress engineer duty, it is not your task to do such calculations. I've understood your client questioned you about considering or not the steam pressure at opened end of PSV discharge as participating to the reaction force.
B31.1 (and me too) assumed that the system is proper designed and you have chocked flow there. That's why B31.1 offers a formula for that pressure. Considering the pressure in addition to steam momentum means to have- in front of your Client- a documented approach, based on B31.1

2. It seems that you try to check the system assures Mach=1 at exit and you are confused about the reducers. You wouldn't expect you have chocked conditions in reducers if your PSV system is proper designed. In the same time, you should expect chocked condition in the end of system, as per B31.1.

3. Cannot help you on the results of software because I have no feeling about how the software tries to deal with your input. For what you call 1-D, may be the fact the final "junction"- where you assigned the flow rate- cannot assure that flowrate because is over the "sonic" one calculated based on your input (typically the software starts with the pressure on the initial source, assumes the flowrate you gave and in the end of system may not be able to reconcile the numbers). But here I just try to speculate, the minimum for you is to consider the warning, errors, etc that software gives you.

4. You've started your calculation with a backpressure, but that one is not a datum- even is written in the datasheet. Why not start with the vessel/ tank specifying the stagnation parameters, inlet pipe in PSV, PSV itself modeled as an orifice (area as per datasheet) and model the rest of discharge system delivering steam in atmosphere. Compare the actual flowrate with the desired one.

Hi Mariog,


Thanks for the advise. Just practicing solving fluid problems. You're correct, as a stress engineer this is not within the scope of my work. I like the advise to complete the whole system including the PSV and go further to proper boundary condition. That would give meaningful results. This would be a very tedious task indeed. The difference I can see in the 1D CFD and 2D CFD calculation is the outlet boundary condition. In the 2D CFD I've modeled a big fluid domain (about 12mx12m rectangle) to represent the atmosphere with 0 gauge pressure at the edges while in 1D CFD I just put mass flow rate at the end of outlet pipe. As we know, most of the fluid software uses the energy balance, mass balance, continuity equation, etc. and with this many variables it's hard to compare results as you have to track down the core basis to have a good comparison.

Any other opinion is greatly appreciated.

Cheers!!!

Hi Mariog,

I have found this in one of the topic of psv. But the links is not accessible anymore. Kindly give me the new link in case you have it. I think in this topic there are two school of thought, so I'm interested to study more on the subject to satisfy my curiosity.

The links are given below:

"It’s a fluid mechanics model.
If you are outside B31.1 scope, you can follow your own model using software like AFT Arrow. Inside B31.1 scope it’s better to follow the appendix.

Just few words.
You may consider a famous work on this subject “75-WA/FE-23 Steam Flow through Safety Valve Vent Pipes by H. E. Brandmaier and M. E. Knebel”. Please see

http://www.coade.com/ubbthreads/ubbthreads.php?ubb=showflat&Board=1&Number=21607

I second Mr. G.S. Liao criticism developed in "Discussion" section of the above article. Arrow software solves the problem just as Mr. Liao hoped.

I’ve tried to make some comments on this subject at:

http://www.coade.com/ubbthreads/ubbthreads.php?ubb=showflat&Number=21000
It would be "informative" or not, it’s not more than my opinion."

Many Thanks,

Dear Borzki,

The article still can be downloaded, see http://65.57.255.42/ubbthreads/ubbthreads.php?ubb=showflat&Number=45529
But you can find a "better" copy on internet, someone posted it on files.engineering.com
(just Google Steam_Flow_through_Safety_Valve_Vent_pipes).

It is useful to see DISCUSSION section of "Analysis of Power Plant Safety and Relief Valve Vent Stacks" (I haven't the last one).
You can find the Discussion section at
http://gasturbinespower.asmedigitalcollection.asme.org/data/journals/jetpez/26720/492_1.pdf
At that time, Brandmaier's work was just submitted to be published, but Mr. Brandmaier included into DISCUSSION a good summary and an useful figure (which was not included later in the article).

Referring the same "Discussion" section mentioned, I second the position of Mr. Liao in "Author's Closure". In fact I made some comments in this forum, you can find them in the same location i.e. http://65.57.255.42/ubbthreads/ubbthreads.php?ubb=showflat&Number=45529

Best regards.

Thanks Mariog & Danb for the info. I've found it. I like the last part of the authors closure.

"Mr. Brandmaier states that the use of his method to solve Example A in Appendix B yields the same answer as the author's.
This is no surprise for the reasons that both his method and the
author's were based on the one-dimensional analysis, and that he
specifically chose the author's conservative approach of assuming a choking condition at the valve exit for comparison. If he had chosen a supersonic velocity instead of sonic, the solution might have been completely different."

I don't know if experiments and physical testing has been done to prove which approach will give near to reality results or maybe it's hard to set-up test like this and also maybe it's not possible to measure local velocity to prove if it's sonic or supersonic velocity at valve exit. How about the back pressure testing (I've seen one test in youtube video), not sure if this can be compared to calculations of this type.

https://www.youtube.com/watch?v=ul1T3Yus8wg

Anyway, many things to study on my part to convince myself which one can I use as a design engineer. As my senior stress engineer told me before when I was still a junior stress engineer "When your in doubt make it stout".

Any other opinion is highly appreciated.

Cheers!!!

I think I know now the why there is a difference in the 1D and 2D CFD software difference in results:

I think the 1D results is based on this one where supersonic jets is not considered inside piping:

"Note. I consider time validated Mr. Liao’s opinion and today regular fluid mechanics software does not consider the supersonic jets inside piping. Maybe they are wrong. Maybe not!"

I'm assuming that the 2D results is based on backward method:

"I think you would consult "Discussions" section of the article (attached) where Mr. Liao expressed serious criticism to the fluid model. The "backward method" mentioned there is what modern calculation software considers today. To understand what does it means, please read the article attached."

So 2 results cannot be compared since they have different basis.

Please correct me if my assumptions are wrong.

Anyway, need to read more and understand. Now I know why they say rocket science is very hard.

Any other opinion is greatly appreciated.

Cheers!!!

In my opinion, the backward method is rather present in "1D" software, for example in AFT Arrow. In Walters' article you can find:

"The only way to solve such a problem accurately is by trial and error: first, assume a flowrate and march down the pipe; if M reaches 1 before the end of the pipe, repeat the procedure with a lower assumed flowrate; repeat until M reaches 1 right at the pipe endpoint. Obviously, this calculation sequence is not practical without a computer."

(However do not be confused on the above- it is valid only for maximum flowrate that the pipe can handle, otherwise of course the calculation with a lower flowrate is possible and in this case the calculation appears more closed to incompressible fluid flow case)

A 3D software would be very sensitive to details as calculating correctly the influence of the boundary layer near wall, turbulence, etc and the results must be evaluated vs. the simplifications considered. A 2D software has anyway much more simplifications.

Thanks Mariog for that info. I think you're right. What I observe in the 1D software is that if I try to put a very high mass flow rate it will give a warning message that my system is beyond sonic so I need to adjust it to get the mass flow rate that will correspond to an exit velocity equal to sonic. While the 2D CFD will continue iterating the transient event even the exit velocity is supersonic.

Anyway, the sizing of discharge pipe in a PSV system to prevent blowback & other criteria is within the process engineer scope in an EPC environment. To officially document my calculation I just need to verify if the forces I consider in my calcs is aligned with process engineer calculation such as the back pressure calcs at discharge pipe exit.

I just feel I need to know both approach so I will be comfortable with my piping restraint system.

This is indeed a very fruitful discussion and I will continue to read, understand, run some simulations and compare results.

Any other opinion is greatly appreciated.

Cheers!!!

Just trying to close this long discussion focused on fluid mechanics.

The B31.1 PSV model is simple and practical one.

In fact, considering the nomenclature of appendix II, there are two chocked sections i.e. sections 1 and 3.
That's why V1=V3 and that's why P3*A3=P1*A1 (as consequence of p_chocked formula and the fact the model considers the same flowrate through all elements, neglecting the "inflow" i.e the air educted into the vent pipe).

The calculation of velocity and pressure in section 1a is a backward by hand method, starting with the fact section 1 is chocked. The same method applied for section 2 vs section 3 which is chocked. The appendix considers Fanno graphs as support of calculation, equally would be applied some equations for this purpose.

As fluid mechanics- that's all. For steady-flow- No supersonic flow, no waves - other than those generated by chocked flow, by which pressure changes. For transient flow- a reference to air inertial effects on discharge but no indication how to consider them other than as pressure.

As mechanics- just forces equilibrium on vertical.

Dear sam,
As you can see, in that appendix are no explicit horizontal forces.
In my opinion you can add anything you want as assumptions in calculation. Just be sure that the level of your determination to be conservative is reasonable. Probably would help to not blame others for acting in a different way, as well.

Thanks Mariog for that very nice closure & clear explanation. It clears my confusion why V1=V3 in ASME B31.1 example (which is based on choked conditions). Also the two enlarging reducers that I have experienced can be compared to the ASME B31.1 example. I've gained a lot of knowledge in this discussion. I will try to run the ASME B31.1 example in a CFD simulation (1D and 2D) and compare some results.

The orifice in the PSV will, I think definitely create a sonic condition at point 1 not the previous one which I assumed that it's a subsonic condition where velocity decrease at point 3 and pressure increase to compensate the energy balance.I just need to figure out how can I simulate this in 1D CFD. Is subsonic condition possible in point 3 for PSV system? I'm assuming this will not happen based on sizing criteria for vent pipe by process engineer.

Any other opinion is greatly appreciated. Just correct if I have some wrong statements

Cheers!!!

I finally figure out how to control the 2D CFD results to match the 1D results. Now I've got 0.75Mach for 2D CFD and 0.78Mach for 1D CFD. The results now make sense compared to ASME B31.1 example (velocities, pressures at points 1,2, and 3 quantities are within reasonable values). Basically, I've controlled the iterations for 2D CFD to stop just right at the point of divergence in the solution (mass and energy are balanced in the system boundaries) with mass flow rate of 12.165 kg/sec and back pressure at point 1 of 45 KPa.

Thank you all for this wonderful discussion.

Cheers!!!

I also observe in the transient analysis of a 2D CFD that as the Mach number transitions to sonic from 0.8 Mach it starts to create a negative pressure or vacuum at point 1 and as I continue to iterate the timestep with a result of 1.6 Mach the result has no physical meaning already where the surrounding atmosphere after point 3 has a 10KPag pressure while at point 1 has a negative pressure or vacuum. Therefore with this result for this particular case it can be validated the max flow is only sonic Mach = 1 (choked flow).

Thanks Mariog for the statement that the inertial effects of air in a transient event so far can only be represented by pressure. I think the next challenge for simulation is the interaction of still air to the moving fluid due to PSV release. Am I right in saying this? Or this can already done in CFD simulation? Please correct if this statement is wrong.

Any other opinion is greatly appreciated.

Many Thanks,

Cheers!!!