Hello All,

PSV Reaction force for closed system.

1) API 520 does not give calculations for reaction force for closed relief system. It says the reaction forces will be less.
The reaction force value calculated as per formula of open system is too large (approx 5 tonnes load) which is too high for the structure around.
I need to lower down the value, is there any way to calculate as this is closed system and the forces will be surely far less than the above value.

2) About direction of reaction force, for closed system I have seen more commonly the reaction forces are modelled at the PSV centre line location and in horizontal direction.
On basis of API 520, For open system the forces will be at last elbow when the discharge pipe is open to atmosphere where there will be sudden change in pressure.
Hence why not we apply the same concept here for closed system where the reaction force to be on last elbow where the the discharge pipe connect to much bigger flare header.

Thanks,

One line answer: Same expression as open system is generally used in the Inudstry ( expepting the PXA term), hence I would recommend the same.

CAESAR II has a load computation module in Dynamic analysis. Check your loads w.r.t that.There should be a vertical component also in the direction of the spring loading.Check for more accurate Dynamic load Factor instead of 2.Also check for correctness of the parameters used in the computation of the Load.

Regards

I risk a long post on this subject. Maybe will help someone to understand …what we are not able to count and why our approach is rather empirical.

Crosby manual says: "There are momentum effects and pressure effects at steady state flow as well as transient dynamic loads caused by opening" and -in my opinion- this is valid for either open or closed systems. There is a kind of similitude between "open" and "closed" PSV’s discharge piping handling gases, so a discussion may be forced on both cases.

Forces that are affecting the PSVs discharge piping are given by:

A.- a free jet effect in steady state flow
B.- unbalanced forces on each "piping leg" due to transient flow.

A. The "free jet effect" is the 3rd law of dynamics.
If a free jet is released in atmosphere or in a large volume, the piping system will receive a reactive force. This is the force that API counts and is:
Reactive_Force= [mass flow-rate]*[jet_velocity]+ [p_jet]*[area_jet]
where
- mass flow rate must be the actual value (it is greater than the designed flow rate, because the actual PSV orifice is larger than minimum required)
- jet_velocity is the critical speed when the jet gas flow has Mach=1 feature (it is not exactly the speed of sound calculated as for a resting fluid, you may get some details in a fluid Mechanics book on the critical speed and stagnation temperature concept) and is counted as jet_velocity= sqrt(2*R*k*T/ ((k+1)*M)), where notations are as in API, R is the universal perfect-gas constant , in SI is R=8314.5 J/kg mol/K.
- p_jet is the gauge pressure in the released jet (may be considered exactly as a steady state simulation is showing, may be "guessed" with some formulas, may be considered conservative as the pressure just downstream the PSV orifice, but definitely is not the upstream PSV p_set…)
- area_jet is the internal area of piping at the point where the jet is released
You may note this is exactly the API formula, where the numerical coefficient is sqrt(2*R), in SI units sqrt(2*8314.5)=129

This long preliminary discussion is useful because we can be focused now on where this force can appear.

You have this force exactly where there is a FREE jet.
That means:
- in an open system, where really the free fluid jet is released into atmosphere
- in a closed system, at the header connection, presuming your PSV is not pressurizing the header- that is the header is counted as a large volume receiving the jet rather than a path for flow…

And...despite the common opinion, the problem of the true steady state force in the PSV is very questionable. In the PSV orifice there is a flow at Mach=1 i.e a critical flow, but the jet is radial released (it exists thru a lateral cylindrical surface) and it’s not a "free jet", because there isn’t a big volume in the PSV’s body.

Roughly considering the steady state flow, there is a changing in fluid momentum, initially is radial compensated, after that there is an impact with the PSV body- on about 2/3 on the path flow- that generates a lot of turbulence, etc. By the other hand, we may consider a model closed to those proposed by Brandmayer and Knebel, see the article "Steam Flow Through Safety valve Vent Pipes", based on an one-dimensional model of the shocked flow (anindya stress has had the generosity to post it recently, thank you anindya stress, it was very interesting and I appreciate your courtesy and your posts!)…

My opinion is, in fact, we haven’t a realistic model for the steady state flow, exactly here, in the PSV body, where the flow is not one-dimensional. Probably is not a significant value and exactly for this reason, you cannot see, in API520 part II or B31.1 figures, this force as horizontally applied on the PSV body, but for some safety reasons, the stress tradition asks to count as this force exists, and I would say is more a way to be conservative rather to be realistic…. of course, this is just my opinion!


B. The transient dynamic loads caused by opening.

I’ve never seen a "Process Department issued" transient calculation for gas flow near or at Mach=1, maybe you’ll be luckier than me…

What really we know: the PSV generates sonic waves because the flow is at Mach=1 inside the orifice. These waves may be counted as "normal" shock waves, in the terminology of Fluid Mechanics. A shock wave is an one-dimensional wave so "hard" that the front-up profile is vertical. Practically, this wave has a zero ramp time and is a very special wave in fluid dynamics, being a discontinuity in flow. This kind of shock appears in the supersonic flight. You may think it’s possible to have it also along your PSVs discharge piping, so that means you’ll have an unbalanced force at magnitude of API force or larger on each discharge piping leg, because the wave propagates thru all the piping. My opinion: if you consider this scenario, you must consider the same large force (don’t ask me how much…) applied in every piping leg, not applied only on the first piping leg, adjacent to the PSV.

Probably a more realistic scenario is to consider the wave as described by E.C. Goodling in the paper "Simplified analysis of steamhammer pipe supports loads".
CraigB has posted this paper (please search for it in this forum!); the community really has very good reasons to thank him, and BTW, I really thank you CraigB for all your posts and for your generosity!
Basically, the Goodling scenario presumes there is a sonic wave, but the wave profile is given by the valve’s closing or opening time. The Goodling’s paper is not referring to PSVs, but he was presenting his paper as valid for both traveling waves of increasing and decreasing pressure. Again my opinion: it would be engineering satisfactorily to consider such approach for either expansion or compression waves. Theoretically, it is very complicated to confirm or invalidate Goodling approach- in Fluid Mechanics, the "classical" Riemann model predicts the wave shape doesn’t remain stable during the wave propagation, but it’s also recognized that the friction and heat gradient effects – not counted in the theory, counteracts this tendency. Eventually, the theory failed to explain the real case. It remains the Goodling’s engineering approach….and that’s all, you can trust it or not…
Let’s consider the effects of this scenario. The idea is to count the unbalanced force on each leg…If the PSV opening time is 0.050s and the wave speed is 300m/s you can have the maximum force on PSV only if you have 15 m or more distance from PSV to the next elbow. If you have just 1.5m distance and you still consider the same maximum force, that would correspond to an opening time of 0.005 s and your procedure is very conservative since you’ve applied a safety factor of 10. Alternatively, you may follow the Goodling approach and to count only the fraction of this force, corresponding to the real opening time and to tyhe actual length of the leg.
This procedure, applied conservative or realistic- as you want! - can be applied leg by leg in a time history scenario, with the notable exception of the last one where is more probable that the force is given by the steady-state flow "free jet" effect, exactly as you've observed.
Just a remark: to follow the Goodling scenario, first a correction factor must be applied on Vendor time opening; this would secure your calculation against the possibility to have a PSV’s non’linear characteristic instead a linear one (Goodling has made similar correction, see fig 1 of his paper). To know the value, you must have the Vendor opening profile….After that, a "stress approach" safety factor may be applied….it’s after you the value, don’t ask me what is the appropriate safety-factor…

And don’t forget, after all, a history-time profile calculated on this base would be the basis of your dynamic calculation, or a rude DLF of 2 may be applied…


Best regards

There are several programs such as PIPENET-Transient and BOS-Fluids to calculate fluid dynamic forces. You can import force spectrums at any piping leg into CAESAR II dynamic input with the time lag for time history analysis. I personally used these programs with CAESAR II and got satisfactory results. In addition, you can import CAESAR II piping model directly into BOS-Fluids and perform the analisys.