Help w/ Relief Valve Analysis

[dfrenk]

I'm analyzing the inner operations of relief valves to help design a larger variety of valves. I'm working with a valve that has a 150 psig set pressure and a rated capacity of 8.1 #air/min.
It has been designed to "pop" at a pressure of 110% of set pressure. By "pop" I mean open to release air at it's rated capacity. I'm working with a pressure rate increase of 0.5 psi/sec, which is much lower than it would actually be applied too. If it is able to "pop" with this lower pressure rate increase, then it will be able to handle higher rates. These higher rates should "pop" the valve before 110%.
As the pressure increases past the set pressure, the force due to pressure applied to the seat disc equals the spring force, thus rising the seat disc. The seat disc rises, allowing the under-pressure air to be released. As pressure increases, the seat disc rises further to a point where the pressure below the seat disc suddenly causes the valve to "pop" thus releasing at rated capacity. The cause of this sudden "pop" has me stumped.
I'm curious as to what is the driving factor that causes this "pop" to where it releases at it's rated capacity. It tends to close around 90 psig. I'm a newly graduated engineer attempting to apply theory learned in school to real life situations. I appreciate any help you can provide.

dfrenk

 

[xcrosby]

Take a look at the Crosby Valve Engineering Handbook.

http://www.andersongreenwood.com/docnet/library/enghnbk.pdf

 

[MortenA]

I think that maybe you misunderstand "pop" and 110%. The valve actually lifts at 100% of set point. In a normal piping system 10% overpressure is allowed and for that reason max. capacity is at 110%.

The valve may actualy start to "simmer" at a pressure lower than set p.

Look at the referenced link or API 520 for a description and explanation of the various terms used in connection with PSV's

Best REgards

Morten

 

[mcintya]

From my experience, I've found that the &quot;pop&quot; is more dependent on the set pressure of the valve rather than the rate of pressure increase. It is more difficult to obtain a &quot;pop&quot; at lower set pressures < 50 psig than at higher pressures. The pop is produced by means of a &quot;huddling chamber&quot; and &quot;secondary orifice&quot;. When the valve begins to open the flow is restricted by the secondary orifice causing pressure to build up in the huddling chamber, this produces a sudden change in upward force (hence the valve pops). The size of the secondary orifice is often controlled by a &quot;Blowdown ring&quot;, increasing the secondary orifice reduces the severity of the pop (you get more simmer) but also reduces blowdown (blowdown is the difference between set pressure and reseat pressure). Blowdown rings are usually only found in valves which have a specific blowdown requirement. Most other valves have a &quot;fixed&quot; secondary orifice.

As the flow rate increases, the flow gets deflected by the discholder and provides additional upward force causing the disc/discholder assembly to lift further. The valve must reach &quot;full lift&quot; before 110% of the set pressure.

Analytical modeling of a pressure relief valve is quite difficult. The upward force is dependant on flow rate and the flow around the valve internal components. It is difficult to analytically determine the pressures and velocities across the disc and discholder (even for a fixed flowrate). The flowrate is dependant on lift which is a function of both flow rate and spring rate (the problem becomes implicitly defined).

It would probably be a good idea to get some experimental data to correlate your mathematical model with.

Good luck!
-Andrew

 

[xcrosby]

I have seen many attempts to analytically model the operation of a pressure relief valve. No one has been successful. There are too many effects that cannot be modelled. Small changes in geometry can make dramatic differences in performance. It can take many years of experience to understand all of the nuances involved in properly designing a pressure relief valve. Some of the best attempts at analytical models have predicted that valves that worked the best shouldn't work at all.

 

[JAlton]

xcrosby & mcintya have covered it pretty well.
Based on your description, Pop at 150 psig and close at 90 psig, it appears you have either a &quot;fixed blowdown&quot; valve as described by mcintya, a low volume test bench, or the spring range is too low for the set pressure. It is possible that the Nozzle ring is set too close to the disc resulting in long blowdown since you did not mention simmer (an audible escape of fluid at a pressure below set or popping pressure).

Regarding rate of increase, ASME PTC-25, 2001, limits pressure increase on a PRV Test Bench to a maximum of 2 psi per second. I prefer to keep the rate closer to 1 psi/sec. If you are getting a pop without simmer at a rate of .5 psi/sec increase, you must be testing a small valve with a fixed blowdown and possibly an o-ring seat or else the metal seats are extremely tight and the nozzle ring is nearly touching the disc. In either case you will have long blowdown. Rate of increase does not equal full lift or capacity. Full lift is typically achieved at an overpressure near 110% of popping (set) pressure. Just because a valve pops at its nameplate set pressure, does not guarantee full lift or capacity.

As the pressure increases past the set pressure, the force due to pressure in the vessel combines with reaction force as the air changes direction off the disc to overcome the spring force, thus lifting the disc. The disc rises, allowing the pressure in the vessel to be released. As pressure in the vessel increases, reaction force also increases, causing the disc to rise further to a point where the valve reached full capacity lift. The initial &quot;pop&quot; is caused by the sudden expansion of air when the valve first lifts not at the 110% overpressure.