Pressure vessel exploding within an atmospheric chamber

[Ryan26]

I am currently investigating pressure test safety with my current employer. Currently we test pressure vessels inside steel test containers, see attached pdf.

At the moment Boyles law is used to calculate the resultant pressure increase inside the steel container if the pressure vessel was to fail and suddenly release pressurised Nitrogen. However I don't believe this takes into account the volume of air that would be trapped and compressed inside the steel container. This means the actual volume the Nitrogen occupies is less than internal dimensions of the test container and there for the pressure inside after a vessel failure would be higher.

We use this (p1v1= p2v2, p(nitrogen 1kpsi) x v(volume of vessel) = p2 (?) x v(volume of test container).

What can I do to take into account the atmospheric pressure and volume of air already inside the test container to obtain a more accurate p2?

Thank you very much,

 

[Nugatory]

What can I do to take into account the atmospheric pressure and volume of air already inside the test container to obtain a more accurate p2?

You can use $PV=nRT$ (assume T is constant) to calculate the $n$ for the atmosphere inside of the steel test container; use it again to calculate $n$ for the compressed gas inside pressure vessel; and then you'll have the total $n$ value inside the test container if the pressure vessel fails so can calculate the $P$ value after the failure.

For realistic conditions, you'll probably find that the difference from including the air in the container is negligible. I'd be at least as concerned about the steel test container being able to mechanically contain flying shrapnel from the pressure vessel if it blows apart.

 

[Ryan26]

Thank you vey much for your reply. You are correct for pointing out the projectile damage that would occur. I have analysed this via stored energy withing the the vessel, blast, gas expansion, strain etc...

The likelyhood of the vessel failing is very minimal, and the possible projectile caps are aimed at the end walls. I needed the P2 value in order to determine the force that may be applied to the roof of the container if the pressurised gas was to escape. As in reality this is a lid, locked with pins so a shear force is generated.

The information you have provided is what I was after, so thanks again!

 

[Ryan26]

Hello again,

I'm still working on this issue. I can estimate the impact of the projectiles hitting the container walls via calculating the stored energy in the vessel. Converting this directly to kinetic energy to different elements of the vessel, ductile and brittle failure modes. This is a conservative estimate as I understand a lot of energy will be lost through the gas expansion pressure wave.

This is what I'm concerned about, the rapid expansion of gas near the point of exit from the pressure vessel. Assuming all energy from the vessel is converted to pressure wave. How can I estimate the resultant force acting locally on the container walls? Could separation losses in pipeflow be used?

PV=nRT gives me a total gas volume and pressure after the gas is released. Is there anyway I could use the stored energy to show pressure at the instant it escapes? Using the distance from the vessel to the container and container XSA to somehow estimate the pressure wave?

Any help at all would be much appreciated.

Many thanks,