Caesar II has a Relief Valve Thrust tool.
I’m interested to understand what is the theoretical background of the "transient pressure rise on valve opening" approach. Under the Technical reference manual, chapter "Controlling the dynamic solution", some details about this subject are given.

"Transient Pressure Rise on Valve Opening

This is the estimated magnitude of the negative pressure wave that will be superimposed on the line pressure when the relief valve first opens. This negative pressure wave will move back through the relief system piping similar to the pressure wave in the downstream piping of a water hammer type system. The magnitude of this wave is estimated as (Po-Pa)*Ap, where Po is the stagnation pressure at the source, Pa is the atmospheric pressure, and Ap is the area of the header piping"

My first remark is about the magnitude of the force.
The modern Fluid mechanics books don’t say too much on the "negative pressure wave" on the water hammer systems. More elaborate theory can be found on the positive pressure wave. In other words, I cannot recover a reference to a formula Caesar II uses.
Can you give me a reference?

Second, it is really appropriate to extrapolate the water hammer approach for the gas case? For the gas case we may expect a shock wave of this magnitude? This result is associated to a weak shock wave or to a hard shock wave, in the Fluid Mechanics terminology? I’ve studied few fluid mechanics books on this subject (shock waves) and never have I found a reference to such formula for the gas case.

NB. To avoid further discussion about, I kindly ask the board of this forum to consider my question as a part of my effort to comply with the Coade’s requirement "it is the user’s responsibility to verify the results of the program".

The majority of the calculations found in the Relief Load Synthesis processor in CAESAR II Dynamic Input were developed in ASME Publication 75-WA/FE "Steam Flow through Safety Valve Vent Pipes" by H. E. Brandemaier and M. E. Knebel.

Dear Mr. Diehl,

Thank you for answer.
Yes, the majority of the calculation follows 75-WA/FE-23 "Steam Flow through Safety Valve Vent Pipes" by H. E. Brandmaier and M. E. Knebel.

However, it’s not the case of "transient pressure"; the article says "…it is assumed that transient effects due to piping valve opening are small…".
It would be interesting to understand the assumption made for transient case, because in "closed" flare systems it is the only true component. For me, it make more sense to consider the article "Simplified analysis of steamhammer pipe supports loads", by E.C. Goodling.


Just a comment, not related to the "transient" subject.
It is interesting to see that the Brandmaier and Knebel’s article was subject to criticism in the "Discussion" section, by G.S.Liao, Bechtel Power Corp. Mr. Liao’s discussion makes sense and, trying to answer, the article authors concluded in "Author’s Closure" section: "It is unfortunate that published test data do not exist against which to compare the calculated data". The modern software, like AFT Arrow, are successfully applied in industry- including Power applications- and don’t consider any supersonic underexpanded free supersonic jets.
Of course, nothing wrong to consider article method. We may keep in mind that is just an acceptable Fluid Mechanics model, but isn’t the only one.

My best regards,