In evaluating existing PSV installations for affects due to reaction loading, the installations may, or may not, fall into the "Thermodynamic Entropy Limit" and/or "Subsonic Vent Exit Limit" listed in the Relief Load Synthesis limitations.

Are the values for the "Vent Pipe Exit Gas Conditions" then reliable? Specifically the exit pressure, which contributes to the Thrust at Vent Pipe End?

I believe I saw a previous reference to this subject that the basis for the Relief Load Synthesis was the technical paper, "Steam Flow Through Safety Valve Vent Pipes". I have downloaded and attempted to understand, but it's been a long time for this old brain.

We have tried to utilize SolidWorks Flow Simulation software, because that is what we have, to model a nozzle and plot the velocity, pressure, and temperature results through an elbow and along the vent pipe. While the trend of the results looks reasonable: increasing velocity along the vent pipe with decreasing pressure, the reported exit pressure differs from the Caesar report significantly (factor of 3).

So, now we are in the situation of the man with two watches. "Man with one watch always knows what time it is. Man with two watches is never sure."

So, back to my original question, "If the 'Limits' are not satisfied, are any of the computed results reliable?".

Thanks for any insight and /or comments.

I've asked myself the same question.
How about this in the meantime...
Adjust the CAESAR II data so that the two checks pass. Will the same data in the flow package produce the same results in that case? If so, then put more trust in those limit checks. If not, then clearly the correlations are different or the data's different or there's a programming error.
The paper used for this load synthesizer is based on steam. Are you running steam here? We added additional parameters to model different gases and that may be the source of the difference. I recall a decent match between CAESAR II and relief valve manufacturer reaction tables for steam.

Dear waterguy,

In my understanding, "Steam Flow Through Safety Valve Vent Pipes" considers a fluid mechanics model which is not confirmed by other works.

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.

I just quote from that article.

"From the standpoint of pipe design or system operation, sonic choking sets a limit on the maximum possible flowrate for a given set of supply conditions."
You may note that this is in contradiction with "supersonic underexpanded free supersonic jets" considered by "Steam Flow Through Safety Valve Vent Pipes".
And
"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"

Hope this help you,
Best regards.

Dear Mariog,

Thank you for your post, I have always respected your thoughts on other posts that you have authored. I will try to put together that type of analysis. So,

David,
We are running this analysis with Propane. Just for curiosity, I let Caesar design the stack diameter to see what would happen. In all cases, the existing diameters were too small, usually by one pipe size. The exit pressure differences between the two were significant - around 50% and upward.

I also made changes to the stack length, and this may play into what Mariog had suggested. The existing installations have stack lengths (equivalent lengths) of around 10 feet. If the length was changed to 1 foot as an example, then the "Limit" values came pretty close to 1.0. The were corresponding exit pressure differences were around 10% between the models. For this exercise, I am thinking that that is close enough to use.

Thanks for your response.

Dear waterguy,

I will try to continue the discussion of the article "Steam Flow through Safety Valve Vent Pipes"

I would say that with that article , my knowledge on Fluid Mechanics calculations is somehow "under attack". This is not because it is incorrect in math details- btw, it seems to be correct… and I consider the article math is quite funny and exciting (believe or not, even equation 1 is not so easy to be proved and –as I know- cannot be recovered directly from a book of gasdynamics…)….

So the "aggression" isn’t by math, it’s because the author have made a unique work with lot of assumptions that appear to be acceptable for the majority of people. It is not my
case and I cannot say the result is reasonable by chance or by knowledge. Or better said, exactly with the authors words "It appears that while the method may result in a satisfactory vent pipe, the result is fortuitous".. .


I think the true limits of the model are rather inside the model than the imposed "limits".
I think also it is worth a short review of the article- of course it is my interpretation here.

1. They considered a one-dimensional model/ straight flow. At first approach it seems to be acceptable, but … Until now, nobody proved that the valve would be considered a convergent-divergent nozzle. Looking only to the areas ratio- of course we can assume this. Entering in details, there is a huge contrast between friction that exists in PSV and the favorable pressure gradient & boundary-layer (that allows neglecting friction) in a convergent-divergent nozzle. So how we deal with this assumption- it is acceptable or not developing this model?

2. They considered that the fluid jet acts inside the vent pipe as a free jet (a supersonic one) and generates a secondary flow of air into vent pipe. First, one might note the model considers both isentropic exponents as identical (the same k for air and working fluid), which is uncomfortable for a serious work. Other assumptions- there is a continuity of the static pressure at boundary primary-secondary flow and the friction with walls is negligible.

All this stuff is to simplify the calculation, however in the end a lot of questions remain…. Some of them …in which way describes the model the "driving force" of mixing process? It seems that it is necessary to have a sonic condition for secondary flow before mixing- why? It is proved the supersonic flow through the vent pipe?

3. To escape the difficulties of answering such questions, the author considered successions of scenarios for primary and secondary flow. Between sections 1 and 2, there is no mixing of primary and secondary flow- and therefore flows are still isentropic. In section 2 is considered a "sonic" condition for secondary flow, after which a mixing zone begins.

In section 3 the primary and secondary flows are mixed- however no momentum or energy seem to be irreversibly consumed. After mixing, in section 3- there is a normal- shock, which changes the flow regime to subsonic (lambda3- to lambda3prime, with the product of them equals 1 as a confirmation of Prandtl- Meyer formula valid for normal-shock). And after that, the pipe length and friction is driving the flow.

Well, about this point it is worth to reproduce what the author says: "Although mixing and flow deceleration occur simultaneously, this analysis assumes that the primary and secondary flows first mix to yield a uniform supersonic flow". Again, this is quite uncomfortable for a serious work- it is recognized that the model does not accurately describe the reality!

Reviewing the "limits" stated by article:

- The sonic velocity of the secondary flow in section 2. This is strongly linked with the assumption that there is a sonic velocity of the secondary flow in section 2, before the mixing space. Better said, this is tributary to the scenario: supersonic free jet of primary flow, accelerating secondary flow to sonic, mixing, decelerating by normal shock, accelerating to sonic. It is confirmed/ proved?

- Thermodynamic limit- entropy cannot decrease in the direction of flow. True, but again the author says: "in the actual flow where primary and secondary flow mixing and shock interactions occur simultaneously and not in series as assumed in this model, the limit may not exists at all". No comments ...

- A vent pipe outlet pressure greater than atmospheric. I think this is linked with "No blowback" condition. The article considers that, depending on the vent pipe length, the flow at the vent pipe outlet may be sonic with a static pressure greater than atmospheric; supersonic if vent pipe is very short; or subsonic in which case the outlet pressure must equal atmospheric. The limiting condition for no blowback corresponds to zero secondary flow and a pipe length for which the flow accelerates to sonic at the pipe outlet. At greater lengths the shock system moves upstream into the free jet region, the pressure rises and blowback occurs.

- "Lambda3 limit downstream normal-shock". It is a math limit, corresponding to the infinite Mach number upstream normal-shock. This limit depends on the assumption of normal-shock wave.

Last, this is the only work I’ve seen where the "Discussion" section destroys the article!

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!

Best regards.