pressure between regulators in series

[buckley8]

In my system, which is supplied by a 2200 psig, 50 Liter Nitrogen bottle, I am required by NASA safety requirements to use two pressure regulators in series in case one fails.

I need to size a relief valve which will be able to handle the flow at the downstream pressure (55 psia). Although I could play it safe and oversize the valve, I would still need to prove to the safety team that my sizing is adequate. The problem is, I don't know how to determine the flow rate for two regulators in series. For one regulator, I assume choked flow and a formula using the Cv of the regulator (.08) and the inlet pressure.

For two regulators with similar (or even the same) Cv, the flow is assumed to be critical for each, yet the flow rate is more dependent on the second regulator since it has the lower inlet pressure. Unfortunately, I don't know the inlet pressure of the second regulator. Even if I had a formula for pressure drop through the first regulator, I couldn't use it unless I had the flow rate. It sounds like a two equation, two unknown problem, if only I had the right equations.

One approximation I considered to determine the intermediate pressure was to take the geometric mean of the absolute inlet and outlet pressures (sqrt(2215*55)=349 psia). This is a totally wild-a$$ guess and would require the two Cv to be equal.

Another approach would be to find the equivalent Cv of regulators in series. I guessed it to be like springs in series (Cv = 1/(1/Cv1+1/Cv2)) but I am pretty sure this is incorrect--my reasoning is two lengthy for this post.

Jim Buckley
ZIN Technologies
at NASA Glenn Research Center
Brook Park, OH

 

[israelkk]

To size a regulator you have know the minimum and maximum flow rate that should flow through the system because a regulator have a maximum and minimum flow that it can regulate within its specified regulated pressure range.

Secondly, knowing the maximum flow rate "of the system" and the Cv of the second regulator you can calculate the minimum desired inlet pressure to the second regulator that will assure such flow rates. It may be choked or not but the calculation result will reveal it.

Then, knowing this pressure which is in the outlet of the first regulator, the inlet pressure to the first regulator (2200psig) and the regulator Cv you can calculate and see if it can pass and regulate the desired flow rate.

For more accurate total system analysis you may need to write some differential equations and solve them simultaneously to check for intermediate and the whole range of pressures and flow rates. You will need to put in the regulator internal dynamics and pressure deviations behavior as a result of sudden change in the pressure flow etc.

 

[sailoday28]

Are you stating that both pressure regulators have failed open?
If so, with that scenario, is there still a demand of N2 other than flow thru the safety/relief valve?
Can you obtain, the orifice diam of each regulator in the full open position?

 

[btrueblood]

isrealkk is right, it's a very complex analysis task.

You can assume, though, that a flowing gas past a critical (choked) orifice will usually see 70% to 85% downstream recovery of the total pressure when flowing in a pipe. Analyse for both ends of that assumption.

 

[vzeos]

buckley8,
With reference to the code box below: P[sub]1[/sub] is the inlet to R[sub]1[/sub], P[sub]3[/sub] is the outlet of R[sub]2[/sub] and P[sub]2[/sub] is the interstage pressure (all psia).

For sub-critical flow use the simple sizing equation noting that Q is the same through both regulators

Q = K((P[sub]1[/sub][sup]2[/sup]- P[sub]2[/sub][sup]2[/sup])/2)[sup]0.5[/sup] = K((P[sub]2[/sub][sup]2[/sup]- P[sub]3[/sub][sup]2[/sup])/2)[sup]0.5[/sup]

where K is a sizing parameter. Then the interstage pressure can be calculated as,

P[sub]2[/sub] = ((P[sub]1[/sub][sup]2[/sup]+ P[sub]3[/sub][sup]2[/sup])/2)[sup]0.5[/sup]

P[sub]2[/sub] is midpoint between R[sub]1[/sub] and R[sub]2[/sub] and the piping loss would need to be accounted for. The C[sub]v[/sub] values should turn out to be about equal.

 P[sub]1[/sub]        P[sub]2[/sub]       P[sub]3[/sub]  
???????????????
    R[sub]1[/sub]            R[sub]2[/sub]

 

[buckley8]

I think everyone has contributed helpful information except it still doesn't answer the problem.

RGasEng: I agree that this would be simple for sub-critical flow. However, with an inlet pressure of 2215 psia, and an outlet at 55 psia, this is definitely critical flow for at least one regulator. And it is a pretty safe assumption that the intermediate pressure is such (1174 psi > P2 > 104 psia) that both regulators have critical flow.

israelkk: I know what the flow rate of the downstream system is since I control it with mass flow controllers (2.56 scfm). However, the relief valve is not sized for this nominal case. It is sized for the maximum flow which will occur due to a supply bottle at 2200 psig with one failed regulator and one wide open regulator and a normally operating (2.56 scfm or less) downstream system. The critical flow for a single regulator of Cv=.06 would be 66 scfm, much higher than the desired flow. Therefore, if I can show that the inlet pressure of the second regulator is only 400 psia, for example, the flow rate will be much smaller, allowing for a smaller relief valve and a longer emptying of the supply bottle.

sailoday28: I assumed that the listed Cv of the regulator is still applicable for a failed-open situation since the flow path is still tortuous and has the same orifice area as a correctly working regulator. Essentially, I assume that a failed regulator equals a unfailed wide open regulator.

btrueblood: What is the formula for pressure drop as a function of Cv and SCFM in choked flow? I've found equations for orifice area but not Cv. If I could calculate the pressure drop of the first regulator, I could very easily iterate the intermediate pressure and thus the choked flow in the second regulator which is my answer.

 

[sailoday28]

I believe Cv is a function of valve position. Is the Cv=0.06 a failed open value?