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Sizing valve for pressurized vessel to relieve under SUBcritical flow

Sizing valve for pressurized vessel to relieve under SUBcritical flow

Sizing valve for pressurized vessel to relieve under SUBcritical flow

(OP)
I need to size a valve to relieve air from a pressurized tank to drop pressure from 16psia to 14.76psia within 5 seconds. As the outlet pressure is greater than .5283 of the inlet pressure, this will occur as non-choked (i.e. sub-critical) flow. (Note that specification is not critical to safety). Is the following equation the correct approach? If so, how can I estimate the Expansion Factor (Y) if I don't know the Pressure Drop Ratio (Xt)?

From ISA specification for Compressible Gas Flow (EQ 11a) and summarized in this manufacturer brief:


Cv: flow coefficient
q: Volumetric Flow (SCFH)
N9 = 7320; conversion constant assumes units SCFH, PSIA, and R temperature
Fp = 1; pipe geometry factor without reducers
p1: inlet pressure
Y = 1 - x/(3*Fk*Xt); expansion factor
.....Fk = 1; Ratio of Specific Heats (assume air)
.....Xt: Pressure drop ratio factor (huh?)
M = 28.97; dry air
T1: inlet temperature (R)
Z = 1: Compressibility factor (assume air at standard T and P)
x = (P1-P2)/P1; ratio of pressure drop

I assume I can iterate through the equation to find the inlet pressure drop over time.
Thanks in advance for your help.

RE: Sizing valve for pressurized vessel to relieve under SUBcritical flow

That parameter, Xt, is also know as critical pressure drop ratio, and it is the pressure drop ratio corresponding to
choked flow condition

Xt = (P1 - Pchoke)/P1

RE: Sizing valve for pressurized vessel to relieve under SUBcritical flow

(OP)
Would that equation for Xt still apply to non-choked flow?

So using the equation to find the critical pressure: Pchoke = 27.83 psia (air exhausting to atmosphere)



Then Pressure Drop Ratio: Xt = (16psia - 27psia) / 16psia = -0.688

RE: Sizing valve for pressurized vessel to relieve under SUBcritical flow

Upstream pressure in your case is P1 = 16 psia, so Pchoke = 0.5283*P1

RE: Sizing valve for pressurized vessel to relieve under SUBcritical flow

(OP)
Duh! Thank you.

So finishing up, for the initial condition:
Pchoke = 8.5psia
Xt = 0.472
Y = 0.942
Flow = 8.56 SCFM (converted from SCFH)

Iterating every 0.2 sec... I get the following graph of inlet pressure for a valve of Cv = 2.0


Is this a close approximation I can trust?

RE: Sizing valve for pressurized vessel to relieve under SUBcritical flow

I think you'd need an Equation of State as well and not just what you've reported in your OP

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