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.
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
choked flow condition
Xt = (P1 - Pchoke)/P1
RE: Sizing valve for pressurized vessel to relieve under SUBcritical 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
RE: Sizing valve for pressurized vessel to relieve under SUBcritical flow
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