Pressure Relief Valve
Spring-loaded relief valve
Description
Equations
Variables
Connections
Parameters
The Pressure Relief Valve component allows fluid flow in one direction, from port A to port B. The flow is controlled by an adjustable orifice whose area is controlled by the pressure difference from port A to port B.
The Conductance increases linearly from C__min to Cmax as the pressure increases from pclose to popen.
The pressure drop vs. flow rate, for the computed area, comes from the Orifice ISO 6358 component.
Formulation Approaches
Two approaches were taken for formulation of the flow equation inside the device. When the boolean parameter UseRestrictionArea is true, the flow area at the local restriction can be provided which will be converted to Sonic conductance using Gidlund's approximation.
p=pA−pBhflow__X = inStreamportX⋅hflow
Orifice Gas Equations
mflow = {k⋅p1⋅1−p__2p__1T__envT__refp2p1≥b__lamregp__1⋅C⋅ρ__0⋅T__envT__ref⋅ (1−p__2p__1−b1−b2b__lamreg> p__2p__1>bp__1⋅C⋅ρ__0⋅T__0T__1p__2P__1≤b p__1 → Upstream pressure, p__2 → Downstream pressure
Linear Gain k is given by
k = C1−b__lamreg⋅ρ__01− b__lamreg−b1−b2
When UseRestrictionArea is checked, Gidlund's approximation is used to calculate C using Ar__max
C=0.125⋅4⋅Ar__maxπ
Orifice Opening
C={Cminp≤pcloseCmin+p−pcloseCmax−Cminpopen−pclosep<popenCmaxotherwise
Name
Units
Modelica ID
C
m3s⋅Pa
Sonic Conductance
Cmax
p
Pa
Pressure difference
hflowX
kJkg
Specific Enthalpy into port X
mflow
kgs
Mass flow rate across the ports
portA
Pneumatic port on left side
portB
Pneumatic port on right side
Fluid Medium Parameters
The Gas parameters used in the equations are properties defined in the Gas Model component used in the model.
Default
Use default medium
true
When true the default gas properties defined for Air will be used.
useDefaultMedium
medium
−
When Use default medium is false this option gets turned on. The user can specify the name of the Gas model dragged into the canvas.
Orifice Parameters
b__lamreg
0.999
Flow transition constant from turbulent to laminar zone
blamreg
UseRestrictionArea
false
True (checked) means flow restriction area can be given which will be converted to sonic conductance based on Gidlund's approximation
Valve Parameters
pclose
2⋅105
Pressure at which valve is fully closed (C = Cmin)
popen
2.05.105
Pressure at which valve is fully open (C = Copen)
Cmin
1 ⋅ 10−13
Valve Sonic Conductance when closed (leakage)
1.6 ⋅ 10−8
Valve Sonic Conductance when fully open
Amin
0
m2
Restriction Area when closed (leakage); used when Use Restriction Area is true
Ar__max
0.00001
Valve restriction area when fully open; used when Use Restriction Area is true
Armax
b
0.54
Critical pressure ratio
bcr
See Also
Pneumatics Library
Valves
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