Pressure Relief Valve - MapleSim Help
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Pressure Relief Valve

Spring-loaded relief valve

Description

Equations

Variables

Connections

Parameters

Description

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.

Equations

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&equals;{Cminp≤pcloseCmin&plus;p−pclose⁢Cmax−Cminpopen−pclosep<popenCmaxotherwise

Variables

Name

Units

Description

Modelica ID

C

m3s⋅Pa

Sonic Conductance

Cmax

p

Pa

Pressure difference

p

hflowX

kJkg

Specific Enthalpy into port X

hflowX

mflow

kgs

Mass flow rate across the ports

mflow

Connections

Name

Description

Modelica ID

portA

Pneumatic port on left side

portA

portB

Pneumatic port on right side

portB

Parameters

Fluid Medium Parameters

The Gas parameters used in the equations are properties defined in the Gas Model component used in the model.

Name

Default

Units

Description

Modelica ID

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.

medium

Orifice Parameters

Name

Default

Units

Description

Modelica ID

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

UseRestrictionArea

Valve Parameters

Name

Default

Units

Description

Modelica ID

pclose

2⋅105

Pa

Pressure at which valve is fully closed (C = Cmin)

pclose

popen

2.05.105

Pa

Pressure at which valve is fully open (C = Copen)

popen

Cmin

1 ⋅ 10−13

m3s⋅Pa

Valve Sonic Conductance when closed (leakage)

Cmin

Cmax

1.6 ⋅ 10−8

m3s⋅Pa

Valve Sonic Conductance when fully open

Cmax

Amin

0

m2

Restriction Area when closed (leakage); used when Use Restriction Area is true

Amin

Ar__max

0.00001

m2

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