Relief Valve with Pressure Dependency
Relief valve with table-based pressure dependency
Description
Equations
Variables
Connections
Parameters
The Relief Valve with Pressure Dependency component models a check valve where the opening varies with the pressure across the device.
The Conductance and critical pressure ratio are computed as a function of the pressure difference between port A and port B from a data table containing values of pressure difference vs. the corresponding C and b. Based on C and b, the pressure vs. flow rate relationships are derived by the formulation used in 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 sonic conductance is calculated from the restriction area using Gidlund's approximation.
Pressure vs. Conductance and b
For this component, the Conductance and Critical pressure ratio of the orifice must be specified as a function of the pressure difference in the form of a table. The following parameters allows users to specify the necessary data for this calculation.
Data Source: This parameter allows users to specify the nature of the source file for the Pressure vs. C and b table. The available options are file, attachment, and inline.
file: Use this option to specify a source file (an Excel or a CSV file) located on the hard drive. Use the C,BdP parameter to browse to and/or select the data file. The data file will not be attached to the MapleSim model.
attachment: Use this option to specify a data file (an Excel or a CSV file) that is attached to the MapleSim model. To be used as an attachment, data files must be attached to the MapleSim model and be categorized under Data Sets. The attached files in a MapleSim model can be viewed in the Attachments pane under the Data Sets section. For more information, see Attaching a File to a Model. If the required file is not already attached to the MapleSim model, use the C,bdP parameter to attach a new file.
Note:
If the file option is used, subsequent changes to the source file will be incorporated into MapleSim simulations
If the attachment option is used, subsequent changes to the source file will not affect the version attached to the MapleSim model. To ensure updates to the source files are incorporated in the simulation, the file must be reattached.
The Data Generation App can be used to generate table data from mathematical functions using Maple code. For more information about MapleSim apps, see Using MapleSim Apps.
inline: Use this option to directly specify the pressure vs. area relationship in the form of a table. In the C,bdP parameter, enter an m×3 matrix. The first column must contain values of pressure difference and the second column must contain corresponding values of the Conductance and third column must contain the critical pressure ratio b.
Note: To change the dimensions of table, right-click (Control-click for Mac®) the parameter field and select Edit Matrix Dimensions. In the Matrix Dimensions dialog, enter values for the number or rows and columns and then click OK.
Skip rows: This option allows users to specify the number of top rows to be ignored during the calculations. This option can be useful when the Excel file contains header information.
Smoothness: The smoothness option specifies how the data table is interpolated.
Pressure difference unit: This option specifies the unit of pressure used in the supplied data.
Ci=Interpolate1DC,bdP,p, column, smoothness,skipRows,column = 2 B__i =Interpolate1DC,bdP,p, column, smoothness,skipRows,column = 3
Ar=Interpolate1DA,bdP,p, column, smoothness,skipRows,column = 2 if UseRestrictionArea = true
Csonic=max0, C__i bcr=max0, B__i
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
C=0.125⋅4⋅ArPi
Name
Units
Modelica ID
p
Pa
Pressure drop from A to B
pX
Pressure at port X
mflow
kgs
Flow rate from A to B
hflowX
kJkg
Specific Enthalpy into port X
portA
Upstream Pneumatic port
portB
Downstream Pneumatic port
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 Parameter
UseRestrictionArea
false
True (checked) means sonic conductance is calculated from restriction area using Gidlund's approximation
b__lamreg
0.999
Flow transition from turbulent to laminar
b_lamreg
Area vs. Conductance and b
Data sources
inline
Data source
datasourcemode
C,bdP
[1]
Data set
table
A,bdP
[2]
Skip rows
0
Number of rows to skip
skipRows
Smoothness
linear
Smoothness of table interpolation
smoothness
Pressure difference unit
kPa
Unit of pressure used in the data
pressUnit
[1] 100,1e−13,0.54;200,3.2ⅇ−9,0.54; 300, 6.4ⅇ−9, 0.54; 600, 9.6ⅇ−9, 0.54
[2] 100,1e−12,0.54;200,0.0001,0.54; 300, 0.0001, 0.54; 600, 0.0001, 0.54
See Also
Pneumatics Library
Valves
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