The Pressure Relief Valve (G) is a pressure relief valve for the gas mains. At normal pressure, the valve is closed and only releases the leakage flow. When the set pressure is exceeded, the valve begins to open, allowing gas to escape from the high pressure area. The opening area increases as the inlet pressure rises to the maximum value at which the valve is fully open and the pressure rises without stopping.
The valve responds to inlet pressure versus outlet pressure or inlet pressure versus ambient pressure. The selected pressure measurement is the control pressure of the valve. The Control pressure specification parameter determines which of the measurements the unit uses in the simulation.
The relationship between the opening area and the differential pressure depends on the valve parameter settings. This relationship can be a linear analytical expression or a tabular function.
The flow can be laminar or turbulent and can reach sonic velocities. The maximum velocity occurs at the valve seat where the flow is narrowest and fastest. Flow reaches critical mode and maximum velocity when the pressure drop downstream can no longer increase velocity. Flow locking occurs when the pressure drop reaches the critical valve-specific value. The unit does not capture supersonic flow.
Pressure control
The inlet pressure is the control signal for the valve. The more the inlet pressure exceeds the set value for the valve, the larger the orifice area. The amount by which the signal pressure exceeds the set value determines the opening degree of the valve.
If Opening characteristic is set to `Linear', the unit calculates the valve opening degree to scale the flow characteristic parameters. The valve opening degree is defined as:
where
- control pressure.
If Opening pressure specification is set to Pressure difference of port A relative to port B, then
where is the absolute pressure at port A and is the absolute pressure at port B.
If the Opening pressure specification is set to Gauge pressure at port A, then
where is the atmospheric pressure specified in the block Gas Properties (G);
- setting pressure.
If Opening pressure specification is set to Pressure difference of port A relative to port B, is the value of Set pressure differential.
If the Opening pressure specification is set to Gauge pressure at port A, is the value of Set pressure (gauge).
- is the value of the Pressure regulation range parameter.
Numerical smoothing
If Opening characteristic is set to Linear and Smoothing factor is set to a non-zero value, the block applies numerical smoothing to the normalised control pressure, . Enabling smoothing helps maintain the numerical stability of the simulation.
Hole parameterization
The calculation of local resistance capacity depends on the value of the Valve parametrization parameter:
Cv flow coefficient - flow coefficient determines the dependence of the flow capacity on the pressure drop.
Kv flow coefficient - flow coefficient determines the dependence of flow capacity on pressure drop, .
Sonic conductance - steady-state acoustic conductance determines the flow capacity at critical flow, the condition at which the flow velocity is equal to the local speed of sound. Flow becomes critical when the ratio of outlet pressure to inlet pressure reaches a value called the critical pressure ratio.
Orifice area - the orifice area determines the flow capacity.
Orifice characteristic
The flow through the valve depends on the inlet signal that creates it. Valve opening is related to acoustic conductivity, flow coefficient or orifice area defined by the Valve parameterization.
The flow characteristic is usually given in steady-state mode, when the inlet is a constant controlled pressure. The flow characteristic depends only on the valve and can be linear or non-linear. To set the flow characteristic, use the Opening characteristic parameter:
Linear' - the flow rate is proportional to the degree of valve opening. As the opening degree increases from `0 to 1, the capacity value increases from the specified minimum to the specified maximum.
`Tabulated' - the capacity value is calculated using a tabulated function, which can be linear or non-linear, depending on the degree of opening of the orifice. The function is tabulated and the independent variable is specified in the Opening pressure differential vector or Opening pressure (gauge) vector.
Storing a pulse
The Valve parameterization parameter determines which equations will be used to calculate the flow rate. If the Valve parameterization parameter is set to Cv flow coefficient, the mass flow rate will be defined as
where
- is the flow coefficient;
- a constant equal to 27.3 for mass flow rate in kg/hour, pressure in bar and density in kg/m3;
- expansion coefficient;
- inlet pressure;
- outlet pressure;
- inlet density.
The coefficient of expansion is defined as
where
- is the ratio of adiabatic index to 1.4;
- value of the parameter xT pressure differential ratio factor at choked flow.
When the pressure ratio exceeds the value of the Laminar flow pressure ratio parameter, , there is a smooth transition to the use of the linearised equation
where
When the pressure ratio falls below , the flow becomes critical and the equation is used
When the Valve parameterization is set to Kv flow coefficient, the unit uses the same equations but replaces with using the ratio . For more information on the mass flow equations when the Valve parameterization is set to Kv flow coefficient or Cv flow coefficient, see [2] and [3].
When the Valve parameterization is set to `Sonic conductance', the mass flow rate is defined as
where
- acoustic conductivity;
- critical pressure ratio;
- Subsonic index parameter value;
- ISO reference temperature;
- ISO reference density parameter value;
- inlet temperature.
When the pressure ratio exceeds the value of the Laminar flow pressure ratio parameter, , there is a smooth transition to the use of the linearised equation
When the pressure ratio falls below the critical pressure ratio , the flow becomes critical and the equation is used.
For more information on mass flow equations when the Valve parametrization parameter is set to `Sonic conductance', see [1].
When the Valve parametrization is set to Orifice area, the mass flow rate is defined as
where
- is the area of the orifice or valve;
- is the value of Cross-sectional area at ports A and B;
- the value of Discharge coefficient;
- adiabatic coefficient.
When the pressure ratio exceeds the Laminar flow pressure ratio, , there is a smooth transition to the use of the linearised equation.
When the pressure ratio falls below , the flow becomes critical and the equation is used
For more information on mass flow equations when the Valve parametrization parameter is set to `Orifice area', see [4].
Mass conservation
The volume and mass of the gas inside the component are assumed to be very small, and these values are not considered. According to the principle of conservation of mass, the mass flow rate of gas entering through one port is equal to the flow rate of gas leaving through another port:
where is defined as the mass flow rate entering the valve through the port indicated by the subscript A or B.
Energy Conservation
The component being modelled is adiabatic. There is no heat exchange between the gas and the wall that surrounds it. The gas does not do any work as it moves from the inlet to the outlet. Energy can only be transferred by convection through ports A and B. According to the principle of conservation of energy, the sum of energy fluxes in the ports is always zero:
where is the energy flow into the valve via ports A or B.
Assumptions and limitations
The Sonic conductance value of the Valve parameterization parameter is intended for pneumatic systems. If this parameter is used for gases other than air, it may be necessary to correct the acoustic conductance value by the square root of the relative density.
The equation for the `Orifice area' parameterization has less accuracy for gases that are far from ideal.
#Opening pressure specification —
differential pressure used to control the valve
Pressure difference of port A relative to port B | Gauge pressure at port A
Details
Defines the control opening pressure of the valve.
The value `Pressure difference of port A relative to port B' defines the control pressure as the pressure difference between ports A and B.
The `Gauge pressure at port A' defines the control pressure as the gauge pressure at the inlet.
Values
Pressure difference of port A relative to port B | Gauge pressure at port A
Default value
Pressure difference of port A relative to port B
Program usage name
opening_pressure_type
Evaluatable
No
#Valve parameterization —
Method of setting the flow characteristic through the valve
Cv flow coefficient | Kv flow coefficient | Sonic conductance | Orifice area
Details
The mass flow calculation method is based on:
Cv flow coefficient - flow coefficient .
Kv flow coefficient - flow coefficient , which is defined as .
Sonic conductance - steady-state acoustic conductance.
Orifice area - orifice area.
Values
Cv flow coefficient | Kv flow coefficient | Sonic conductance | Orifice area
Default value
Cv flow coefficient
Program usage name
valve_parameterization
Evaluatable
No
#Opening characteristic —
type of capacity characteristic
Linear | Tabulated
Details
The method the block uses to calculate the valve opening area. The following values are available:
Linear - the opening area is defined as a linear function depending on the degree of opening of the orifice;
Tabulated - the opening area is defined as a non-linear dependency that you specify in tabular form.
Values
Linear | Tabulated
Default value
Linear
Program usage name
opening_characteristic
Evaluatable
No
#Set pressure differential —
set pressure
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar
Details
The differential pressure above which the valve is actuated. This pressure is set when the control pressure is the differential pressure between ports A and B.
Dependencies
To use this parameter, set the Opening pressure specification to `Pressure difference at port A relative to port B' and the Opening characteristic to `Linear'.
Values
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar
Default value
0.0 MPa
Program usage name
delta_p_set
Evaluatable
Yes
#Set pressure (gauge) —
set pressure
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar
Details
The overpressure above which the valve is actuated. This pressure is set when the control pressure is the differential pressure between the A ports and the atmospheric pressure.
Dependencies
To use this parameter, set the Opening pressure specification to `Gauge pressure at port A' and the Opening characteristic to `Linear'.
Values
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar
Default value
0.1 MPa
Program usage name
p_set_gauge
Evaluatable
Yes
#Pressure regulation range —
operating pressure range of the valve
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar
Details
The working pressure range of the valve. The valve starts opening at the set pressure value and opens fully at the maximum value of the working range , where .
Dependencies
To use this parameter, set the Opening characteristic parameter to `Linear'.
Values
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar
Default value
0.1 MPa
Program usage name
p_regulation_range
Evaluatable
Yes
#Maximum Cv flow coefficient —
flow coefficient corresponding to the maximum orifice area
Details
The value of the flow coefficient , when the cross-sectional area available for flow is maximised. This parameter measures the degree to which the gas overcomes the resistive element due to the pressure drop.
Dependencies
To use this parameter, set the Valve parameterization to `Cv flow coefficient' and the Opening characteristic to `Linear'.
Default value
4.0
Program usage name
C_v_max
Evaluatable
Yes
#Opening pressure differential vector —
set pressures
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar
Details
A vector of setting pressures at which the selected valve opening measure - sound conductivity, flow coefficient or opening area - should be specified. This vector must be equal in size to the vector containing the valve opening data. The elements of the vector should be positive and monotonically increasing from left to right. These pressure values represent the pressure drop from inlet to outlet.
The first element of this parameter is the pressure setting at which the valve starts to open. The last element is the maximum pressure at which the valve is fully open. The difference between these two values is the pressure control range of the valve.
Dependencies
To use this parameter, set the Opening pressure specification to `Pressure difference at port A relative to port B' and the Opening characteristic to `Tabulated'.
The Valve parameterization must be set to `Cv flow coefficient'.
Values
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar
Default value
[0.2 : 0.2 : 1.2…] MPa
Program usage name
delta_p_vector_C_v
Evaluatable
Yes
#Opening pressure (gauge) vector —
set pressures
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar
Details
A vector of setting pressures at which the selected valve opening measure - sound conductivity, flow coefficient or opening area - should be specified. This vector must be equal in size to the vector containing the valve opening data. The elements of the vector should be positive and monotonically increasing from left to right. These pressure values represent the pressure drop from inlet to outlet.
The first element of this parameter is the pressure setting at which the valve starts to open. The last element is the maximum pressure at which the valve is fully open. The difference between these two values is the pressure control range of the valve.
Dependencies
To use this parameter, set the Opening pressure specification to `Gauge pressure at port A' and the Opening characteristic to `Tabulated'.
The Valve parameterization must be set to `Cv flow coefficient'.
Values
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar
Default value
[0.2 : 0.2 : 1.2…] MPa
Program usage name
p_gauge_vector_C_v
Evaluatable
Yes
#Cv flow coefficient vector —
vector of flow coefficient values
Details
Vector of flow coefficients . Values should be listed in ascending order.
Dependencies
To use this parameter, set Valve parameterization to Cv flow coefficient and Opening characteristic to Linear.
Default value
[1e-6, 0.8, 1.6, 2.4, 3.2, 4.0]
Program usage name
C_v_vector
Evaluatable
Yes
#xT pressure differential ratio factor at choked flow —
critical differential pressure ratio
Details
The ratio between the inlet pressure and the outlet pressure , defined as , at which the flow becomes critical. If this value is not known, it can be found in Table 2 in ISA-75.01.01 3.
By default the value 0.7 is suitable for many valves.
Dependencies
To use this parameter, set the Valve parameterization parameter to Cv flow coefficient.
Default value
0.7
Program usage name
delta_p_ratio_C_v
Evaluatable
Yes
#Maximum Kv flow coefficient —
flow coefficient corresponding to the maximum orifice area
Details
Flow coefficient value, , when the orifice cross-sectional area is maximum.
Dependencies
To use this parameter, set the Valve parameterization to Kv flow coefficient and the Opening characteristic to Linear.
Default value
3.6
Program usage name
K_v_max
Evaluatable
Yes
#Opening pressure differential vector —
set pressures
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar
Details
A vector of setting pressures at which the selected valve opening degree - sound conductivity, flow coefficient or opening area - is to be specified. This vector must be equal in size to the vector containing the valve opening data. The elements of the vector should be positive and monotonically increasing from left to right. These pressure values represent the pressure drop from inlet to outlet.
The first element of this parameter is the pressure setting at which the valve starts to open. The last element is the maximum pressure at which the valve is fully open. The difference between these two values is the pressure control range of the valve.
Dependencies
To use this parameter, set the Opening pressure specification to `Pressure difference at port A relative to port B' and the Opening characteristic to `Tabulated'.
The Valve parameterization must be set to `Kv flow coefficient'.
Values
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar
Default value
[0.2 : 0.2 : 1.2…] MPa
Program usage name
delta_p_vector_K_v
Evaluatable
Yes
#Opening pressure (gauge) vector —
set pressures
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar
Details
A vector of setting pressures at which the selected valve opening degree - sound conductivity, flow coefficient or opening area - is to be specified. This vector must be equal in size to the vector containing the valve opening data. The elements of the vector shall be positive and monotonically increasing in value from left to right. These values represent the inlet overpressure.
The first element of this parameter is the valve setting pressure at which the valve starts to open. The last element is the maximum pressure at which the valve is fully open. The difference between these two values is the pressure control range of the valve.
Dependencies
To use this parameter, set the Opening pressure specification to `Gauge pressure at port A' and the Opening characteristic to `Tabulated'.
The Valve parameterization must be set to `Kv flow coefficient'.
Values
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar
Default value
[0.2 : 0.2 : 1.2…] MPa
Program usage name
p_gauge_vector_K_v
Evaluatable
Yes
#Kv flow coefficient vector —
vector of flow coefficient values
Details
Vector of flow coefficients . The values must be specified in ascending order. The dimensionality of the vector corresponds to that of the Opening fraction vector.
Dependencies
To use this parameter, set the Valve parameterization to `Kv flow coefficient' and the Opening characteristic to `Tabulated'.
Default value
[1e-6, 0.72, 1.44, 2.16, 2.88, 3.6]
Program usage name
K_v_vector
Evaluatable
Yes
#xT pressure differential ratio factor at choked flow —
critical differential pressure ratio
Details
The ratio between the inlet pressure and the outlet pressure , defined as , at which the flow becomes critical. If this value is not known, it can be found in Table 2 in ISA-75.01.01 3.
By default the value 0.7 is suitable for many valves.
Dependencies
To use this parameter, set the Valve parameterization parameter to Kv flow coefficient.
Default value
0.7
Program usage name
delta_p_ratio_K_v
Evaluatable
Yes
#Maximum sonic conductance —
acoustic conductivity corresponding to the maximum aperture area
l/(bar*s) | gal/(min*psi) | m^3/(Pa*s)
Details
The value of acoustic conductivity when the orifice cross-sectional area is maximised.
Dependencies
To use this parameter, set the Valve parameterization to Sonic conductance and the Opening characteristic to Linear.
Values
l/(bar*s) | gal/(min*psi) | m^3/(Pa*s)
Default value
12.0 l/(bar*s)
Program usage name
C_max
Evaluatable
Yes
#Critical pressure ratio —
critical pressure ratio
Details
The ratio of pressures at which the flow becomes critical and the flow velocity reaches a maximum determined by the local speed of sound.
The ratio between the outlet pressure and the inlet pressure : .
Dependencies
To use this parameter, set the Valve parameterization to Sonic conductance and the Opening characteristic to Linear.
Default value
0.3
Program usage name
B_critical_linear
Evaluatable
Yes
#Opening pressure differential vector —
set pressures
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar
Details
A vector of setting pressures at which the selected valve opening degree - sound conductivity, flow coefficient or opening area - is to be specified. This vector must be equal in size to the vector containing the valve opening data. The elements of the vector should be positive and monotonically increasing from left to right. These pressure values represent the pressure drop from inlet to outlet.
The first element of this parameter is the pressure setting at which the valve starts to open. The last element is the maximum pressure at which the valve is fully open. The difference between these two values is the pressure control range of the valve.
Dependencies
To use this parameter, set the Opening pressure specification to `Pressure difference at port A relative to port B' and the Opening characteristic to `Tabulated'.
The Valve parameterization must be set to `Sonic conductance'.
Values
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar
Default value
[0.2 : 0.2 : 1.2…] MPa
Program usage name
delta_p_vector_C
Evaluatable
Yes
#Opening pressure (gauge) vector —
set pressures
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar
Details
A vector of setting pressures at which the selected valve opening degree - sound conductivity, flow coefficient or opening area - is to be specified. This vector must be equal in size to the vector containing the valve opening data. The elements of the vector shall be positive and monotonically increasing in value from left to right. These values represent the inlet overpressure.
The first element of this parameter is the valve setting pressure at which the valve starts to open. The last element is the maximum pressure at which the valve is fully open. The difference between these two values is the pressure control range of the valve.
Dependencies
To use this parameter, set the Opening pressure specification to `Gauge pressure at port A' and the Opening characteristic to `Tabulated'.
The Valve parameterization must be set to `Sonic conductance'.
Values
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar
Vector of acoustic conductivity values. The values should be listed in ascending order.
Dependencies
To use this parameter, set the Valve parameterization parameter to Sonic conductance.
Values
l/(bar*s) | gal/(min*psi) | m^3/(Pa*s)
Default value
[1e-5, 2.4, 4.8, 7.2, 9.6, 12.0] l/(bar*s)
Program usage name
C_vector
Evaluatable
Yes
#Critical pressure ratio vector —
vector of critical pressure ratio values
Details
Vector of critical pressure ratios. The critical pressure ratio is the ratio of the outlet pressure to the inlet pressure at which the flow becomes critical and the flow velocity reaches a maximum determined by the local speed of sound.
Dependencies
To use this parameter, set the Valve parameterization to `Sonic conductance' and the Opening characteristic to `Tabulated'.
Default value
0.3 * ones(6)
Program usage name
B_critical_vector
Evaluatable
Yes
#Subsonic index —
degree value used to calculate the mass flow rate in subsonic flow regime
Details
An empirical value used to more accurately calculate the mass flow rate in subsonic flow regime.
Dependencies
To use this parameter, set the Valve parameterization parameter to `Sonic conductance'.
Default value
0.5
Program usage name
m
Evaluatable
Yes
#ISO reference temperature —
reference temperature according to ISO 8778
K | degC | degF | degR | deltaK | deltadegC | deltadegF | deltadegR
Details
The temperature in the standard reference atmosphere in ISO 8778.
The values of the ISO reference parameters only need to be adjusted if acoustic conductivity values obtained with different reference values are used.
Dependencies
To use this parameter, set the Valve parameterization parameter to `Sonic conductance'.
#ISO reference density —
reference density according to ISO 8778
g/cm^3 | kg/m^3 | lbm/gal
Details
Density in a standard reference atmosphere in ISO 8778.
The values of the ISO reference parameters need only be adjusted if acoustic conductivity values obtained with different reference values are used.
Dependencies
To use this parameter, set the Valve parameterization parameter to `Sonic conductance'.
Values
g/cm^3 | kg/m^3 | lbm/gal
Default value
1.185 kg/m^3
Program usage name
rho_reference
Evaluatable
Yes
#Maximum orifice area —
flow cross-sectional area corresponding to the maximum orifice area
m^2 | cm^2 | ft^2 | in^2 | km^2 | mi^2 | mm^2 | um^2 | yd^2
Details
Maximum cross-sectional flow area when the cross-sectional area of the orifice is maximum.
Dependencies
To use this parameter, set Valve parameterization to Orifice area and Opening characteristic to Linear.
#Opening pressure differential vector —
set pressures
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar
Details
A vector of setting pressures at which the selected valve opening degree - sound conductivity, flow coefficient or opening area - is to be specified. This vector must be equal in size to the vector containing the valve opening data. The elements of the vector should be positive and monotonically increasing from left to right. These pressure values represent the pressure drop from inlet to outlet.
The first element of this parameter is the pressure setting at which the valve starts to open. The last element is the maximum pressure at which the valve is fully open. The difference between these two values is the pressure control range of the valve.
Dependencies
To use this parameter, set the Opening pressure specification to `Pressure difference at port A relative to port B' and the Opening characteristic to `Tabulated'.
The Valve parameterization must be set to `Orifice area'.
Values
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar
Default value
[0.2 : 0.2 : 1.2…] MPa
Program usage name
delta_p_vector_area
Evaluatable
Yes
#Opening pressure (gauge) vector —
set pressures
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar
Details
A vector of setting pressures at which the selected valve opening degree - sound conductivity, flow coefficient or opening area - is to be specified. This vector must be equal in size to the vector containing the valve opening data. The elements of the vector shall be positive and monotonically increasing in value from left to right. These values represent the inlet overpressure.
The first element of this parameter is the valve setting pressure at which the valve starts to open. The last element is the maximum pressure at which the valve is fully open. The difference between these two values is the pressure control range of the valve.
Dependencies
To use this parameter, set the Opening pressure specification to `Gauge pressure at port A' and the Opening characteristic to `Tabulated'.
The Valve parameterization must be set to `Orifice area'.
Values
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar
Default value
[0.2 : 0.2 : 1.2…] MPa
Program usage name
p_gauge_vector_area
Evaluatable
Yes
#Orifice area vector —
vector of hole area values
m^2 | cm^2 | ft^2 | in^2 | km^2 | mi^2 | mm^2 | um^2 | yd^2
Details
Vector of the areas of the hole cross-section. The dimensionality of the vector corresponds to the Opening fraction vector. The first element of this vector is the leakage area and the last element is the maximum orifice area.
Dependencies
To use this parameter, set the Valve parameterization to `Orifice area' and the Opening characteristic to `Tabulated'.
ISO 6358-3. "Pneumatic fluid power - Determination of flow-rate characteristics of components using compressible fluids - Part 3: Method for calculating steady-state flow rate characteristics of systems". 2014.
IEC 60534-2-3. "Industrial-process control valves - Part 2-3: Flow capacity - Test procedures". 2015.
ANSI/ISA-75.01.01. "Industrial-Process Control Valves - Part 2-1: Flow capacity - Sizing equations for fluid flow underinstalled conditions". 2012.
P. Beater. "Pneumatic Drives." Springer-Verlag Berlin Heidelberg. 2007.