Pressure Reducing Valve (G)

Pressure reducing valve in the gas network.

pressure reducing valve g

Description

The Pressure Reducing Valve (G) unit is a pressure reducing valve in the gas flow network. The valve remains open when the pressure at port B is less than the set point. When the pressure at port B reaches or exceeds the set point, the valve closes. The unit is controlled by the difference between the set pressure and the pressure at port B. The opening area decreases as the pressure drops to a minimum, when the valve is completely closed and only leakage flow remains.

The relationship between the opening area and the pressure drop depends on the valve parameterization. This relationship can take the form of a linear analytical expression or a tabular function.

The flow can be laminar or turbulent and can reach sonic velocities. The maximum velocity is reached at the valve throat where the flow is narrowest and fastest. The flow reaches the critical regime and and maximum velocity when the pressure drop downstream can no longer increase the velocity. The unit does not capture supersonic flow.

Pressure control

The Pressure-Reducing Valve (G) unit regulates the pressure between the set pressure and the maximum pressure. The outlet pressure is the control signal for the valve. The more the outlet pressure exceeds the setting pressure of the valve, the smaller the opening area becomes.

The signal pressure, , is equal to

where

- is the pressure at the port ;
- is the atmospheric pressure specified in the Gas Properties (G) block of the model.

Both pressures are defined during the simulation as absolute pressures.

The pressure setting, , of the valve is the value of the Set pressure parameter (gauge pressure) when the Opening characteristic parameter is set to Linear. When Opening characteristic is set to Tabulated, is the first element of the vector parameter Pressure at port B (gauge).

The maximum pressure, , is equal to , where is the pressure control range of the valve when Linear is set to Opening characteristic. When Opening characteristic is set to `Tabulated', is the last element of the vector parameter Pressure at port B (gauge).

Valve opening degree

The degree to which the control pressure exceeds the set pressure determines how much the valve opens. When Opening characteristic is set to `Linear', the unit calculates the degree of valve opening to scale the flow characteristic parameters. The valve opening degree is:

where

- control pressure;
- is the pressure setting specified by the Set pressure (gauge) parameter;
- the pressure regulation range set by the Pressure regulation range parameter.

The fraction is normalised so that it is 0 when the valve is fully closed and 1 when the valve is fully open. If the calculation returns a value outside these limits, the block saturates the value to the nearest of the two limits.

Numerical smoothing

If the Opening characteristic parameter is set to Linear and the Smoothing factor parameter is set to a non-zero value, the block applies numerical smoothing to the normalised control pressure, . The smoothing helps to 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.

pressure reducing valve g 1

`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 parameter Pressure at port B (gauge) vector.

pressure reducing valve g 2

Saving 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 expansion coefficient is defined as

where

- is the ratio of the adiabatic ratio to 1.4;
- is the 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 parametrization 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 parametrization is set to Kv flow coefficient or Cv flow coefficient, see [2] and [3].

If the Valve parametrization 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 liquid entering through one port is equal to the gas flow rate leaving through the other port:

where is defined as the mass flow rate entering the valve through the port labelled by the subscript A or B.

Energy Conservation

The component being modelled is adiabatic. There is no heat transfer between the fluid and the wall that surrounds it. The fluid 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.
This block does not model supersonic flow.

Ports

Conserving

# A — valve inlet
gas

Details

Gas port associated with the valve inlet.

Program usage name

port_a

# B — valve outlet
gas

Details

Gas port associated with the valve outlet.

Program usage name

port_b

Parameters

# Valve parameterization — method of specifying the flow characteristic through the orifice
Cv flow coefficient | Kv flow coefficient | Sonic conductance | Orifice area

Details

The method of mass flow calculation 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

Method for calculating the valve opening area into the selected capacity measure.

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 dependence that you specify in tabular form.

Values	`Linear` \| `Tabulated`
Default value	`Linear`
Program usage name	`opening_characteristic`
Evaluatable	No

# 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 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

Flow coefficient value , when the orifice cross-sectional area is maximum.

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

# Pressure at port B (gauge) vector — values at which the valve opening data must be specified
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar

Details

A vector of control pressures at which the selected valve opening degree is specified - sound conductivity, flow coefficient or opening area. This vector must be equal in size to the vector containing the valve opening data. The elements of the vector must be positive and monotonically increasing in value from left to right.

The first element of the vector gives the pressure value at which the valve begins to close. This element is equivalent to the parameter Set pressure (gauge) at `Linear' of the parameter Opening characteristic. The latter element gives the maximum pressure at which the valve is maximally closed and only the leakage flow remains. The difference between the two gives the pressure control range of the valve.

Dependencies

To use this parameter, set the Opening characteristic to `Tabulated' and the Valve parameterization 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 . 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 `Cv flow coefficient' and the Opening characteristic to `Tabulated'.

Default value	`[4.0, 3.2, 2.4, 1.6, 0.8, 1e-6]`
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

# Pressure at port B (gauge) vector — vector of control pressures at which the valve opening data must be specified
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar

Details

A vector of control pressures at which to specify the selected valve opening degree - sound conductivity, flow coefficient or opening area. This vector must be equal in size to the vector containing the valve opening data. The elements of the vector must be positive and monotonically increasing in value from left to right.

Dependencies

To use this parameter, set the Opening characteristic to `Tabulated' and the Valve parameterization 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	`[3.6, 2.88, 2.16, 1.44, 0.72, 1e-6]`
Program usage name	`K_v_vector`
Evaluatable	Yes

# xT pressure differential ratio factor at choked flow — critical differential pressure ratio

Details

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/(bars)` \| `gal/(minpsi)` \| `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

# Pressure at port B (gauge) vector — vector of control pressures at which the valve opening data must be specified
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar

Details

Dependencies

To use this parameter, set the Opening characteristic to `Tabulated' and the Valve parameterization 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	`p_gauge_vector_C`
Evaluatable	Yes

# Sonic conductance vector — vector of acoustic conductivity values
l/(bar*s) | gal/(min*psi) | m^3/(Pa*s)

Details

Vector of acoustic conductivity values. The values should be specified in ascending order. The dimensionality of the vector corresponds to the Opening fraction vector.

Dependencies

To use this parameter, set the Valve parameterization parameter to Sonic conductance.

Values	`l/(bars)` \| `gal/(minpsi)` \| `m^3/(Pa*s)`
Default value	`[12.0, 9.6, 7.2, 4.8, 2.4, 1e-5] 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. The dimensionality of the vector corresponds to that of the Opening fraction vector.

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

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'.

Values	`K` \| `degC` \| `degF` \| `degR` \| `deltaK` \| `deltadegC` \| `deltadegF` \| `deltadegR`
Default value	`293.15 K`
Program usage name	`T_reference`
Evaluatable	Yes

# 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.

Values	`m^2` \| `cm^2` \| `ft^2` \| `in^2` \| `km^2` \| `mi^2` \| `mm^2` \| `um^2` \| `yd^2`
Default value	`1e-4 m^2`
Program usage name	`max_restriction_area`
Evaluatable	Yes

# Pressure at port B (gauge) vector — vector of control pressures at which the valve opening data must be specified
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar

Details

Dependencies

To use this parameter, set the Opening characteristic to `Tabulated' and the Valve parameterization 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'.

Values	`m^2` \| `cm^2` \| `ft^2` \| `in^2` \| `km^2` \| `mi^2` \| `mm^2` \| `um^2` \| `yd^2`
Default value	`[1e-4, 0.8e-4, 0.6e-4, 0.4e-4, 0.2e-4, 1e-10] m^2`
Program usage name	`restriction_area_vector`
Evaluatable	Yes

# Discharge coefficient — correction factor

Details

The correction factor is the ratio of the actual mass flow rate to the theoretical mass flow rate.

Dependencies

To use this parameter, set the Valve parameterization parameter to Orifice area.

Default value	`0.64`
Program usage name	`C_d`
Evaluatable	Yes

# Leakage flow fraction — cost ratio

Details

The ratio of the flow rate through a closed orifice to that through an open orifice.

Dependencies

To use this parameter, set the Opening characteristic to `Linear'.

Default value	`1e-6`
Program usage name	`leakage_fraction`
Evaluatable	Yes

# Smoothing factor — numerical smoothing factor

Details

A continuous smoothing factor that ensures smooth opening by correcting the orifice characteristic in the nearly open and nearly closed positions.

Dependencies

To use this parameter, set Opening characteristic to `Linear'.

Default value	`0.01`
Program usage name	`smoothing_factor`
Evaluatable	Yes

# Laminar flow pressure ratio — pressure ratio at which the flow transitions between laminar and turbulent regimes

Details

The ratio of outlet pressure to inlet pressure at which the flow transitions between laminar and turbulent flow regimes.

Typical values range from 0.995 to 0.999.

Default value	`0.999`
Program usage name	`B_laminar`
Evaluatable	Yes

# Cross-sectional area at ports A and B — inlet or outlet area
m^2 | cm^2 | ft^2 | in^2 | km^2 | mi^2 | mm^2 | um^2 | yd^2

Details

This area is used when calculating the mass flow rate through the ports.

The ports are all the same size. The value of this parameter must match the inlet port area of the component to which the unit is connected.

Values	`m^2` \| `cm^2` \| `ft^2` \| `in^2` \| `km^2` \| `mi^2` \| `mm^2` \| `um^2` \| `yd^2`
Default value	`0.01 m^2`
Program usage name	`port_area`
Evaluatable	Yes

Pressure Reducing Valve (G)

Description

Pressure control

Valve opening degree

Numerical smoothing

Hole parameterization

Orifice characteristic

Saving a pulse

Mass conservation

Energy Conservation

Assumptions and limitations

Ports

Conserving

Parameters

Parameters

See also