Pilot-Operated Check Valve (G)

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A check valve with a control port in the gas network.

blockType: EngeeFluids.Gas.Valves.DirectionalControl.PilotOperatedCheck

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Description

Block Pilot-Operated Check Valve (G) simulates a valve with a forced-opening mechanism that, when activated, allows reverse flow. A check valve is an opening with a unidirectional opening mechanism that prevents backflow.

The X port of the block is a control port that serves as a forced opening mechanism. In normal operation, the control port is inactive and the valve behaves like a non-return valve. In a non-return valve, the opening opens only when the pressure gradient on the valve is directed from the inlet to the outlet. Opening the opening prevents backflow, which requires a reverse pressure gradient, and protects the upstream valve components from pressure surges, temperature fluctuations, and chemical contamination.

With sufficient pressure in port X, the unit increases the pressure in the control port and pushes the valve control element out of the seat, providing a return flow. After that, the valve opens for flow in both directions, and the reverse pressure drop from the outlet to the inlet ensures flow in the opposite direction. The seat located in the flow path determines whether the valve is open. When the seat is closed, the flow is blocked and the valve closes.

The valve starts to open at the actuation pressure and continues to open until the end of the pressure control range. The actuation pressure is the initial resistance due to friction or elastic forces that the valve must overcome in order to open slightly. Below this threshold, the valve is closed and only allows leakage flow. After the end of the pressure control range, the valve is fully open, and the flow rate at maximum opening is determined by the instantaneous pressure values.

The flow can be laminar or turbulent and can reach sonic velocities. The maximum speed is reached in the smallest section of the valve. The flow becomes critical and the velocity reaches saturation when reducing the outlet pressure can no longer increase the velocity. The critical mode occurs when the back pressure ratio reaches a critical value characteristic of the valve. The block does not simulate supersonic flow.

Regulation and other pressure parameters

The opening of the valve depends on the control pressure and the pressure difference between the inlet and outlet. The pressure opening the valve is determined as follows:

where

— control pressure drop;
— pilot ratio;
— overpressure in port A;
— overpressure in port B.

During the simulation, the unit determines the pressure in the ports relative to absolute zero.

The control pressure drop can be set relative to the inlet, port A, or relative to the environment. The control pressure drop can be selected by setting the parameter Pilot pressure specification meaning Pressure difference of port X relative to port A or Gauge pressure at port X.

If the value is set to Gauge pressure at port X, the control pressure drop is

where — the atmospheric pressure set in the block Gas Properties (G) models, and — the absolute pressure value in the control port.

If the value is set to Pressure difference of port X relative to port A, the control pressure drop is

where — the absolute pressure value at the valve inlet, in port A.

If for the parameter Pilot configuration the value is set Rigidly connected pilot spool and poppet The control spool transmits both positive and negative forces of the control pressure, and the unit uses as it is in the equation for . If for the parameter Pilot configuration the value is set Disconnected pilot spool and poppet, the control spool transmits only the positive forces of the control pressure, and limited to positive values. In the equation for the block uses .

Degree of valve opening

The degree to which the control pressure exceeds the actuation pressure determines how much the valve opens. The degree of valve opening is equal to

where

— control pressure;
— the actuation pressure set in the parameter Cracking pressure differential;
— the maximum opening pressure set in the parameter Maximum opening pressure differential.

The degree of opening is normalized so that it is equal to 0 with the valve fully closed and 1 with the valve fully open. If the calculation returns a value outside this range, the block equates it to the nearest of the two limits.

calculated smoothing

If the parameter value is Smoothing factor non-zero, the unit applies numerical smoothing to the normalized control pressure . Enabling anti-aliasing helps maintain the numerical stability of the simulation.

Parameterization of the valve

The behavior of the block depends on the selected parameter value. Valve parameterization:

Cv flow coefficient — expense ratio determines the bandwidth. The flow coefficient characterizes how easily the gas passes under the influence of a given pressure drop.
Kv flow coefficient — expense ratio , where , defines the bandwidth. The flow coefficient characterizes how easily the gas passes under the influence of a given pressure drop.
Sonic conductance — acoustic conductivity in stationary mode determines the throughput. Acoustic conductivity determines the throughput in a critical flow when the flow velocity is equal to the local speed of sound. The critical mode occurs when the ratio of outlet pressure to inlet pressure reaches a critical value, called the critical pressure ratio.
Orifice area — the area of the hole determines the throughput.

The unit scales the set flow rate depending on the degree of valve opening. As the degree of valve opening increases from 0 before 1 The throughput indicator is scaled from a set minimum to a set maximum.

The mass flow equation

The block equations depend on the parameter Valve parameterization. If for the parameter Valve parameterization the value is set Cv flow coefficient, mass consumption equal to

where

— expense ratio;
— a constant equal to 27.3 for mass flow rate in kg/h, pressure in bars and density in kg/m3³;
— expansion coefficient;
— inlet pressure;
— outlet pressure;
— density at the entrance.

The expansion coefficient is

where

— the ratio of the adiabatic index to 1.4;
— parameter value xT pressure differential ratio factor at choked flow.

The block smoothly transitions to the linearized form of the equation when the pressure ratio exceeds the value the parameter Laminar flow pressure ratio:

where

When is the pressure ratio falls lower , the flow becomes critical, and the block uses the equation

If for the parameter Valve parameterization the value is set Kv flow coefficient, the block uses the same equations, but replaces on using the ratio . More information about the mass flow equations for the values Kv flow coefficient and Cv flow coefficient the parameter Valve parameterization see [2], << ansi-isa-75-01-01, [3]>>.

If for the parameter Valve parameterization the value is set Sonic conductance, mass consumption equal to

where

— acoustic conductivity;
— critical pressure ratio;
— parameter value Subsonic index;
— parameter value ISO reference temperature;
— parameter value ISO reference density;
— temperature at the entrance.

The block smoothly transitions to the linearized form of the equation when the pressure ratio exceeds the value the parameter Laminar flow pressure ratio:

When is the pressure ratio falls below the critical pressure ratio , the flow becomes critical, and the block uses the equation

For more information about the mass flow equations for the value Sonic conductance the parameter Valve parameterization see [1].

If for the parameter Valve parameterization the value is set Orifice area, mass consumption equal to

where

— the area of the hole or valve;
— parameter value Cross-sectional area at ports A and B;
— parameter value Discharge coefficient;
— the adiabatic index.

The block smoothly transitions to the linearized form of the equation when the pressure ratio exceeds the value the parameter Laminar flow pressure ratio:

When is the pressure ratio falls lower , the flow becomes critical, and the block uses the equation

For more information about the mass flow equations for the value Orifice area the parameter Valve parameterization see [4].

Conservation of mass

The block assumes that the volume and mass of gas inside the valve are very small, and does not take these values into account. As a result, gas cannot accumulate in the valve. According to the principle of conservation of mass, the mass flow rate of gas entering the valve through one port is equal to the mass flow rate of gas exiting through the other port:

where — the mass flow rate of the gas entering the valve through the port indicated by the subscript A or B.

Energy conservation

The modeled component is adiabatic. There is no heat exchange between the gas and the surrounding wall. When the gas is moved from the inlet to the outlet, no work is performed on it. Energy can only be transferred by convection through ports A and B. According to the principle of energy conservation, the sum of energy flows in ports is always zero:

where — the flow of energy entering the valve through port A or B.

Assumptions and limitations

Meaning Sonic conductance the parameter Valve parameterization designed for pneumatic systems. If this value is used for gases other than air, it may be necessary to scale the acoustic conductivity by the square root of the relative density.
The equation for parameterization Orifice area less accurate for gases that are far from ideal.
This block does not simulate supersonic flow.

Ports

Conserving

# A — valve inlet
gas

Details

A non-directional port connected to the opening through which the flow should flow into the valve during normal operation when the control mechanism is turned off. This port can only serve as an outlet if there is sufficient pressure in the control port.

Program usage name

inlet

# B — valve outlet
gas

Details

A non-directional port connected to the opening through which the flow should exit the valve during normal operation when the control mechanism is disabled.

Program usage name

outlet

# X — managing port
gas

Details

A non-directional port connected to an opening through which, when sufficient pressure is applied, a control mechanism is activated that opens the valve for reverse flow.

Program usage name

port_x

Parameters

Main

# Pilot ratio — the ratio of the areas of the control ports

Details

The ratio of the area of the control port X to the area of the input port A.

Default value	`1.0`
Program usage name	`pilot_ratio`
Evaluatable	Yes

# Valve parameterization — parameterization to determine the characteristics of the flow through the hole
Cv flow coefficient | Kv flow coefficient | Sonic conductance | Orifice area

Details

Mass flow calculation method:

Cv flow coefficient — expense ratio .
Kv flow coefficient — expense ratio , where .
Sonic conductance — steady-state acoustic conductivity.
Orifice area — the area of the hole.

Values	`Cv flow coefficient` \| `Kv flow coefficient` \| `Sonic conductance` \| `Orifice area`
Default value	`Cv flow coefficient`
Program usage name	`valve_parameterization`
Evaluatable	No

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

Details

The ratio between the inlet pressure and outlet pressure , defined as at which point the flow becomes critical. If this value is unknown, it can be found in table 2 in ISA-75.01.01 [3]. Otherwise, the default value is 0.7 suitable for many valves.

Dependencies

To use this parameter, set for the parameter Valve parameterization meaning Cv flow coefficient or Kv flow coefficient.

Default value	`0.7`
Program usage names	`delta_p_ratio_K_v`, `delta_p_ratio_C_v`
Evaluatable	Yes

# Critical pressure ratio — critical pressure ratio

Details

The ratio of inlet and outlet pressures at which the flow becomes critical and the flow velocity reaches a maximum determined by the local speed of sound. The pressure ratio is the outlet pressure divided by the inlet pressure.

Dependencies

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

Default value	`0.3`
Program usage name	`B_critical_linear`
Evaluatable	Yes

# Maximum opening pressure differential — maximum pressure drop when the valve is open
Pa | uPa | hPa | kPa | MPa | GPa | kgf/m^2 | kgf/cm^2 | kgf/mm^2 | mbar | bar | kbar | atm | ksi | psi | mmHg | inHg

Details

Maximum pressure drop when the valve is open. This difference is equal to the sum of the pressure drop from the inlet to the outlet and the product of the control pressure by the pilot ratio. The control pressure used depends on the parameter value Pilot pressure specification.

Units	`Pa` \| `uPa` \| `hPa` \| `kPa` \| `MPa` \| `GPa` \| `kgf/m^2` \| `kgf/cm^2` \| `kgf/mm^2` \| `mbar` \| `bar` \| `kbar` \| `atm` \| `ksi` \| `psi` \| `mmHg` \| `inHg`
Default value	`0.1 MPa`
Program usage name	`max_delta_p`
Evaluatable	Yes

# Pilot configuration — valve geometry
Rigidly connected pilot spool and poppet | Disconnected pilot spool and poppet

Details

The method that the unit uses when the control pressure is negative:

Rigidly connected pilot spool and poppet — the control spool transmits both positive and negative forces of the control pressure, so the unit uses as it is.
Disconnected pilot spool and poppet — the control spool transmits only the positive forces of the control pressure, so the block limits positive values. The block replaces negative values with zero.

Values	`Rigidly connected pilot spool and poppet` \| `Disconnected pilot spool and poppet`
Default value	`Rigidly connected pilot spool and poppet`
Program usage name	`pilot_configuration`
Evaluatable	No

# Cracking pressure differential — threshold pressure
Pa | uPa | hPa | kPa | MPa | GPa | kgf/m^2 | kgf/cm^2 | kgf/mm^2 | mbar | bar | kbar | atm | ksi | psi | mmHg | inHg

Details

The pressure drop at which the valve starts to open. This difference is equal to the sum of the pressure drop from the inlet to the outlet and the product of the control pressure by the pilot ratio. The control pressure used depends on the parameter value Pilot pressure specification.

Units	`Pa` \| `uPa` \| `hPa` \| `kPa` \| `MPa` \| `GPa` \| `kgf/m^2` \| `kgf/cm^2` \| `kgf/mm^2` \| `mbar` \| `bar` \| `kbar` \| `atm` \| `ksi` \| `psi` \| `mmHg` \| `inHg`
Default value	`0.01 MPa`
Program usage name	`delta_p_cracking`
Evaluatable	Yes

# Discharge coefficient — expense ratio

Details

A correction factor that takes into account discharge losses in theoretical flows.

Dependencies

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

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

# Maximum sonic conductance — acoustic conductivity corresponding to the maximum hole area
l/(bar*s) | gal/(min*psi) | m^3/(Pa*s)

Details

The value of acoustic conductivity is when the cross-sectional area available for flow is maximal.

Dependencies

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

Units	`l/(bars)` \| `gal/(minpsi)` \| `m^3/(Pa*s)`
Default value	`12.0 l/(bar*s)`
Program usage name	`C_max`
Evaluatable	Yes

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

Details

The pressure ratio at which the flow transitions between laminar and turbulent flow modes. The pressure ratio is the outlet pressure divided by the inlet pressure. Typical values range from 0.995 before 0.999.

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

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

Details

The cross-sectional area at ports A and B. The ports have the same size. The value of this parameter must correspond to the area of the inlet of the components to which the unit is connected.

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

# Maximum orifice area — the flow area corresponding to the maximum open component
m^2 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac

Details

The cross-sectional area of the hole is when the cross-sectional area available for flow is at its maximum.

Dependencies

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

Units	`m^2` \| `um^2` \| `mm^2` \| `cm^2` \| `km^2` \| `in^2` \| `ft^2` \| `yd^2` \| `mi^2` \| `ha` \| `ac`
Default value	`0.0001 m^2`
Program usage name	`max_orifice_area`
Evaluatable	Yes

# Subsonic index — exponent for calculating mass flow in subsonic mode

Details

An empirical value used for more accurate calculation of mass flow rate in subsonic flow mode.

Dependencies

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

Default value	`0.5`
Program usage name	`m`
Evaluatable	Yes

# Maximum Cv flow coefficient — ratio corresponding to the maximum hole area

Details

The value of the flow coefficient when the cross-sectional area available for the flow is maximal. This parameter characterizes how easily the gas passes through the unit under the influence of a pressure drop.

Dependencies

To use this parameter, set for the parameter Valve parameterization meaning Cv flow coefficient.

Default value	`4.0`
Program usage name	`C_v_max`
Evaluatable	Yes

Details

The temperature in the standard reference atmosphere, defined as 293.15 K according to ISO 8778.

The values of the ISO reference parameters need to be adjusted only if acoustic conductivity values obtained with other reference values are used.

Dependencies

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

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

# Maximum Kv flow coefficient — ratio corresponding to the maximum hole area

Details

Maximum value of the flow coefficient when the cross-sectional area available for the flow is maximal. This parameter characterizes how easily the gas passes through the unit under the influence of a pressure drop.

Dependencies

To use this parameter, set for the parameter Valve parameterization meaning Kv flow coefficient.

Default value	`3.6`
Program usage name	`K_v_max`
Evaluatable	Yes

# ISO reference density — reference density according to ISO 8778
kg/m^3 | g/m^3 | g/cm^3 | g/mm^3 | lbm/ft^3 | lbm/gal | lbm/in^3

Details

The density in the standard reference atmosphere, defined as 1.185 kg/m³ according to ISO 8778.

The values of the ISO reference parameters need to be adjusted only if acoustic conductivity values obtained with other reference values are used.

Dependencies

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

Units	`kg/m^3` \| `g/m^3` \| `g/cm^3` \| `g/mm^3` \| `lbm/ft^3` \| `lbm/gal` \| `lbm/in^3`
Default value	`1.185 kg/m^3`
Program usage name	`rho_reference`
Evaluatable	Yes

# Smoothing factor — numerical smoothing factor

Details

The continuous smoothing coefficient, which introduces a level of gradual change based on the flow characteristic when the valve is in the nearly open and nearly closed positions. Set a non-zero value less than one to increase the stability of the simulation in these modes.

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

# Pilot pressure specification — differential pressure for valve control
Pressure difference of port X relative to port A | Gauge pressure at port X

Details

The pressure drop used to control the valve. The unit uses this parameter to determine when the valve starts opening.

Pressure difference of port X relative to port A — The valve opening pressure is expressed as the pressure drop from the control port X to the inlet A.
Gauge pressure at port X — The valve opening pressure is expressed as the excess pressure at the control port, measured relative to the ambient pressure.

Values	`Pressure difference of port X relative to port A` \| `Gauge pressure at port X`
Default value	`Pressure difference of port X relative to port A`
Program usage name	`p_control_type`
Evaluatable	No

# Leakage flow fraction — expense ratio

Details

The ratio of the flow rate through the closed hole to the flow rate through the open hole.

Default value	`1.0e-6`
Program usage name	`leakage_fraction`
Evaluatable	Yes

Literature

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 under installed conditions». 2012.
P. Beater. Pneumatic Drives. Springer-Verlag Berlin Heidelberg. 2007.