Orifice (G)

Flow constriction in the gas network.

Variable Orifice (G)

Orifice (G)

Description

The Orifice (G) unit simulates the pressure loss in a gas network due to a local resistance, which can be a constriction, orifice or valve with a constant or variable cross-sectional area.

Orifice parameterization

The calculation of the local resistance capacity depends on the value of the Orifice 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

When Orifice type is set to Variable, the input value at port L is used as the control signal for the degree of orifice opening. The value of the degree of opening varies from 0 to 1. If a smaller or larger value is specified, the block equates the value to the nearest of the two limits.

The conversion of the control signal to the selected capacity measure depends on the value of the Opening characteristic parameter. Flow is maximally restricted when the control signal is 0 and minimally restricted when the control signal is 1. In between these values, the flow through the orifice depends on whether the throughput value is a linear function or based on tabulated data:

Linear - the capacity value is proportional to the control signal at port L.

If the Orifice parameterization is set to Sonic conductance', the critical pressure ratio Critical pressure ratio and subsonic index Subsonic index are assumed to be constant and independent of the control signal. If the Orifice parameterization is set to `Cv flow coefficient or Kv flow coefficient, the xT pressure differential ratio factor at choked flow is assumed to be constant and independent of the control signal.
Tabulated - the throughput value is calculated by means of a tabulated function from the value of the control signal at the L port. The values in the table must be specified in ascending order.

If Orifice parameterization is set to Sonic conductance', the critical pressure ratio Critical pressure ratio is a function of the control signal and the subsonic index Subsonic index is a constant. If the Orifice parameterization is set to `Cv flow coefficient or Kv flow coefficient, then the xT pressure differential ratio factor at choked flow is a constant value.

Numerical smoothing

When Orifice type is set to Variable, Opening characteristic is set to Linear, and Smoothing factor is set to a non-zero value, numerical smoothing is applied to the control signal from port L. Smoothing helps to maintain the numerical stability of the simulation.

Pulse Save

The Orifice parameterization parameter determines which equations will be used to calculate the flow rate. If the Orifice parametrization parameter is set to Cv flow coefficient parameterization, then 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 Orifice parametrization is set to Kv flow coefficient parameterization, the unit uses the same equations but replaces with using the ratio . For more information on the mass flow equations when the Orifice parametrization is set to Kv flow coefficient parameterization or Cv flow coefficient parameterization, see [2] and [3].

When the Orifice parametrization is set to Sonic conductance parameterization, 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 the mass flow equations when the Orifice parametrization is set to `Sonic conductance parameterization', see [1].

When the Orifice parametrization is set to Orifice area parameterization, 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 Orifice parametrization parameter is set to `Orifice area parameterization', see [4].

Mass conservation

The volume and mass of the fluid inside the component are assumed to be very small and these values are not considered. According to the principle of mass conservation, the mass flow rate of fluid entering through one port is equal to the flow rate of fluid exiting through the other port:

where is defined as the mass flow rate entering the valve through the port designated 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 Orifice 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 — gas inlet or outlet
gas

Details

Non-directional port, corresponds to flow in or flow out.

Program usage name

port_a

# B — gas inlet or outlet
gas

Details

Non-directional port, corresponds to flow in or flow out.

Program usage name

port_b

Input

# L — degree of opening
scalar

Details

An input port that determines the degree of opening. The port is fully closed at 0 and fully open at 1.

Dependencies

To use this port, set the Orifice type parameter to Variable.

Data types	`Float64`.
Complex numbers support	No

Parameters

# Orifice type — possibility to change the cross-sectional area of the bore
Constant | Variable

Details

Determines whether the hole cross-sectional area can be changed during simulation:

Variable - The input signal at port L determines the degree of opening.
Constant - the orifice area is constant.

Values	`Constant` \| `Variable`
Default value	`—`
Program usage name	`type`
Evaluatable	No

# Orifice 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	`orifice_parameterization`
Evaluatable	No

# Opening characteristic — type of capacity characteristic
Linear | Tabulated

Details

The method of converting the control signal on the L port to the selected bandwidth measure.

Dependencies

To use this parameter, set the Orifice type parameter to Variable.

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

# Cv flow coefficient — flow coefficient

Details

Value of constant flow coefficient . The flow coefficient determines the dependence of the flow capacity on the pressure drop.

Dependencies

To use this parameter, set the Orifice type parameter to Constant and the Orifice parameterization parameter to Cv flow coefficient.

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

# Maximum Cv flow coefficient — flow coefficient corresponding to the maximum orifice area

Details

The value of the flow coefficient is , when the value of the control signal at port L is 1 and the orifice area is maximum.

Dependencies

To use this parameter, set Orifice type to Variable, Orifice parameterization to Cv flow coefficient, Opening characteristic to Linear.

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

# Opening fraction vector — values of the control signal for the opening degree

Details

The vector of control signal values at which the capacity measure Cv coefficient vector is set. The control signal value is equal to the opening degree only in the range from 0 to 1.

The values must be specified in ascending order. The dimensionality of the vector corresponds to the dimensionality of the Cv coefficient vector.

Dependencies

To use this parameter, set Orifice type to Variable, Opening characteristic to Tabulated, Orifice parameterization to Cv flow coefficient.

Default value	`[0:0.2:1…]`
Program usage name	`opening_fraction_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 Orifice type to `Variable', Opening characteristic to `Tabulated', Orifice parameterization to `Cv flow coefficient'.

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 Orifice parameterization parameter to Cv flow coefficient.

Default value	`0.7`
Program usage name	`delta_p_ratio_C_v`
Evaluatable	Yes

# Kv flow coefficient — flow coefficient

Details

Value of the constant flow coefficient . The flow coefficient defines the dependence of the flow rate on the pressure drop.

Dependencies

To use this parameter, set the Orifice type parameter to `Constant' and the Orifice parameterization parameter to `Kv flow coefficient'.

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

# Maximum Kv flow coefficient — flow coefficient corresponding to the maximum orifice area

Details

The value of the flow coefficient is , when the value of the control signal at port L is 1 and the orifice area is maximum.

Dependencies

To use this parameter, set Orifice type to Variable, Orifice parameterization to Kv flow coefficient, Opening characteristic to Linear.

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

# Opening fraction vector — values of the control signal for the opening degree

Details

The vector of control signal values at which the capacity measure Kv coefficient vector is set. The control signal value is equal to the opening degree only in the range from 0 to 1.

The values must be specified in ascending order. The dimensionality of the vector corresponds to the dimensionality of the Kv coefficient vector.

Dependencies

To use this parameter, set Orifice type to Variable, Opening characteristic to Tabulated, Orifice parameterization to Kv flow coefficient.

Default value	`[0:0.2:1…]`
Program usage name	`opening_fraction_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 Orifice type to `Variable', Opening characteristic to `Tabulated', Orifice parameterization to `Kv flow coefficient'.

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

Dependencies

To use this parameter, set the Orifice parameterization parameter to Kv flow coefficient.

Default value	`0.7`
Program usage name	`delta_p_ratio_K_v`
Evaluatable	Yes

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

Details

The ratio of the mass flow rate through an orifice to the product of the inlet pressure and density at standard conditions defined in ISO 8778, measured at the onset of critical flow. This parameter determines the maximum flow rate allowed at a given inlet pressure.

Dependencies

To use this parameter, set the Orifice type parameter to `Constant' and the Orifice parameterization parameter to `Sonic conductance'.

Values	`l/(bars)` \| `gal/(minpsi)` \| `m^3/(Pa*s)`
Default value	`12.0 l/(bar*s)`
Program usage name	`C_fixed`
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 Orifice type parameter to Constant and the Orifice parameterization parameter to Sonic conductance.

Default value	`0.3`
Program usage name	`B_critical_fixed`
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 value of the control signal on the L port is 1 and the orifice cross-sectional area is maximised.

Dependencies

To use this parameter, set Orifice type to `Variable', Orifice parameterization to `Sonic conductance', and 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

Dependencies

To use this parameter, set Orifice type to Variable, Orifice parameterization to Sonic conductance, Opening characteristic to Linear.

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

# Opening fraction vector — values of the control signal for the opening degree

Details

The vector of control signal values at which the throughput measure Sonic conductance vector is set. The control signal value is equal to the opening degree only in the range from 0 to 1.

The values must be specified in ascending order. The dimensionality of the vector corresponds to the dimensionality of the Sonic conductance vector.

Dependencies

To use this parameter, set Orifice type to `Variable', Opening characteristic to `Tabulated', Orifice parameterization to `Sonic conductance'.

Default value	`[0:0.2:1…]`
Program usage name	`opening_fraction_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 Orifice type to `Variable', Orifice parameterization to `Sonic conductance', Opening characteristic to `Tabulated'.

Values	`l/(bars)` \| `gal/(minpsi)` \| `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. The dimensionality of the vector corresponds to the Opening fraction vector.

Dependencies

To use this parameter, set Orifice type to `Variable', Orifice parameterization to `Sonic conductance' and 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 Orifice 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 Orifice 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 Orifice 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

# Orifice area — hole area
m^2 | cm^2 | ft^2 | in^2 | km^2 | mi^2 | mm^2 | um^2 | yd^2

Details

Cross-sectional area of the bore.

Dependencies

To use this parameter, set the Orifice type parameter to `Constant' and the Orifice parameterization parameter to `Orifice area'.

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	`fixed_restriction_area`
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 flow area when the value of the control signal at port L is 1.

Dependencies

To use this parameter, set Orifice type to `Variable', Orifice 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

# Opening fraction vector — values of the control signal for the opening degree

Details

The vector of control signal values at which the capacity measure Orifice area vector is set. The control signal value is equal to the opening degree only in the range from 0 to 1.

The values must be specified in ascending order. The dimensionality of the vector corresponds to the dimensionality of the Orifice area vector.

Dependencies

To use this parameter, set the Orifice type parameter to `Variable', the Opening characteristic parameter to `Tabulated', and the Orifice parameterization parameter to `Orifice area'.

Default value	`[0:0.2:1…]`
Program usage name	`opening_fraction_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 Orifice type to `Variable', Orifice parameterization to `Orifice area' and 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-10, 0.2e-4, 0.4e-4, 0.6e-4, 0.8e-4, 1e-4] m^2`
Program usage name	`restriction_area_vector`
Evaluatable	Yes

# Discharge coefficient — flow coefficient

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 Orifice 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 Orifice type parameter to Variable and the Orifice parameterization parameter to Orifice area.

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 Orifice type to `Variable' and 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

Literature

[1] 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.

[2] IEC 60534-2-3. "Industrial-process control valves - Part 2-3: Flow capacity - Test procedures". 2015.

[3] ANSI/ISA-75.01.01. "Industrial-Process Control Valves - Part 2-1: Flow capacity - Sizing equations for fluid flow underinstalled conditions". 2012.

[4] P. Beater. Pneumatic Drives. Springer-Verlag Berlin Heidelberg. 2007.