Engee documentation

Orifice (G)

Flow constriction in the gas network.

blockType: EngeeFluids.Gas.Orifices.LocalRestriction

orifice g

Orifice (G)

Path in the library:

/Physical Modeling/Fluids/Gas/Valves & Orifices/Orifices/Orifice (G)

variable orifice g

Variable Orifice (G)

Path in the library:

/Physical Modeling/Fluids/Gas/Valves & Orifices/Orifices/Variable 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.

Hole parameterization

The calculation of the capacity of the local resistance 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 the Orifice type parameters are 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 bandwidth measure depends on the value of the Opening characteristic parameters. 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 parameter 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 the 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, the value of the parameter xT pressure differential ratio factor at choked flow is a constant value.

Numerical smoothing

When the Orifice type parameter is set to Variable, the Opening characteristic parameter is set to Linear, and the Smoothing factor parameter 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, 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 parameters xT pressure differential ratio factor at choked flow.

When the pressure ratio exceeds the value of the Laminar flow pressure ratio parameters, , there is a smooth transition to usage of the linearised equation

where

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

When the Orifice parametrization parameter 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 parameter is set to Sonic conductance parameterization, the mass flow rate is defined as

where

  • - acoustic conductivity;

  • - critical pressure ratio;

  • - value of the Subsonic index parameters;

  • - ISO reference temperature parameters;

  • - ISO reference density parameters;

  • - inlet temperature.

When the pressure ratio exceeds the value of the Laminar flow pressure ratio parameters, , there is a smooth transition to usage 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 parameter is set to `Sonic conductance parameterization', see [1].

When the Orifice parametrization parameter 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 the Cross-sectional area at ports A and B parameters;

  • - the value of the Discharge coefficient parameters;

  • - adiabatic coefficient.

When the pressure ratio exceeds the Laminar flow pressure ratio parameters, , there is a smooth transition to usage 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 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

Parameters

# Orifice type — the possibility of changing the area of the passage section of the hole
Constant | Variable

Details

Determines whether the cross-sectional area of the hole can change during simulation:

  • Variable — the input signal on the L port determines the degree of opening.

  • Constant — the hole area is constant.

Values

Constant | Variable
Default value

—
Program usage name

type
Evaluatable

No

# Orifice parameterization — the method of defining the characteristics of the flow through the hole
Cv flow coefficient | Kv flow coefficient | Sonic conductance | Orifice area

Details

The method of calculating the mass flow is based on:

  • Cv flow coefficient — the expense ratio .

  • Kv flow coefficient — the expense ratio , which is defined as .

  • Sonic conductance — acoustic conductivity in steady-state mode.

  • 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

orifice_parameterization
Evaluatable

No

# Opening characteristic — type of bandwidth characteristic
Linear | Tabulated

Details

A method for converting the control signal on port L to a 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 — expense ratio

Details

The value of the constant flow rate . The flow coefficient determines the dependence of the throughput on the pressure drop.

Dependencies

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

Default value

4.0
Program usage name

C_v_fixed
Evaluatable

Yes

# Maximum Cv flow coefficient — the flow rate corresponding to the maximum opening area

Details

The value of the flow coefficient when the value of the control signal on port L is equal to 1, and the cross-sectional area of the hole is maximal.

Dependencies

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

Default value

4.0
Program usage name

C_v_max
Evaluatable

Yes

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

Details

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

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

Dependencies

To use this parameter, set the Orifice type parameter to Variable, for the Opening characteristic parameter , the value is Tabulated, for the Orifice parameterization parameter , the value 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 should be listed in ascending order. The dimension of the vector corresponds to the dimension of the Opening fraction vector.

Dependencies

To use this parameter, set the Orifice type parameter to Variable, for the Opening characteristic parameter , the value is Tabulated, for the Orifice parameterization parameter , the value 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 pressure drop ratio

Details

The ratio between inlet pressure and the outlet pressure , defined as at which point the flow becomes critical. If this value is not known, then it can be found in Table 2 in ISA-75.01.01 [3]. Default value 0.7 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 — expense ratio

Details

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

Dependencies

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

Default value

3.6
Program usage name

K_v_fixed
Evaluatable

Yes

# Maximum Kv flow coefficient — the flow rate corresponding to the maximum opening area

Details

The value of the flow coefficient when the value of the control signal on port L is equal to 1, and the cross-sectional area of the hole is maximal.

Dependencies

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

Default value

3.6
Program usage name

K_v_max
Evaluatable

Yes

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

Details

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

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

Dependencies

To use this parameter, set the Orifice type parameter to Variable, for the Opening characteristic parameter , the value is Tabulated, for the Orifice parameterization parameter , the value 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 should be listed in ascending order. The dimension of the vector corresponds to the dimension of the Opening fraction vector.

Dependencies

To use this parameter, set the Orifice type parameter to Variable, for the Opening characteristic parameter , the value is Tabulated, for the Orifice parameterization parameter , the value 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 pressure drop ratio

Details

The ratio between inlet pressure and the outlet pressure , defined as at which point the flow becomes critical. If this value is not known, then it can be found in Table 2 in ISA-75.01.01 [3]. Default value 0.7 suitable for many valves.

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 through the orifice to the product of the inlet pressure and density under the standard conditions defined in ISO 8778, measured at the time of 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, for the Orifice parameterization parameter , the value Sonic conductance.

Units

l/(bar*s) | gal/(min*psi) | 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 pressure ratio 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 inlet pressure : .

Dependencies

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

Default value

0.3
Program usage name

B_critical_fixed
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 when the value of the control signal on port L is equal to 1, and the cross-sectional area of the hole is maximal.

Dependencies

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

Units

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 pressure ratio 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 inlet pressure : .

Dependencies

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

Default value

0.3
Program usage name

B_critical_linear
Evaluatable

Yes

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

Details

A vector of control signal values at which a measure of bandwidth is set Sonic conduction vector. The value of the control signal is equal to the degree of opening only in the range from 0 before 1.

The values should be listed in ascending order. The dimension of the vector corresponds to the dimension of the Sonic conduction vector vector.

Dependencies

To use this parameter, set the Orifice type parameter to Variable, for the Opening characteristic parameter , the value is Tabulated, for the Orifice parameterization parameter , the value 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

The vector of acoustic conductivities. The values must be specified in ascending order. The dimension of the vector corresponds to the dimension of the Opening fraction vector.

Dependencies

To use this parameter, set the Orifice type parameter to Variable, for the Orifice parameterization parameter , the value Sonic conductance, for the Opening characteristic parameter , the value is Tabulated.

Units

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 — the vector of values of the critical pressure ratio

Details

The vector of critical pressure relations. 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 dimension of the vector corresponds to the dimension of the Opening fraction vector.

Dependencies

To use this parameter, set the Orifice type parameter to Variable, for the Orifice parameterization parameter , the value Sonic conductance, for the Opening characteristic parameter , the value is Tabulated.

Default value

0.3 * ones(6)
Program usage name

B_critical_vector
Evaluatable

Yes

# Subsonic index — the value of the degree used to calculate the mass flow rate in subsonic flow mode

Details

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

Dependencies

To use this parameter, set the Orifice 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 the ISO 8778 standard.

The ISO reference parameter values need to be adjusted only if acoustic conductivity values obtained with excellent reference values are used.

Dependencies

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

Units

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
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 in the ISO 8778 standard.

The ISO reference parameter values need to be adjusted only if acoustic conductivity values obtained with excellent reference values are used.

Dependencies

To use this parameter, set the Orifice parameterization parameter to 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

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

Details

The area of the passage section of the hole.

Dependencies

To use this parameter, set the Orifice type parameter to Constant, and for the Orifice parameterization parameter , the value 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

1e-4 m^2
Program usage name

fixed_orifice_area
Evaluatable

Yes

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

Details

The maximum flow cross-sectional area when the value of the control signal on port L is equal to 1.

Dependencies

To use this parameter, set the Orifice type parameter to Variable, for the Orifice parameterization parameter , the value Orifice area, for the Opening characteristic parameter , the value is Linear.

Units

m^2 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac
Default value

1e-4 m^2
Program usage name

max_orifice_area
Evaluatable

Yes

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

Details

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

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

Dependencies

To use this parameter, set the Orifice type parameter to Variable, for the Opening characteristic parameter , the value is Tabulated, for the Orifice parameterization parameter , the value 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 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac

Details

The vector of the areas of the passage section of the hole. The dimension of the vector corresponds to the Opening fraction vector vector. The first element of this vector is the area of the leak, and the last element is the maximum area of the hole.

Dependencies

To use this parameter, set the Orifice type parameter to Variable, for the Orifice parameterization parameter , the value Orifice area, for the Opening characteristic parameter , the value is Tabulated.

Units

m^2 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac
Default value

[1e-10, 0.2e-4, 0.4e-4, 0.6e-4, 0.8e-4, 1e-4] m^2
Program usage name

orifice_area_vector
Evaluatable

Yes

# Discharge coefficient — expense ratio

Details

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

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 flow through a closed and through an open hole.

Dependencies

To use this parameter, set the Orifice type parameter to Variable, and for the Orifice parameterization parameter , the value Orifice area.

Default value

1e-6
Program usage name

leakage_fraction
Evaluatable

Yes

# Smoothing factor — numerical smoothing coefficient

Details

The continuous smoothing coefficient, which ensures smooth opening by correcting the characteristic of the hole in the almost open and almost closed positions.

Dependencies

To use this parameter, set the Orifice type parameter to Variable, and for the Opening characteristic parameter , the value Linear.

Default value

0.01
Program usage name

smoothing_factor
Evaluatable

Yes

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

Details

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

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 entrance or exit
m^2 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac

Details

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

The ports have the same size. The value of this parameter must correspond to the area of the inlet of the component 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

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.