Orifice (MA)

Narrowing of the humid air flow in the network.

blockType: EngeeFluids.MoistAir.Orifices.LocalRestriction

Orifice (MA)

Path in the library:

/Physical Modeling/Fluids/Moist Air/Valves & Orifices/Orifices/Orifice (MA)

Variable Orifice (MA)

Path in the library:

/Physical Modeling/Fluids/Moist Air/Valves & Orifices/Orifices/Variable Orifice (MA)

Description

Block Orifice (MA) simulates pressure loss in a humid air network due to local resistance, which may be a constriction, an opening, or a valve with a constant or variable cross-sectional area. For variable openings, the control element connected to the S port sets the opening position.

The unit calculates the properties of the humid air inside the valve based on the input conditions. There is no heat exchange between the moist air and the environment, so the phase transition inside the hole occurs only due to a pressure drop or the propagation of a phase transition from another part of the model.

Parameterization of the hole

The calculation of the local resistance throughput depends on the parameter value Orifice parameterization:

Cv flow coefficient — expense ratio determines the dependence of the throughput on the pressure drop. The flow coefficient measures the ease with which moist air can flow under the influence of a certain pressure drop.
Kv flow coefficient — expense ratio determines the dependence of throughput on pressure drop, . The flow coefficient measures the ease with which moist air can flow under the influence of a certain pressure drop.
Sonic conductance — steady-state acoustic conductivity determines the throughput at critical flow, a condition in which the flow velocity is equal to the local speed of sound. The flow becomes critical when the ratio of outlet pressure to inlet pressure reaches a value called the critical pressure ratio.
Orifice area — the area of the hole determines the throughput.

Hole Characteristic

If for the parameter Orifice type the value is set Variable, and for the parameter Opening characteristic — Linear, the unit uses the input signal of the port S as a control signal for the degree of opening of the hole:

where

— the value of the signal on port S;
— parameter value Control member position at closed orifice;
— parameter value Control member travel between closed and open orifice.

If for the parameter Orifice type the value is set Variable, and for the parameter Opening characteristic — Tabulated, the block interpolates the characteristics of the hole based on the parameter Control member position vector and the input signal on the S port.

For variable openings, the conversion of the control signal to the selected bandwidth measure depends on the parameter value. Opening characteristic:

Linear — the amount of bandwidth is proportional to the control signal on port S. As the control signal increases, the bandwidth indicator changes from a set minimum to a set maximum.

If for the parameter Orifice parameterization the value is set Cv flow coefficient or Kv flow coefficient, parameter value xT pressure differential ratio factor at choked flow It is assumed to be constant and independent of the control signal.
Tabulated — the bandwidth value is calculated using a tabular function from the value of the control signal on port S. This function uses a one-dimensional interpolation table.

If for the parameter Orifice parameterization the value is set Cv flow coefficient or Kv flow coefficient, the value of the parameter xT pressure differential ratio factor at choked flow It is a function of the value of the control signal.

Conservation of momentum

Parameter Orifice parameterization determines which equations will be used to calculate the flow rate. If for the parameter Orifice parameterization the value is set Cv flow coefficient, then the mass flow rate will be defined as

where

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

The expansion coefficient is defined as

where

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

When is the pressure ratio exceeds the value of the parameter Laminar flow pressure ratio, , there is a smooth transition to using the linearized equation

where

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

If for the parameter Orifice parameterization the value is set Kv flow coefficient, then the block uses the same equations, but replaces on using a relationship .

If for the parameter Orifice parameterization the value is set Sonic conductance, then the mass flow rate is defined as

where

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

When is the pressure ratio exceeds the value of the parameter Laminar flow pressure ratio, , there is a smooth transition to using the linearized equation

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

Meaning Sonic conductance the parameter Orifice parameterization designed for pneumatic applications. If you are using this parameter for humid air with a high content of impurity gases or modeling a working environment other than air, you may need to multiply the acoustic conductivity by the square root of the relative density of the mixture.

If for the parameter Orifice parameterization the value is set Orifice area, then the mass flow rate is defined as

where

— parameter value Discharge coefficient;
— the adiabatic index.

When is the pressure ratio exceeds the value of the parameter Laminar flow pressure ratio, , there is a smooth transition to using the linearized equation

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

Conservation of mass

The mass conservation equations for moist air, water vapor, impurity gases, and water droplets through the valve are as follows:

where

— mass consumption;
Lower indexes and — ports A and B respectively;
Lower indexes and They indicate the properties of water vapor, gas impurities, and water droplets, respectively.

Energy conservation

The equation of conservation of energy in a hole:

where

— power consumption via port A;
— power consumption through port B.

Assumptions and limitations

The unit does not exchange heat with the environment.

Ports

Input

# S — position of the control element, m
scalar

Details

The position of the control element, which determines the degree of opening.

Dependencies

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

Data types	`Float64`
Complex numbers support	No

Conserving

# B — humid air inlet or outlet
humid air

Details

A non-directional port connected to the inlet or outlet of a stream of humid air.

Program usage name

port_b

# A — humid air inlet or outlet
humid air

Details

A non-directional port connected to the inlet or outlet of a stream of humid air.

Program usage name

port_a

Parameters

Main

# Control member position vector — vector of positions of control elements
m | um | mm | cm | km | in | ft | yd | mi | nmi

Details

Vector of positions of control elements for tabular parameterizations of the hole. The elements of the vector correspond to the values in the parameters Orifice area vector, Cv flow coefficient vector or Kv flow coefficient vector.

Dependencies

To use this parameter, set for the parameter Orifice type meaning Variable, and for the parameter Opening characteristic meaning Tabulated.

Units	`m` \| `um` \| `mm` \| `cm` \| `km` \| `in` \| `ft` \| `yd` \| `mi` \| `nmi`
Default value	`[0.0, 0.003, 0.006, 0.009, 0.012, 0.015] m`
Program usage names	`control_displacement_vector_C_v`, `control_displacement_vector_area`, `control_displacement_vector_K_v`, `control_displacement_vector_C`
Evaluatable	Yes

# Kv flow coefficient vector — vector of flow coefficient values

Details

Vector of flow coefficients . Each coefficient corresponds to an element of the parameter Control member position vector. This parameter determines the dependence of the throughput on the pressure drop. The dimension of the vector corresponds to the dimension Control member position vector.

Dependencies

To use this parameter, set for the parameter Orifice type meaning Variable, for the parameter Orifice parameterization meaning Kv flow coefficient, and for the parameter Opening characteristic meaning Tabulated.

Default value	`[1.0e-6, 0.72, 1.44, 2.16, 2.88, 3.6]`
Program usage name	`K_v_vector`
Evaluatable	Yes

# 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 rate is based on:

Cv flow coefficient — the expense ratio ;
Kv flow coefficient — the expense ratio ;
Sonic conductance — acoustic conductivity in steady state;
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

# 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.

Dependencies

To use this parameter, set for the parameter Orifice 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 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 compose .

Dependencies

To use this parameter, set:

for the parameter Orifice type meaning Constant and for the parameter Orifice parameterization meaning Sonic conductance, or
for the parameter Orifice type meaning Variable, for the parameter Orifice parameterization meaning Sonic conductance and for the parameter Opening characteristic meaning Linear.

Default value	`0.3`
Program usage names	`B_critical_linear`, `B_critical_fixed`
Evaluatable	Yes

# Control member position at closed orifice — displacement of the control element
m | um | mm | cm | km | in | ft | yd | mi | nmi

Details

The offset of the control element, or the value on the port S when the hole is completely closed.

Dependencies

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

Units	`m` \| `um` \| `mm` \| `cm` \| `km` \| `in` \| `ft` \| `yd` \| `mi` \| `nmi`
Default value	`0 m`
Program usage name	`min_control_displacement`
Evaluatable	Yes

# Control member travel between closed and open orifice — the stroke of the control element
m | um | mm | cm | km | in | ft | yd | mi | nmi

Details

The distance by which the control element is shifted between the closed and open positions of the hole. If set for the parameter Opening orientation meaning Positive control member displacement opens orifice, the hole opens completely when the sum of the parameter values is reached Control member position at closed orifice and Control member travel between closed and open orifice. If set for the parameter Opening orientation meaning Negative control member displacement opens orifice, the hole opens completely when the parameter values are different Control member position at closed orifice and Control member travel between closed and open orifice.

Dependencies

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

Units	`m` \| `um` \| `mm` \| `cm` \| `km` \| `in` \| `ft` \| `yd` \| `mi` \| `nmi`
Default value	`0.005 m`
Program usage name	`delta_control_displacement`
Evaluatable	Yes

# Discharge coefficient — expense ratio

Details

The correction factor is the ratio of the actual mass flow to the theoretical mass flow. This parameter takes into account the actual losses, which are not reflected in the equations for the hole.

Dependencies

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

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

# Opening characteristic — type of bandwidth characteristic
Linear | Tabulated

Details

A method for converting the control signal on port S to a selected bandwidth measure.

Dependencies

To use this parameter, set for the parameter Orifice type meaning Variable.

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

# Sonic conductance — critical mode throughput indicator
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 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 for the parameter Orifice type meaning Constant, and for the parameter Orifice parameterization meaning Sonic conductance.

Units	`l/(bars)` \| `gal/(minpsi)` \| `m^3/(Pa*s)`
Default value	`12 l/(bar*s)`
Program usage name	`C_fixed`
Evaluatable	Yes

# 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 for the parameter Orifice type meaning Constant, and for the parameter Orifice parameterization meaning Cv flow coefficient.

Default value	`4`
Program usage name	`C_v_fixed`
Evaluatable	Yes

# Critical pressure ratio vector — the vector of values of the critical pressure ratio

Details

The vector of critical pressure ratios at which the flow becomes critical for the first time, with each critical pressure ratio corresponding to an element of the parameter Control member position vector. 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 Control member position vector.

Dependencies

To use this parameter, set for the parameter Orifice type meaning Variable, for the parameter Orifice parameterization meaning Sonic conductance, and for the parameter Opening characteristic meaning Tabulated.

Default value	`[0.3, 0.3, 0.3, 0.3, 0.3, 0.3]`
Program usage name	`B_critical_vector`
Evaluatable	Yes

# Cv flow coefficient vector — vector of flow coefficient values

Details

Dependencies

To use this parameter, set for the parameter Orifice type meaning Variable, for the parameter Orifice parameterization meaning Cv flow coefficient, and for the parameter Opening characteristic meaning Tabulated.

Default value	`[1.0e-6, 0.8, 1.6, 2.4, 3.2, 4.0]`
Program usage name	`C_v_vector`
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 S is equal to 1, and the cross-sectional area of the hole is maximal.

Dependencies

Units	`l/(bars)` \| `gal/(minpsi)` \| `m^3/(Pa*s)`
Default value	`12 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 ratio of outlet pressure to inlet pressure at which the flow transitions between laminar and turbulent flow modes. In laminar flows, pressure losses depend linearly on the mass flow rate, while in turbulent flows they depend quadratically.

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

# Opening orientation — the direction of the displacement opening the hole
Positive control member displacement opens orifice | Negative control member displacement opens orifice

Details

The direction of displacement of the element opening the adjustable hole. A positive orientation means that increasing the signal on port S opens the hole. A negative orientation means that reducing the signal on port S opens a hole.

Dependencies

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

Values	`Positive control member displacement opens orifice` \| `Negative control member displacement opens orifice`
Default value	`Positive control member displacement opens orifice`
Program usage name	`opening_orientation`
Evaluatable	No

# 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

The area of ports A and B.

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 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 area of the flow passage section in the fully open state.

Dependencies

To use this parameter, set for the parameter Orifice type meaning Variable, and for the parameter Orifice parameterization meaning Orifice area, and for the parameter Opening characteristic meaning Linear.

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

# 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 for the parameter Orifice type meaning Constant, and for the parameter Orifice 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	`fixed_orifice_area`
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 for the parameter Orifice parameterization meaning Sonic conductance.

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

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

Details

The value of the flow coefficient when the hole is fully open and the cross-sectional area of the hole is maximum. This parameter determines the dependence of the throughput on the pressure drop.

Dependencies

Default value	`4`
Program usage name	`C_v_max`
Evaluatable	Yes

Details

The temperature in the standard reference atmosphere, defined as 293.15 For example, in the ISO 8778 standard.

The ISO reference parameter values need to be adjusted only if acoustic conductivity values obtained at values other than the reference values are used.

Dependencies

To use this parameter, set for the parameter Orifice 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

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

Details

The vector of acoustic conductivities. Each conductivity corresponds to an element of the parameter Control member position vector. The dimension of the vector corresponds to the dimension Control member position vector.

Dependencies

Units	`l/(bars)` \| `gal/(minpsi)` \| `m^3/(Pa*s)`
Default value	`[1.0e-5, 2.4, 4.8, 7.2, 9.6, 12.0] l/(bar*s)`
Program usage name	`C_vector`
Evaluatable	Yes

# 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 S port determines the degree of opening.
Constant — the hole area is constant.

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

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

Details

The value of the flow coefficient when the hole is fully open and the cross-sectional area of the hole is maximum. This parameter determines the dependence of the throughput on the pressure drop.

Dependencies

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 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 for the parameter Orifice 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

# 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 vector Control member position vector.

Dependencies

To use this parameter, set for the parameter Orifice type meaning Variable, for the parameter Orifice parameterization meaning Orifice area, and for the parameter Opening characteristic meaning Tabulated.

Units	`m^2` \| `um^2` \| `mm^2` \| `cm^2` \| `km^2` \| `in^2` \| `ft^2` \| `yd^2` \| `mi^2` \| `ha` \| `ac`
Default value	`[1.0e-10, 2.0e-5, 4.0e-5, 6.0e-5, 8.0e-5, 0.0001] m^2`
Program usage name	`orifice_area_vector`
Evaluatable	Yes

# Kv 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 for the parameter Orifice type meaning Constant, and for the parameter Orifice parameterization meaning Kv flow coefficient.

Default value	`3.6`
Program usage name	`K_v_fixed`
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. Set this parameter to a non-zero value less than one to increase the stability of modeling in these areas.

Dependencies

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

Default value	`0.01`
Program usage name	`smoothing_factor`
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 for the parameter Orifice type meaning Variable, and for the parameter Opening characteristic meaning Linear.

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