4-Way 2-Position Directional Valve (MA)

4-way 2-position directional valve in a moist air network

Since R2025a

Libraries:
Simscape / Fluids / Moist Air / Valves & Orifices / Directional Control Valves

Description

The 4-Way 2-Position Directional Valve (MA) models a valve with four openings — such as the valves between an actuator, pump, and tank — in a moist air network. A single spool controls the valve operation according to the signal at port S. You can set the baseline configuration of your valve by specifying the orifices that are open when the spool moves in the positive direction and negative directions in the Positive spool position open connections and Negative spool position open connections parameters, respectively. You can set the valve opening model in the Orifice parameterization parameter as a linear relationship or function of user-provided data, which you can apply to one or all flow paths in the valve.

This block is a composite component that comprises of multiple instances of the Orifice (MA) block. Refer to the Orifice (MA) block for more details about valve parameterizations and block calculations. In some configurations, this valve resembles a 3-way valve. To set additional flow paths when the spool is in the neutral position, see the 4-Way 3-Position Directional Valve (MA) block.

This image shows an example valve setup where the valve is connected to a tank, actuator, and pump and the Positive spool position open connections parameter is P-B, A-T:

This image shows the valve when the Negative spool position open connections parameter is P-A, B-T:

In this configuration, when the signal at port S moves the spool to a negative position, the paths between ports P and A and between ports B and T are open to flow. The paths between ports P and B and ports A and T are closed to flow.

This image shows the valve when the Positive spool position open connections parameter is P-B, A-T:

In this configuration, when the signal at port S moves the spool to a positive position, the paths between ports P and B and between ports A and T are open to flow and the paths between ports P and A and between ports B and T are closed.

The schematic that represents this configuration is:

The left-hand side corresponds to the positive position and the right-hand side corresponds to the negative position. The valve transitions through positions in the neutral mid-section.

Spool Displacement and Valve Configuration

The spool stroke is the amount of spool travel an orifice takes to fully open from a closed position. You can use the Orifice parameterization and Area characteristics parameters to specify the flow path characteristics:

Orifice Parameterization	Identical for All Flow Paths	Different for Each Flow Path
`Linear - Area vs. spool travel`	The Spool travel between closed and open orifice parameter defines the spool stroke	The Spool travel between closed and open orifice parameter defines the spool stroke for each orifice
`Tabulated data - Area vs. spool travel`	The difference between the first and last element of the Spool travel vector parameter defines the spool stroke	The difference between the first and last element of the Spool travel vector parameter for each orifice
`Tabulated data - Volumetric flow rate vs. spool travel and pressure drop`or `Tabulated data - Mass flow rate vs. spool travel and pressure drop`	The difference between the first and last element of the Spool travel vector, ds parameter defines the spool stroke	The difference between the first and last element of the Spool travel vector, ds parameter defines the spool stroke for each orifice

The direction of the spool movement depends on the spool stroke, orifice orientation, and signal at port S. This table shows the spool travel for an orifice depending on the selections for the Positive spool position open connection and Negative spool position open connection parameters:

Spool Position When Orifice Is Open	Spool Travel, ΔS
Orifice always closed: orifice not selected for the Positive spool position open connection or Negative spool position open connection parameters	N/A
Orifice always open: orifice selected for both the Positive spool position open connection and Negative spool position open connection parameters	N/A
Negative: orifice selected for only Negative spool position open connection parameter	S_{orifice_max} + spool stroke – S
Positive: orifice selected for only Positive spool position open connection parameter	S_{orifice_max} – spool stroke + S

Where S_{orifice_max} is the spool position at the maximum orifice area defined for each orifice. The orifice area saturates at the leakage area when ΔS is negative and saturates at the maximum orifice area when the orifice is fully open. When the orifice is fully open, ΔS is equal to the spool stroke, so ΔS greater than the spool stroke does not further increase the orifice area.

This table shows the possible configurations of the 4-Way 2-Position Directional Valve (MA) block:

Configuration	Parameter Values
All four paths are closed during transition.	Positive spool position open connections: `P-A, B-T` Negative spool position open connections: `P-B, A-T` Spool position at maximum P-A orifice area > P-A spool stroke Spool position at maximum P-B orifice area < –P-B spool stroke Spool position at maximum A-T orifice area < –A-T spool stroke Spool position at maximum B-T orifice area > B-T spool stroke
All four paths are open during transition.	Positive spool position open connections: `P-A, B-T` Negative spool position open connections: `P-B, A-T` Spool position at maximum P-A orifice area < P-A spool stroke Spool position at maximum P-B orifice area > –P-B spool stroke Spool position at maximum A-T orifice area > –A-T spool stroke Spool position at maximum B-T orifice area < B-T spool stroke
A-T and B-T are closed during transition.	Positive spool position open connections: `P-A, B-T` Negative spool position open connections: `P-B, A-T` Spool position at maximum P-A orifice area < P-A spool stroke Spool position at maximum P-B orifice area > –P-B spool stroke Spool position at maximum A-T orifice area < –A-T spool stroke Spool position at maximum B-T orifice area > B-T spool stroke
P-A and P-B are closed during transition.	Positive spool position open connections: `P-A` Negative spool position open connections: `P-B` Spool position at maximum P-A orifice area > P-A spool stroke Spool position at maximum P-B orifice area < –P-B spool stroke
P-B and B-T are closed during transition.	Positive spool position open connections: `P-B, A-T` Negative spool position open connections: `P-A, B-T` Spool position at maximum P-A orifice area < P-A spool stroke Spool position at maximum P-B orifice area > P-B spool stroke Spool position at maximum A-T orifice area > A-T spool stroke Spool position at maximum B-T orifice area < –B-T spool stroke
P-A and A-T are closed during transition.	Positive spool position open connections: `P-B, A-T` Negative spool position open connections: `P-A, B-T` Spool position at maximum P-A orifice area < –P-A spool stroke Spool position at maximum P-B orifice area < P-B spool stroke Spool position at maximum A-T orifice area > A-T spool stroke Spool position at maximum B-T orifice area > –B-T spool stroke
P-A, P-B, and B-T are open during transition.	Positive spool position open connections: `P-A, P-B` Negative spool position open connections: `P-A, B-T` Spool position at maximum P-A orifice area < P-A spool stroke Spool position at maximum P-B orifice area < P-B spool stroke Spool position at maximum A-T orifice area = any value Spool position at maximum B-T orifice area > –B-T spool stroke
P-A, A-T, and B-T are open during transition.	Positive spool position open connections: `P-B, A-T` Negative spool position open connections: `P-A, P-B` Spool position at maximum P-A orifice area > –P-A spool stroke Spool position at maximum A-T orifice area < A-T spool stroke Spool position at maximum B-T orifice area = any value
P-A and P-B are closed during transition. A-T is always closed.	Positive spool position open connections: `P-A, P-B` Negative spool position open connections: `P-A, B-T` Spool position at maximum P-B orifice area > P-B spool stroke Spool position at maximum B-T orifice area < –B-T spool stroke
All paths are closed during transition.	Positive spool position open connections: `P-B, A-T` Negative spool position open connections: `P-A, P-B` Spool position at maximum P-A orifice area < –P-A spool stroke Spool position at maximum P-B orifice area > P-B spool stroke Spool position at maximum A-T orifice area > A-T spool stroke
A-T is open during transition. P-A is closed during transition.	Positive spool position open connections: `P-A, P-B` Negative spool position open connections: `P-A, B-T` Spool position at maximum P-A orifice area > P-A spool stroke Spool position at maximum P-B orifice area > P-B spool stroke Spool position at maximum A-T orifice area = any value Spool position at maximum B-T orifice area > –B-T spool stroke
B-T is open during transition. P-B is closed during transition.	Positive spool position open connections: `P-B, A-T` Negative spool position open connections: `P-A, P-B` Spool position at maximum P-A orifice area < –P-A spool stroke Spool position at maximum P-B orifice area > P-B spool stroke Spool position at maximum A-T orifice area < A-T spool stroke Spool position at maximum B-T orifice area = any value
P-A is closed during transition.	Positive spool position open connections: `P-A, B-T` Negative spool position open connections: `P-A, P-B` Spool position at maximum P-A orifice area > P-A spool stroke Spool position at maximum P-B orifice area < –P-B spool stroke Spool position at maximum B-T orifice area > B-T spool stroke
P-B is closed during transition.	Positive spool position open connections: `P-A, P-B` Negative spool position open connections: `P-B, A-T` Spool position at maximum P-A orifice area > P-A spool stroke Spool position at maximum P-B orifice area > P-B spool stroke Spool position at maximum A-T orifice area > –A-T spool stroke

Valve Orifice Parameterizations

The Orifice parameterization parameter specifies the model for the open area or flow rate through one or all of the valve orifices. If you set Area characteristics to Identical for all flow paths, the block applies the same data for all flow paths. When you select Different for all flow paths, the block uses individual parameterizations for each flow path.

The method the block uses to control each orifice depends on the Opening characteristic parameter:

Linear — The measure of flow capacity depends on the spool position at port S. As the spool displaces to open to orifice, the measure of flow capacity scales from the specified minimum to the specified maximum.
Tabulated — The block calculates the measure of flow capacity as a function of the spool position at port S. This function uses a one-dimensional lookup table.

The Orifice parameterization parameter determines how the block calculates the flow rate in each orifice:

Cv flow coefficient — The flow coefficient C_v scales the flow rate in each orifice. The flow coefficient measures the ease with which a fluid can flow when driven by a certain pressure differential.
Kv flow coefficient — The flow coefficient K_v, where $K_{v} = 0.865 C_{v}$ , scales the flow rate in each orifice. The flow coefficient measures the ease with which a fluid can flow when driven by a certain pressure differential.
Orifice area — The size of the orifice area scales the flow rate in each orifice.

Visualize Orifice Openings

To visualize the spool offsets and maximum displacement, right-click the block and select Fluids > Plot Valve Characteristics. The plot shows the sonic conductance, K_v flow coefficient, C_v flow coefficient, or orifice area as a function of spool position.

To update the data after changing the block parameters, click Reload Data in the figure window.

This figure shows the valve configuration with default values.

Assumptions and Limitations

The Sonic conductance setting of the Valve parameterization parameter is for pneumatic applications. If you use this setting for moist air with high levels of trace gasses or are modeling a fluid other than air, you may need to scale the sonic conductance by the square root of the mixture specific gravity.
This block does not model supersonic flow.
There is no heat exchange between the valve and the environment.

Ports

Conserving

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A — Entry or exit port
moist air

Moist air conserving port associated with the entry or exit port to the valve.

B — Entry or exit port
moist air

Moist air conserving port associated with the entry or exit port to the valve.

P — Entry or exit port
moist air

Moist air conserving port associated with the entry or exit port to the valve.

T — Entry or exit port
moist air

Moist air conserving port associated with the entry or exit port to the valve.

Input

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S — Spool displacement, m
physical signal

Physical signal associated with the spool displacement, in m.

Parameters

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Valve Configuration

Positive spool position open connections — Flow paths open when the spool is in positive position
`All closed` (default) | `P-A, B-T` | `P-A, P-B` | `P-B, A-T` | `P-A` | `P-B` | `P-A, P-B, A-T, B-T`

Flow paths open when the spool is in a positive position. This parameter sets the valve configuration and defines the direction of spool movement according to the signal received at port S.

Negative spool position open connections — Flow paths open when spool moves in negative direction
`All closed` (default) | `P-A, B-T` | `P-A, P-B` | `P-B, A-T` | `P-A` | `P-B` | `P-A, P-B, A-T, B-T`

Flow paths open when the spool moves in the negative direction. This parameter sets the valve configuration and defines the direction of spool movement according to the signal received at port S.

Model Parameterization

Area characteristics — Flow equations for orifices
`Identical for all flow paths` (default) | `Different for each flow path`

Whether to apply uniform or individual flow equations for the valve orifice area. When you set this parameter to Identical for all flow paths, the block uses the same orifice and spool geometries, flow rates, pressure, and area vectors for all valve orifices. When you set this parameter to Different for each flow path, you can specify these parameters individually for each orifice. For both settings, orifices A, B, P, and T have the same cross-sectional areas, discharge coefficients, and Reynolds numbers when you set Orifice parameterization to Linear - Area vs. spool travel or Tabulated data - Area vs. spool travel.

Orifice parameterization — Variable or constant orifice parameterization
`Cv flow coefficient` (default) | `Kv flow coefficient` | `Sonic conductance` | `Orifice area`

Method the block uses to calculate the mass flow rate from the pressure difference across the orifice or the pressure difference from the mass flow rate.

Spool travel between closed and open orifice — Maximum spool stroke
`0.005 m` (default) | positive scalar

Maximum distance of spool travel.

Dependencies

To enable this parameter, set Area characteristics to Identical for all flow paths and Opening characteristic to Linear.

Opening characteristic — Method to convert control signal to measure of flow capacity
`Linear` (default) | `Tabulated`

Method by which to convert the control signal specified at port S to the chosen measure of flow capacity.

Spool travel vector — Vector of spool opening distances relative to fully closed position
`[0, .00125, .0025, .00375, .005] m` (default) | 1-by-n vector

Vector of spool travel distances when parameterizing the orifice according to the tabulated valve area data. The vector elements must correspond one-to-one with the elements in the Orifice area vector parameter. List the values in ascending order. The first element must be 0. The block uses linear interpolation between table data points.

Dependencies

To enable this parameter, set Area characteristics to Identical for all flow paths and Opening characteristic to Tabulated.

Maximum Cv flow coefficient — C_v coefficient that corresponds to maximally open component
`4` (default) | positive scalar

Value of the C_v flow coefficient when the orifice is fully open and the area available for flow is at a maximum. This parameter measures the ease with which the vapor traverses the resistive element when driven by a pressure differential.

Dependencies

To enable this parameter, set Area characteristics to Identical for all flow paths, Orifice parameterization to Cv flow coefficient, and Opening characteristic to Linear.

Cv flow coefficient vector — C_v coefficients for values in member position vector
`[1e-06, .8, 1.6, 2.4, 3.2, 4]` (default) | 1-by-n vector

Vector of C_v flow coefficients. Each coefficient corresponds to a value in the Control member position vector parameter. This parameter measures the ease with which the vapor traverses the resistive element when driven by a pressure differential. The size of the vector must be the same as the Control member position vector parameter.

Dependencies

To enable this parameter, set Area characteristics to Identical for all flow paths, Orifice parameterization to Cv flow coefficient, and Opening characteristic to Tabulated.

Maximum Kv flow coefficient — K_v coefficient that corresponds to maximally open component
`3.6` (default) | positive scalar

Value of the K_v flow coefficient when the orifice is fully open and the area available for flow is at a maximum. This parameter measures the ease with which the vapor traverses the resistive element when driven by a pressure differential.

Dependencies

To enable this parameter, set Area characteristics to Identical for all flow paths, Orifice parameterization to Kv flow coefficient, and Opening characteristic to Linear.

Kv flow coefficient vector — K_v coefficients for values in member position vector
`[1e-06, .72, 1.44, 2.16, 2.88, 3.6]` (default) | 1-by-n vector

Vector of K_v flow coefficients. Each coefficient corresponds to a value in the Control member position vector parameter. This parameter measures the ease with which the vapor traverses the resistive element when driven by a pressure differential. The size of the vector must be the same as the Control member position vector parameter.

Dependencies

To enable this parameter, set Area characteristics to Identical for all flow paths, Orifice parameterization to Kv flow coefficient, and Opening characteristic to Tabulated.

Maximum orifice area — Maximum orifice opening area
`1e-4 m^2` (default) | positive scalar

Largest open area of each orifice during the operation of the valve.

Dependencies

To enable this parameter, set Area characteristics to Identical for all flow paths, Orifice parameterization to Orifice area, and Opening characteristic to Linear.

Orifice area vector — Vector of valve opening areas
`[1e-10, 1e-05, 4e-05, 6e-05, .0001] m^2` (default) | 1-by-n vector

Vector of opening areas when parameterizing the orifice according to the tabulated valve area data. The vector elements must correspond one-to-one with the elements in the Spool travel vector parameter. List the values in ascending order. The elements must be greater than 0.

Dependencies

To enable this parameter, set Area characteristics to Identical for all flow paths, Orifice parameterization to Orifice area, and Opening characteristic to Tabulated.

xT pressure differential ratio factor at choked flow — Ratio of pressure differentials
`0.7` (default) | positive scalar

Ratio between the inlet pressure, p_in, and the outlet pressure, p_out, defined as $(p_{i n} - p_{o u t}) / p_{i n}$ where choking first occurs.

Dependencies

To enable this parameter, set Area characteristics to Identical for all flow paths, and Orifice parameterization to Cv flow coefficient or Kv flow coefficient.

Discharge coefficient — Discharge coefficient
`0.64` (default) | positive scalar

Correction factor that accounts for discharge losses in theoretical flows.

Dependencies

To enable this parameter, set Orifice parameterization to Orifice area.

Maximum sonic conductance — Sonic conductance corresponding to maximally open component
`12 l/(bar*s)` (default) | positive scalar

Value of the sonic conductance when the control signal specified at port S is 1 and cross-sectional area available for flow is at a maximum.

Dependencies

To enable this parameter, set Area characteristics to Identical for all flow paths, Orifice parameterization to Sonic conductance, and Opening characteristic to Linear.

Critical pressure ratio — Ratio of downstream and upstream pressures at which the flow first chokes
`0.3` (default) | positive scalar

Pressure ratio at which flow first begins to choke and the flow velocity reaches its maximum, given by the local speed of sound. The pressure ratio is the outlet pressure divided by inlet pressure.

Dependencies

To enable this parameter, set Area characteristics to Identical for all flow paths, Orifice parameterization to Sonic conductance, and Opening characteristic to Linear.

Subsonic index — Exponent used to characterize mass flow in subsonic flow regime
`0.5` (default) | positive scalar

Empirical value used to more accurately calculate the mass flow rate in the subsonic flow regime.

Dependencies

To enable this parameter, set Area characteristics to Identical for all flow paths and Orifice parameterization to Sonic conductance.

ISO reference temperature — ISO 8778 reference temperature
`293.15 K` (default) | scalar

Temperature at standard reference atmosphere, defined as 293.15 K in ISO 8778.

You only need to adjust the ISO reference parameter values if you are using sonic conductance values that are obtained at difference reference values.

Dependencies

To enable this parameter, set Area characteristics to Identical for all flow paths and Orifice parameterization to Sonic conductance.

ISO reference density — ISO 8778 reference density
`1.185 kg/m^3` (default) | positive scalar

Density at standard reference atmosphere, defined as 1.185 kg/m3 in ISO 8778.

You only need to adjust the ISO reference parameter values if you are using sonic conductance values that are obtained at difference reference values.

Dependencies

To enable this parameter, set Area characteristics to Identical for all flow paths and Orifice parameterization to Sonic conductance.

Sonic conductance vector — Sonic conductances corresponding to values in spool travel vector
`[1e-05, 2.4, 4.8, 7.2, 9.6, 12] l/(bar*s)` (default) | vector of positive values

Vector of sonic conductances inside the resistive element. Each conductance corresponds to a value in the Spool travel vector parameter. The size of the vector must be the same as the Spool travel vector parameter.

Dependencies

To enable this parameter, set Area characteristics to Identical for all flow paths, Orifice parameterization to Sonic conductance, and Opening characteristic to Tabulated.

Critical pressure ratio vector — Critical pressure ratios corresponding to values in spool travel vector
`0.3 * ones(1,6)` (default) | vector of positive numbers

Vector of critical pressure ratios at which the flow first chokes, with each critical pressure ratio corresponding to a value in the Spool travel vector parameter. The critical pressure ratio is the fraction of downstream-to-upstream pressures at which the flow velocity reaches the local speed of sound. The size of the vector must be the same as the Spool travel vector parameter.

Dependencies

To enable this parameter, set Area characteristics to Identical for all flow paths, Orifice parameterization to Sonic conductance, and Opening characteristic to Tabulated.

Leakage flow fraction — Ratio of flow rates
`1e-6` (default) | positive scalar

Ratio of the flow rate of the orifice when it is closed to when it is open.

Dependencies

To enable this parameter, set Opening characteristic to Linear.

Smoothing factor — Numerical smoothing factor
`0.01` (default) | positive scalar in the range of [0,1]

Continuous smoothing factor that introduces a layer of gradual change based on the flow response when the valve is in the near-open and near-closed positions. To increase the stability of your simulation in these regimes, set this parameter to a nonzero value less than one.

Dependencies

To enable this parameter, set Opening characteristic to Linear.

Laminar flow pressure ratio — Laminar-turbulent transition pressure ratio
`0.999` (default) | positive scalar

Ratio of the orifice outlet pressure to orifice inlet pressure at which the fluid transitions between the laminar and turbulent regimes. The pressure loss corresponds to the mass flow rate linearly in laminar flows and quadratically in turbulent flows.

Cross-sectional area at ports P, T, A, and B — Area at conserving ports
`0.01 m^2` (default) | positive scalar

Maximum cross-sectional areas at the entry and exit ports P, T, A, and B, which the block uses in the pressure-flow rate equation that determines the mass flow rate through the valve.

P-A Orifice

Spool position at maximum P-A orifice area — Spool offset for fully open P-A orifice
`5e-3 m` (default) | positive scalar

Spool offset from the neutral position for a fully open P-A orifice.

Dependencies

To enable this parameter, set one of these parameters.

Positive spool position open connections to:

P-A, B-T
P-A, P-B
P-A
P-A, P-B, A-T, B-T

Negative spool position open connections to:

P-A, B-T
P-A, P-B
P-A
P-A, P-B, A-T, B-T

Note:

This parameter is enabled only when the P-A orifice settings do not appear in both the Positive spool position open connections and Negative spool position open connections parameters.

P-A spool travel between closed and open orifice — Maximum spool stroke
`0.005 m` (default) | positive scalar

Maximum distance of spool travel. This value provides an upper limit to calculations so that simulations do not return unphysical values.

Dependencies

To enable this parameter, set Area characteristics to Different for each flow path, Opening characteristic to Linear, and one of the following parameters:

Positive spool position open connections to:

P-A, B-T
P-A, P-B
P-A
P-A, P-B, A-T, B-T

Negative spool position open connections to:

P-A, B-T
P-A, P-B
P-A
P-A, P-B, A-T, B-T

P-A constant orifice Cv flow coefficient — Flow coefficient
`4` (default) | positive scalar

Value of the constant C_v flow coefficient for the P-A orifice. This parameter measures the ease with which the vapor traverses the resistive element when driven by a pressure differential.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Cv flow coefficient
One of the following settings in each parameter:
Positive spool position open connections to:
- P-A, B-T
- P-A, P-B
- P-A
- P-A, P-B, A-T, B-T
Negative spool position open connections to:
- P-A, B-T
- P-A, P-B
- P-A
- P-A, P-B, A-T, B-T

Note:

This parameter is enabled only when the P-A orifice settings appear in both spool position parameters: Positive spool position open connections and Negative spool position open connections.

P-A orifice maximum Cv flow coefficient — C_v coefficient that corresponds to maximally open component
`4` (default) | positive scalar

Value of the C_v flow coefficient when the P-A orifice is fully open and the area available for flow is at a maximum. This parameter measures the ease with which the vapor traverses the resistive element when driven by a pressure differential.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Cv flow coefficient
Opening characteristic to Linear
One of the following parameters:
Positive spool position open connections to:
- P-A, B-T
- P-A, P-B
- P-A
- P-A, P-B, A-T, B-T
Negative spool position open connections to:
- P-A, B-T
- P-A, P-B
- P-A
- P-A, P-B, A-T, B-T

P-A orifice Cv flow coefficient vector — C_v coefficients for values in member position vector
`[1e-06, .8, 1.6, 2.4, 3.2, 4]` (default) | 1-by-n vector

Vector of C_v flow coefficients. Each coefficient corresponds to a value in the P-A orifice spool travel vector parameter. This parameter measures the ease with which the vapor traverses the resistive element when driven by a pressure differential. The size of the vector must be the same as the P-A orifice spool travel vector parameter.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Cv flow coefficient
Opening characteristic to Tabulated
One of the following parameters:
Positive spool position open connections to:
- P-A, B-T
- P-A, P-B
- P-A
- P-A, P-B, A-T, B-T
Negative spool position open connections to:
- P-A, B-T
- P-A, P-B
- P-A
- P-A, P-B, A-T, B-T

P-A constant orifice Kv flow coefficient — Flow coefficient
`3.6` (default) | positive scalar

Value of the constant K_v flow coefficient for the P-A orifice. This parameter measures the ease with which the vapor traverses the resistive element when driven by a pressure differential.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Kv flow coefficient
One of the following settings in each parameter:
Positive spool position open connections to:
- P-A, B-T
- P-A, P-B
- P-A
- P-A, P-B, A-T, B-T
Negative spool position open connections to:
- P-A, B-T
- P-A, P-B
- P-A
- P-A, P-B, A-T, B-T

Note:

This parameter is enabled only when the P-A orifice settings appear in both spool position parameters: Positive spool position open connections and Negative spool position open connections.

P-A orifice maximum Kv flow coefficient — K_v coefficient that corresponds to maximally open component
`3.6` (default) | positive scalar

Value of the K_v flow coefficient when the P-A orifice is fully open and the area available for flow is at a maximum. This parameter measures the ease with which the vapor traverses the resistive element when driven by a pressure differential.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Kv flow coefficient
Opening characteristic to Linear
One of the following parameters:
Positive spool position open connections to:
- P-A, B-T
- P-A, P-B
- P-A
- P-A, P-B, A-T, B-T
Negative spool position open connections to:
- P-A, B-T
- P-A, P-B
- P-A
- P-A, P-B, A-T, B-T

P-A orifice Kv flow coefficient vector — K_v coefficients for values in member position vector
`[1e-06, .72, 1.44, 2.16, 2.88, 3.6]` (default) | 1-by-n vector

Vector of K_v flow coefficients. Each coefficient corresponds to a value in the P-A orifice spool travel vector parameter. This parameter measures the ease with which the vapor traverses the resistive element when driven by a pressure differential. The size of the vector must be the same as the P-A orifice spool travel vector parameter.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Kv flow coefficient
Opening characteristic to Tabulated
One of the following parameters:
Positive spool position open connections to:
- P-A, B-T
- P-A, P-B
- P-A
- P-A, P-B, A-T, B-T
Negative spool position open connections to:
- P-A, B-T
- P-A, P-B
- P-A
- P-A, P-B, A-T, B-T

P-A orifice spool travel vector — Vector of spool opening distances relative to fully closed position
`[0, .00125, .0025, .00375, .005] m` (default) | 1-by-n vector

Vector of spool travel distances for the tabular parameterization of the valve area. List the values in ascending order. The first element must be 0. The block uses linear interpolation between table data points.

Dependencies

To enable this parameter, set Area characteristics to Different for each flow path, Opening characteristic to Tabulated, and one of the following parameters:

Positive spool position open connections to:

P-A, B-T
P-A, P-B
P-A
P-A, P-B, A-T, B-T

Negative spool position open connections to:

P-A, B-T
P-A, P-B
P-A
P-A, P-B, A-T, B-T

P-A maximum orifice area — Maximum orifice opening area
`1e-4 m^2` (default) | positive scalar

Largest open area of the P-A orifice during the operation of the valve.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Orifice area
Opening characteristic to Linear
One of the following parameters:
Positive spool position open connections to:
- P-A, B-T
- P-A, P-B
- P-A
- P-A, P-B, A-T, B-T
Negative spool position open connections to:
- P-A, B-T
- P-A, P-B
- P-A
- P-A, P-B, A-T, B-T

P-A orifice area vector — Vector of valve opening areas
`[1e-10, 1e-05, 4e-05, 6e-05, .0001] m^2` (default) | 1-by-n vector

Vector of opening areas for the tabular parameterization of the valve area. The vector elements must correspond one-to-one with the elements in the P-A orifice spool travel vector parameter. The elements must be greater than 0 and listed in ascending order.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Orifice area
Opening characteristic to Tabulated
One of the following parameters:
Positive spool position open connections to:
- P-A, B-T
- P-A, P-B
- P-A
- P-A, P-B, A-T, B-T
Negative spool position open connections to:
- P-A, B-T
- P-A, P-B
- P-A
- P-A, P-B, A-T, B-T

P-A constant orifice area — Cross-sectional area for constant orifice
`1e-4 m^2` (default) | positive scalar

Orifice area when the positive and negative spool positions include the same orifice.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Orifice area
One of the following settings in each parameter:
Positive spool position open connections to:
- P-A, B-T
- P-A, P-B
- P-A
- P-A, P-B, A-T, B-T
Negative spool position open connections to:
- P-A, B-T
- P-A, P-B
- P-A
- P-A, P-B, A-T, B-T

Note:

This parameter is enabled only when the P-A orifice settings appear in both spool position parameters: Positive spool position open connections and Negative spool position open connections.

P-A orifice xT pressure differential ratio factor at choked flow — Ratio of pressure differentials
`0.7` (default) | positive scalar

Ratio between the inlet pressure, p_in, and the outlet pressure, p_out, defined as $(p_{i n} - p_{o u t}) / p_{i n}$ where choking first occurs for the P-A orifice.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Kv flow coefficient or Cv flow coefficient
At least one of the following parameters:
Positive spool position open connections to:
- P-A, B-T
- P-A, P-B
- P-A
- P-A, P-B, A-T, B-T
Negative spool position open connections to:
- P-A, B-T
- P-A, P-B
- P-A
- P-A, P-B, A-T, B-T

P-A constant orifice sonic conductance — Sonic conductance for constant orifice
`12` `l/(bar*s)` (default) | positive scalar

Sonic conductance when the positive and negative spool positions include the same orifice. This value is the ratio, measured at the onset of choking, of the mass flow rate through the resistive element to the product of the upstream pressure and mass density at standard conditions as defined in ISO 8778. This parameter determines the maximum flow rate allowed at a given upstream pressure.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Sonic conductance
One of the following settings in each parameter:
Positive spool position open connections to:
- P-A, B-T
- P-A, P-B
- P-A
- P-A, P-B, A-T, B-T
Negative spool position open connections to:
- P-A, B-T
- P-A, P-B
- P-A
- P-A, P-B, A-T, B-T

Note:

This parameter is enabled only when the P-A orifice settings appear in both spool position parameters: Positive spool position open connections and Negative spool position open connections.

P-A constant orifice critical pressure ratio — Ratio of downstream and upstream pressures at which the flow first chokes for constant orifice
`0.3` (default) | positive scalar

Critical pressure ratio when the positive and negative spool positions include the same orifice. This value is the pressure ratio at which flow first begins to choke and the flow velocity reaches its maximum, given by the local speed of sound. The pressure ratio is the outlet pressure divided by inlet pressure.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Sonic conductance
One of the following settings in each parameter:
Positive spool position open connections to:
- P-A, B-T
- P-A, P-B
- P-A
- P-A, P-B, A-T, B-T
Negative spool position open connections to:
- P-A, B-T
- P-A, P-B
- P-A
- P-A, P-B, A-T, B-T

Note:

This parameter is enabled only when the P-A orifice settings appear in both spool position parameters: Positive spool position open connections and Negative spool position open connections.

P-A orifice maximum sonic conductance — Sonic conductance corresponding to maximally open orifice
`12` `l/(bar*s)` (default) | positive scalar

Value of the sonic conductance when the P-A orifice is fully open and the area available for flow is at a maximum.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Sonic conductance
Opening characteristic to Linear
One of the following parameters:
Positive spool position open connections to:
- P-A, B-T
- P-A, P-B
- P-A
- P-A, P-B, A-T, B-T
Negative spool position open connections to:
- P-A, B-T
- P-A, P-B
- P-A
- P-A, P-B, A-T, B-T

P-A orifice critical pressure ratio — Ratio of downstream and upstream pressures at which the flow first chokes
`0.3` (default) | positive scalar

Pressure ratio at which flow first begins to choke and the flow velocity reaches its maximum, given by the local speed of sound. The pressure ratio is the outlet pressure divided by inlet pressure.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Sonic conductance
Opening characteristic to Linear
One of the following parameters:
Positive spool position open connections to:
- P-A, B-T
- P-A, P-B
- P-A
- P-A, P-B, A-T, B-T
Negative spool position open connections to:
- P-A, B-T
- P-A, P-B
- P-A
- P-A, P-B, A-T, B-T

P-A orifice sonic conductance vector — Sonic conductances corresponding to values in spool travel vector
`[1e-05, 2.4, 4.8, 7.2, 9.6, 12]` `l/(bar*s)` (default) | 1-by-n vector

Vector of sonic conductances inside the resistive element. Each conductance corresponds to a value in the P-A orifice spool travel vector parameter. The size of the vector must be the same as the P-A orifice spool travel vector parameter.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Sonic conductance
Opening characteristic to Tabulated
One of the following parameters:
Positive spool position open connections to:
- P-A, B-T
- P-A, P-B
- P-A
- P-A, P-B, A-T, B-T
Negative spool position open connections to:
- P-A, B-T
- P-A, P-B
- P-A
- P-A, P-B, A-T, B-T

P-A orifice critical pressure ratio vector — Critical pressure ratios corresponding to values in spool travel vector
`0.3 * ones(1, 6)` (default) | 1-by-n vector

Vector of critical pressure ratios at which the flow first chokes, with each critical pressure ratio corresponding to a value in the P-A orifice spool travel vector parameter. The critical pressure ratio is the fraction of downstream-to-upstream pressures at which the flow velocity reaches the local speed of sound. The size of the vector must be the same as the P-A orifice spool travel vector parameter.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Sonic conductance
Opening characteristic to Tabulated
One of the following parameters:
Positive spool position open connections to:
- P-A, B-T
- P-A, P-B
- P-A
- P-A, P-B, A-T, B-T
Negative spool position open connections to:
- P-A, B-T
- P-A, P-B
- P-A
- P-A, P-B, A-T, B-T

P-A orifice subsonic index — Exponent used to characterize mass flow in subsonic flow regime
`0.5` (default) | positive scalar

Empirical value used to more accurately calculate the mass flow rate in the subsonic flow regime.

Dependencies

To enable this parameter, set Area characteristics to Different for each flow path, Orifice parameterization to Sonic conductance, and at least one of the following parameters:

Positive spool position open connections to:

P-A, B-T
P-A, P-B
P-A
P-A, P-B, A-T, B-T

Negative spool position open connections to:

P-A, B-T
P-A, P-B
P-A
P-A, P-B, A-T, B-T

P-A orifice ISO reference temperature — ISO 8778 reference temperature
`293.15` `K` (default) | scalar

Temperature at standard reference atmosphere, defined as 293.15 K in ISO 8778.

You only need to adjust the ISO reference parameter values if you are using sonic conductance values that are obtained at difference reference values.

Dependencies

To enable this parameter, set Area characteristics to Different for each flow path, Orifice parameterization to Sonic conductance, and at least one of the following parameters:

Positive spool position open connections to:

P-A, B-T
P-A, P-B
P-A
P-A, P-B, A-T, B-T

Negative spool position open connections to:

P-A, B-T
P-A, P-B
P-A
P-A, P-B, A-T, B-T

P-A orifice ISO reference density — ISO 8778 reference density
`1.185 kg/m^3` (default) | positive scalar

Density at standard reference atmosphere, defined as 1.185 kg/m3 in ISO 8778.

You only need to adjust the ISO reference parameter values if you are using sonic conductance values that are obtained at difference reference values.

Dependencies

To enable this parameter, set Area characteristics to Different for each flow path, Orifice parameterization to Sonic conductance, and at least one of the following parameters:

Positive spool position open connections to:

P-A, B-T
P-A, P-B
P-A
P-A, P-B, A-T, B-T

Negative spool position open connections to:

P-A, B-T
P-A, P-B
P-A
P-A, P-B, A-T, B-T

P-B Orifice

Spool position at maximum P-B orifice area — Spool offset for fully open P-B orifice
`5e-3 m` (default) | positive scalar

Spool offset from the neutral position for a fully open P-B orifice.

Dependencies

To enable this parameter, set one of these parameters:

Positive spool position open connections to:

P-B, A-T
P-A, P-B
P-B
P-A, P-B, A-T, B-T

or set Negative spool position open connections to:

P-B, A-T
P-A, P-B
P-B
P-A, P-B, A-T, B-T

Note:

This parameter is enabled only when the P-B orifice settings do not appear in both the Positive spool position open connections and Negative spool position open connections parameters.

P-B spool travel between closed and open orifice — Maximum spool stroke
`0.005 m` (default) | positive scalar

Maximum distance of spool travel. This value provides an upper limit to calculations so that simulations do not return unphysical values.

Dependencies

To enable this parameter, set Area characteristics to Different for each flow path, Opening characteristic to Linear, and one of the following parameters:

Positive spool position open connections to:

P-B, A-T
P-A, P-B
P-B
P-A, P-B, A-T, B-T

or set Negative spool position open connections to:

P-B, A-T
P-A, P-B
P-B
P-A, P-B, A-T, B-T

P-B constant orifice Cv flow coefficient — Flow coefficient
`4` (default) | positive scalar

Value of the constant C_v flow coefficient for the P-B orifice. This parameter measures the ease with which the vapor traverses the resistive element when driven by a pressure differential.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Cv flow coefficient
One of the following settings in each parameter:
Positive spool position open connections to:
- P-B, A-T
- P-A, P-B
- P-B
- P-A, P-B, A-T, B-T
or set Negative spool position open connections to:
- P-B, A-T
- P-A, P-B
- P-B
- P-A, P-B, A-T, B-T

Note:

This parameter is enabled only when the P-B orifice settings appear in both spool position parameters: Positive spool position open connections and Negative spool position open connections.

P-B orifice maximum Cv flow coefficient — C_v coefficient that corresponds to maximally open component
`4` (default) | positive scalar

Value of the C_v flow coefficient when the P-B orifice is fully open and the area available for flow is at a maximum. This parameter measures the ease with which the vapor traverses the resistive element when driven by a pressure differential.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Cv flow coefficient
Opening characteristic to Linear
One of the following parameters:
Positive spool position open connections to:
- P-B, A-T
- P-A, P-B
- P-B
- P-A, P-B, A-T, B-T
or set Negative spool position open connections to:
- P-B, A-T
- P-A, P-B
- P-B
- P-A, P-B, A-T, B-T

P-B orifice Cv flow coefficient vector — C_v coefficients for values in member position vector
`[1e-06, .8, 1.6, 2.4, 3.2, 4]` (default) | 1-by-n vector

Vector of C_v flow coefficients. Each coefficient corresponds to a value in the P-B orifice spool travel vector parameter. This parameter measures the ease with which the vapor traverses the resistive element when driven by a pressure differential. The size of the vector must be the same as the P-B orifice spool travel vector parameter.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Cv flow coefficient
Opening characteristic to Tabulated
One of the following parameters:
Positive spool position open connections to:
- P-B, A-T
- P-A, P-B
- P-B
- P-A, P-B, A-T, B-T
or set Negative spool position open connections to:
- P-B, A-T
- P-A, P-B
- P-B
- P-A, P-B, A-T, B-T

P-B constant orifice Kv flow coefficient — Flow coefficient
`3.6` (default) | positive scalar

Value of the constant K_v flow coefficient for the P-B orifice. This parameter measures the ease with which the vapor traverses the resistive element when driven by a pressure differential.

Dependencies

To enable this parameter, set:

Modeling option to Vapor operating condition
Area characteristics to Different for each flow path
Orifice parameterization to Kv flow coefficient
One of the following settings in each parameter:
Positive spool position open connections to:
- P-B, A-T
- P-A, P-B
- P-B
- P-A, P-B, A-T, B-T
or set Negative spool position open connections to:
- P-B, A-T
- P-A, P-B
- P-B
- P-A, P-B, A-T, B-T

Note:

This parameter is enabled only when the P-B orifice settings appear in both spool position parameters: Positive spool position open connections and Negative spool position open connections.

P-B orifice maximum Kv flow coefficient — K_v coefficient that corresponds to maximally open component
`3.6` (default) | positive scalar

Value of the K_v flow coefficient when the P-B orifice is fully open and the area available for flow is at a maximum. This parameter measures the ease with which the vapor traverses the resistive element when driven by a pressure differential.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Kv flow coefficient
Opening characteristic to Linear
One of the following parameters:
Positive spool position open connections to:
- P-B, A-T
- P-A, P-B
- P-B
- P-A, P-B, A-T, B-T
or set Negative spool position open connections to:
- P-B, A-T
- P-A, P-B
- P-B
- P-A, P-B, A-T, B-T

P-B orifice Kv flow coefficient vector — K_v coefficients for values in member position vector
`[1e-06, .72, 1.44, 2.16, 2.88, 3.6]` (default) | 1-by-n vector

Vector of K_v flow coefficients. Each coefficient corresponds to a value in the P-B orifice spool travel vector parameter. This parameter measures the ease with which the vapor traverses the resistive element when driven by a pressure differential. The size of the vector must be the same as the P-B orifice spool travel vector parameter.

Dependencies

To enable this parameter, set:

Modeling option to Vapor operating condition
Area characteristics to Different for each flow path
Orifice parameterization to Kv flow coefficient
Opening characteristic to Tabulated
One of the following parameters:
Positive spool position open connections to:
- P-B, A-T
- P-A, P-B
- P-B
- P-A, P-B, A-T, B-T
or set Negative spool position open connections to:
- P-B, A-T
- P-A, P-B
- P-B
- P-A, P-B, A-T, B-T

P-B orifice spool travel vector — Vector of spool opening distances relative to fully closed position
`[0, .00125, .0025, .00375, .005] m` (default) | 1-by-n vector

Dependencies

To enable this parameter, set Area characteristics to Different for each flow path, Opening characteristic to Tabulated, and one of the following parameters:

Positive spool position open connections to:

P-B, A-T
P-A, P-B
P-B
P-A, P-B, A-T, B-T

or set Negative spool position open connections to:

P-B, A-T
P-A, P-B
P-B
P-A, P-B, A-T, B-T

P-B maximum orifice area — Maximum orifice opening area
`1e-4 m^2` (default) | positive scalar

Largest open area of the P-B orifice during the operation of the valve.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Orifice area
Opening characteristic to Tabulated
One of the following parameters:
Positive spool position open connections to:
- P-B, A-T
- P-A, P-B
- P-B
- P-A, P-B, A-T, B-T
or set Negative spool position open connections to:
- P-B, A-T
- P-A, P-B
- P-B
- P-A, P-B, A-T, B-T

P-B orifice area vector — Vector of valve opening areas
`[1e-10, 1e-05, 4e-05, 6e-05, .0001] m^2` (default) | 1-by-n vector

Vector of opening areas for the tabular parameterization of the valve area. The vector elements must correspond one-to-one with the elements in the P-B orifice spool travel vector parameter. The elements must be greater than 0 and listed in ascending order.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Orifice area
Opening characteristic to Tabulated
One of the following parameters:
Positive spool position open connections to:
- P-B, A-T
- P-A, P-B
- P-B
- P-A, P-B, A-T, B-T
or set Negative spool position open connections to:
- P-B, A-T
- P-A, P-B
- P-B
- P-A, P-B, A-T, B-T

P-B constant orifice area — Cross-sectional area for constant orifice
`1e-4 m^2` (default) | positive scalar

Orifice area when the positive and negative spool positions include the same orifice.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Orifice area
One of the following settings in each parameter:
Positive spool position open connections to:
- P-B, A-T
- P-A, P-B
- P-B
- P-A, P-B, A-T, B-T
or set Negative spool position open connections to:
- P-B, A-T
- P-A, P-B
- P-B
- P-A, P-B, A-T, B-T

Note:

This parameter is enabled only when the P-B orifice settings appear in both spool position parameters: Positive spool position open connections and Negative spool position open connections.

P-B orifice xT pressure differential ratio factor at choked flow — Ratio of pressure differentials
`0.7` (default) | positive scalar

Ratio between the inlet pressure, p_in, and the outlet pressure, p_out, defined as $(p_{i n} - p_{o u t}) / p_{i n}$ where choking first occurs for the P-B orifice.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Kv flow coefficient or Cv flow coefficient
At least one of the following parameters:
Positive spool position open connections to:
- P-B, A-T
- P-A, P-B
- P-B
- P-A, P-B, A-T, B-T
or set Negative spool position open connections to:
- P-B, A-T
- P-A, P-B
- P-B
- P-A, P-B, A-T, B-T

P-B constant orifice sonic conductance — Sonic conductance for constant orifice
`12` `l/(bar*s)` (default) | positive scalar

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Sonic conductance
One of the following settings in each parameter:
Positive spool position open connections to:
- P-B, A-T
- P-A, P-B
- P-B
- P-A, P-B, A-T, B-T
or set Negative spool position open connections to:
- P-B, A-T
- P-A, P-B
- P-B
- P-A, P-B, A-T, B-T

Note:

This parameter is enabled only when the P-B orifice settings appear in both spool position parameters: Positive spool position open connections and Negative spool position open connections.

P-B constant orifice critical pressure ratio — Ratio of downstream and upstream pressures at which the flow first chokes for constant orifice
`0.3` (default) | positive scalar

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Sonic conductance
One of the following settings in each parameter:
Positive spool position open connections to:
- P-B, A-T
- P-A, P-B
- P-B
- P-A, P-B, A-T, B-T
or set Negative spool position open connections to:
- P-B, A-T
- P-A, P-B
- P-B
- P-A, P-B, A-T, B-T

Note:

This parameter is enabled only when the P-B orifice settings appear in both spool position parameters: Positive spool position open connections and Negative spool position open connections.

P-B orifice maximum sonic conductance — Sonic conductance corresponding to maximally open orifice
`12` `l/(bar*s)` (default) | positive scalar

Value of the sonic conductance when the P-B orifice is fully open and the area available for flow is at a maximum.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Sonic conductance
Opening characteristic to Linear
One of the following parameters:
Positive spool position open connections to:
- P-B, A-T
- P-A, P-B
- P-B
- P-A, P-B, A-T, B-T
or set Negative spool position open connections to:
- P-B, A-T
- P-A, P-B
- P-B
- P-A, P-B, A-T, B-T

P-B orifice critical pressure ratio — Ratio of downstream and upstream pressures at which the flow first chokes
`0.3` (default) | positive scalar

Pressure ratio at which flow first begins to choke and the flow velocity reaches its maximum, given by the local speed of sound. The pressure ratio is the outlet pressure divided by inlet pressure.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Sonic conductance
Opening characteristic to Linear
One of the following parameters:
Positive spool position open connections to:
- P-B, A-T
- P-A, P-B
- P-B
- P-A, P-B, A-T, B-T
or set Negative spool position open connections to:
- P-B, A-T
- P-A, P-B
- P-B
- P-A, P-B, A-T, B-T

P-B orifice sonic conductance vector — Sonic conductances corresponding to values in spool travel vector
`[1e-05, 2.4, 4.8, 7.2, 9.6, 12]` `l/(bar*s)` (default) | 1-by-n vector

Vector of sonic conductances inside the resistive element. Each conductance corresponds to a value in the P-B orifice spool travel vector parameter. The size of the vector must be the same as the P-B orifice spool travel vector parameter.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Sonic conductance
Opening characteristic to Tabulated
One of the following parameters:
Positive spool position open connections to:
- P-B, A-T
- P-A, P-B
- P-B
- P-A, P-B, A-T, B-T
or set Negative spool position open connections to:
- P-B, A-T
- P-A, P-B
- P-B
- P-A, P-B, A-T, B-T

P-B orifice critical pressure ratio vector — Critical pressure ratios corresponding to values in spool travel vector
`0.3 * ones(1, 6)` (default) | 1-by-n vector

Vector of critical pressure ratios at which the flow first chokes, with each critical pressure ratio corresponding to a value in the P-B orifice spool travel vector parameter. The critical pressure ratio is the fraction of downstream-to-upstream pressures at which the flow velocity reaches the local speed of sound. The size of the vector must be the same as the P-B orifice spool travel vector parameter.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Sonic conductance
Opening characteristic to Tabulated
One of the following parameters:
Positive spool position open connections to:
- P-B, A-T
- P-A, P-B
- P-B
- P-A, P-B, A-T, B-T
or set Negative spool position open connections to:
- P-B, A-T
- P-A, P-B
- P-B
- P-A, P-B, A-T, B-T

P-B orifice subsonic index — Exponent used to characterize mass flow in subsonic flow regime
`0.5` (default) | positive scalar

Empirical value used to more accurately calculate the mass flow rate in the subsonic flow regime.

Dependencies

To enable this parameter, set Area characteristics to Different for each flow path, Orifice parameterization to Sonic conductance, and at least one of the following parameters:

Positive spool position open connections to:

P-B, A-T
P-A, P-B
P-B
P-A, P-B, A-T, B-T

or set Negative spool position open connections to:

P-B, A-T
P-A, P-B
P-B
P-A, P-B, A-T, B-T

P-B orifice ISO reference temperature — ISO 8778 reference temperature
`293.15` `K` (default) | scalar

Temperature at standard reference atmosphere, defined as 293.15 K in ISO 8778.

You only need to adjust the ISO reference parameter values if you are using sonic conductance values that are obtained at difference reference values.

Dependencies

To enable this parameter, set Area characteristics to Different for each flow path, Orifice parameterization to Sonic conductance, and at least one of the following parameters:

Positive spool position open connections to:

P-B, A-T
P-A, P-B
P-B
P-A, P-B, A-T, B-T

or set Negative spool position open connections to:

P-B, A-T
P-A, P-B
P-B
P-A, P-B, A-T, B-T

P-B orifice ISO reference density — ISO 8778 reference density
`1.185 kg/m^3` (default) | positive scalar

Density at standard reference atmosphere, defined as 1.185 kg/m3 in ISO 8778.

You only need to adjust the ISO reference parameter values if you are using sonic conductance values that are obtained at difference reference values.

Dependencies

To enable this parameter, set Area characteristics to Different for each flow path, Orifice parameterization to Sonic conductance, and at least one of the following parameters:

Positive spool position open connections to:

P-B, A-T
P-A, P-B
P-B
P-A, P-B, A-T, B-T

or set Negative spool position open connections to:

P-B, A-T
P-A, P-B
P-B
P-A, P-B, A-T, B-T

A-T Orifice

Spool position at maximum A-T orifice area — Spool offset for fully open A-T orifice
`5e-3 m` (default) | positive scalar

Spool offset from the neutral position for a fully open A-T orifice.

Dependencies

To enable this parameter, set one of these parameters.

Positive spool position open connections to P-B, A-T or P-A, P-B, A-T, B-T.
Negative spool position open connections to P-B, A-T or P-A, P-B, A-T, B-T.

Note:

This parameter is enabled only when the A-T orifice settings do not appear in both the Positive spool position open connections and Negative spool position open connections parameters.

A-T spool travel between closed and open orifice — Maximum spool stroke
`0.005 m` (default) | positive scalar

Maximum distance of spool travel. This value provides an upper limit to calculations so that simulations do not return unphysical values.

Dependencies

To enable this parameter, set Area characteristics to Different for each flow path, Opening characteristic to Linear, and one of the following parameters:

Positive spool position open connections to P-B, A-T or P-A, P-B, A-T, B-T.
Negative spool position open connections to P-B, A-T or P-A, P-B, A-T, B-T.

A-T constant orifice Cv flow coefficient — Flow coefficient
`4` (default) | positive scalar

Value of the constant C_v flow coefficient for the A-T orifice. This parameter measures the ease with which the vapor traverses the resistive element when driven by a pressure differential.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Cv flow coefficient
One of the following settings in each parameter:
- Positive spool position open connections to P-B, A-T or P-A, P-B, A-T, B-T.
- Negative spool position open connections to P-B, A-T or P-A, P-B, A-T, B-T.

Note:

This parameter is enabled only when the A-T orifice settings appear in both spool position parameters: Positive spool position open connections and Negative spool position open connections.

A-T orifice maximum Cv flow coefficient — C_v coefficient that corresponds to maximally open component
`4` (default) | positive scalar

Value of the C_v flow coefficient when the A-T orifice is fully open and the area available for flow is at a maximum. This parameter measures the ease with which the vapor traverses the resistive element when driven by a pressure differential.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Cv flow coefficient
Opening characteristic to Linear
One of the following parameters:
- Positive spool position open connections to P-B, A-T or P-A, P-B, A-T, B-T.
- Negative spool position open connections to P-B, A-T or P-A, P-B, A-T, B-T.

A-T orifice Cv flow coefficient vector — C_v coefficients for values in member position vector
`[1e-06, .8, 1.6, 2.4, 3.2, 4]` (default) | 1-by-n vector

Vector of C_v flow coefficients. Each coefficient corresponds to a value in the A-T orifice spool travel vector parameter. This parameter measures the ease with which the vapor traverses the resistive element when driven by a pressure differential. The size of the vector must be the same as the A-T orifice spool travel vector parameter.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Cv flow coefficient
Opening characteristic to Tabulated
One of the following parameters:
- Positive spool position open connections to P-B, A-T or P-A, P-B, A-T, B-T.
- Negative spool position open connections to P-B, A-T or P-A, P-B, A-T, B-T.

A-T constant orifice Kv flow coefficient — Flow coefficient
`3.6` (default) | positive scalar

Value of the constant K_v flow coefficient for the A-T orifice. This parameter measures the ease with which the vapor traverses the resistive element when driven by a pressure differential.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Kv flow coefficient
One of the following settings in each parameter:
- Positive spool position open connections to P-B, A-T or P-A, P-B, A-T, B-T.
- Negative spool position open connections to P-B, A-T or P-A, P-B, A-T, B-T.

Note:

This parameter is enabled only when the A-T orifice settings appear in both spool position parameters: Positive spool position open connections and Negative spool position open connections.

A-T orifice maximum Kv flow coefficient — K_v coefficient that corresponds to maximally open component
`3.6` (default) | positive scalar

Value of the K_v flow coefficient when the A-T orifice is fully open and the area available for flow is at a maximum. This parameter measures the ease with which the vapor traverses the resistive element when driven by a pressure differential.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Kv flow coefficient
Opening characteristic to Linear
One of the following parameters:
- Positive spool position open connections to P-B, A-T or P-A, P-B, A-T, B-T.
- Negative spool position open connections to P-B, A-T or P-A, P-B, A-T, B-T.

A-T orifice Kv flow coefficient vector — K_v coefficients for values in member position vector
`[1e-06, .72, 1.44, 2.16, 2.88, 3.6]` (default) | 1-by-n vector

Vector of K_v flow coefficients. Each coefficient corresponds to a value in the A-T orifice spool travel vector parameter. This parameter measures the ease with which the vapor traverses the resistive element when driven by a pressure differential. The size of the vector must be the same as the A-T orifice spool travel vector parameter.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Kv flow coefficient
Opening characteristic to Tabulated
One of the following parameters:
- Positive spool position open connections to P-B, A-T or P-A, P-B, A-T, B-T.
- Negative spool position open connections to P-B, A-T or P-A, P-B, A-T, B-T.

A-T orifice spool travel vector — Vector of spool opening distances relative to fully closed position
`[0, .00125, .0025, .00375, .005] m` (default) | 1-by-n vector

Dependencies

To enable this parameter, set Area characteristics to Different for each flow path, Opening characteristic to Tabulated, and one of the following parameters:

Positive spool position open connections to P-B, A-T or P-A, P-B, A-T, B-T.
Negative spool position open connections to P-B, A-T or P-A, P-B, A-T, B-T.

A-T maximum orifice area — Maximum orifice opening area
`1e-4 m^2` (default) | positive scalar

Largest open area of the A-T orifice during the operation of the valve.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Orifice area
Opening characteristic to Linear
One of the following parameters:
- Positive spool position open connections to P-B, A-T or P-A, P-B, A-T, B-T.
- Negative spool position open connections to P-B, A-T or P-A, P-B, A-T, B-T.

A-T orifice area vector — Vector of valve opening areas
`[1e-10, 1e-05, 4e-05, 6e-05, .0001] m^2` (default) | 1-by-n vector

Vector of opening areas for the tabular parameterization of the valve area. The vector elements must correspond one-to-one with the elements in the A-T orifice spool travel vector parameter. The elements must be greater than 0 and listed in ascending order.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Orifice area
Opening characteristic to Tabulated
One of the following parameters:
- Positive spool position open connections to P-B, A-T or P-A, P-B, A-T, B-T.
- Negative spool position open connections to P-B, A-T or P-A, P-B, A-T, B-T.

A-T constant orifice area — Cross-sectional area for constant orifice
`1e-4 m^2` (default) | positive scalar

Orifice area when the positive and negative spool positions include the same orifice.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Orifice area
One of the following settings in each parameter:
- Positive spool position open connections to P-B, A-T or P-A, P-B, A-T, B-T.
- Negative spool position open connections to P-B, A-T or P-A, P-B, A-T, B-T.

Note:

This parameter is enabled only when the A-T orifice settings appear in both spool position parameters: Positive spool position open connections and Negative spool position open connections.

A-T orifice xT pressure differential ratio factor at choked flow — Ratio of pressure differentials
`0.7` (default) | positive scalar

Ratio between the inlet pressure, p_in, and the outlet pressure, p_out, defined as $(p_{i n} - p_{o u t}) / p_{i n}$ where choking first occurs for the A-T orifice.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Kv flow coefficient or Cv flow coefficient
At least one of the following parameters:
- Positive spool position open connections to P-B, A-T or P-A, P-B, A-T, B-T.
- Negative spool position open connections to P-B, A-T or P-A, P-B, A-T, B-T.

A-T constant orifice sonic conductance — Sonic conductance for constant orifice
`12` `l/(bar*s)` (default) | positive scalar

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Sonic conductance
One of the following settings in each parameter:
- Positive spool position open connections to P-B, A-T or P-A, P-B, A-T, B-T.
- Negative spool position open connections to P-B, A-T or P-A, P-B, A-T, B-T.

Note:

This parameter is enabled only when the A-T orifice settings appear in both spool position parameters: Positive spool position open connections and Negative spool position open connections.

A-T constant orifice critical pressure ratio — Ratio of downstream and upstream pressures at which the flow first chokes for constant orifice
`0.3` (default) | positive scalar

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Sonic conductance
One of the following settings in each parameter:
- Positive spool position open connections to P-B, A-T or P-A, P-B, A-T, B-T.
- Negative spool position open connections to P-B, A-T or P-A, P-B, A-T, B-T.

Note:

This parameter is enabled only when the A-T orifice settings appear in both spool position parameters: Positive spool position open connections and Negative spool position open connections.

A-T orifice maximum sonic conductance — Sonic conductance corresponding to maximally open orifice
`12` `l/(bar*s)` (default) | positive scalar

Value of the sonic conductance when the A-T orifice is fully open and the area available for flow is at a maximum.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Sonic conductance
Opening characteristic to Linear
One of the following parameters:
- Positive spool position open connections to P-B, A-T or P-A, P-B, A-T, B-T.
- Negative spool position open connections to P-B, A-T or P-A, P-B, A-T, B-T.

A-T orifice critical pressure ratio — Ratio of downstream and upstream pressures at which the flow first chokes
`0.3` (default) | positive scalar

Pressure ratio at which flow first begins to choke and the flow velocity reaches its maximum, given by the local speed of sound. The pressure ratio is the outlet pressure divided by inlet pressure.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Sonic conductance
Opening characteristic to Linear
One of the following parameters:
- Positive spool position open connections to P-B, A-T or P-A, P-B, A-T, B-T.
- Negative spool position open connections to P-B, A-T or P-A, P-B, A-T, B-T.

A-T orifice sonic conductance vector — Sonic conductances corresponding to values in spool travel vector
`[1e-05, 2.4, 4.8, 7.2, 9.6, 12]` `l/(bar*s)` (default) | 1-by-n vector

Vector of sonic conductances inside the resistive element. Each conductance corresponds to a value in the A-T orifice spool travel vector parameter. The size of the vector must be the same as the A-T orifice spool travel vector parameter.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Sonic conductance
Opening characteristic to Tabulated
One of the following parameters:
- Positive spool position open connections to P-B, A-T or P-A, P-B, A-T, B-T.
- Negative spool position open connections to P-B, A-T or P-A, P-B, A-T, B-T.

A-T orifice critical pressure ratio vector — Critical pressure ratios corresponding to values in spool travel vector
`0.3 * ones(1, 6)` (default) | 1-by-n vector

Vector of critical pressure ratios at which the flow first chokes, with each critical pressure ratio corresponding to a value in the A-T orifice spool travel vector parameter. The critical pressure ratio is the fraction of downstream-to-upstream pressures at which the flow velocity reaches the local speed of sound. The size of the vector must be the same as the A-T orifice spool travel vector parameter.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Sonic conductance
Opening characteristic to Tabulated
One of the following parameters:
- Positive spool position open connections to P-B, A-T or P-A, P-B, A-T, B-T.
- Negative spool position open connections to P-B, A-T or P-A, P-B, A-T, B-T.

A-T orifice subsonic index — Exponent used to characterize mass flow in subsonic flow regime
`0.5` (default) | positive scalar

Empirical value used to more accurately calculate the mass flow rate in the subsonic flow regime.

Dependencies

To enable this parameter, set Area characteristics to Different for each flow path, Orifice parameterization to Sonic conductance, and at least one of the following parameters:

Positive spool position open connections to P-B, A-T or P-A, P-B, A-T, B-T.
Negative spool position open connections to P-B, A-T or P-A, P-B, A-T, B-T.

A-T orifice ISO reference temperature — ISO 8778 reference temperature
`293.15` `K` (default) | scalar

Temperature at standard reference atmosphere, defined as 293.15 K in ISO 8778.

You only need to adjust the ISO reference parameter values if you are using sonic conductance values that are obtained at difference reference values.

Dependencies

To enable this parameter, set Area characteristics to Different for each flow path, Orifice parameterization to Sonic conductance, and at least one of the following parameters:

Positive spool position open connections to P-B, A-T or P-A, P-B, A-T, B-T.
Negative spool position open connections to P-B, A-T or P-A, P-B, A-T, B-T.

A-T orifice ISO reference density — ISO 8778 reference density
`1.185 kg/m^3` (default) | positive scalar

Density at standard reference atmosphere, defined as 1.185 kg/m3 in ISO 8778.

You only need to adjust the ISO reference parameter values if you are using sonic conductance values that are obtained at difference reference values.

Dependencies

To enable this parameter, set Area characteristics to Different for each flow path, Orifice parameterization to Sonic conductance, and at least one of the following parameters:

Positive spool position open connections to P-B, A-T or P-A, P-B, A-T, B-T.
Negative spool position open connections to P-B, A-T or P-A, P-B, A-T, B-T.

B-T Orifice

Spool position at maximum B-T orifice area — Spool offset for fully open B-T orifice
`5e-3 m` (default) | positive scalar

Spool offset from the neutral position for a fully open B-T orifice.

Dependencies

To enable this parameter, set one of these parameters.

Positive spool position open connections to P-A, B-T or P-A, P-B, A-T, B-T.
Negative spool position open connections to P-A, B-T or P-A, P-B, A-T, B-T.

Note:

This parameter is enabled only when the B-T orifice settings do not appear in both the Positive spool position open connections and Negative spool position open connections parameters.

B-T spool travel between closed and open orifice — Maximum spool stroke
`0.005 m` (default) | positive scalar

Maximum distance of spool travel. This value provides an upper limit to calculations so that simulations do not return unphysical values.

Dependencies

To enable this parameter, set Area characteristics to Different for each flow path, Opening characteristic to Linear, and one of the following parameters:

Positive spool position open connections to P-A, B-T or P-A, P-B, A-T, B-T.
Negative spool position open connections to P-A, B-T or P-A, P-B, A-T, B-T.

B-T constant orifice Cv flow coefficient — Flow coefficient
`4` (default) | positive scalar

Value of the constant C_v flow coefficient for the B-T orifice. This parameter measures the ease with which the vapor traverses the resistive element when driven by a pressure differential.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Cv flow coefficient
One of the following settings in each parameter:
- Positive spool position open connections to P-A, B-T or P-A, P-B, A-T, B-T.
- Negative spool position open connections to P-A, B-T or P-A, P-B, A-T, B-T.

Note:

This parameter is enabled only when the B-T orifice settings appear in both spool position parameters: Positive spool position open connections and Negative spool position open connections.

B-T orifice maximum Cv flow coefficient — C_v coefficient that corresponds to maximally open component
`4` (default) | positive scalar

Value of the C_v flow coefficient when the B-T orifice is fully open and the area available for flow is at a maximum. This parameter measures the ease with which the vapor traverses the resistive element when driven by a pressure differential.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Cv flow coefficient
Opening characteristic to Linear
One of the following parameters:
- Positive spool position open connections to P-A, B-T or P-A, P-B, A-T, B-T.
- Negative spool position open connections to P-A, B-T or P-A, P-B, A-T, B-T.

B-T orifice Cv flow coefficient vector — C_v coefficients for values in member position vector
`[1e-06, .8, 1.6, 2.4, 3.2, 4]` (default) | 1-by-n vector

Vector of C_v flow coefficients. Each coefficient corresponds to a value in the B-T orifice spool travel vector parameter. This parameter measures the ease with which the vapor traverses the resistive element when driven by a pressure differential. The size of the vector must be the same as the B-T orifice spool travel vector parameter.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Cv flow coefficient
Opening characteristic to Tabulated
One of the following parameters:
- Positive spool position open connections to P-A, B-T or P-A, P-B, A-T, B-T.
- Negative spool position open connections to P-A, B-T or P-A, P-B, A-T, B-T.

B-T constant orifice Kv flow coefficient — Flow coefficient
`3.6` (default) | positive scalar

Value of the constant K_v flow coefficient for the B-T orifice. This parameter measures the ease with which the vapor traverses the resistive element when driven by a pressure differential.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Kv flow coefficient
One of the following settings in each parameter:
- Positive spool position open connections to P-A, B-T or P-A, P-B, A-T, B-T.
- Negative spool position open connections to P-A, B-T or P-A, P-B, A-T, B-T.

Note:

This parameter is enabled only when the B-T orifice settings appear in both spool position parameters: Positive spool position open connections and Negative spool position open connections.

B-T orifice maximum Kv flow coefficient — K_v coefficient that corresponds to maximally open component
`3.6` (default) | positive scalar

Value of the K_v flow coefficient when the B-T orifice is fully open and the area available for flow is at a maximum. This parameter measures the ease with which the vapor traverses the resistive element when driven by a pressure differential.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Kv flow coefficient
Opening characteristic to Linear
One of the following parameters:
- Positive spool position open connections to P-A, B-T or P-A, P-B, A-T, B-T.
- Negative spool position open connections to P-A, B-T or P-A, P-B, A-T, B-T.

B-T orifice Kv flow coefficient vector — K_v coefficients for values in member position vector
`[1e-06, .72, 1.44, 2.16, 2.88, 3.6]` (default) | 1-by-n vector

Vector of K_v flow coefficients. Each coefficient corresponds to a value in the B-T orifice spool travel vector parameter. This parameter measures the ease with which the vapor traverses the resistive element when driven by a pressure differential. The size of the vector must be the same as the B-T orifice spool travel vector parameter.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Kv flow coefficient
Opening characteristic to Tabulated
One of the following parameters:
- Positive spool position open connections to P-A, B-T or P-A, P-B, A-T, B-T.
- Negative spool position open connections to P-A, B-T or P-A, P-B, A-T, B-T.

B-T orifice spool travel vector — Vector of spool opening distances relative to fully closed position
`[0, .00125, .0025, .00375, .005] m` (default) | 1-by-n vector

Dependencies

To enable this parameter, set Area characteristics to Different for each flow path, Opening characteristic to Tabulated, and one of the following parameters:

Positive spool position open connections to P-A, B-T or P-A, P-B, A-T, B-T.
Negative spool position open connections to P-A, B-T or P-A, P-B, A-T, B-T.

B-T maximum orifice area — Maximum orifice opening area
`1e-4 m^2` (default) | positive scalar

Largest open area of the B-T orifice during the operation of the valve.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Orifice area
Opening characteristic to Linear
One of the following parameters:
- Positive spool position open connections to P-A, B-T or P-A, P-B, A-T, B-T.
- Negative spool position open connections to P-A, B-T or P-A, P-B, A-T, B-T.

B-T orifice area vector — Vector of valve opening areas
`[1e-10, 1e-05, 4e-05, 6e-05, .0001] m^2` (default) | 1-by-n vector

Vector of opening areas for the tabular parameterization of the valve area. The vector elements must correspond one-to-one with the elements in the B-T orifice spool travel vector parameter. The elements must be greater than 0 and listed in ascending order.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Orifice area
Opening characteristic to Tabulated
One of the following parameters:
- Positive spool position open connections to P-A, B-T or P-A, P-B, A-T, B-T.
- Negative spool position open connections to P-A, B-T or P-A, P-B, A-T, B-T.

B-T constant orifice area — Cross-sectional area for constant orifice
`1e-4 m^2` (default) | positive scalar

Orifice area when the positive and negative spool positions include the same orifice.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Orifice area
One of the following settings in each parameter:
- Positive spool position open connections to P-A, B-T or P-A, P-B, A-T, B-T.
- Negative spool position open connections to P-A, B-T or P-A, P-B, A-T, B-T.

Note:

This parameter is enabled only when the B-T orifice settings appear in all both spool position parameters: Positive spool position open connections and Negative spool position open connections.

B-T orifice xT pressure differential ratio factor at choked flow — Ratio of pressure differentials
`0.7` (default) | positive scalar

Ratio between the inlet pressure, p_in, and the outlet pressure, p_out, defined as $(p_{i n} - p_{o u t}) / p_{i n}$ where choking first occurs for the B-T orifice.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Kv flow coefficient or Cv flow coefficient
At least one of the following parameters:
- Positive spool position open connections to P-A, B-T or P-A, P-B, A-T, B-T.
- Negative spool position open connections to P-A, B-T or P-A, P-B, A-T, B-T.

B-T constant orifice sonic conductance — Sonic conductance for constant orifice
`12` `l/(bar*s)` (default) | positive scalar

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Sonic conductance
One of the following settings in each parameter:
- Positive spool position open connections to P-A, B-T or P-A, P-B, A-T, B-T.
- Negative spool position open connections to P-A, B-T or P-A, P-B, A-T, B-T.

Note:

This parameter is enabled only when the B-T orifice settings appear in both spool position parameters: Positive spool position open connections and Negative spool position open connections.

B-T constant orifice critical pressure ratio — Ratio of downstream and upstream pressures at which the flow first chokes for constant orifice
`0.3` (default) | positive scalar

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Sonic conductance
One of the following settings in each parameter:
- Positive spool position open connections to P-A, B-T or P-A, P-B, A-T, B-T.
- Negative spool position open connections to P-A, B-T or P-A, P-B, A-T, B-T.

Note:

This parameter is enabled only when the B-T orifice settings appear in both spool position parameters: Positive spool position open connections and Negative spool position open connections.

B-T orifice maximum sonic conductance — Sonic conductance corresponding to maximally open orifice
`12` `l/(bar*s)` (default) | positive scalar

Value of the sonic conductance when the B-T orifice is fully open and the area available for flow is at a maximum.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Sonic conductance
Opening characteristic to Linear
One of the following parameters:
- Positive spool position open connections to P-A, B-T or P-A, P-B, A-T, B-T.
- Negative spool position open connections to P-A, B-T or P-A, P-B, A-T, B-T.

B-T orifice critical pressure ratio — Ratio of downstream and upstream pressures at which the flow first chokes
`0.3` (default) | positive scalar

Pressure ratio at which flow first begins to choke and the flow velocity reaches its maximum, given by the local speed of sound. The pressure ratio is the outlet pressure divided by inlet pressure.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Sonic conductance
Opening characteristic to Linear
One of the following parameters:
- Positive spool position open connections to P-A, B-T or P-A, P-B, A-T, B-T.
- Negative spool position open connections to P-A, B-T or P-A, P-B, A-T, B-T.

B-T orifice sonic conductance vector — Sonic conductances corresponding to values in spool travel vector
`[1e-05, 2.4, 4.8, 7.2, 9.6, 12]` `l/(bar*s)` (default) | 1-by-n vector

Vector of sonic conductances inside the resistive element. Each conductance corresponds to a value in the B-T orifice spool travel vector parameter. The size of the vector must be the same as the B-T orifice spool travel vector parameter.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Sonic conductance
Opening characteristic to Tabulated
One of the following parameters:
- Positive spool position open connections to P-A, B-T or P-A, P-B, A-T, B-T.
- Negative spool position open connections to P-A, B-T or P-A, P-B, A-T, B-T.

B-T orifice critical pressure ratio vector — Critical pressure ratios corresponding to values in spool travel vector
`0.3 * ones(1, 6)` (default) | 1-by-n vector

Vector of critical pressure ratios at which the flow first chokes, with each critical pressure ratio corresponding to a value in the B-T orifice spool travel vector parameter. The critical pressure ratio is the fraction of downstream-to-upstream pressures at which the flow velocity reaches the local speed of sound. The size of the vector must be the same as the B-T orifice spool travel vector parameter.

Dependencies

To enable this parameter, set:

Area characteristics to Different for each flow path
Orifice parameterization to Sonic conductance
Opening characteristic to Tabulated
One of the following parameters:
- Positive spool position open connections to P-A, B-T or P-A, P-B, A-T, B-T.
- Negative spool position open connections to P-A, B-T or P-A, P-B, A-T, B-T.

B-T orifice subsonic index — Exponent used to characterize mass flow in subsonic flow regime
`0.5` (default) | positive scalar

Empirical value used to more accurately calculate the mass flow rate in the subsonic flow regime.

Dependencies

To enable this parameter, set Area characteristics to Different for each flow path, Orifice parameterization to Sonic conductance, and at least one of the following parameters:

Positive spool position open connections to P-A, B-T or P-A, P-B, A-T, B-T.
Negative spool position open connections to P-A, B-T or P-A, P-B, A-T, B-T.

B-T orifice ISO reference temperature — ISO 8778 reference temperature
`293.15` `K` (default) | scalar

Temperature at standard reference atmosphere, defined as 293.15 K in ISO 8778.

You only need to adjust the ISO reference parameter values if you are using sonic conductance values that are obtained at difference reference values.

Dependencies

To enable this parameter, set Area characteristics to Different for each flow path, Orifice parameterization to Sonic conductance, and at least one of the following parameters:

Positive spool position open connections to P-A, B-T or P-A, P-B, A-T, B-T.
Negative spool position open connections to P-A, B-T or P-A, P-B, A-T, B-T.

B-T orifice ISO reference density — ISO 8778 reference density
`1.185 kg/m^3` (default) | positive scalar

Density at standard reference atmosphere, defined as 1.185 kg/m3 in ISO 8778.

You only need to adjust the ISO reference parameter values if you are using sonic conductance values that are obtained at difference reference values.

Dependencies

To enable this parameter, set Area characteristics to Different for each flow path, Orifice parameterization to Sonic conductance, and at least one of the following parameters:

Positive spool position open connections to P-A, B-T or P-A, P-B, A-T, B-T.
Negative spool position open connections to P-A, B-T or P-A, P-B, A-T, B-T.

References

[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.

Extended Capabilities

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C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2025a

4-Way 2-Position Directional Valve (MA)

Description

Spool Displacement and Valve Configuration

Valve Orifice Parameterizations

Visualize Orifice Openings

Assumptions and Limitations

Ports

Conserving

A — Entry or exit port moist air

B — Entry or exit port moist air

P — Entry or exit port moist air

T — Entry or exit port moist air

Input

S — Spool displacement, m physical signal

Parameters

Valve Configuration

Positive spool position open connections — Flow paths open when the spool is in positive position All closed (default) | P-A, B-T | P-A, P-B | P-B, A-T | P-A | P-B | P-A, P-B, A-T, B-T

Negative spool position open connections — Flow paths open when spool moves in negative direction All closed (default) | P-A, B-T | P-A, P-B | P-B, A-T | P-A | P-B | P-A, P-B, A-T, B-T

Model Parameterization

Area characteristics — Flow equations for orifices Identical for all flow paths (default) | Different for each flow path

Orifice parameterization — Variable or constant orifice parameterization Cv flow coefficient (default) | Kv flow coefficient | Sonic conductance | Orifice area

Spool travel between closed and open orifice — Maximum spool stroke 0.005 m (default) | positive scalar

Dependencies

Opening characteristic — Method to convert control signal to measure of flow capacity Linear (default) | Tabulated

Spool travel vector — Vector of spool opening distances relative to fully closed position [0, .00125, .0025, .00375, .005] m (default) | 1-by-n vector

Dependencies

Maximum Cv flow coefficient — Cv coefficient that corresponds to maximally open component 4 (default) | positive scalar

Dependencies

Cv flow coefficient vector — Cv coefficients for values in member position vector [1e-06, .8, 1.6, 2.4, 3.2, 4] (default) | 1-by-n vector

Dependencies

Maximum Kv flow coefficient — Kv coefficient that corresponds to maximally open component 3.6 (default) | positive scalar

Dependencies

Kv flow coefficient vector — Kv coefficients for values in member position vector [1e-06, .72, 1.44, 2.16, 2.88, 3.6] (default) | 1-by-n vector

Dependencies

Maximum orifice area — Maximum orifice opening area 1e-4 m^2 (default) | positive scalar

Dependencies

Orifice area vector — Vector of valve opening areas [1e-10, 1e-05, 4e-05, 6e-05, .0001] m^2 (default) | 1-by-n vector

Dependencies

xT pressure differential ratio factor at choked flow — Ratio of pressure differentials 0.7 (default) | positive scalar

Dependencies

Discharge coefficient — Discharge coefficient 0.64 (default) | positive scalar

Dependencies

Maximum sonic conductance — Sonic conductance corresponding to maximally open component 12 l/(bar*s) (default) | positive scalar

Dependencies

Critical pressure ratio — Ratio of downstream and upstream pressures at which the flow first chokes 0.3 (default) | positive scalar

Dependencies

Subsonic index — Exponent used to characterize mass flow in subsonic flow regime 0.5 (default) | positive scalar

Dependencies

ISO reference temperature — ISO 8778 reference temperature 293.15 K (default) | scalar

Dependencies

ISO reference density — ISO 8778 reference density 1.185 kg/m^3 (default) | positive scalar

Dependencies

Sonic conductance vector — Sonic conductances corresponding to values in spool travel vector [1e-05, 2.4, 4.8, 7.2, 9.6, 12] l/(bar*s) (default) | vector of positive values

Dependencies

Critical pressure ratio vector — Critical pressure ratios corresponding to values in spool travel vector 0.3 * ones(1,6) (default) | vector of positive numbers

Dependencies

Leakage flow fraction — Ratio of flow rates 1e-6 (default) | positive scalar

Dependencies

Smoothing factor — Numerical smoothing factor 0.01 (default) | positive scalar in the range of [0,1]

Dependencies

Laminar flow pressure ratio — Laminar-turbulent transition pressure ratio 0.999 (default) | positive scalar

Cross-sectional area at ports P, T, A, and B — Area at conserving ports 0.01 m^2 (default) | positive scalar

P-A Orifice

Spool position at maximum P-A orifice area — Spool offset for fully open P-A orifice 5e-3 m (default) | positive scalar

Dependencies

P-A spool travel between closed and open orifice — Maximum spool stroke 0.005 m (default) | positive scalar

Dependencies

P-A constant orifice Cv flow coefficient — Flow coefficient 4 (default) | positive scalar

Dependencies

P-A orifice maximum Cv flow coefficient — Cv coefficient that corresponds to maximally open component 4 (default) | positive scalar

Dependencies

P-A orifice Cv flow coefficient vector — Cv coefficients for values in member position vector [1e-06, .8, 1.6, 2.4, 3.2, 4] (default) | 1-by-n vector

Dependencies

P-A constant orifice Kv flow coefficient — Flow coefficient 3.6 (default) | positive scalar

Dependencies

P-A orifice maximum Kv flow coefficient — Kv coefficient that corresponds to maximally open component 3.6 (default) | positive scalar

Dependencies

P-A orifice Kv flow coefficient vector — Kv coefficients for values in member position vector [1e-06, .72, 1.44, 2.16, 2.88, 3.6] (default) | 1-by-n vector

Dependencies

P-A orifice spool travel vector — Vector of spool opening distances relative to fully closed position [0, .00125, .0025, .00375, .005] m (default) | 1-by-n vector

A — Entry or exit port
moist air

B — Entry or exit port
moist air

P — Entry or exit port
moist air

T — Entry or exit port
moist air

S — Spool displacement, m
physical signal

Positive spool position open connections — Flow paths open when the spool is in positive position
`All closed` (default) | `P-A, B-T` | `P-A, P-B` | `P-B, A-T` | `P-A` | `P-B` | `P-A, P-B, A-T, B-T`

Negative spool position open connections — Flow paths open when spool moves in negative direction
`All closed` (default) | `P-A, B-T` | `P-A, P-B` | `P-B, A-T` | `P-A` | `P-B` | `P-A, P-B, A-T, B-T`

Area characteristics — Flow equations for orifices
`Identical for all flow paths` (default) | `Different for each flow path`

Orifice parameterization — Variable or constant orifice parameterization
`Cv flow coefficient` (default) | `Kv flow coefficient` | `Sonic conductance` | `Orifice area`

Spool travel between closed and open orifice — Maximum spool stroke
`0.005 m` (default) | positive scalar

Opening characteristic — Method to convert control signal to measure of flow capacity
`Linear` (default) | `Tabulated`

Spool travel vector — Vector of spool opening distances relative to fully closed position
`[0, .00125, .0025, .00375, .005] m` (default) | 1-by-n vector

Maximum Cv flow coefficient — C_v coefficient that corresponds to maximally open component
`4` (default) | positive scalar

Cv flow coefficient vector — C_v coefficients for values in member position vector
`[1e-06, .8, 1.6, 2.4, 3.2, 4]` (default) | 1-by-n vector

Maximum Kv flow coefficient — K_v coefficient that corresponds to maximally open component
`3.6` (default) | positive scalar

Kv flow coefficient vector — K_v coefficients for values in member position vector
`[1e-06, .72, 1.44, 2.16, 2.88, 3.6]` (default) | 1-by-n vector

Maximum orifice area — Maximum orifice opening area
`1e-4 m^2` (default) | positive scalar

Orifice area vector — Vector of valve opening areas
`[1e-10, 1e-05, 4e-05, 6e-05, .0001] m^2` (default) | 1-by-n vector

xT pressure differential ratio factor at choked flow — Ratio of pressure differentials
`0.7` (default) | positive scalar

Discharge coefficient — Discharge coefficient
`0.64` (default) | positive scalar

Maximum sonic conductance — Sonic conductance corresponding to maximally open component
`12 l/(bar*s)` (default) | positive scalar

Critical pressure ratio — Ratio of downstream and upstream pressures at which the flow first chokes
`0.3` (default) | positive scalar

Subsonic index — Exponent used to characterize mass flow in subsonic flow regime
`0.5` (default) | positive scalar

ISO reference temperature — ISO 8778 reference temperature
`293.15 K` (default) | scalar

ISO reference density — ISO 8778 reference density
`1.185 kg/m^3` (default) | positive scalar

Sonic conductance vector — Sonic conductances corresponding to values in spool travel vector
`[1e-05, 2.4, 4.8, 7.2, 9.6, 12] l/(bar*s)` (default) | vector of positive values

Critical pressure ratio vector — Critical pressure ratios corresponding to values in spool travel vector
`0.3 * ones(1,6)` (default) | vector of positive numbers

Leakage flow fraction — Ratio of flow rates
`1e-6` (default) | positive scalar

Smoothing factor — Numerical smoothing factor
`0.01` (default) | positive scalar in the range of [0,1]

Laminar flow pressure ratio — Laminar-turbulent transition pressure ratio
`0.999` (default) | positive scalar

Cross-sectional area at ports P, T, A, and B — Area at conserving ports
`0.01 m^2` (default) | positive scalar

Spool position at maximum P-A orifice area — Spool offset for fully open P-A orifice
`5e-3 m` (default) | positive scalar

P-A spool travel between closed and open orifice — Maximum spool stroke
`0.005 m` (default) | positive scalar

P-A constant orifice Cv flow coefficient — Flow coefficient
`4` (default) | positive scalar

P-A orifice maximum Cv flow coefficient — C_v coefficient that corresponds to maximally open component
`4` (default) | positive scalar

P-A orifice Cv flow coefficient vector — C_v coefficients for values in member position vector
`[1e-06, .8, 1.6, 2.4, 3.2, 4]` (default) | 1-by-n vector

P-A constant orifice Kv flow coefficient — Flow coefficient
`3.6` (default) | positive scalar

P-A orifice maximum Kv flow coefficient — K_v coefficient that corresponds to maximally open component
`3.6` (default) | positive scalar

P-A orifice Kv flow coefficient vector — K_v coefficients for values in member position vector
`[1e-06, .72, 1.44, 2.16, 2.88, 3.6]` (default) | 1-by-n vector

P-A orifice spool travel vector — Vector of spool opening distances relative to fully closed position
`[0, .00125, .0025, .00375, .005] m` (default) | 1-by-n vector

P-A maximum orifice area — Maximum orifice opening area
`1e-4 m^2` (default) | positive scalar

P-A orifice area vector — Vector of valve opening areas
`[1e-10, 1e-05, 4e-05, 6e-05, .0001] m^2` (default) | 1-by-n vector

P-A constant orifice area — Cross-sectional area for constant orifice
`1e-4 m^2` (default) | positive scalar

P-A orifice xT pressure differential ratio factor at choked flow — Ratio of pressure differentials
`0.7` (default) | positive scalar

P-A constant orifice sonic conductance — Sonic conductance for constant orifice
`12` `l/(bar*s)` (default) | positive scalar

P-A constant orifice critical pressure ratio — Ratio of downstream and upstream pressures at which the flow first chokes for constant orifice
`0.3` (default) | positive scalar

P-A orifice maximum sonic conductance — Sonic conductance corresponding to maximally open orifice
`12` `l/(bar*s)` (default) | positive scalar

P-A orifice critical pressure ratio — Ratio of downstream and upstream pressures at which the flow first chokes
`0.3` (default) | positive scalar

P-A orifice sonic conductance vector — Sonic conductances corresponding to values in spool travel vector
`[1e-05, 2.4, 4.8, 7.2, 9.6, 12]` `l/(bar*s)` (default) | 1-by-n vector

P-A orifice critical pressure ratio vector — Critical pressure ratios corresponding to values in spool travel vector
`0.3 * ones(1, 6)` (default) | 1-by-n vector

P-A orifice subsonic index — Exponent used to characterize mass flow in subsonic flow regime
`0.5` (default) | positive scalar

P-A orifice ISO reference temperature — ISO 8778 reference temperature
`293.15` `K` (default) | scalar

P-A orifice ISO reference density — ISO 8778 reference density
`1.185 kg/m^3` (default) | positive scalar

Spool position at maximum P-B orifice area — Spool offset for fully open P-B orifice
`5e-3 m` (default) | positive scalar

P-B spool travel between closed and open orifice — Maximum spool stroke
`0.005 m` (default) | positive scalar

P-B constant orifice Cv flow coefficient — Flow coefficient
`4` (default) | positive scalar

P-B orifice maximum Cv flow coefficient — C_v coefficient that corresponds to maximally open component
`4` (default) | positive scalar

P-B orifice Cv flow coefficient vector — C_v coefficients for values in member position vector
`[1e-06, .8, 1.6, 2.4, 3.2, 4]` (default) | 1-by-n vector

P-B constant orifice Kv flow coefficient — Flow coefficient
`3.6` (default) | positive scalar

P-B orifice maximum Kv flow coefficient — K_v coefficient that corresponds to maximally open component
`3.6` (default) | positive scalar

P-B orifice Kv flow coefficient vector — K_v coefficients for values in member position vector
`[1e-06, .72, 1.44, 2.16, 2.88, 3.6]` (default) | 1-by-n vector

P-B orifice spool travel vector — Vector of spool opening distances relative to fully closed position
`[0, .00125, .0025, .00375, .005] m` (default) | 1-by-n vector

P-B maximum orifice area — Maximum orifice opening area
`1e-4 m^2` (default) | positive scalar

P-B orifice area vector — Vector of valve opening areas
`[1e-10, 1e-05, 4e-05, 6e-05, .0001] m^2` (default) | 1-by-n vector

P-B constant orifice area — Cross-sectional area for constant orifice
`1e-4 m^2` (default) | positive scalar

P-B orifice xT pressure differential ratio factor at choked flow — Ratio of pressure differentials
`0.7` (default) | positive scalar

P-B constant orifice sonic conductance — Sonic conductance for constant orifice
`12` `l/(bar*s)` (default) | positive scalar

P-B constant orifice critical pressure ratio — Ratio of downstream and upstream pressures at which the flow first chokes for constant orifice
`0.3` (default) | positive scalar

P-B orifice maximum sonic conductance — Sonic conductance corresponding to maximally open orifice
`12` `l/(bar*s)` (default) | positive scalar

P-B orifice critical pressure ratio — Ratio of downstream and upstream pressures at which the flow first chokes
`0.3` (default) | positive scalar

P-B orifice sonic conductance vector — Sonic conductances corresponding to values in spool travel vector
`[1e-05, 2.4, 4.8, 7.2, 9.6, 12]` `l/(bar*s)` (default) | 1-by-n vector

P-B orifice critical pressure ratio vector — Critical pressure ratios corresponding to values in spool travel vector
`0.3 * ones(1, 6)` (default) | 1-by-n vector

P-B orifice subsonic index — Exponent used to characterize mass flow in subsonic flow regime
`0.5` (default) | positive scalar

P-B orifice ISO reference temperature — ISO 8778 reference temperature
`293.15` `K` (default) | scalar