Engee documentation

4-Way 2-Position Directional Valve (IL)

A four-line two-position distributor in an isothermal fluid network.

blockType: EngeeFluids.IsothermalLiquid.Valves.DirectionalControl.FourWayTwoPosition

4 way 2 position directional valve il

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/Physical Modeling/Fluids/Isothermal Liquid/Valves & Orifices/Directional Control Valves/4-Way 2-Position Directional Valve (IL)

Description

Block 4-Way 2-Position Directional Valve (IL) It is a spool distributor with four plug-in lines, usually located between a hydraulic cylinder, a pump and a reservoir in an isothermal fluid network. The operation of the distributor is controlled by a single spool, which moves according to the signal on port S. The distributor has two positions, then they are indicated as positive and negative. You can set the basic configuration of the distributor by specifying the channels that open when the spool moves in the positive and negative directions in the parameters Positive spool position open connections and Negative spool position open connections, respectively.

You can set the flow characteristics of the distributor channels in the Orifice parameterization parameter as a linear relationship or a tabular function provided by the user, which can be applied to one or all distributor channels.

An example of distributor configuration is shown in the figure.

4 way 2 position directional valve il 1 en

In the configuration shown below, the distributor is connected to a tank, a hydraulic drive and a pump, and the Negative spool position open connections parameter is set to P-A, B-T. When the signal on port S moves the spool to the negative position (to the left of the neutral position), the channels between ports P and A and between ports B and T are open. The channels between ports P and B and ports A and T are closed.

4 way 2 position directional valve il 2 1

In the configuration below, the Positive spool position open connections parameter is set to P-B, A-T. When the signal on port S moves the spool to the positive position (to the right of the neutral position), the channels between ports P and B and between ports A and T are open, and the channels between ports P and A and between ports B and T are closed.

4 way 2 position directional valve il 2 2

Spool movement and distributor configuration

The stroke of the spool is the amount of movement of the spool between the fully open and fully closed channel. You can use the Orifice parameterization and Area characteristics parameters to set the channel characteristics, as shown in the table.

Orifice Parameterization Identical for All Flow Paths Different for Each Flow Path

Linear - Area vs. spool travel

The stroke of the spool is equal to the value of the parameter Spool travel between closed and open orifice

The stroke of the spool is equal to the value of the parameter Spool travel between closed and open orifice for each channel

Tabulated data - Area vs. spool travel

The stroke of the spool is equal to the difference between the first and last element of the parameter Spool travel vector

The stroke of the spool is equal to the difference between the first and last element of the Spool travel vector parameter for each channel

Tabulated data - Volumetric flow rate vs. spool travel and pressure drop

The stroke of the spool is equal to the difference between the first and last element of the parameter Spool travel vector, ds

The stroke of the spool is equal to the difference between the first and last element of the parameter Spool travel vector, ds for each channel

The table below shows the methods for determining the relative position of the spool for the channel, depending on the choice of values for the parameters Positive spool position open connection and Negative spool position open connection.

The position of the spool when the channel is open Relative position of the spool

The channel is always closed: the channel is not selected in the parameters Positive spool position open connection or Negative spool position open connection

Not used

The channel is always open: the channel is selected in the parameters Positive spool position open connection and Negative spool position open connection

Not used

Negative position: the channel is selected only in the Negative spool position open connection parameter.

− S + spool stroke

Positive position: the channel is selected only in the parameter Positive spool position open connection

S − + spool stroke

Where — this is the position of the spool at the maximum cross-sectional area (the value of the parameter Spool position at maximum orifice area), set for each channel. The cross-sectional area is equal to the leakage area when the value negative, and is equal to the maximum when the channel is fully open. When the channel is fully open, the relative position is equal to the stroke of the spool, so if the value exceeds the stroke of the spool, this does not lead to a further increase in the cross-sectional area of the channel.

The table below shows the possible block configurations. 4-Way 2-Position Directional Valve (IL).

Configuration Parameter values

All four channels are closed in the intermediate position (neutral position).

4 way 2 position directional valve il 1

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 stroke of the spool

Spool position at maximum A-T orifice area < −A-T stroke of the spool

Spool position at maximum B-T orifice area > B-T spool stroke

All four channels are open in the intermediate position (neutral position).

4 way 2 position directional valve il 1

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 stroke of the spool

Spool position at maximum A-T orifice area > −A-T stroke of the spool

Spool position at maximum B-T orifice area < B-T spool stroke

A-T and B-T are closed in the intermediate position (neutral position).

4 way 2 position directional valve il 1

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 stroke of the spool

Spool position at maximum A-T orifice area < −A-T stroke of the spool

Spool position at maximum B-T orifice area > B-T spool stroke

P-A and P-B are closed in the intermediate position (neutral position).

4 way 2 position directional valve il 2

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 stroke of the spool

P-B and B-T are closed in the intermediate position (neutral position).

4 way 2 position directional valve il 3

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 stroke of the spool

P-A and A-T are closed in the intermediate position (neutral position).

4 way 2 position directional valve il 3

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 stroke of the spool

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 stroke of the spool

P-A, P-B and B-T are open in the intermediate position (neutral position).

4 way 2 position directional valve il 4

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 stroke of the spool

P-A, A-T and B-T are open in the intermediate position (neutral position).

4 way 2 position directional valve il 5

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 stroke of the spool

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 in the intermediate position (neutral position). A-T is always closed.

4 way 2 position directional valve il 4

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 stroke of the spool

All channels are closed in the intermediate position (neutral position).

4 way 2 position directional valve il 5

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 stroke of the spool

Spool position at maximum P-B orifice area > P-B spool stroke

Spool position at maximum A-T orifice area > A-T spool stroke

In the intermediate position (neutral position) A-T is open, P-A is closed.

4 way 2 position directional valve il 6

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 stroke of the spool

In the intermediate position (neutral position) B-T is open, P-B is closed.

4 way 2 position directional valve il 5

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 stroke of the spool

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

The P-A is closed in the intermediate position (neutral position).

4 way 2 position directional valve il 7

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 stroke of the spool

Spool position at maximum B-T orifice area > B-T spool stroke

The P-B is closed in the intermediate position (neutral position).

4 way 2 position directional valve il 8

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 stroke of the spool

Parameterization of distributor channels

The Orifice parameterization parameter specifies a method for calculating the cross-sectional area. The calculation is performed either by channel parameters or by tabular datasets that are specified in the parameters of the Model Parameterization section. The block uses the same data for all channels if the Area characteristics parameter is set to Identical for all flow paths, and if the value is set to Different for all flow paths, then individual values are set for each channel.

Parameterization of distributor channels Orifice parameterization can be linear and tabular.

linear parameterization

If the value is selected for parameterization Orifice parameterization Linear — Area vs. spool travel, then the area of the passage section of the channel linearly depends on the stroke of the spool and the value received at port S:

,

where

  • — the maximum area of the passage section of the channel (the value of the parameter Maximum orifice area);

  • — leakage area (value of the Leakage area parameter);

  • — spool travel between closed and open channel states (value of the parameter Spool travel between closed and open orifice);

  • — relative position of the spool, from 0 to .

equates to When the value is negative, and equates to when the channel is fully open. When the channel is fully open, the relative position is equal to the stroke of the spool, so the value exceeding the stroke of the spool does not lead to an increase in the cross-sectional area.

Note the linear growth from before in the picture:

Static

When the channel is in an almost open or almost closed position with linear parameterization, it is possible to maintain the numerical stability of the simulation by adjusting the smoothing factor, the value of the Smoothing factor parameter. If the value of the Smoothing factor parameter is not zero, a smooth change in the cross-sectional area between and .

table parameterization

If the value is selected for parameterization Orifice parameterization Tabulated data — Area vs. spool travel, then it is necessary to set the vectors of the relationship between the area of the passage section and the relative position of the spool. Interpolation is used to determine the area of the hole between the specified data points. and — the first and last elements of the vector of the cross-sectional area Opening area vector, respectively.

Static

If the value is selected for the parameterization of Orifice parameterization Tabulated data — Volumetric flow rate vs. spool travel and pressure drop, then it is necessary to set the vectors of the relative position of the spool and the pressure drop. The volumetric flow rate is calculated based on the relationship between the pressure drop and the relative position of the spool. Interpolation is used to determine the flow rate between the specified data points. Mass flow is the product of volume flow and density.

Static

Ports

Conserving

# P — isothermal liquid port
isothermal liquid

Details

Working fluid supply.

Program usage name

port_p

# T — isothermal liquid port
isothermal liquid

Details

Working fluid outlet.

Program usage name

port_t

# A — isothermal liquid port
isothermal liquid

Details

Working line.

Program usage name

port_a

# B — isothermal liquid port
isothermal liquid

Details

Working line.

Program usage name

port_b

Input

# S — distributor spool position
scalar

Details

Position of the distributor spool valve in m. Channels set open in the positive position of the spool valve are opened at positive travel. Channels set open in the negative position of the spool valve open at negative travel.

Data types

Float64.
Complex numbers support

No

Parameters

Valve Configuration

# Positive spool position open connections — channels opened in a positive position
All closed | P-A and B-T | P-A and P-B | P-B and A-T | A-T only | B-T only | P-A only | P-B only | P-A, P-B, A-T, and B-T

Details

Channels open in positive position. This parameters sets the distributor configuration and determines the relative position of the spool valve according to the signal received at port S.

Values

All closed | P-A and B-T | P-A and P-B | P-B and A-T | A-T only | B-T only | P-A only | P-B only | P-A, P-B, A-T, and B-T
Default value

P-A and B-T
Program usage name

positive_position_open_orifices
Evaluatable

No

# Negative spool position open connections — channels opened in a negative position
All closed | P-A and B-T | P-A and P-B | P-B and A-T | A-T only | B-T only | P-A only | P-B only | P-A, P-B, A-T, and B-T

Details

Channels open in negative position. This parameters sets the distributor configuration and determines the relative position of the spool valve according to the signal received at port S.

Values

All closed | P-A and B-T | P-A and P-B | P-B and A-T | A-T only | B-T only | P-A only | P-B only | P-A, P-B, A-T, and B-T
Default value

P-B and A-T
Program usage name

negative_position_open_orifices
Evaluatable

No

Model Parameterization

# Area characteristics — channel characterisation method
Identical for all flow paths | Different for each flow path

Details

Sets identical or individual flow characteristics for the channel cross-section:

  • Identical for all flow paths - identical characteristics for all flow paths of the distributor.

  • Different for each flow path - individual characteristics are set for each channel.

In both cases ports A, B, P and T have identical cross-sectional areas, flow coefficients and Reynolds numbers if the Orifice parameterization parameters are set to Linear - Area vs. spool travel or Tabulated data - Area vs. spool travel.

Values

Identical for all flow paths | Different for each flow path
Default value

Identical for all flow paths
Program usage name

area_characteristics
Evaluatable

No

# Orifice parameterization — channel area calculation method
Linear - Area vs. spool travel | Tabulated data - Area vs. spool travel | Tabulated data - Volumetric flow rate vs. spool travel and pressure drop

Details

A method for calculating the area of a channel cross-sectional area in modelling.

At tabular parameterization it is possible to specify a non-linear profile of the flow characteristic of the channels in the form of dependence of the flow area on the spool position or dependence of the volume flow rate on the pressure drop and spool position.

Values

Linear - Area vs. spool travel | Tabulated data - Area vs. spool travel | Tabulated data - Volumetric flow rate vs. spool travel and pressure drop
Default value

Linear - Area vs. spool travel
Program usage name

orifice_parameterization
Evaluatable

No

# Spool travel between closed and open orifice — maximum spool stroke
m | um | mm | cm | km | in | ft | yd | mi | nmi

Details

Spool stroke between closed and open channel states.

Dependencies

To use this parameter, set the Area characteristics parameter to `Identical for all flow paths' and the Orifice parameterization parameter to `Linear - Area vs. spool travel'.

Units

m | um | mm | cm | km | in | ft | yd | mi | nmi
Default value

0.005 m
Program usage name

max_spool_travel
Evaluatable

Yes

# Maximum orifice area — maximum cross-sectional area of the channel
m^2 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac

Details

Maximum cross-sectional area of the channel.

Dependencies

To use this parameter, set the Area characteristics parameter to `Identical for all flow paths' and the Orifice parameterization parameter to `Linear - Area vs. spool travel'.

Units

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

1e-4 m^2
Program usage name

max_area
Evaluatable

Yes

# Spool travel vector — vector of values of the spool relative position
m | um | mm | cm | km | in | ft | yd | mi | nmi

Details

Vector of values of the spool relative position. The dimensionality of the vector corresponds to the Orifice area vector. The values are listed in ascending order and the first element must be equal to 0. Linear interpolation is used between the data points in the table.

Dependencies

To use this parameter, set the Area characteristics parameter to `Identical for all flow paths' and the Orifice parameterization parameter to `Tabulated data - Area vs. spool travel'.

Units

m | um | mm | cm | km | in | ft | yd | mi | nmi
Default value

[0.0, 1.25e-3, 2.5e-3, 3.75e-3, 5e-3] m
Program usage name

spool_travel_vector
Evaluatable

Yes

# Orifice area vector — vector of values of the channel cross-sectional area
m^2 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac

Details

Vector of channel cross-sectional area values for tabular parameterization. The dimension of the vector corresponds to the Spool travel vector. The values are listed in ascending order. The first element is the leakage area, the last element is the maximum channel cross-sectional area. Linear interpolation is used between data points.

Dependencies

To use this parameter, set the Area characteristics parameter to `Identical for all flow paths' and the Orifice parameterization parameter to `Tabulated data - Area vs. spool travel'.

Units

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

[1e-10, 1e-5, 4e-5, 6e-5, 1e-4] m^2
Program usage name

valve_area_vector
Evaluatable

Yes

# Spool travel vector, ds — vector of values of the spool relative position
m | um | mm | cm | km | in | ft | yd | mi | nmi

Details

Vector of spool position values for the table parameterization of the volumetric flow rate table. The dimension of the spool position vector corresponds to the differential pressure vector Pressure drop vector, dp and the volumetric flow rate table Volumetric flow rate table, q(ds,dp). The values are listed in ascending order and the first element must be 0. Linear interpolation is used to calculate intermediate values.

Dependencies

To use this parameter, set the Area characteristics parameter to `Identical for all flow paths' and the Orifice parameterization parameter to `Tabulated data - Volumetric flow rate vs. spool travel and pressure drop'.

Units

m | um | mm | cm | km | in | ft | yd | mi | nmi
Default value

[0.0, 1.25e-3, 2.5e-3, 3.75e-3, 5e-3] m
Program usage name

spool_travel_vector_2D
Evaluatable

Yes

# Pressure drop vector, dp — vector of differential pressure values
Pa | uPa | hPa | kPa | MPa | GPa | kgf/m^2 | kgf/cm^2 | kgf/mm^2 | mbar | bar | kbar | atm | ksi | psi | mmHg | inHg

Details

Vector of differential pressure values for tabular parameterization by volumetric flow rate. The dimension of the differential pressure vector corresponds to the spool position vector Spool travel vector, ds and the volumetric flow rate table Volumetric flow rate table, q(ds,dp). The values are listed in ascending order. Linear interpolation is used to calculate intermediate values.

Dependencies

To use this parameter, set the Area characteristics parameter to `Identical for all flow paths' and the Orifice parameterization parameter to `Tabulated data - Volumetric flow rate vs. spool travel and pressure drop'.

Units

Pa | uPa | hPa | kPa | MPa | GPa | kgf/m^2 | kgf/cm^2 | kgf/mm^2 | mbar | bar | kbar | atm | ksi | psi | mmHg | inHg
Default value

[-0.1, 0.3, 0.5, 0.7] MPa
Program usage name

delta_p_vector_2D
Evaluatable

Yes

# Volumetric flow rate table, q(ds,dp) — table of volumetric flow rates
m^3/s | mm^3/s | cm^3/s | m^3/hr | m^3/min | l/hr | l/min | l/s | gal/hr | gal/min | gal/s | ft^3/hr | ft^3/min | ft^3/s

Details

Matrix to of volume flow rates corresponding to differential pressure and spool position values. to - dimensions of the corresponding vectors:

  • - number of elements in the spool position vector Spool travel vector, ds.

  • - number of elements in the pressure drop vector Pressure drop vector, dp.

Dependencies

To use this parameter, set the Area characteristics parameter to `Identical for all flow paths' and the Orifice parameterization parameter to `Tabulated data - Volumetric flow rate vs. spool travel and pressure drop'.

Units

m^3/s | mm^3/s | cm^3/s | m^3/hr | m^3/min | l/hr | l/min | l/s | gal/hr | gal/min | gal/s | ft^3/hr | ft^3/min | ft^3/s
Default value

[-1e-8 2.2e-8 2.8e-8 3.4e-8; -9e-6 1.5e-4 2e-4 2.4e-4; -3.6e-4 6.3e-4 8.1e-4 9.6e-4; -5.4e-4 9.4e-4 1.2e-3 1.4e-3; -9.1e-4 1.6e-3 2.0e-3 2.4e-3] m^3/s
Program usage name

Vdot_matrix_2D
Evaluatable

Yes

# Constant orifice area — cross-sectional area for permanently open channels
m^2 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac

Details

Cross-sectional area of channels defined open in both positions.

Dependencies

To use this parameter, set for parameters:

  • Area characteristics to Identical for all flow paths.

  • Orifice parameterization to Linear - area vs. spool travel or Tabulated data - Area vs. spool travel.

  • Positive spool position open connections and Negative spool position open connections - at least one channel is set in both positions.

Units

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

1e-4 m^2
Program usage name

area_fixed
Evaluatable

Yes

# Constant orifice pressure drop vector — vector of differential pressure values for permanently open channels
Pa | uPa | hPa | kPa | MPa | GPa | kgf/m^2 | kgf/cm^2 | kgf/mm^2 | mbar | bar | kbar | atm | ksi | psi | mmHg | inHg

Details

Vector of differential pressure values for channels defined open in both positions. The dimension of the differential pressure vector corresponds to the Constant orifice volumetric flow rate vector. The values are listed in ascending order. Linear interpolation is used to calculate intermediate values.

Dependencies

To use this parameter, set the parameters to:

  • Area characteristics to Identical for all flow paths.

  • Orifice parameterization value Tabulated data - Volumetric flow rate vs. spool travel and pressure drop.

  • Positive spool position open connections and Negative spool position open connections - at least one channel is set in both positions.

Units

Pa | uPa | hPa | kPa | MPa | GPa | kgf/m^2 | kgf/cm^2 | kgf/mm^2 | mbar | bar | kbar | atm | ksi | psi | mmHg | inHg
Default value

[-0.1, 0.3, 0.5, 0.7] MPa
Program usage name

delta_p_vector_fixed
Evaluatable

Yes

# Constant orifice volumetric flow rate vector — vector of volume flow rates for permanently open channels
m^3/s | mm^3/s | cm^3/s | m^3/hr | m^3/min | l/hr | l/min | l/s | gal/hr | gal/min | gal/s | ft^3/hr | ft^3/min | ft^3/s

Details

Vector of volume flow values for channels set open in both positions. The dimension of the pressure drop vector corresponds to the Constant orifice pressure drop vector. The values are listed in ascending order. Linear interpolation is used to calculate intermediate values.

Dependencies

To use this parameter, set the parameters to:

  • Area characteristics to Identical for all flow paths.

  • Orifice parameterization value Tabulated data - Volumetric flow rate vs. spool travel and pressure drop.

  • Positive spool position open connections and Negative spool position open connections - at least one channel is set in both positions.

Units

m^3/s | mm^3/s | cm^3/s | m^3/hr | m^3/min | l/hr | l/min | l/s | gal/hr | gal/min | gal/s | ft^3/hr | ft^3/min | ft^3/s
Default value

[-9e-4, 1.6e-3, 2.0e-3, 2.4e-3] m^3/s
Program usage name

Vdot_vector_fixed
Evaluatable

Yes

# Leakage area — leakage area through the channel in fully closed position
m^2 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac

Details

The sum of all clearances when the channel is completely closed. Any area less than this value equates to the specified leakage area. This parameter contributes to the stability of the numerical solution by maintaining flow continuity.

Dependencies

To use this parameter, set the Area characteristics parameter to `Identical for all flow paths' and the Orifice parameterization parameter to `Linear - area vs. spool travel'.

Units

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

1e-10 m^2
Program usage name

leakage_area
Evaluatable

Yes

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

Details

The cross-sectional area at ports A, B, P, and T. This area is used in calculating the mass flow rate through the distributor.

Dependencies

To use this parameter, set the Area characteristics parameter to `Identical for all flow paths' and the Orifice parameterization parameter to `Linear - area vs. spool travel' or `Tabulated data - Area vs. spool travel'.

Units

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

Inf m^2
Program usage name

port_area
Evaluatable

Yes

# Discharge coefficient — flow coefficient

Details

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

Dependencies

To use this parameter, set the Orifice parameterization parameters to `Linear - area vs. spool travel' or `Tabulated data - Area vs. spool travel'.

Default value

0.64
Program usage name

C_d
Evaluatable

Yes

# Critical Reynolds number — upper limit of Reynolds number for laminar flow

Details

Upper Reynolds number limit for laminar flow through a channel.

Dependencies

To use this parameter, set the Orifice parameterization parameters to `Linear - area vs. spool travel' or `Tabulated data - Area vs. spool travel'.

Default value

150.0
Program usage name

Re_critical
Evaluatable

Yes

# Smoothing factor — numerical smoothing factor

Details

A continuous smoothing factor that ensures smooth opening by correcting the channel characteristic in the nearly open and nearly closed positions.

Dependencies

To use this parameter, set the Orifice parameterization parameters to Linear - area vs. spool travel.

Default value

0.01
Program usage name

smoothing_factor
Evaluatable

Yes

# Pressure recovery — whether to take into account the increase in pressure when expanding the area

Details

Whether to take into account the pressure increase when the fluid flows from a region with a smaller cross-sectional area to a region with a larger cross-sectional area.

Dependencies

To use this parameter, set the Orifice parameterization parameters to `Linear - area vs. spool travel' or `Tabulated data - Area vs. spool travel'.

Default value

false (switched off)
Program usage name

pressure_recovery
Evaluatable

No

P-A Orifice

# Spool position at maximum P-A orifice area — spool position at maximum channel area between ports P and A
m | um | mm | cm | km | in | ft | yd | mi | nmi

Details

Spool position corresponding to a fully open channel between ports P and A.

Dependencies

To use this parameter, set the Positive spool position open connections or Negative spool position open connections parameters to one of the following values:

  • `P-A and B-T

  • `P-A and P-B

  • `P-A only

  • P-A, P-B, A-T, and B-T.

This parameter is enabled only if the P-A channel is not set simultaneously in both parameters Positive spool position open connections and Negative spool position open connections.

Units

m | um | mm | cm | km | in | ft | yd | mi | nmi
Default value

5e-3 m
Program usage name

spool_offset_pa
Evaluatable

Yes

# P-A spool travel between closed and open orifice — maximum spool stroke between ports P and A
m | um | mm | cm | km | in | ft | yd | mi | nmi

Details

Maximum spool stroke between ports P and A.

Dependencies

To use this parameter, set for parameters:

  • Area characteristics to Different for each flow path.

  • Orifice parameterization value Linear - Area vs. spool travel.

  • Positive spool position open connections or Negative spool position open connections one of the following values:

    • `P-A and B-T

    • `P-A and P-B

    • `P-A only

    • `P-A, P-B, A-T, and B-T'.

Units

m | um | mm | cm | km | in | ft | yd | mi | nmi
Default value

0.005 m
Program usage name

max_spool_travel_pa
Evaluatable

Yes

# P-A maximum orifice area — maximum area between ports P and A
m^2 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac

Details

The channel cross-sectional area between ports P and A in the fully open position.

Dependencies

To use this parameter, set for parameters:

  • Area characteristics to Different for each flow path.

  • Orifice parameterization value Linear - Area vs. spool travel.

  • Positive spool position open connections or Negative spool position open connections one of the following values:

    • `P-A and B-T

    • `P-A and P-B

    • `P-A only

    • `P-A, P-B, A-T, and B-T'.

Units

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

1e-4 m^2
Program usage name

max_area_pa
Evaluatable

Yes

# P-A orifice spool travel vector — vector of spool relative positions
m | um | mm | cm | km | in | ft | yd | mi | nmi

Details

Vector of spool positions. The dimensionality of the vector corresponds to the P-A orifice area vector. The values are listed in ascending order and the first element must be 0. Linear interpolation is used between the data points in the table.

Dependencies

To use this parameter, set the parameters to:

  • Area characteristics to Different for each flow path.

  • Orifice parameterization value `Tabulated data - Area vs. spool travel'.

  • Positive spool position open connections or Negative spool position open connections one of the following values:

    • `P-A and B-T

    • `P-A and P-B

    • `P-A only

    • `P-A, P-B, A-T, and B-T'.

Units

m | um | mm | cm | km | in | ft | yd | mi | nmi
Default value

[0.0, 1.25e-3, 2.5e-3, 3.75e-3, 5e-3] m
Program usage name

spool_travel_vector_pa
Evaluatable

Yes

# P-A orifice area vector — vector of values of the channel cross-sectional area
m^2 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac

Details

Vector of channel cross-sectional area values for the tabular parameterization of the valve area. The dimension of the vector corresponds to the P-A orifice spool travel vector. The values are listed in ascending order and must be greater than 0.

Dependencies

To use this parameter, set the parameters to:

  • Area characteristics to Different for each flow path.

  • Orifice parameterization value `Tabulated data - Area vs. spool travel'.

  • Positive spool position open connections or Negative spool position open connections one of the following values:

    • `P-A and B-T

    • `P-A and P-B

    • `P-A only

    • `P-A, P-B, A-T, and B-T'.

Units

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

[1e-10, 1e-5, 4e-5, 6e-5, 1e-4] m^2
Program usage name

valve_area_vector_pa
Evaluatable

Yes

# P-A orifice spool travel vector, ds — vector of values of the spool relative position
m | um | mm | cm | km | in | ft | yd | mi | nmi

Details

Vector of spool positions for tabular parameterization by volume flow. The dimension of the spool position vector corresponds to the pressure drop vector P-A orifice pressure drop vector,dp and the volumetric flow rate table P-A orifice volumetric flow rate table, q(s,dp). The values are listed in ascending order and the first element must be 0. Linear interpolation is used to calculate intermediate values.

Dependencies

To use this parameter, set the parameters to:

  • Area characteristics to `Different for each flow path'.

  • Orifice parameterization value Tabulated data - Volumetric flow rate vs. spool travel and pressure drop.

  • Positive spool position open connections or Negative spool position open connections one of the following values:

    • `P-A and B-T

    • `P-A and P-B

    • `P-A only

    • `P-A, P-B, A-T, and B-T'.

Units

m | um | mm | cm | km | in | ft | yd | mi | nmi
Default value

[0.0, 1.25e-3, 2.5e-3, 3.75e-3, 5e-3] m
Program usage name

spool_travel_vector_2D_pa
Evaluatable

Yes

# P-A orifice pressure drop vector, dp — vector of differential pressure values
Pa | uPa | hPa | kPa | MPa | GPa | kgf/m^2 | kgf/cm^2 | kgf/mm^2 | mbar | bar | kbar | atm | ksi | psi | mmHg | inHg

Details

Vector of differential pressure values for tabular parameterization by volume flow. The differential pressure vector corresponds to the position vector of the spool valve. P-A orifice spool travel vector, ds and volumetric flow rate table, q(ds,ds). P-A orifice volumetric flow rate table, q(ds,dp). The values are listed in ascending order. Linear interpolation is used to calculate intermediate values.

Dependencies

To use this parameter, set the parameters to:

  • Area characteristics to `Different for each flow path'.

  • Orifice parameterization value Tabulated data - Volumetric flow rate vs. spool travel and pressure drop.

  • Positive spool position open connections or Negative spool position open connections one of the following values:

    • `P-A and B-T

    • `P-A and P-B

    • `P-A only

    • `P-A, P-B, A-T, and B-T'.

Units

Pa | uPa | hPa | kPa | MPa | GPa | kgf/m^2 | kgf/cm^2 | kgf/mm^2 | mbar | bar | kbar | atm | ksi | psi | mmHg | inHg
Default value

[-0.1, 0.3, 0.5, 0.7] MPa
Program usage name

delta_p_vector_2D_pa
Evaluatable

Yes

# P-A orifice volumetric flow rate table, q(ds,dp) — table of volumetric flow rates
m^3/s | mm^3/s | cm^3/s | m^3/hr | m^3/min | l/hr | l/min | l/s | gal/hr | gal/min | gal/s | ft^3/hr | ft^3/min | ft^3/s

Details

Matrix to of volume flow rates corresponding to differential pressure and spool position values. to - dimensions of the corresponding vectors:

  • - number of elements in the spool position vector P-A orifice spool travel vector, ds.

  • - number of elements in the pressure drop vector P-A orifice pressure drop vector, dp.

Dependencies

To use this parameter, set the parameters to:

  • Area characteristics to `Different for each flow path'.

  • Orifice parameterization value Tabulated data - Volumetric flow rate vs. spool travel and pressure drop.

  • Positive spool position open connections or Negative spool position open connections one of the following values:

    • `P-A and B-T

    • `P-A and P-B

    • `P-A only

    • `P-A, P-B, A-T, and B-T'.

Units

m^3/s | mm^3/s | cm^3/s | m^3/hr | m^3/min | l/hr | l/min | l/s | gal/hr | gal/min | gal/s | ft^3/hr | ft^3/min | ft^3/s
Default value

[-1e-8 2.2e-8 2.8e-8 3.4e-8; -9e-6 1.5e-4 2e-4 2.4e-4; -3.6e-4 6.3e-4 8.1e-4 9.6e-4; -5.4e-4 9.4e-4 1.2e-3 1.4e-3; -9.1e-4 1.6e-3 2.0e-3 2.4e-3] m^3/s
Program usage name

Vdot_matrix_2D_pa
Evaluatable

Yes

# P-A constant orifice area — cross-sectional area for a permanently open channel
m^2 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac

Details

Cross-sectional area of a channel defined as open in both positions.

Dependencies

To use this parameter, set for parameters:

  • Area characteristics to Different for each flow path.

  • Orifice parameterization to Linear - area vs. spool travel or Tabulated data - Area vs. spool travel.

  • Positive spool position open connections and Negative spool position open connections one of the channels:

    • `P-A and B-T

    • `P-A and P-B

    • `P-A only

    • P-A, P-B, A-T, and B-T

This parameter is enabled only if the P-A channel is set in both the Positive spool position open connections and Negative spool position open connections parameters.

Units

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

1e-4 m^2
Program usage name

area_fixed_pa
Evaluatable

Yes

# P-A constant orifice pressure drop vector — vector of differential pressure values of a permanently open channel
Pa | uPa | hPa | kPa | MPa | GPa | kgf/m^2 | kgf/cm^2 | kgf/mm^2 | mbar | bar | kbar | atm | ksi | psi | mmHg | inHg

Details

Vector of differential pressure values for a channel defined open in both positions. The dimension of the differential pressure vector corresponds to the P-A constant orifice volumetric flow rate vector. The values are listed in ascending order. Linear interpolation is used to calculate intermediate values.

Dependencies

To use this parameter, set the parameters to:

  • Area characteristics to Different for each flow path.

  • Orifice parameterization value Tabulated data - Volumetric flow rate vs. spool travel and pressure drop.

  • Positive spool position open connections and Negative spool position open connections one of the channels:

    • `P-A and B-T

    • `P-A and P-B

    • `P-A only

    • P-A, P-B, A-T, and B-T

This parameter is enabled only if the P-A channel is set in both the Positive spool position open connections and Negative spool position open connections parameters.

Units

Pa | uPa | hPa | kPa | MPa | GPa | kgf/m^2 | kgf/cm^2 | kgf/mm^2 | mbar | bar | kbar | atm | ksi | psi | mmHg | inHg
Default value

[-0.1, 0.3, 0.5, 0.7] MPa
Program usage name

delta_p_vector_fixed_pa
Evaluatable

Yes

# P-A constant volumetric flow rate vector — vector of values of volume flow rate of a permanently open channel
m^3/s | mm^3/s | cm^3/s | m^3/hr | m^3/min | l/hr | l/min | l/s | gal/hr | gal/min | gal/s | ft^3/hr | ft^3/min | ft^3/s

Details

Vector of volume flow values for a channel defined open in both positions. The dimension of the pressure drop vector corresponds to the P-A constant orifice pressure drop vector. The values are listed in ascending order. Linear interpolation is used to calculate intermediate values.

Dependencies

To use this parameter, set the parameters to:

  • Area characteristics to Different for each flow path.

  • Orifice parameterization value Tabulated data - Volumetric flow rate vs. spool travel and pressure drop.

  • Positive spool position open connections and Negative spool position open connections one of the channels:

    • `P-A and B-T

    • `P-A and P-B

    • `P-A only

    • P-A, P-B, A-T, and B-T

This parameter is enabled only if the P-A channel is set in both the Positive spool position open connections and Negative spool position open connections parameters.

Units

m^3/s | mm^3/s | cm^3/s | m^3/hr | m^3/min | l/hr | l/min | l/s | gal/hr | gal/min | gal/s | ft^3/hr | ft^3/min | ft^3/s
Default value

[-9e-4, 1.6e-3, 2.0e-3, 2.4e-3] m^3/s
Program usage name

Vdot_vector_fixed_pa
Evaluatable

Yes

P-B Orifice

# Spool position at maximum P-B orifice area — spool position at maximum channel area between ports P and B
m | um | mm | cm | km | in | ft | yd | mi | nmi

Details

Spool position corresponding to a fully open channel between ports P and B.

Dependencies

To use this parameter, set the Positive spool position open connections or Negative spool position open connections parameters to one of the following values:

  • `P-B and A-T

  • `P-A and P-B

  • `P-B only

  • `P-A, P-B, A-T, and B-T'.

This parameter is enabled only if the P-B channel is not set simultaneously in both parameters Positive spool position open connections and Negative spool position open connections.

Units

m | um | mm | cm | km | in | ft | yd | mi | nmi
Default value

-5e-3 m
Program usage name

spool_offset_pb
Evaluatable

Yes

# P-B spool travel between closed and open orifice — maximum spool stroke between ports P and B
m | um | mm | cm | km | in | ft | yd | mi | nmi

Details

Maximum spool stroke between ports P and B.

Dependencies

To use this parameter, set for parameters:

  • Area characteristics to Different for each flow path.

  • Orifice parameterization value Linear - Area vs. spool travel.

  • Positive spool position open connections or Negative spool position open connections one of the following values:

    • `P-B and A-T

    • `P-A and P-B

    • `P-B only

    • `P-A, P-B, A-T, and B-T'.

Units

m | um | mm | cm | km | in | ft | yd | mi | nmi
Default value

0.005 m
Program usage name

max_spool_travel_pb
Evaluatable

Yes

# P-B maximum orifice area — maximum area between ports P and B
m^2 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac

Details

The cross-sectional area between ports P and B in the fully open position.

Dependencies

To use this parameter, set for parameters:

  • Area characteristics to Different for each flow path.

  • Orifice parameterization value Linear - Area vs. spool travel.

  • Positive spool position open connections or Negative spool position open connections one of the following values:

    • `P-B and A-T

    • `P-A and P-B

    • `P-B only

    • `P-A, P-B, A-T, and B-T'.

Units

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

1e-4 m^2
Program usage name

max_area_pb
Evaluatable

Yes

# P-B orifice spool travel vector — vector of spool relative positions
m | um | mm | cm | km | in | ft | yd | mi | nmi

Details

Vector of spool positions. The dimensionality of the vector corresponds to the P-B orifice area vector. The values are listed in ascending order and the first element must be 0. Linear interpolation is used between the data points in the table.

Dependencies

To use this parameter, set the parameters to:

  • Area characteristics to Different for each flow path.

  • Orifice parameterization value `Tabulated data - Area vs. spool travel'.

  • Positive spool position open connections or Negative spool position open connections one of the following values:

    • `P-B and A-T

    • `P-A and P-B

    • `P-B only

    • `P-A, P-B, A-T, and B-T'.

Units

m | um | mm | cm | km | in | ft | yd | mi | nmi
Default value

[0.0, 1.25e-3, 2.5e-3, 3.75e-3, 5e-3] m
Program usage name

spool_travel_vector_pb
Evaluatable

Yes

# P-B orifice area vector — vector of values of the channel cross-sectional area
m^2 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac

Details

Vector of channel cross-sectional area values for the tabular parameterization of the valve area. The dimension of the vector corresponds to the P-B orifice spool travel vector. The values are listed in ascending order and must be greater than 0.

Dependencies

To use this parameter, set the parameters to:

  • Area characteristics to Different for each flow path.

  • Orifice parameterization value `Tabulated data - Area vs. spool travel'.

  • Positive spool position open connections or Negative spool position open connections one of the following values:

    • `P-B and A-T

    • `P-A and P-B

    • `P-B only

    • `P-A, P-B, A-T, and B-T'.

Units

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

[1e-10, 1e-5, 4e-5, 6e-5, 1e-4] m^2
Program usage name

valve_area_vector_pb
Evaluatable

Yes

# P-B orifice spool travel vector, ds — vector of values of the spool relative position
m | um | mm | cm | km | in | ft | yd | mi | nmi

Details

Vector of spool positions for tabular parameterization by volume flow. The dimension of the spool position vector corresponds to the differential pressure vector P-B orifice pressure drop vector,dp and the volumetric flow rate table P-B orifice volumetric flow rate table, q(s,dp). The values are listed in ascending order and the first element must be 0. Linear interpolation is used to calculate intermediate values.

Dependencies

To use this parameter, set the parameters to:

  • Area characteristics to `Different for each flow path'.

  • Orifice parameterization value Tabulated data - Volumetric flow rate vs. spool travel and pressure drop.

  • Positive spool position open connections or Negative spool position open connections one of the following values:

    • `P-B and A-T

    • `P-A and P-B

    • `P-B only

    • `P-A, P-B, A-T, and B-T'.

Units

m | um | mm | cm | km | in | ft | yd | mi | nmi
Default value

[0.0, 1.25e-3, 2.5e-3, 3.75e-3, 5e-3] m
Program usage name

spool_travel_vector_2D_pb
Evaluatable

Yes

# P-B orifice pressure drop vector, dp — vector of differential pressure values
Pa | uPa | hPa | kPa | MPa | GPa | kgf/m^2 | kgf/cm^2 | kgf/mm^2 | mbar | bar | kbar | atm | ksi | psi | mmHg | inHg

Details

Vector of differential pressure values for tabular parameterization by volume flow. The differential pressure vector corresponds to the position vector of the spool valve. P-B orifice spool travel vector, ds and volumetric flow rate table, q(ds,ds). P-B orifice volumetric flow rate table, q(ds,dp). The values are listed in ascending order. Linear interpolation is used to calculate intermediate values.

Dependencies

To use this parameter, set the parameters to:

  • Area characteristics to `Different for each flow path'.

  • Orifice parameterization value Tabulated data - Volumetric flow rate vs. spool travel and pressure drop.

  • Positive spool position open connections or Negative spool position open connections one of the following values:

    • `P-B and A-T

    • `P-A and P-B

    • `P-B only

    • `P-A, P-B, A-T, and B-T'.

Units

Pa | uPa | hPa | kPa | MPa | GPa | kgf/m^2 | kgf/cm^2 | kgf/mm^2 | mbar | bar | kbar | atm | ksi | psi | mmHg | inHg
Default value

[-0.1, 0.3, 0.5, 0.7] MPa
Program usage name

delta_p_vector_2D_pb
Evaluatable

Yes

# P-B orifice volumetric flow rate table, q(ds,dp) — table of volumetric flow rates
m^3/s | mm^3/s | cm^3/s | m^3/hr | m^3/min | l/hr | l/min | l/s | gal/hr | gal/min | gal/s | ft^3/hr | ft^3/min | ft^3/s

Details

Matrix to of volume flow rates corresponding to differential pressure and spool position values. to - dimensions of the corresponding vectors:

  • - number of elements in the spool position vector P-B orifice spool travel vector, ds.

  • - number of elements in the pressure drop vector P-B orifice pressure drop vector, dp.

Dependencies

To use this parameter, set the parameters to:

  • Area characteristics to `Different for each flow path'.

  • Orifice parameterization value Tabulated data - Volumetric flow rate vs. spool travel and pressure drop.

  • Positive spool position open connections or Negative spool position open connections one of the following values:

    • `P-B and A-T

    • `P-A and P-B

    • `P-B only

    • `P-A, P-B, A-T, and B-T'.

Units

m^3/s | mm^3/s | cm^3/s | m^3/hr | m^3/min | l/hr | l/min | l/s | gal/hr | gal/min | gal/s | ft^3/hr | ft^3/min | ft^3/s
Default value

[-1e-8 2.2e-8 2.8e-8 3.4e-8; -9e-6 1.5e-4 2e-4 2.4e-4; -3.6e-4 6.3e-4 8.1e-4 9.6e-4; -5.4e-4 9.4e-4 1.2e-3 1.4e-3; -9.1e-4 1.6e-3 2.0e-3 2.4e-3] m^3/s
Program usage name

Vdot_matrix_2D_pb
Evaluatable

Yes

# P-B constant orifice area — cross-sectional area of the permanently open channel
m^2 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac

Details

Cross-sectional area of a channel defined as open in both positions.

Dependencies

To use this parameter, set for parameters:

  • Area characteristics to Different for each flow path.

  • Orifice parameterization to Linear - area vs. spool travel or Tabulated data - Area vs. spool travel.

  • Positive spool position open connections and Negative spool position open connections one of the channels:

    • `P-B and A-T

    • `P-A and P-B

    • `P-B only

    • P-A, P-B, A-T, and B-T

This parameter is enabled only if the P-B channel is present in both the Positive spool position open connections and Negative spool position open connections parameters.

Units

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

1e-4 m^2
Program usage name

area_fixed_pb
Evaluatable

Yes

# P-B constant orifice pressure drop vector — vector of differential pressure values for a permanently open channel
Pa | uPa | hPa | kPa | MPa | GPa | kgf/m^2 | kgf/cm^2 | kgf/mm^2 | mbar | bar | kbar | atm | ksi | psi | mmHg | inHg

Details

Vector of differential pressure values for a channel defined open in both positions. The dimension of the differential pressure vector corresponds to the P-B constant orifice volumetric flow rate vector. The values are listed in ascending order. Linear interpolation is used to calculate intermediate values.

Dependencies

To use this parameter, set the parameters to:

  • Area characteristics to Different for each flow path.

  • Orifice parameterization value Tabulated data - Volumetric flow rate vs. spool travel and pressure drop.

  • Positive spool position open connections and Negative spool position open connections one of the channels:

    • `P-B and A-T

    • `P-A and P-B

    • `P-B only

    • P-A, P-B, A-T, and B-T

This parameter is enabled only if the P-B channel is present in both the Positive spool position open connections and Negative spool position open connections parameters.

Units

Pa | uPa | hPa | kPa | MPa | GPa | kgf/m^2 | kgf/cm^2 | kgf/mm^2 | mbar | bar | kbar | atm | ksi | psi | mmHg | inHg
Default value

[-0.1, 0.3, 0.5, 0.7] MPa
Program usage name

delta_p_vector_fixed_pb
Evaluatable

Yes

# P-B constant volumetric flow rate vector — vector of values of the volume constant open channel
m^3/s | mm^3/s | cm^3/s | m^3/hr | m^3/min | l/hr | l/min | l/s | gal/hr | gal/min | gal/s | ft^3/hr | ft^3/min | ft^3/s

Details

Vector of volumetric flow rate values for a channel defined open in both positions. The dimension of the pressure drop vector corresponds to the P-B constant orifice pressure drop vector. The values are listed in ascending order. Linear interpolation is used to calculate intermediate values.

Dependencies

To use this parameter, set the parameters to:

  • Area characteristics to Different for each flow path.

  • Orifice parameterization value Tabulated data - Volumetric flow rate vs. spool travel and pressure drop.

  • Positive spool position open connections and Negative spool position open connections one of the channels:

    • `P-B and A-T

    • `P-A and P-B

    • `P-B only

    • P-A, P-B, A-T, and B-T

This parameter is enabled only if the P-B channel is present in both the Positive spool position open connections and Negative spool position open connections parameters.

Units

m^3/s | mm^3/s | cm^3/s | m^3/hr | m^3/min | l/hr | l/min | l/s | gal/hr | gal/min | gal/s | ft^3/hr | ft^3/min | ft^3/s
Default value

[-9e-4, 1.6e-3, 2.0e-3, 2.4e-3] m^3/s
Program usage name

Vdot_vector_fixed_pb
Evaluatable

Yes

A-T Orifice

# Spool position at maximum A-T orifice area — spool position at maximum channel area between ports A and T
m | um | mm | cm | km | in | ft | yd | mi | nmi

Details

Spool position corresponding to a fully open channel between ports A and T.

Dependencies

To use this parameter, set the Positive spool position open connections or Negative spool position open connections parameters to one of the following values:

  • A-T only.

  • `P-B and A-T

  • `P-A, P-B, A-T, and B-T'.

This parameter is enabled only if the A-T channel is not set simultaneously in both parameters Positive spool position open connections and Negative spool position open connections.

Units

m | um | mm | cm | km | in | ft | yd | mi | nmi
Default value

-5e-3 m
Program usage name

spool_offset_at
Evaluatable

Yes

# A-T spool travel between closed and open orifice — maximum spool stroke between ports A and T
m | um | mm | cm | km | in | ft | yd | mi | nmi

Details

Maximum spool stroke between ports A and T.

Dependencies

To use this parameter, set the parameters to:

  • Area characteristics to Different for each flow path.

  • Orifice parameterization value Linear - Area vs. spool travel.

  • Positive spool position open connections or Negative spool position open connections one of the following values:

    • A-T only.

    • `P-B and A-T

    • `P-A, P-B, A-T, and B-T'.

Units

m | um | mm | cm | km | in | ft | yd | mi | nmi
Default value

0.005 m
Program usage name

max_spool_travel_at
Evaluatable

Yes

# A-T maximum orifice area — maximum area between ports A and T
m^2 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac

Details

The cross-sectional area between ports A and T in the fully open position.

Dependencies

To use this parameter, set for parameters:

  • Area characteristics to Different for each flow path.

  • Orifice parameterization value Linear - Area vs. spool travel.

  • Positive spool position open connections or Negative spool position open connections one of the following values:

    • A-T only.

    • `P-B and A-T

    • `P-A, P-B, A-T, and B-T'.

Units

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

1e-4 m^2
Program usage name

max_area_at
Evaluatable

Yes

# A-T orifice spool travel vector — vector of spool relative positions
m | um | mm | cm | km | in | ft | yd | mi | nmi

Details

Vector of spool positions. The dimensionality of the vector corresponds to the A-T orifice area vector. The values are listed in ascending order and the first element must be 0. Linear interpolation is used between the data points in the table.

Dependencies

To use this parameter, set the parameters to:

  • Area characteristics value Different for each flow path.

  • Orifice parameterization value `Tabulated data - Area vs. spool travel'.

  • Positive spool position open connections or Negative spool position open connections one of the following values:

    • A-T only.

    • `P-B and A-T

    • `P-A, P-B, A-T, and B-T'.

Units

m | um | mm | cm | km | in | ft | yd | mi | nmi
Default value

[0.0, 1.25e-3, 2.5e-3, 3.75e-3, 5e-3] m
Program usage name

spool_travel_vector_at
Evaluatable

Yes

# A-T orifice area vector — vector of values of the channel cross-sectional area
m^2 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac

Details

Vector of channel cross-sectional area values for the tabular parameterization of the valve area. The dimension of the vector corresponds to the A-T orifice spool travel vector. The values are listed in ascending order and must be greater than 0.

Dependencies

To use this parameter, set the parameters to:

  • Area characteristics to Different for each flow path.

  • Orifice parameterization value `Tabulated data - Area vs. spool travel'.

  • Positive spool position open connections or Negative spool position open connections one of the following values:

    • A-T only.

    • `P-B and A-T

    • `P-A, P-B, A-T, and B-T'.

Units

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

[1e-10, 1e-5, 4e-5, 6e-5, 1e-4] m^2
Program usage name

valve_area_vector_at
Evaluatable

Yes

# A-T orifice spool travel vector, ds — vector of values of the spool relative position
m | um | mm | cm | km | in | ft | yd | mi | nmi

Details

Vector of spool positions for tabular parameterization by volume flow. The dimension of the spool position vector corresponds to the differential pressure vector A-T orifice pressure drop vector,dp and the volumetric flow rate table A-T orifice volumetric flow rate table, q(s,dp). The values are listed in ascending order and the first element must be 0. Linear interpolation is used to calculate intermediate values.

Dependencies

To use this parameter, set the parameters to:

  • Area characteristics to `Different for each flow path'.

  • Orifice parameterization value Tabulated data - Volumetric flow rate vs. spool travel and pressure drop.

  • Positive spool position open connections or Negative spool position open connections one of the following values:

    • A-T only.

    • `P-B and A-T

    • `P-A, P-B, A-T, and B-T'.

Units

m | um | mm | cm | km | in | ft | yd | mi | nmi
Default value

[0.0, 1.25e-3, 2.5e-3, 3.75e-3, 5e-3] m
Program usage name

spool_travel_vector_2D_at
Evaluatable

Yes

# A-T orifice pressure drop vector, dp — vector of differential pressure values
Pa | uPa | hPa | kPa | MPa | GPa | kgf/m^2 | kgf/cm^2 | kgf/mm^2 | mbar | bar | kbar | atm | ksi | psi | mmHg | inHg

Details

Vector of differential pressure values for tabular parameterization by volume flow. The differential pressure vector corresponds to the position vector of the spool valve. A-T orifice spool travel vector, ds and the volumetric flow rate table A-T orifice volumetric flow rate table, q(ds,dp). The values are listed in ascending order. Linear interpolation is used to calculate intermediate values.

Dependencies

To use this parameter, set the parameters to:

  • Area characteristics to `Different for each flow path'.

  • Orifice parameterization value Tabulated data - Volumetric flow rate vs. spool travel and pressure drop.

  • Positive spool position open connections or Negative spool position open connections one of the following values:

    • A-T only.

    • `P-B and A-T

    • `P-A, P-B, A-T, and B-T'.

Units

Pa | uPa | hPa | kPa | MPa | GPa | kgf/m^2 | kgf/cm^2 | kgf/mm^2 | mbar | bar | kbar | atm | ksi | psi | mmHg | inHg
Default value

[-0.1, 0.3, 0.5, 0.7] MPa
Program usage name

delta_p_vector_2D_at
Evaluatable

Yes

# A-T orifice volumetric flow rate table, q(ds,dp) — table of volumetric flow rates
m^3/s | mm^3/s | cm^3/s | m^3/hr | m^3/min | l/hr | l/min | l/s | gal/hr | gal/min | gal/s | ft^3/hr | ft^3/min | ft^3/s

Details

Matrix to of volume flow rates corresponding to differential pressure and spool position values. to - dimensions of the corresponding vectors:

  • - number of elements in the spool position vector A-T orifice spool travel vector, ds.

  • - number of elements in the pressure drop vector A-T orifice pressure drop vector, dp.

Dependencies

To use this parameter, set the parameters to:

  • Area characteristics to `Different for each flow path'.

  • Orifice parameterization value Tabulated data - Volumetric flow rate vs. spool travel and pressure drop.

  • Positive spool position open connections or Negative spool position open connections one of the following values:

    • A-T only.

    • `P-B and A-T

    • `P-A, P-B, A-T, and B-T'.

Units

m^3/s | mm^3/s | cm^3/s | m^3/hr | m^3/min | l/hr | l/min | l/s | gal/hr | gal/min | gal/s | ft^3/hr | ft^3/min | ft^3/s
Default value

[-1e-8 2.2e-8 2.8e-8 3.4e-8; -9e-6 1.5e-4 2e-4 2.4e-4; -3.6e-4 6.3e-4 8.1e-4 9.6e-4; -5.4e-4 9.4e-4 1.2e-3 1.4e-3; -9.1e-4 1.6e-3 2.0e-3 2.4e-3] m^3/s
Program usage name

Vdot_matrix_2D_at
Evaluatable

Yes

# A-T constant orifice area — cross-sectional area of the permanently open channel
m^2 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac

Details

Cross-sectional area of a channel defined as open in both positions.

Dependencies

To use this parameter, set for parameters:

  • Area characteristics to Different for each flow path.

  • Orifice parameterization to Linear - area vs. spool travel or Tabulated data - Area vs. spool travel.

  • Positive spool position open connections and Negative spool position open connections one of the channels:

    • A-T only.

    • `P-B and A-T

    • P-A, P-B, A-T, and B-T

This parameter is enabled only if the A-T channel is present in both the Positive spool position open connections and Negative spool position open connections parameters.

Units

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

1e-4 m^2
Program usage name

area_fixed_at
Evaluatable

Yes

# A-T constant orifice pressure drop vector — vector of differential pressure values for a permanently open channel
Pa | uPa | hPa | kPa | MPa | GPa | kgf/m^2 | kgf/cm^2 | kgf/mm^2 | mbar | bar | kbar | atm | ksi | psi | mmHg | inHg

Details

Vector of differential pressure values for a channel defined open in both positions. The dimension of the differential pressure vector corresponds to the A-T constant orifice volumetric flow rate vector. The values are listed in ascending order. Linear interpolation is used to calculate intermediate values.

Dependencies

To use this parameter, set the parameters to:

  • Area characteristics to Different for each flow path.

  • Orifice parameterization value Tabulated data - Volumetric flow rate vs. spool travel and pressure drop.

  • Positive spool position open connections and Negative spool position open connections one of the channels:

    • A-T only.

    • `P-B and A-T

    • P-A, P-B, A-T, and B-T

This parameter is enabled only if the A-T channel is present in both the Positive spool position open connections and Negative spool position open connections parameters.

Units

Pa | uPa | hPa | kPa | MPa | GPa | kgf/m^2 | kgf/cm^2 | kgf/mm^2 | mbar | bar | kbar | atm | ksi | psi | mmHg | inHg
Default value

[-0.1, 0.3, 0.5, 0.7] MPa
Program usage name

delta_p_vector_fixed_at
Evaluatable

Yes

# A-T constant volumetric flow rate vector — vector of values of the volume constant open channel
m^3/s | mm^3/s | cm^3/s | m^3/hr | m^3/min | l/hr | l/min | l/s | gal/hr | gal/min | gal/s | ft^3/hr | ft^3/min | ft^3/s

Details

Vector of volumetric flow rate values for a channel defined open in both positions. The dimension of the pressure drop vector corresponds to the A-T constant orifice pressure drop vector. The values are listed in ascending order. Linear interpolation is used to calculate intermediate values.

Dependencies

To use this parameter, set the parameters to:

  • Area characteristics to Different for each flow path.

  • Orifice parameterization value Tabulated data - Volumetric flow rate vs. spool travel and pressure drop.

  • Positive spool position open connections and Negative spool position open connections one of the channels:

    • A-T only.

    • `P-B and A-T

    • P-A, P-B, A-T, and B-T

This parameter is enabled only if the A-T channel is present in both the Positive spool position open connections and Negative spool position open connections parameters.

Units

m^3/s | mm^3/s | cm^3/s | m^3/hr | m^3/min | l/hr | l/min | l/s | gal/hr | gal/min | gal/s | ft^3/hr | ft^3/min | ft^3/s
Default value

[-9e-4, 1.6e-3, 2.0e-3, 2.4e-3] m^3/s
Program usage name

Vdot_vector_fixed_at
Evaluatable

Yes

B-T Orifice

# Spool position at maximum B-T orifice area — spool position at maximum channel area between ports B and T
m | um | mm | cm | km | in | ft | yd | mi | nmi

Details

Spool position corresponding to a fully open channel between ports B and T.

Dependencies

To use this parameter, set the parameters Positive spool position open connections or Negative spool position open connections to `P-A and B-T'.

To use this parameter, set the Positive spool position open connections or Negative spool position open connections parameters to one of the following values:

  • B-T only.

  • `P-A and B-T

  • P-A, P-B, A-T, and B-T.

This parameter is enabled only if the B-T channel is not set simultaneously in both parameters Positive spool position open connections and Negative spool position open connections.

Units

m | um | mm | cm | km | in | ft | yd | mi | nmi
Default value

5e-3 m
Program usage name

spool_offset_bt
Evaluatable

Yes

# B-T spool travel between closed and open orifice — maximum spool stroke between ports B and T
m | um | mm | cm | km | in | ft | yd | mi | nmi

Details

Maximum spool stroke between ports B and T.

Dependencies

To use this parameter, set for parameters:

  • Area characteristics to Different for each flow path.

  • Orifice parameterization value Linear - Area vs. spool travel.

  • Positive spool position open connections or Negative spool position open connections one of the following values:

    • B-T only.

    • `P-A and B-T

    • `P-A, P-B, A-T, and B-T'.

Units

m | um | mm | cm | km | in | ft | yd | mi | nmi
Default value

0.005 m
Program usage name

max_spool_travel_bt
Evaluatable

Yes

# B-T maximum orifice area — maximum area between ports B and T
m^2 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac

Details

The cross-sectional area between ports B and T in the fully open position.

Dependencies

To use this parameter, set for parameters:

  • Area characteristics to Different for each flow path.

  • Orifice parameterization value Linear - Area vs. spool travel.

  • Positive spool position open connections or Negative spool position open connections one of the following values:

    • B-T only.

    • `P-A and B-T

    • `P-A, P-B, A-T, and B-T'.

Units

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

1e-4 m^2
Program usage name

max_area_bt
Evaluatable

Yes

# B-T orifice spool travel vector — vector of spool relative positions
m | um | mm | cm | km | in | ft | yd | mi | nmi

Details

Vector of spool positions. The dimension of the vector corresponds to the B-T orifice area vector. The values are listed in ascending order and the first element must be 0. Linear interpolation is used between the data points in the table.

Dependencies

To use this parameter, set the parameters to:

  • Area characteristics value Different for each flow path.

  • Orifice parameterization value `Tabulated data - Area vs. spool travel'.

  • Positive spool position open connections or Negative spool position open connections one of the following values:

    • B-T only.

    • `P-A and B-T

    • `P-A, P-B, A-T, and B-T'.

Units

m | um | mm | cm | km | in | ft | yd | mi | nmi
Default value

[0.0, 1.25e-3, 2.5e-3, 3.75e-3, 5e-3] m
Program usage name

spool_travel_vector_bt
Evaluatable

Yes

# B-T orifice area vector — vector of values of the channel cross-sectional area
m^2 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac

Details

Vector of channel cross-sectional area values for the tabular parameterization of the valve area. The dimension of the vector corresponds to the B-T orifice spool travel vector. The values are listed in ascending order and must be greater than 0.

Dependencies

To use this parameter, set the parameters to:

  • Area characteristics to Different for each flow path.

  • Orifice parameterization value `Tabulated data - Area vs. spool travel'.

  • Positive spool position open connections or Negative spool position open connections one of the following values:

    • B-T only.

    • `P-A and B-T

    • `P-A, P-B, A-T, and B-T'.

Units

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

[1e-10, 1e-5, 4e-5, 6e-5, 1e-4] m^2
Program usage name

valve_area_vector_bt
Evaluatable

Yes

# B-T orifice spool travel vector, ds — vector of values of the spool relative position
m | um | mm | cm | km | in | ft | yd | mi | nmi

Details

Vector of spool positions for tabular parameterization by volume flow. The dimension of the spool position vector corresponds to the differential pressure vector B-T orifice pressure drop vector,dp and the volumetric flow rate table B-T orifice volumetric flow rate table, q(s,dp). The values are listed in ascending order and the first element must be 0. Linear interpolation is used to calculate intermediate values.

Dependencies

To use this parameter, set the parameters to:

  • Area characteristics to `Different for each flow path'.

  • Orifice parameterization value Tabulated data - Volumetric flow rate vs. spool travel and pressure drop.

  • Positive spool position open connections or Negative spool position open connections one of the following values:

    • B-T only.

    • `P-A and B-T

    • `P-A, P-B, A-T, and B-T'.

Units

m | um | mm | cm | km | in | ft | yd | mi | nmi
Default value

[0.0, 1.25e-3, 2.5e-3, 3.75e-3, 5e-3] m
Program usage name

spool_travel_vector_2D_bt
Evaluatable

Yes

# B-T orifice pressure drop vector, dp — vector of differential pressure values
Pa | uPa | hPa | kPa | MPa | GPa | kgf/m^2 | kgf/cm^2 | kgf/mm^2 | mbar | bar | kbar | atm | ksi | psi | mmHg | inHg

Details

Vector of differential pressure values for tabular parameterization by volume flow. The differential pressure vector corresponds to the spool position vector B-T orifice spool travel vector, ds and the volumetric flow rate table B-T orifice volumetric flow rate table, q(ds,dp). The values are listed in ascending order. Linear interpolation is used to calculate intermediate values.

Dependencies

To use this parameter, set the parameters to:

  • Area characteristics to `Different for each flow path'.

  • Orifice parameterization value Tabulated data - Volumetric flow rate vs. spool travel and pressure drop.

  • Positive spool position open connections or Negative spool position open connections one of the following values:

    • B-T only.

    • `P-A and B-T

    • `P-A, P-B, A-T, and B-T'.

Units

Pa | uPa | hPa | kPa | MPa | GPa | kgf/m^2 | kgf/cm^2 | kgf/mm^2 | mbar | bar | kbar | atm | ksi | psi | mmHg | inHg
Default value

[-0.1, 0.3, 0.5, 0.7] MPa
Program usage name

delta_p_vector_2D_bt
Evaluatable

Yes

# B-T orifice volumetric flow rate table, q(ds,dp) — table of volumetric flow rates
m^3/s | mm^3/s | cm^3/s | m^3/hr | m^3/min | l/hr | l/min | l/s | gal/hr | gal/min | gal/s | ft^3/hr | ft^3/min | ft^3/s

Details

Matrix to of volume flow rates corresponding to differential pressure and spool position values. to - dimensions of the corresponding vectors:

  • - number of elements in the spool position vector B-T orifice spool travel vector, ds.

  • - number of elements in the pressure drop vector B-T orifice pressure drop vector, dp.

Dependencies

To use this parameter, set the parameters to:

  • Area characteristics to `Different for each flow path'.

  • Orifice parameterization value Tabulated data - Volumetric flow rate vs. spool travel and pressure drop.

  • Positive spool position open connections or Negative spool position open connections one of the following values:

    • B-T only.

    • `P-A and B-T

    • `P-A, P-B, A-T, and B-T'.

Units

m^3/s | mm^3/s | cm^3/s | m^3/hr | m^3/min | l/hr | l/min | l/s | gal/hr | gal/min | gal/s | ft^3/hr | ft^3/min | ft^3/s
Default value

[-1e-8 2.2e-8 2.8e-8 3.4e-8; -9e-6 1.5e-4 2e-4 2.4e-4; -3.6e-4 6.3e-4 8.1e-4 9.6e-4; -5.4e-4 9.4e-4 1.2e-3 1.4e-3; -9.1e-4 1.6e-3 2.0e-3 2.4e-3] m^3/s
Program usage name

Vdot_matrix_2D_bt
Evaluatable

Yes

# B-T constant orifice area — cross-sectional area of the permanently open channel
m^2 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac

Details

Cross-sectional area of a channel defined as open in both positions.

Dependencies

To use this parameter, set for parameters:

  • Area characteristics to Different for each flow path.

  • Orifice parameterization to Linear - area vs. spool travel or Tabulated data - Area vs. spool travel.

  • Positive spool position open connections or Negative spool position open connections one of the following values:

    • B-T only.

    • `P-A and B-T

    • `P-A, P-B, A-T, and B-T'.

This parameter is enabled only if the B-T channel is present in both the Positive spool position open connections and Negative spool position open connections parameters.

Units

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

1e-4 m^2
Program usage name

area_fixed_bt
Evaluatable

Yes

# B-T constant orifice pressure drop vector — vector of differential pressure values for a permanently open channel
Pa | uPa | hPa | kPa | MPa | GPa | kgf/m^2 | kgf/cm^2 | kgf/mm^2 | mbar | bar | kbar | atm | ksi | psi | mmHg | inHg

Details

Vector of differential pressure values for a channel set open in both positions. The dimension of the differential pressure vector corresponds to the B-T constant orifice volumetric flow rate vector. The values are listed in ascending order. Linear interpolation is used to calculate intermediate values.

Dependencies

To use this parameter, set the parameters to:

  • Area characteristics to Different for each flow path.

  • Orifice parameterization value Tabulated data - Volumetric flow rate vs. spool travel and pressure drop.

  • Positive spool position open connections or Negative spool position open connections one of the following values:

    • B-T only.

    • `P-A and B-T

    • `P-A, P-B, A-T, and B-T'.

This parameter is enabled only if the B-T channel is present in both the Positive spool position open connections and Negative spool position open connections parameters.

Units

Pa | uPa | hPa | kPa | MPa | GPa | kgf/m^2 | kgf/cm^2 | kgf/mm^2 | mbar | bar | kbar | atm | ksi | psi | mmHg | inHg
Default value

[-0.1, 0.3, 0.5, 0.7] MPa
Program usage name

delta_p_vector_fixed_bt
Evaluatable

Yes

# B-T constant volumetric flow rate vector — vector of values of the volume constant open channel
m^3/s | mm^3/s | cm^3/s | m^3/hr | m^3/min | l/hr | l/min | l/s | gal/hr | gal/min | gal/s | ft^3/hr | ft^3/min | ft^3/s

Details

Vector of volumetric flow rate values for a channel defined open in both positions. The dimension of the pressure drop vector corresponds to the B-T constant orifice pressure drop vector. The values are listed in ascending order. Linear interpolation is used to calculate intermediate values.

Dependencies

To use this parameter, set the parameters to:

  • Area characteristics to Different for each flow path.

  • Orifice parameterization value Tabulated data - Volumetric flow rate vs. spool travel and pressure drop.

  • Positive spool position open connections or Negative spool position open connections one of the following values:

    • B-T only.

    • `P-A and B-T

    • `P-A, P-B, A-T, and B-T'.

This parameter is enabled only if the B-T channel is present in both the Positive spool position open connections and Negative spool position open connections parameters.

Units

m^3/s | mm^3/s | cm^3/s | m^3/hr | m^3/min | l/hr | l/min | l/s | gal/hr | gal/min | gal/s | ft^3/hr | ft^3/min | ft^3/s
Default value

[-9e-4, 1.6e-3, 2.0e-3, 2.4e-3] m^3/s
Program usage name

Vdot_vector_fixed_bt
Evaluatable

Yes