3-Way Directional Valve (TL)

Three-line two-position distributor in a thermal liquid network.

3 way directional valve tl

Description

Unit 3-Way Directional Valve (TL) is a spool distributor with three connected lines in the thermal liquid network, usually located between the hydraulic cylinder, pump and tank. The operation of the distributor is controlled by a single spool valve moving according to the signal on the S port. The spreader has two positions, hereafter referred to as positive and negative. The basic configuration of the spreader can be set by specifying the holes that open when the spool moves in positive and negative directions in the parameters Positive spool position open connections and Negative spool position open connections respectively.

It is possible to set the flow characteristic of the distributor channels in the Orifice parameterization in the form of a linear dependence or a tabular function provided by the user, which can be applied to one or all channels of the distributor.

An example of distributor configuration is shown in the figure.

3 way directional valve il 1 en

In the configuration shown below, the Positive spool position open connections parameters are set to A-T only. When the signal at port S moves the spool to a positive position (to the right of the neutral position), the channel between ports A and T is open. The channels between ports P and A and between ports P and T are closed.

3 way directional valve il 2

In the configuration below, the Negative spool position open connections parameters are set to P-A only. When the signal at port S moves the spool to a negative position (to the left of the neutral position), the channel between ports P and A is open, and the channels between ports T and A and between ports P and T are closed.

3 way directional valve il 3

You can set the channel between ports P and T by setting the Positive spool position open connections or Negative spool position open connections parameters to P-T only or P-A, A-T, and P-T.

A channel can be open in either positive or negative spool position, but not both.

Parameterization of the distributor channels

The Orifice parameterization parameter specifies the method of calculating the area of the through section. Calculation is performed either by channel parameters or by tabular data sets, which are set in parameters of 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 Different for all flow paths is set, then individual values are set for each channel.

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

Linear parameterization

If Linear - Area vs. spool travel is selected for the Orifice parameterization, the flow area of the channel depends linearly on the spool travel and the value supplied to the port S:

where

- is the maximum cross-sectional area of the channel (value of the Maximum orifice area parameters);
- leakage area (value of parameters Leakage area);
- spool travel between closed and open states of the channel (value of parameter Spool travel between closed and open orifice);
- spool relative position from 0 to .

For channels open in positive position:

.

For channels open in a negative position:

,

where - spool position corresponding to fully open channel section (value of parameter Spool position at maximum orifice area).

Note the linear growth from to in the figure:

Static

When the channel is in the nearly open or nearly closed position in the linear parameterization, you can maintain the numerical stability of the simulation by adjusting the smoothing factor - the value of the Smoothing factor parameter. If the Smoothing factor parameter value is not zero, a smooth change in the cross-sectional area between and is ensured.

Table parameterization

If Tabulated data - Area vs. spool travel is selected for the Orifice parameterization, the dependencies between the bore area and the relative position of the spool valve must be defined. Interpolation is used to determine the orifice area between the given data points. and are the first and last elements of the Opening area vector respectively.

Static

If Tabulated data - Volumetric flow rate vs. spool travel and pressure drop is selected for the Orifice parameterization, the relative spool position and pressure drop vectors must be set. The volumetric flow rate is calculated from the relationship between pressure drop and relative spool position. Interpolation is used to determine the flow rate between given data points. The mass flow rate is the product of the volumetric flow rate and density.

Static

If Tabulated data - Mass flow rate vs. opening and pressure drop is selected for parameterization Orifice parameterization, the block uses the mass flow rate table Mass flow rate table, mdot(ds,dp), the relative pressure drop vector Pressure drop vector, dp and the spool travel vector Spool travel vector, ds to determine the mass flow rate, .

Static

Approximations

Inertia of the fluid is not taken into account.
The load on the spool valve due to inertial, elastic and other forces is not taken into account.
It is assumed that all distributor channels are identical, unless otherwise stated.

Ports

Conserving

# P — thermal liquid port
thermal liquid

Details

Working fluid supply.

Program usage name

port_p

# T — port of thermal liquid
thermal liquid

Details

Drainage of the working fluid.

Program usage name

port_t

# A — thermal liquid port
thermal liquid

Details

Working Line.

Program usage name

port_a

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

Model Parameterization

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

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, A-T, and P-T` \| `P-A only` \| `A-T only` \| `P-T only`
Default value	`P-A only`
Program usage name	`positive_position_open_orifices`
Evaluatable	No

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

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, A-T, and P-T` \| `P-A only` \| `A-T only` \| `P-T only`
Default value	`A-T only`
Program usage name	`negative_position_open_orifices`
Evaluatable	No

# 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 the channels between ports P and A, ports A and T, ports P and T.

In both cases, ports A, P and T have the same cross-sectional areas, flow coefficients and Reynolds numbers. Orifice parameterization is also applied to all channels of the distributor.

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

Details

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

In the tabular parameterization it is possible to set 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 volumetric 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` \| `Tabulated data - Mass 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 | cm | ft | in | km | mi | mm | um | yd

Details

Spool stroke between closed and open channel states.

Dependencies

To use this parameter, set the Area characteristics parameters to Identical for all flow paths.

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

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

Details

Maximum cross-sectional area of the channel.

Dependencies

To use this parameter, set the Area characteristics parameters to Identical for all flow paths.

Values	`m^2` \| `cm^2` \| `ft^2` \| `in^2` \| `km^2` \| `mi^2` \| `mm^2` \| `um^2` \| `yd^2`
Default value	`0.0001 m^2`
Program usage name	`max_area`
Evaluatable	Yes

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

Details

Vector of spool positions. 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'.

Values	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`[0.0, 0.00125, 0.0025, 0.00375, 0.005] m`
Program usage name	`control_displacement_vector_1D`
Evaluatable	Yes

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

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'.

Values	`m^2` \| `cm^2` \| `ft^2` \| `in^2` \| `km^2` \| `mi^2` \| `mm^2` \| `um^2` \| `yd^2`
Default value	`[1.0e-10, 1.0e-5, 4.0e-5, 8.0e-5, 1.0e-4] m^2`
Program usage name	`restriction_area_vector_1D`
Evaluatable	Yes

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

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'.

Values	`m^2` \| `cm^2` \| `ft^2` \| `in^2` \| `km^2` \| `mi^2` \| `mm^2` \| `um^2` \| `yd^2`
Default value	`1e-10 m^2`
Program usage name	`leakage_area`
Evaluatable	Yes

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

Details

Vector of spool valve positions for tabular flow parameterization. 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) or the mass flow rate table Mass flow rate table, mdot(ds,dp). The values are listed in ascending order and the first element must be equal to 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' or `Tabulated data - Mass flow rate vs. spool travel and pressure drop'.

Values	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`[0.0, 0.00125, 0.0025, 0.00375, 0.005] m`
Program usage name	`control_displacement_vector_2D`
Evaluatable	Yes

# Pressure drop vector, dp — vector of differential pressure values
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar

Details

Vector of differential pressure values for tabular flow parameterization. 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) or the mass flow rate table Mass flow rate table, mdot(ds,dp). The values are listed in ascending order and must be greater than 0. Linear interpolation is used to calculate intermediate values.

Dependencies

Values	`Pa` \| `GPa` \| `MPa` \| `atm` \| `bar` \| `kPa` \| `ksi` \| `psi` \| `uPa` \| `kbar`
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 | m^3/h | cm^3/s | mm^3/s | ft^3/s | lpm | l/s | gpm | gal/s | gal/h

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

Values	`m^3/s` \| `m^3/h` \| `cm^3/s` \| `mm^3/s` \| `ft^3/s` \| `lpm` \| `l/s` \| `gpm` \| `gal/s` \| `gal/h`
Default value	`[-9.05e-10 1.57e-9 2.02e-9 2.39e-9; -9.05e-5 1.57e-4 2.02e-4 2.39e-4; -3.62e-4 6.27e-4 8.10e-4 9.58e-4; -7.24e-4 1.25e-3 1.62e-3 1.92e-3; -9.05e-4 1.56e-3 2.00e-3 2.39e-3] m^3/s`
Program usage name	`Vdot_matrix_2D`
Evaluatable	Yes

# Mass flow rate table, mdot(ds,dp) — mass flow rate table
kg/s | N*s/m | N/(m/s) | lbf/(ft/s) | lbf/(in/s)

Details

Matrix to of mass 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 - Mass flow rate vs. spool travel and pressure drop'.

Values	`kg/s` \| `N*s/m` \| `N/(m/s)` \| `lbf/(ft/s)` \| `lbf/(in/s)`
Default value	`1.0e3 * [-9.05e-10 1.57e-9 2.02e-9 2.39e-9; -9.05e-5 1.57e-4 2.02e-4 2.39e-4; -3.62e-4 6.27e-4 8.10e-4 9.58e-4; -7.24e-4 1.25e-3 1.62e-3 1.92e-3; -9.05e-4 1.56e-3 2.00e-3 2.39e-3] kg/s`
Program usage name	`mdot_matrix_2D`
Evaluatable	Yes

Details

Temperature for which the tabulated mass flow data is set.

Dependencies

To use this parameter, set the Orifice parameterization parameters to Tabulated data - Mass flow rate vs. spool travel and pressure drop.

Values	`K` \| `degC` \| `degF` \| `degR` \| `deltaK` \| `deltadegC` \| `deltadegF` \| `deltadegR`
Default value	`293.15 K`
Program usage name	`T_inflow_ref`
Evaluatable	Yes

# Reference inflow pressure — pressure for which the tabulated mass flow rate data are set
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar

Details

The pressure for which the tabulated mass flow rate data is set. The unit uses this parameter to calculate the corresponding density.

Dependencies

To use this parameter, set the Orifice parameterization parameters to `Tabulated data - Mass flow rate vs. spool travel and pressure drop'.

Values	`Pa` \| `GPa` \| `MPa` \| `atm` \| `bar` \| `kPa` \| `ksi` \| `psi` \| `uPa` \| `kbar`
Default value	`0.101325 MPa`
Program usage name	`p_inflow_ref`
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.

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.

Default value	`150.0`
Program usage name	`Re_critical`
Evaluatable	Yes

# Smoothing factor — numerical smoothing factor

Details

A continuous smoothing factor that provides a smooth opening by correcting the channel characteristic in the nearly open and nearly closed positions. Set a non-zero value less than one to increase the stability of the simulation in these modes.

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.

Default value	`false (switched off)`
Program usage name	`pressure_recovery`
Evaluatable	No

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

Details

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

Values	`m^2` \| `cm^2` \| `ft^2` \| `in^2` \| `km^2` \| `mi^2` \| `mm^2` \| `um^2` \| `yd^2`
Default value	`0.01 m^2`
Program usage name	`port_area`
Evaluatable	Yes

P-A Orifice

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

Details

Spool position corresponding to a fully open channel between ports P and A. By default value characterises the channel with partial overlap.

If the value Spool position at maximum P-A orifice area is less than P-A spool travel between closed and open orifice, the channel has negative overlap, i.e. it is partially open when the spool position is 0m.
If the value Spool position at maximum P-A orifice area is greater than the value P-A spool travel between closed and open orifice, the channel has positive overlap. This means that the channel remains closed in a certain range of spool positions.
If the value of Spool position at maximum P-A orifice area is equal to the value of P-A spool travel between closed and open orifice, the channel has zero overlap. This means that the channel is closed when the spool position is 0 and starts to open as soon as the spool position changes.

Values	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`0.0045 m`
Program usage name	`max_control_displacement_pa`
Evaluatable	Yes

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

Details

Maximum spool stroke for the channel between ports P and A.

Dependencies

To use this parameter, set the Area characteristics parameter to Different for each flow path.

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

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

Details

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

Dependencies

To use this parameter, set the Area characteristics parameter to Different for each flow path and the Orifice parameterization parameter to Linear - area vs. spool travel.

Values	`m^2` \| `cm^2` \| `ft^2` \| `in^2` \| `km^2` \| `mi^2` \| `mm^2` \| `um^2` \| `yd^2`
Default value	`0.0001 m^2`
Program usage name	`max_area_pa`
Evaluatable	Yes

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

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 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 `Different for each flow path' and the Orifice parameterization parameter to `Tabulated data - Area vs. spool travel'.

Values	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`[0.0, 0.00125, 0.0025, 0.00375, 0.005] m`
Program usage name	`control_displacement_vector_1D_pa`
Evaluatable	Yes

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

Details

Vector of channel cross-sectional area values for the tabular parameterization of the valve area. The dimensionality of the vector corresponds to the P-A orifice spool travel vector. The values are listed in ascending order. The first element is the leakage area and 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 `Different for each flow path' and the Orifice parameterization parameter to `Tabulated data - Area vs. spool travel'.

Values	`m^2` \| `cm^2` \| `ft^2` \| `in^2` \| `km^2` \| `mi^2` \| `mm^2` \| `um^2` \| `yd^2`
Default value	`[1.0e-10, 1.0e-5, 4.0e-5, 8.0e-5, 1.0e-4] m^2`
Program usage name	`restriction_area_vector_1D_pa`
Evaluatable	Yes

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

Details

Vector of spool positions for tabular flow parameterization. The dimension of the spool position vector corresponds to the differential pressure vector P-A orifice pressure drop vector, dp and the volumetric flow rate table P-A orifice volumetric flow rate table, q(s,dp) or the mass flow rate table P-A orifice mass flow rate table, mdot(ds,dp). Linear interpolation is used to calculate intermediate values.

Dependencies

To use this parameter, set the Area characteristics parameter to `Different for each flow path' and the Orifice parameterization parameter to `Tabulated data - Volumetric flow rate vs. spool travel and pressure drop' or `Tabulated data - Mass flow rate vs. spool travel and pressure drop'.

Values	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`[0.0, 0.00125, 0.0025, 0.00375, 0.005] m`
Program usage name	`control_displacement_vector_2D_pa`
Evaluatable	Yes

# P-A orifice pressure drop vector, dp — vector of differential pressure values
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar

Details

Vector of differential pressure values for tabular flow parameterization. The dimension of the differential pressure vector corresponds to the spool position vector P-A orifice spool travel vector, ds and the volumetric flow rate table P-A orifice volumetric flow rate table, q(ds,dp) or the mass flow rate table P-A orifice mass flow rate table, mdot(ds,dp). The values are listed in ascending order and must be greater than 0. Linear interpolation is used to calculate intermediate values.

Dependencies

Values	`Pa` \| `GPa` \| `MPa` \| `atm` \| `bar` \| `kPa` \| `ksi` \| `psi` \| `uPa` \| `kbar`
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 | m^3/h | cm^3/s | mm^3/s | ft^3/s | lpm | l/s | gpm | gal/s | gal/h

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

Values	`m^3/s` \| `m^3/h` \| `cm^3/s` \| `mm^3/s` \| `ft^3/s` \| `lpm` \| `l/s` \| `gpm` \| `gal/s` \| `gal/h`
Default value	`[-9.05e-10 1.57e-9 2.02e-9 2.39e-9; -9.05e-5 1.57e-4 2.02e-4 2.39e-4; -3.62e-4 6.27e-4 8.10e-4 9.58e-4; -7.24e-4 1.25e-3 1.62e-3 1.92e-3; -9.05e-4 1.56e-3 2.00e-3 2.39e-3] m^3/s`
Program usage name	`Vdot_matrix_2D_pa`
Evaluatable	Yes

# P-A orifice mass flow rate table, mdot(ds,dp) — mass flow rate table
kg/s | N*s/m | N/(m/s) | lbf/(ft/s) | lbf/(in/s)

Details

Matrix to of mass 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 Area characteristics parameter to `Different for each flow path' and the Orifice parameterization parameter to `Tabulated data - Mass flow rate vs. spool travel and pressure drop'.

Values	`kg/s` \| `N*s/m` \| `N/(m/s)` \| `lbf/(ft/s)` \| `lbf/(in/s)`
Default value	`1.0e3 * [-9.05e-10 1.57e-9 2.02e-9 2.39e-9; -9.05e-5 1.57e-4 2.02e-4 2.39e-4; -3.62e-4 6.27e-4 8.10e-4 9.58e-4; -7.24e-4 1.25e-3 1.62e-3 1.92e-3; -9.05e-4 1.56e-3 2.00e-3 2.39e-3] kg/s`
Program usage name	`mdot_matrix_2D_pa`
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 | cm | ft | in | km | mi | mm | um | yd

Details

Spool position corresponding to a fully open channel between ports A and T. By default value characterises the channel with partial overlap.

If value Spool position at maximum A-T orifice area is less than value A-T spool travel between closed and open orifice, the channel has negative overlap, i.e. it is partially open when spool position is equal to 0m.
If the value Spool position at maximum A-T orifice area is greater than the value A-T spool travel between closed and open orifice, the channel has positive overlap. This means that the channel remains closed in a certain range of spool positions.
If the value of Spool position at maximum A-T orifice area is equal to the value of A-T spool travel between closed and open orifice, the channel has zero overlap. This means that the channel is closed when the spool position is 0 and starts to open as soon as the spool position changes.

Values	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`-0.0045 m`
Program usage name	`max_control_displacement_at`
Evaluatable	Yes

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

Details

Maximum spool stroke for the channel between ports A and T.

Dependencies

To use this parameter, set the Area characteristics parameter to Different for each flow path.

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

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

Details

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

Dependencies

To use this parameter, set the Area characteristics parameter to Different for each flow path and the Orifice parameterization parameter to Linear - area vs. spool travel.

Values	`m^2` \| `cm^2` \| `ft^2` \| `in^2` \| `km^2` \| `mi^2` \| `mm^2` \| `um^2` \| `yd^2`
Default value	`0.0001 m^2`
Program usage name	`max_area_at`
Evaluatable	Yes

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

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 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 `Different for each flow path' and the Orifice parameterization parameter to `Tabulated data - Area vs. spool travel'.

Values	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`[0.0, 0.00125, 0.0025, 0.00375, 0.005] m`
Program usage name	`control_displacement_vector_1D_at`
Evaluatable	Yes

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

Details

Vector of channel cross-sectional area values for the tabular parameterization of the valve area. The dimensionality of the vector corresponds to the A-T orifice spool travel vector. The values are listed in ascending order. The first element is the leakage area and 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 `Different for each flow path' and the Orifice parameterization parameter to `Tabulated data - Area vs. spool travel'.

Values	`m^2` \| `cm^2` \| `ft^2` \| `in^2` \| `km^2` \| `mi^2` \| `mm^2` \| `um^2` \| `yd^2`
Default value	`[1.0e-10, 1.0e-5, 4.0e-5, 8.0e-5, 1.0e-4] m^2`
Program usage name	`restriction_area_vector_1D_at`
Evaluatable	Yes

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

Details

Vector of spool positions for tabular flow parameterization. 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(ds,dp) or the mass flow rate table A-T orifice mass flow rate table, mdot(ds,dp). Linear interpolation is used to calculate intermediate values.

Dependencies

Values	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`[0.0, 0.00125, 0.0025, 0.00375, 0.005] m`
Program usage name	`control_displacement_vector_2D_at`
Evaluatable	Yes

# A-T orifice pressure drop vector, dp — vector of differential pressure values
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar

Details

Vector of differential pressure values for tabular flow parameterization. The dimension of the differential pressure vector corresponds to the spool position vector A-T orifice spool travel vector, ds and the volumetric flow rate table A-T orifice volumetric flow rate table, q(ds,dp) or the mass flow rate table A-T orifice mass flow rate table, mdot(ds,dp). Values are listed in ascending order and must be greater than 0. Linear interpolation is used to calculate intermediate values.

Dependencies

Values	`Pa` \| `GPa` \| `MPa` \| `atm` \| `bar` \| `kPa` \| `ksi` \| `psi` \| `uPa` \| `kbar`
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 | m^3/h | cm^3/s | mm^3/s | ft^3/s | lpm | l/s | gpm | gal/s | gal/h

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

Values	`m^3/s` \| `m^3/h` \| `cm^3/s` \| `mm^3/s` \| `ft^3/s` \| `lpm` \| `l/s` \| `gpm` \| `gal/s` \| `gal/h`
Default value	`[-9.05e-10 1.57e-9 2.02e-9 2.39e-9; -9.05e-5 1.57e-4 2.02e-4 2.39e-4; -3.62e-4 6.27e-4 8.10e-4 9.58e-4; -7.24e-4 1.25e-3 1.62e-3 1.92e-3; -9.05e-4 1.56e-3 2.00e-3 2.39e-3] m^3/s`
Program usage name	`Vdot_matrix_2D_at`
Evaluatable	Yes

# A-T orifice mass flow rate table, mdot(ds,dp) — mass flow rate table
kg/s | N*s/m | N/(m/s) | lbf/(ft/s) | lbf/(in/s)

Details

Matrix to of mass 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

Values	`kg/s` \| `N*s/m` \| `N/(m/s)` \| `lbf/(ft/s)` \| `lbf/(in/s)`
Default value	`1.0e3 * [-9.05e-10 1.57e-9 2.02e-9 2.39e-9; -9.05e-5 1.57e-4 2.02e-4 2.39e-4; -3.62e-4 6.27e-4 8.10e-4 9.58e-4; -7.24e-4 1.25e-3 1.62e-3 1.92e-3; -9.05e-4 1.56e-3 2.00e-3 2.39e-3] kg/s`
Program usage name	`mdot_matrix_2D_at`
Evaluatable	Yes

P-T Orifice

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

Details

Spool position corresponding to a fully open channel between ports P and T. By default value characterises the channel with partial overlap.

If value Spool position at maximum P-T orifice area is less than value P-T spool travel between closed and open orifice, the channel has negative overlap, i.e. it is partially open when spool position is equal to 0 m.
If the value Spool position at maximum P-T orifice area is greater than the value P-T spool travel between closed and open orifice, the channel has positive overlap. This means that the channel remains closed in a certain range of spool positions.
If the value of Spool position at maximum P-T orifice area is equal to the value of P-T spool travel between closed and open orifice, the channel has zero overlap. This means that the channel is closed when the spool position is 0 and starts to open as soon as the spool position changes.

Values	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`0.0045 m`
Program usage name	`max_control_displacement_pt`
Evaluatable	Yes

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

Details

Maximum spool stroke for the channel between ports P and T.

Dependencies

To use this parameter, set the Area characteristics parameters to Different for each flow path.

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

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

Details

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

Dependencies

To use this parameter, set the Area characteristics parameter to Different for each flow path and the Orifice parameterization parameter to Linear - area vs. spool travel.

Values	`m^2` \| `cm^2` \| `ft^2` \| `in^2` \| `km^2` \| `mi^2` \| `mm^2` \| `um^2` \| `yd^2`
Default value	`0.0001 m^2`
Program usage name	`max_area_pt`
Evaluatable	Yes

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

Details

Vector of spool positions. The dimensionality of the vector corresponds to the P-T 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 `Different for each flow path' and the Orifice parameterization parameter to `Tabulated data - Area vs. spool travel'.

Values	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`[0.0, 0.00125, 0.0025, 0.00375, 0.005] m`
Program usage name	`control_displacement_vector_1D_pt`
Evaluatable	Yes

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

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-T orifice spool travel vector. The values are listed in ascending order. The first element is the leakage area and 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 `Different for each flow path' and the Orifice parameterization parameter to `Tabulated data - Area vs. spool travel'.

Values	`m^2` \| `cm^2` \| `ft^2` \| `in^2` \| `km^2` \| `mi^2` \| `mm^2` \| `um^2` \| `yd^2`
Default value	`[1.0e-10, 1.0e-5, 4.0e-5, 8.0e-5, 1.0e-4] m^2`
Program usage name	`restriction_area_vector_1D_pt`
Evaluatable	Yes

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

Details

Vector of spool positions for tabular flow parameterization. The dimension of the spool position vector corresponds to the differential pressure vector P-T orifice pressure drop vector, dp and the volumetric flow rate table P-T orifice volumetric flow rate table, q(ds,dp) or the mass flow rate table P-T orifice mass flow rate table, mdot(ds,dp). Linear interpolation is used to calculate intermediate values.

Dependencies

Values	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`[0.0, 0.00125, 0.0025, 0.00375, 0.005] m`
Program usage name	`control_displacement_vector_2D_pt`
Evaluatable	Yes

# P-T orifice pressure drop vector, dp — vector of differential pressure values
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar

Details

Vector of differential pressure values for tabular flow parameterization. The dimension of the differential pressure vector corresponds to the spool position vector P-T orifice spool travel vector, ds and the volumetric flow rate table P-T orifice volumetric flow rate table, q(ds,dp) or the mass flow rate table P-T orifice mass flow rate table, mdot(ds,dp). The values are listed in ascending order and must be greater than 0. Linear interpolation is used to calculate intermediate values.

Dependencies

Values	`Pa` \| `GPa` \| `MPa` \| `atm` \| `bar` \| `kPa` \| `ksi` \| `psi` \| `uPa` \| `kbar`
Default value	`[-0.1, 0.3, 0.5, 0.7] MPa`
Program usage name	`delta_p_vector_2D_pt`
Evaluatable	Yes

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

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-T orifice spool travel vector, ds.
- number of elements in the pressure drop vector P-T orifice pressure drop vector, dp.

Dependencies

Values	`m^3/s` \| `m^3/h` \| `cm^3/s` \| `mm^3/s` \| `ft^3/s` \| `lpm` \| `l/s` \| `gpm` \| `gal/s` \| `gal/h`
Default value	`[-9.05e-10 1.57e-9 2.02e-9 2.39e-9; -9.05e-5 1.57e-4 2.02e-4 2.39e-4; -3.62e-4 6.27e-4 8.10e-4 9.58e-4; -7.24e-4 1.25e-3 1.62e-3 1.92e-3; -9.05e-4 1.56e-3 2.00e-3 2.39e-3] m^3/s`
Program usage name	`Vdot_matrix_2D_pt`
Evaluatable	Yes

# P-T orifice mass flow rate table, mdot(ds,dp) — mass flow rate table
kg/s | N*s/m | N/(m/s) | lbf/(ft/s) | lbf/(in/s)

Details

Matrix to of mass 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-T orifice spool travel vector, ds.
- number of elements in the pressure drop vector P-T orifice pressure drop vector, dp.

Dependencies

Values	`kg/s` \| `N*s/m` \| `N/(m/s)` \| `lbf/(ft/s)` \| `lbf/(in/s)`
Default value	`1.0e3 * [-9.05e-10 1.57e-9 2.02e-9 2.39e-9; -9.05e-5 1.57e-4 2.02e-4 2.39e-4; -3.62e-4 6.27e-4 8.10e-4 9.58e-4; -7.24e-4 1.25e-3 1.62e-3 1.92e-3; -9.05e-4 1.56e-3 2.00e-3 2.39e-3] kg/s`
Program usage name	`mdot_matrix_2D_pt`
Evaluatable	Yes