3-Way Directional Valve (TL)

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

blockType: EngeeFluids.ThermalLiquid.Valves.DirectionalControl.ThreeWay

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/Physical Modeling/Fluids/Thermal Liquid/Valves & Orifices/Directional Control Valves/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 that are open in a positive position
All closed | P-A, A-T, and P-T | P-A only | A-T only | P-T only

Details

Channels that are open in a positive position. This parameter sets the distributor configuration and determines the relative position of the spool 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 that are open in a negative position
All closed | P-A, A-T, and P-T | P-A only | A-T only | P-T only

Details

Channels that are open in a negative position. This parameter sets the distributor configuration and determines the relative position of the spool 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 — the method of defining channel characteristics
Identical for all flow paths | Different for each flow path

Details

Sets identical or individual flow characteristics for the passage section of the channels:

Identical for all flow paths — identical characteristics for all distributor channels.
Different for each flow path — Individual characteristics are set for 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 also applies to all distributor channels.

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 — the method of calculating the area of channels
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 cross-sectional area of channels during modeling.

In the tabular parameterization, you can set a non-linear profile of the flow characteristics of the channels, in the form of a dependence of the flow area on the position of the spool, or a dependence of the volume flow on the pressure drop and the position of the spool.

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 stroke of the spool
m | um | mm | cm | km | in | ft | yd | mi | nmi

Details

The stroke of the spool between the closed and open channel states.

Dependencies

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

Units	`m` \| `um` \| `mm` \| `cm` \| `km` \| `in` \| `ft` \| `yd` \| `mi` \| `nmi`
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 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac

Details

The maximum cross-sectional area of the channel.

Dependencies

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

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

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

Details

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

Dependencies

Units	`m` \| `um` \| `mm` \| `cm` \| `km` \| `in` \| `ft` \| `yd` \| `mi` \| `nmi`
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 area of the passage section of the channel
m^2 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac

Details

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

Dependencies

Units	`m^2` \| `um^2` \| `mm^2` \| `cm^2` \| `km^2` \| `in^2` \| `ft^2` \| `yd^2` \| `mi^2` \| `ha` \| `ac`
Default value	`[1.0e-10, 1.0e-5, 4.0e-5, 8.0e-5, 1.0e-4] m^2`
Program usage name	`orifice_area_vector_1D`
Evaluatable	Yes

# Leakage area — leakage area through the channel in the 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 gaps when the channel is completely blocked. Any area less than this value is equal to the specified leakage area. This parameter contributes to the stability of the numerical solution by maintaining the continuity of the flow.

Dependencies

To use this parameter, set the Area characteristics parameter to Identical for all flow paths, and for the Orifice parameterization parameter , the value 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

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

Details

A vector of spool positions for tabular flow parameterization. The dimension of the position vector of the spool corresponds to the pressure drop vector Pressure drop vector, dp and the table of volume flow values Volumetric flow rate table, q(ds,dp) or the table of mass flow values Mass flow rate table, mdot(ds,dp). The values are listed in ascending order, and the first element should be equal to 0. Linear interpolation is used to calculate the intermediate values.

Dependencies

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

Units	`m` \| `um` \| `mm` \| `cm` \| `km` \| `in` \| `ft` \| `yd` \| `mi` \| `nmi`
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 pressure drop 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 flow parameterization. The pressure drop vector corresponds to the position vector of the spool Spool travel vector, ds and the table of volume flow values Volumetric flow rate table, q(ds,dp) or the table of mass flow values Mass flow rate table, mdot(ds,dp). The values are listed in ascending order and must be greater. 0. Linear interpolation is used to calculate the intermediate values.

Dependencies

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 volume flow values
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

The matrix on volume flow rates corresponding to the values of the differential pressure and the position of the spool. on — the sizes of the corresponding vectors:

— the number of elements in the spool position vector Spool travel vector, ds.
— the number of elements in the pressure drop vector Pressure drop vector, dp.

Dependencies

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	`[-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

Details

The matrix on the mass flow rates corresponding to the values of the pressure drop and the position of the spool. on — the sizes of the corresponding vectors:

— the number of elements in the spool position vector Spool travel vector, ds.
— the 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 for the Orifice parameterization parameter , the value Tabulated data - Mass flow rate vs. spool travel and pressure drop.

Units	`kg/s` \| `kg/hr` \| `kg/min` \| `g/hr` \| `g/min` \| `g/s` \| `t/hr` \| `lbm/hr` \| `lbm/min` \| `lbm/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

The temperature for which tabular mass flow data is set.

Dependencies

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

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

# Reference inflow pressure — the pressure for which tabular mass flow data is set
Pa | uPa | hPa | kPa | MPa | GPa | kgf/m^2 | kgf/cm^2 | kgf/mm^2 | mbar | bar | kbar | atm | ksi | psi | mmHg | inHg

Details

The pressure for which tabular mass flow data is set. The block uses this parameter to calculate the corresponding density.

Dependencies

To use this parameter, set the Orifice parameterization parameter to Tabulated data - Mass 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	`0.101325 MPa`
Program usage name	`p_inflow_ref`
Evaluatable	Yes

# Discharge coefficient — expense ratio

Details

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

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

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

Details

The upper limit of the Reynolds number for laminar flow through a channel.

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

# Smoothing factor — numerical smoothing coefficient

Details

The continuous smoothing coefficient, which ensures smooth opening by correcting the channel characteristics in the almost open and almost 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 — should the pressure increase be taken into account when expanding the area

Details

Should the pressure increase be taken into account when liquid flows from an area with a smaller cross-sectional area to an area 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 — the 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 in ports A, P and T. This area is used when calculating the mass flow through the distributor.

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

P-A Orifice

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

Details

The position of the spool corresponding to the fully open channel between ports P and A. The default value characterizes a channel with partial overlap.

If the value of Spool position at maximum P-A orifice area is less than the value of P-A spool travel between closed and open orifice, then the channel has a negative overlap, that is, it is partially open when the spool position is 0 m.
If the value of Spool position at maximum P-A orifice area is greater than the value of P-A spool travel between closed and open orifice, then the channel has a 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, then the channel has zero overlap. This means that the channel is closed when the position of the spool is 0, and begins to open as soon as the position of the spool changes.

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

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

Details

The maximum stroke of the spool for the channel between ports P and A.

Dependencies

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

Units	`m` \| `um` \| `mm` \| `cm` \| `km` \| `in` \| `ft` \| `yd` \| `mi` \| `nmi`
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 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac

Details

The cross-sectional area of the channel 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 for the Orifice parameterization parameter , the value 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	`0.0001 m^2`
Program usage name	`max_area_pa`
Evaluatable	Yes

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

Details

The position vector of the spool. The dimension of the vector corresponds to the vector P-A orifice area vector. The values are listed in ascending order, and the first element should be equal to 0. Linear interpolation is used between the data points in the table.

Dependencies

Units	`m` \| `um` \| `mm` \| `cm` \| `km` \| `in` \| `ft` \| `yd` \| `mi` \| `nmi`
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 area of the passage section of the channel
m^2 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac

Details

The vector of values of the area of the passage section of the channel for tabular parameterization of the valve area. The dimension of the vector corresponds to the vector P-A orifice spool travel vector. The values are listed in ascending order. The first element is the leakage area, the last element is the maximum cross—sectional area of the channel. Linear interpolation is used between data points.

Dependencies

Units	`m^2` \| `um^2` \| `mm^2` \| `cm^2` \| `km^2` \| `in^2` \| `ft^2` \| `yd^2` \| `mi^2` \| `ha` \| `ac`
Default value	`[1.0e-10, 1.0e-5, 4.0e-5, 8.0e-5, 1.0e-4] m^2`
Program usage name	`orifice_area_vector_1D_pa`
Evaluatable	Yes

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

Details

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

Dependencies

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

Units	`m` \| `um` \| `mm` \| `cm` \| `km` \| `in` \| `ft` \| `yd` \| `mi` \| `nmi`
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 pressure drop 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 flow parameterization. The dimension of the differential pressure vector corresponds to the position vector of the spool P-A orifice spool travel vector, ds and the table of volume flow values P-A orifice volumetric flow rate table, q(ds,dp) or the table of mass flow values P-A orifice mass flow rate table, mdot(ds,dp). The values are listed in ascending order and must be greater. 0. Linear interpolation is used to calculate the intermediate values.

Dependencies

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 volume flow values
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

The matrix on volume flow rates corresponding to the values of the differential pressure and the position of the spool. on — the sizes of the corresponding vectors:

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

Dependencies

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	`[-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

Details

The matrix on the mass flow rates corresponding to the values of the pressure drop and the position of the spool. on — the sizes of the corresponding vectors:

— the number of elements in the spool position vector P-A orifice spool travel vector, ds.
— the 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 for the Orifice parameterization parameter , the value Tabulated data - Mass flow rate vs. spool travel and pressure drop.

Units	`kg/s` \| `kg/hr` \| `kg/min` \| `g/hr` \| `g/min` \| `g/s` \| `t/hr` \| `lbm/hr` \| `lbm/min` \| `lbm/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 — the position of the spool at the maximum channel area between ports A and T
m | um | mm | cm | km | in | ft | yd | mi | nmi

Details

The position of the spool corresponding to the fully open channel between ports A and T. The default value characterizes a channel with partial overlap.

If the value of Spool position at maximum A-T orifice area is less than the value of A-T spool travel between closed and open orifice, then the channel has a negative overlap, that is, it is partially open when the spool position is 0 m.
If the value of Spool position at maximum A-T orifice area is greater than the value of A-T spool travel between closed and open orifice, then the channel has a 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, then the channel has zero overlap. This means that the channel is closed when the position of the spool is 0, and begins to open as soon as the position of the spool changes.

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

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

Details

The maximum stroke of the spool for the channel between ports A and T.

Dependencies

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

Units	`m` \| `um` \| `mm` \| `cm` \| `km` \| `in` \| `ft` \| `yd` \| `mi` \| `nmi`
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 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac

Details

The cross-sectional area of the channel 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 for the Orifice parameterization parameter , the value 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	`0.0001 m^2`
Program usage name	`max_area_at`
Evaluatable	Yes

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

Details

The position vector of the spool. The dimension of the vector corresponds to the vector A-T orifice area vector. The values are listed in ascending order, and the first element should be equal to 0. Linear interpolation is used between the data points in the table.

Dependencies

Units	`m` \| `um` \| `mm` \| `cm` \| `km` \| `in` \| `ft` \| `yd` \| `mi` \| `nmi`
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 area of the passage section of the channel
m^2 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac

Details

The vector of values of the area of the passage section of the channel for tabular parameterization of the valve area. The dimension of the vector corresponds to the A-T orifice spool travel vector vector. The values are listed in ascending order. The first element is the leakage area, the last element is the maximum cross–sectional area of the channel. Linear interpolation is used between data points.

Dependencies

Units	`m^2` \| `um^2` \| `mm^2` \| `cm^2` \| `km^2` \| `in^2` \| `ft^2` \| `yd^2` \| `mi^2` \| `ha` \| `ac`
Default value	`[1.0e-10, 1.0e-5, 4.0e-5, 8.0e-5, 1.0e-4] m^2`
Program usage name	`orifice_area_vector_1D_at`
Evaluatable	Yes

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

Details

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

Dependencies

Units	`m` \| `um` \| `mm` \| `cm` \| `km` \| `in` \| `ft` \| `yd` \| `mi` \| `nmi`
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 pressure drop 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 flow parameterization. The dimension of the differential pressure vector corresponds to the position vector of the spool A-T orifice spool travel vector, ds and the table of volume flow values A-T orifice volumetric flow rate table, q(ds,dp) or the table of mass flow values A-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 the intermediate values.

Dependencies

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 volume flow values
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

The matrix on volume flow rates corresponding to the values of the differential pressure and the position of the spool. on — the sizes of the corresponding vectors:

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

Dependencies

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	`[-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

Details

The matrix on the mass flow rates corresponding to the values of the differential pressure and the position of the spool. on — the sizes of the corresponding vectors:

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

Dependencies

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

Units	`kg/s` \| `kg/hr` \| `kg/min` \| `g/hr` \| `g/min` \| `g/s` \| `t/hr` \| `lbm/hr` \| `lbm/min` \| `lbm/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 — the position of the spool at the maximum channel area between ports P and T
m | um | mm | cm | km | in | ft | yd | mi | nmi

Details

The position of the spool corresponding to the fully open channel between ports P and T. The default value characterizes a channel with partial overlap.

If the value of Spool position at maximum P-T orifice area is less than the value of P-T spool travel between closed and open orifice, then the channel has a negative overlap, that is, it is partially open when the spool position is 0 m.
If the value of Spool position at maximum P-T orifice area is greater than the value of P-T spool travel between closed and open orifice, then the channel has a 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, then the channel has zero overlap. This means that the channel is closed when the position of the spool is 0, and begins to open as soon as the position of the spool changes.

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

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

Details

The maximum stroke of the spool for the channel between ports P and T.

Dependencies

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

Units	`m` \| `um` \| `mm` \| `cm` \| `km` \| `in` \| `ft` \| `yd` \| `mi` \| `nmi`
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 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac

Details

The cross-sectional area of the channel 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 for the Orifice parameterization parameter , the value 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	`0.0001 m^2`
Program usage name	`max_area_pt`
Evaluatable	Yes

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

Details

The position vector of the spool. The dimension of the vector corresponds to the vector P-T orifice area vector. The values are listed in ascending order, and the first element should be equal to 0. Linear interpolation is used between the data points in the table.

Dependencies

Units	`m` \| `um` \| `mm` \| `cm` \| `km` \| `in` \| `ft` \| `yd` \| `mi` \| `nmi`
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 area of the passage section of the channel
m^2 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac

Details

The vector of values of the area of the passage section of the channel for tabular parameterization of the valve area. The dimension of the vector corresponds to the vector P-T orifice spool travel vector. The values are listed in ascending order. The first element is the leakage area, the last element is the maximum cross—sectional area of the channel. Linear interpolation is used between data points.

Dependencies

Units	`m^2` \| `um^2` \| `mm^2` \| `cm^2` \| `km^2` \| `in^2` \| `ft^2` \| `yd^2` \| `mi^2` \| `ha` \| `ac`
Default value	`[1.0e-10, 1.0e-5, 4.0e-5, 8.0e-5, 1.0e-4] m^2`
Program usage name	`orifice_area_vector_1D_pt`
Evaluatable	Yes

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

Details

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

Dependencies

Units	`m` \| `um` \| `mm` \| `cm` \| `km` \| `in` \| `ft` \| `yd` \| `mi` \| `nmi`
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 pressure drop 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 flow parameterization. The dimension of the differential pressure vector corresponds to the position vector of the spool P-T orifice spool travel vector, ds and the table of volume flow values P-T orifice volumetric flow rate table, q(ds,dp) or the table of mass flow values P-T orifice mass flow rate table, mdot(ds,dp). The values are listed in ascending order and must be greater. 0. Linear interpolation is used to calculate the intermediate values.

Dependencies

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_pt`
Evaluatable	Yes

# P-T orifice volumetric flow rate table, q(ds,dp) — table of volume flow values
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

The matrix on volume flow rates corresponding to the values of the differential pressure and the position of the spool. on — the sizes of the corresponding vectors:

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

Dependencies

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	`[-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

Details

The matrix on the mass flow rates corresponding to the values of the pressure drop and the position of the spool. on — the sizes of the corresponding vectors:

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

Dependencies

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

Units	`kg/s` \| `kg/hr` \| `kg/min` \| `g/hr` \| `g/min` \| `g/s` \| `t/hr` \| `lbm/hr` \| `lbm/min` \| `lbm/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

Examples

Recirculating drive with differential cylinders