# 3-Way Directional Valve (TL)

3-position directional valve in a thermal liquid network

**Library:**Simscape / Fluids / Thermal Liquid / Valves & Orifices / Directional Control Valves

## Description

The 3-Way Directional Valve (TL) block represents a
valve with three openings in a thermal liquid network, typically between an actuator,
pump, and tank. The valve operation is controlled by a single spool displaced according
to the signal at port **S**. You can set the baseline configuration of
your valve by specifying the orifices that are open when the spool moves in the positive
direction and negative directions in the **Positive spool position open
connections** and **Negative spool position open
connections** parameters, respectively.

You can set the model for valve opening in the **Orifice
parameterization** parameter as a linear relationship or function of
user-provided data, which can be applied to one or all flow paths in the valve.

**Example Valve Configuration**

In this configuration, **Positive spool position open connections**
is set to `A-T only`

. When the signal at port
**S** moves the spool to a positive position, the path between
ports **A** and **T** is open to flow. The paths
between ports **P** and **A** and between ports
**P** and **T** are closed:

In this configuration, **Negative spool position open connections**
is set to `P-A only`

. When the signal at port
**S** moves the spool to a negative position, the path between
ports **P** and **A** is open to flow and the paths
between ports **T** and **A** and between ports
**P** and **T** are closed:

You can open the path between ports **P** and **T**
by setting either **Positive spool position open connections** or
**Negative spool position open connections** to ```
P-T
only
```

or `P-A, A-T, and P-T`

.

A flow path can be open in either the positive or negative spool positions, but not both.

### Valve Orifice Parameterizations

The **Orifice parameterization** sets the method for calculating
the valve open area. The calculations are based either on the orifice parameters or
tabulated data sets specified in the **Model Parameterization**
tab. The block uses the same data for all flow paths if **Area
characteristics** is set to ```
Identical for all flow
paths
```

; otherwise, individual values are applied in the
`Different for all flow paths`

setting. The orifice
parameterizations are:

`Linear - area vs. spool travel`

The opening area is a linear function of the spool travel distance and the signal received at port

**S**:$${A}_{orifice}=\frac{\left({A}_{\mathrm{max}}-{A}_{leak}\right)}{\Delta {S}_{\mathrm{max}}}\Delta S+{A}_{leak},$$

where:

*A*_{max}is the**Maximum orifice area**.*A*_{leak}is the**Leakage area**.*ΔS*_{max}is the**Spool travel between closed and open orifice**.*ΔS*is the spool travel distance. For flow paths that are open in the positive position:$$\Delta S={S}_{orifice\_\mathrm{max}}-\Delta {S}_{\mathrm{max}}+S,$$

and for flow paths that are open in the negative position:

$$\Delta S={S}_{orifice\_\mathrm{max}}+\Delta {S}_{\mathrm{max}}-S,$$

where

*S*is the_{orifice_max}**Spool position at maximum orifice area**.

`Tabulated data - Area vs. spool travel`

Provide spool travel vectors for your system or for individual flow paths between ports

**P**and**A**,**A**and**T**, and**P**and**T**. This data will be used to calculate the relationship between the orifice opening area and spool travel distance. Interpolation is used to determine the opening area between given data points.*A*_{leak}and*A*_{max}are the first and last parameters of the**Opening area vector**, respectively.`Tabulated data - Volumetric flow rate vs. spool travel and pressure drop`

Provide spool travel and pressure drop vectors. The volumetric flow rate is calculated based on the relationship between pressure change and the spool travel distance. Interpolation is used to determine flow rate between given data points. The mass flow rate is the product of the volumetric flow rate and the local density.

When you set

**Orifice parameterization**to`Tabulated data - Mass flow rate vs. spool travel and pressure drop`

the block calculates the mass flow rate directly from the control member position and the pressure drop across the valve. The relationship between the three variables can be nonlinear and it is given by the tabulated data in the**Spool travel vector, ds**,**Pressure drop vector, dp**, and**Mass flow rate table, mdot(ds,dp)**parameters.

### Numerically-Smoothed Valve Area in the Linear Parameterization

When the valve is in a near-open or near-closed position in the linear
parameterization, you can maintain numerical robustness in your simulation by
adjusting the block **Smoothing factor**. A smoothing function is
applied to all calculated areas, but primarily influences the simulation at the
extremes of the valve area.

The normalized valve area is calculated as:

$$\widehat{A}=\frac{\left({A}_{orifice}-{A}_{leak}\right)}{\left({A}_{\mathrm{max}}-{A}_{leak}\right)}.$$

The **Smoothing factor**, *s*,
is applied to the normalized area:

$${\widehat{A}}_{smoothed}=\frac{1}{2}+\frac{1}{2}\sqrt{{\widehat{A}}_{}^{2}+{\left(\frac{s}{4}\right)}^{2}}-\frac{1}{2}\sqrt{{\left(\widehat{A}-1\right)}^{2}+{\left(\frac{s}{4}\right)}^{2}}.$$

The smoothed valve area is:

$${A}_{smoothed}={\widehat{A}}_{smoothed}\left({A}_{\mathrm{max}}-{A}_{leak}\right)+{A}_{leak}.$$

### Assumptions

Fluid inertia is ignored.

Spool loading due to inertial, spring, and other forces is ignored.

All valve orifices are assumed to be identical in size unless otherwise specified.

## Ports

### Input

`S`

— Control member displacement

physical signal

Displacement of the valve control member, in m. This is equivalent to the spool position.

### Conserving

`P`

— Flow passage

thermal liquid

Opening through which the flow can enter or exit the valve. This port is typically connected to a fluid supply line.

`T`

— Flow passage

thermal liquid

Opening through which the flow can enter or exit the valve. This port is typically connected to a fluid return line.

`A`

— Flow passage

thermal liquid

Opening through which the flow can enter or exit the valve. This port is typically connected to an actuation line.

## Parameters

### Model Parameterization

`Positive spool position open connections`

— Flow paths open when the spool is in a positive position

`P-A only`

(default) | `All closed`

| `P-A, A-T, and P-T`

| `P-T only`

| `A-T only`

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

`Negative spool position open connections`

— Flow paths open when the spool moves in the negative direction

`A-T only`

(default) | `All closed`

| `P-A, A-T, and P-T`

| `P-A only`

| `P-T only`

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

`Area characteristics`

— Flow equations for orifices

```
Identical for all flow
paths
```

(default) | `Different for each flow path`

Applies uniform or individual flow equations for the valve orifice
area. `Identical for all flow paths`

uses the
same orifice and spool geometries, flow rates, pressure, and area
vectors for all valve orifices. When using ```
Different for
each flow path
```

, the spool offsets and tabulated data
are assigned to the orifices between ports **P** and
**A**, ports **A** and
**T**, and ports **P** and
**T**. In both cases, ports **A**,
**P**, and **T** have the same
cross-sectional areas, discharge coefficients, and Reynolds numbers. The
same **Orifice parameterization** is also applied to
all flow paths.

`Orifice parameterization`

— Method of calculating opening area

```
Linear area vs. spool
travel
```

(default) | ```
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
```

Method of calculating the valve opening area. In the tabulated data parameterizations, you can provide your own valve area and spool travel data for nonlinear valve opening profiles, or you can provide data in terms of volumetric flow rate, spool travel, and pressure drop over the flow path. The thermal liquid domain allows you to parameterize the orifice using tabulated mass flow rate data.

`Spool travel between closed and open orifice`

— Maximum spool stroke

`5e-3 m`

(default) | positive scalar

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

#### Dependencies

To enable this parameter, set **Area
characteristics** to ```
Identical for all
flow paths
```

.

`Maximum orifice area`

— Maximum orifice opening area

`1e-4 m^2`

(default) | positive scalar

Largest open area during operation of valve.

#### Dependencies

To enable this parameter, set **Area
characteristics** to ```
Identical for all
flow paths
```

.

`Spool travel vector`

— Vector of valve opening distance

```
[0, .002, .004, .007, .017]
```

m (default) | 1-by*n* vector

Vector of control member travel distances for the tabular
parameterization of valve area. The vector elements must correspond
one-to-one with the elements in the **Orifice area
vector** parameter. The values are listed in ascending
order and the first element must be 0. Linear interpolation is employed
between table data points.

#### Dependencies

To enable this parameter, set **Area
characteristics** to ```
Identical for all
flow paths
```

and **Orifice
parameterization** to ```
Tabulated data -
Area vs. spool travel
```

.

`Orifice area vector`

— Vector of valve opening areas

```
[1e-09, 2.0352e-07, 4.0736e-05, .00011438,
.00034356]
```

m^2 (default) | 1-by*n* vector

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

#### Dependencies

To enable this parameter, set **Area
characteristics** to ```
Identical for all
flow paths
```

and **Opening
parameterization** to ```
Tabulated data -
Area vs. spool travel
```

.

`Leakage area`

— Gap area when in fully closed position

`1e-10 m^2`

(default) | positive scalar

Sum of all gaps when the valve is in its fully closed position. Any area smaller than this value is maintained at the specified leakage area. This contributes to numerical stability by maintaining continuity in the flow.

#### Dependencies

To enable this parameter, set **Area
characteristics** to ```
Identical for all
flow paths
```

and **Orifice
parameterization** to ```
Linear - area vs.
spool travel
```

.

`Smoothing factor`

— Numerical smoothing factor

`0.01`

(default) | positive scalar in the range [0,1]

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

`Spool travel vector, ds`

— Vector of valve opening distances

```
[0, .002, .004, .007, .017]
m
```

(default) | 1-by-*n* vector

Vector of control member travel distances for tabular parametrization
of volumetric flow rate. The spool travel vector forms an independent
axis with the **Pressure drop vector, dp** parameter
for the 3-D dependent **Volumetric flow rate table,
q(ds,dp)** or **Mass flow rate table,
mdot(ds,dp)** parameters. A positive displacement
corresponds to valve opening. The values are listed in ascending order
and the first element must be 0. Linear interpolation is employed
between table data points.

#### Dependencies

To enable this parameter, set **Area
characteristics** to ```
Identical for all
flow paths
```

and **Orifice
parameterization** to ```
Volumetric flow rate
vs. spool travel and pressure drop
```

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

.

`Pressure drop vector, dp`

— Vector of valve pressure drop values

`[.3, .5, .7] MPa`

(default) | 1-by-*n* vector

Vector of pressure drop values for tabular parametrization of
volumetric flow rate. The pressure drop vector forms an independent axis
with the **Spool travel vector, s** parameter for the
3-D dependent **Volumetric flow rate table, q(ds,dp)**
or **Mass flow rate table, mdot(ds,dp)** parameters.
The values are listed in ascending order and must be greater than 0.
Linear interpolation is employed between table data points.

#### Dependencies

To enable this parameter, set **Area
characteristics** to ```
Identical for all
flow paths
```

and **Orifice
parameterization** to ```
Volumetric flow rate
vs. spool travel and pressure drop
```

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

.

`Volumetric flow rate table, q(ds,dp)`

— Array of volumetric flow rates

```
1e-3 * [1.7e-05, 2e-05, 2.6e-05; .0035,
.0045, .0053; .7, .9, 1.06; 1.96, 2.5, 3; 6, 7.7, 9.13]
m^3/s
```

(default) | *M*-by-*N* matrix

*M*-by-*N* matrix of volumetric flow
rates based on independent values of pressure drop and spool travel
distance. *M* and *N* are the sizes of
the corresponding vectors:

*M*is the number of elements in the**Spool travel vector, ds**parameter.*N*is the number of elements in the**Pressure drop vector, dp**parameter.

#### Dependencies

To enable this parameter, set **Area
characteristics** to ```
Identical for all
flow paths
```

and **Orifice
parameterization** to ```
Tabulated data -
Volumetric flow rate vs. spool travel and pressure
drop
```

.

`Reference inflow temperature`

— Temperature at which pressure-drop data is specified

`293.15 K`

(default) | positive scalar

Temperature at which the tabulated pressure-drop data is specified.

#### Dependencies

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

.

`Reference inflow pressure`

— Pressure at which pressure-drop tabulated data is specified

`0.101325 MPa`

(default) | positive scalar

Pressure at which the tabulated pressure-drop data is specified. The block uses this parameter to calculate a third reference parameter, the reference density. The reference that it uses to scale the tabulated pressure drop data for pressures and temperatures deviating from the reference conditions.

#### Dependencies

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

.

`Mass flow rate table, mdot(ds,dp)`

— Mass flow rate

```
[1.7e-05, 2e-05, 2.6e-05; .0035, .0045,
.0053; .7, .9, 1.06; 1.96, 2.5, 3; 6, 7.7, 9.13]
kg/s
```

(default) | M-by-N matrix

Mass flow rate for *M* given control member positions
and *N* given pressure drops over the orifice. The
control member position represents a spool or other mechanism that
controls the opening area.

#### Dependencies

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

.

`Discharge coefficient`

— Discharge coefficient

`0.7`

(default) | positive scalar

Correction factor that accounts for discharge losses in theoretical flows.

`Critical Reynolds number`

— Upper Reynolds number limit for laminar flow

`12`

(default) | positive scalar

Upper Reynolds number limit for laminar flow through the valve.

`Pressure recovery`

— Whether to account for pressure increase in area expansions

`On`

(default) | `Off`

Select to account for pressure increase when fluid flows from a region of a smaller cross-sectional area to a region of larger cross-sectional area.

`Cross-sectional area at ports A, P and T`

— Area at valve entry or exit

`0.01 m^2`

(default) | positive scalar

Cross-sectional area at the entry and exit ports
**A**, **P**, and
**T**. These areas are used in the pressure-flow
rate equation that determines volumetric flow rate through the
valve.

### P-A Orifice

`Spool position at maximum P-A orifice area`

— Spool offset at maximum area between ports P and A

`2.5e-3 m`

(default) | scalar

Initial orifice opening distance between ports **P**
and **A**. The default represents a zero-lapped
system.

`P-A spool travel between closed and open orifice`

— Maximum stroke for the spool between ports P and A

`0.005 m`

(default) | positive scalar

Maximum distance of spool travel for the orifice between ports
**P** and **A**. This value
provides an upper limit to calculations so that simulations do not
return unphysical values.

#### Dependencies

To enable this parameter, set **Area
characteristics** to ```
Different for each
flow path
```

.

`P-A maximum orifice area`

— Maximum area between ports P and A

`1e-4 m^2`

(default) | positive scalar

Cross-sectional area of the orifice between ports
**P** and **A** in its fully open
position.

#### Dependencies

To enable this parameter, set **Area
characteristics** to ```
Different for each
flow path
```

and **Orifice
parameterization** to ```
Linear - area vs.
spool travel
```

.

`P-A orifice spool travel vector`

— Vector of valve opening distance

```
[0, .002, .004, .007, .017]
m
```

(default) | 1-by*n* vector

Vector of control member travel distances for the tabular
parameterization of valve area. The vector elements must correspond
one-to-one with the elements in the **P-A orifice area
vector** parameter. The values are listed in ascending
order and the first element must be 0. Linear interpolation is employed
between table data points.

#### Dependencies

To enable this parameter, set **Area
characteristics** to ```
Different for each
flow path
```

and **Orifice
parameterization** to ```
Tabulated data -
Area vs. spool travel
```

.

`P-A orifice area vector`

— Vector of valve opening areas

```
[1e-09, 2.0352e-07, 4.0736e-05, .00011438,
.00034356] m^2
```

(default) | 1-by-*n* vector

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

#### Dependencies

To enable this parameter, set **Area
characteristics** to ```
Different for each
flow path
```

and **Opening
parameterization** to ```
Tabulated data -
Area vs. spool travel
```

.

`P-A orifice spool travel vector, ds`

— Vector of valve opening distances

```
[0, .002, .004, .007, .017]
m
```

(default) | 1-by-*n* vector

Vector of control member travel distances for tabular parametrization
of volumetric flow rate. The spool travel vector forms an independent
axis with the **P-A orifice pressure drop vector, dp**
parameter for the 3-D dependent **P-A orifice volumetric flow
rate table, q(s,dp)** or **Mass flow rate table,
mdot(ds,dp)** parameters. A positive displacement
corresponds to valve opening. The values are listed in ascending order
and the first element must be 0. Linear interpolation is employed
between table data points.

#### Dependencies

To enable this parameter, set **Area
characteristics** to ```
Identical for all
flow paths
```

and **Orifice
parameterization** to ```
Volumetric flow rate
vs. spool travel and pressure drop
```

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

.

`P-A orifice pressure drop vector, dp`

— Vector of pressure drop values over the valve

`[.3, .5, .7] MPa`

(default) | 1-by-*n* vector

Vector of pressure drop values for tabular parametrization of
volumetric flow rate. The pressure drop vector forms an independent axis
with the **P-A orifice spool travel vector, s**
parameter for the 3-D dependent **P-A orifice volumetric flow
rate table, q(s,dp)** or **Mass flow rate table,
mdot(ds,dp)** parameters. The values are listed in
ascending order and must be greater than 0. Linear interpolation is
employed between table data points.

#### Dependencies

**Area
characteristics** to ```
Identical for all
flow paths
```

and **Orifice
parameterization** to ```
Volumetric flow rate
vs. spool travel and pressure drop
```

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

.

`P-A orifice volumetric flow rate table, q(ds,dp)`

— Vector of valve volumetric flow rates

```
[1.7e-05, 2e-05, 2.6e-05; .0035, .0045,
.0053; .7, .9, 1.06; 1.96, 2.5, 3; 6, 7.7, 9.13] .* 1e-3
m^3/s
```

(default) | *M*-by-*N* matrix

*M*-by-*N* matrix of volumetric flow
rates based on independent values of pressure drop and spool travel
distance. *M* and *N* are the sizes of
the corresponding vectors:

*M*is the number of elements in the**P-A orifice pressure drop vector, dp**parameter.*N*is the number of elements in the**P-A orifice spool travel vector, s**parameter.

#### Dependencies

To enable this parameter, set **Area
characteristics** to ```
Different for each
flow path
```

and **Orifice
parameterization** to ```
Tabulated data -
Volumetric flow rate vs. spool travel and pressure
drop
```

.

`P-A orifice mass flow rate table, mdot(ds,dp)`

— Vector of valve mass flow rates

```
[1.7e-05, 2e-05, 2.6e-05; .0035, .0045,
.0053; .7, .9, 1.06; 1.96, 2.5, 3; 6, 7.7, 9.13]
kg/s
```

(default) | *M*-by-*N* matrix

*M*-by-*N* matrix of mass flow rates
based on independent values of pressure drop and spool travel distance.
*M* and *N* are the sizes of the
corresponding vectors:

*M*is the number of elements in the**P-A orifice pressure drop vector, dp**parameter.*N*is the number of elements in the**P-A orifice spool travel vector, s**parameter.

#### Dependencies

To enable this parameter, set **Area
characteristics** to ```
Different for each
flow path
```

and **Orifice
parameterization** to ```
Tabulated data -
Mass flow rate vs. spool travel and pressure
drop
```

.

### A-T Orifice

`Spool position at maximum A-T orifice area`

— Spool offset at maximum area between ports A and T

`-2.5e-3 m`

(default) | scalar

Initial orifice opening distance between ports **A**
and **T**. The default represents a zero-lapped
system.

`A-T spool travel between closed and open orifice`

— Maximum stroke for the spool between ports A and T

`0.005 m`

(default) | positive scalar

Maximum distance of spool travel for the orifice between ports
**A** and **T**. This value
provides an upper limit to calculations so that simulations do not
return unphysical values.

#### Dependencies

To enable this parameter, set **Area
characteristics** type to ```
Different for
each flow path
```

.

`A-T maximum orifice area`

— Maximum area between ports A and T

`1e-4 m^2`

(default) | positive scalar

Cross-sectional area of the orifice between ports
**A** and **T** in its fully open
position.

#### Dependencies

To enable this parameter, set **Area
characteristics** to ```
Different for each
flow path
```

and **Orifice
parameterization** to ```
Linear - area vs.
spool travel
```

.

`A-T orifice spool travel vector`

— Vector of valve opening distances

```
[0, .002, .004, .007, .017]
m
```

(default) | 1-by-*n* vector

Vector of control member travel distances for the tabular
parameterization of valve area. The vector elements must correspond
one-to-one with the elements in the **A-T orifice area
vector** parameter. The values are listed in ascending
order and the first element must be 0. Linear interpolation is employed
between table data points.

#### Dependencies

To enable this parameter, set **Area
characteristics** to ```
Different for each
flow path
```

and **Orifice
parameterization** to ```
Tabulated data -
Area vs. spool travel
```

.

`A-T orifice area vector`

— Vector of valve opening areas

```
[1e-09, 2.0352e-07, 4.0736e-05, .00011438,
.00034356] m^2
```

(default) | 1-by-*n* vector

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

#### Dependencies

To enable this parameter, set **Area
characteristics** to ```
Different for each
flow path
```

and **Opening
parameterization** to ```
Tabulated data -
Area vs. spool travel
```

.

`A-T orifice spool travel vector, ds`

— Vector of valve opening distances

```
[0, .002, .004, .007, .017]
m
```

(default) | 1-by-*n* vector

Vector of control member travel distances for tabular parametrization
of volumetric flow rate. The spool travel vector forms an independent
axis with the **A-T orifice pressure drop vector, dp**
parameter for the 3-D dependent **A-T orifice volumetric flow
rate table, q(ds,dp)** or **Mass flow rate table,
mdot(ds,dp)** parameters. A positive displacement
corresponds to valve opening. The values are listed in ascending order
and the first element must be 0. Linear interpolation is employed
between table data points.

#### Dependencies

**Area
characteristics** to ```
Identical for all
flow paths
```

and **Orifice
parameterization** to ```
Volumetric flow rate
vs. spool travel and pressure drop
```

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

.

`A-T orifice pressure drop vector, dp`

— Vector of pressure drop values over the valve

`[.3, .5, .7] MPa`

(default) | 1-by-*n* vector

Vector of pressure drop values for tabular parametrization of
volumetric flow rate. The pressure drop vector forms an independent axis
with the **A-T orifice spool travel vector, s**
parameter for the 3-D dependent **A-T orifice volumetric flow
rate table, q(ds,dp)** or **Mass flow rate table,
mdot(ds,dp)** parameters. The values are listed in
ascending order and must be greater than 0. Linear interpolation is
employed between table data points.

#### Dependencies

**Area
characteristics** to ```
Identical for all
flow paths
```

and **Orifice
parameterization** to ```
Volumetric flow rate
vs. spool travel and pressure drop
```

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

.

`A-T orifice volumetric flow rate table, q(ds,dp)`

— Vector of volumetric flow rate for tabular parameterization - different flow paths

```
[1.7e-05, 2e-05, 2.6e-05; .0035, .0045,
.0053; .7, .9, 1.06; 1.96, 2.5, 3; 6, 7.7, 9.13] .* 1e-3
m^3/s
```

(default) | *M*-by-*N* matrix

*M*-by-*N* matrix of volumetric flow
rates based on independent values of pressure drop and spool travel
distance. *M* and *N* are the sizes of
the corresponding vectors:

*M*is the number of elements in the**A-T orifice pressure drop vector, dp**parameter.*N*is the number of elements in the**A-T orifice spool travel vector, s**parameter.

#### Dependencies

To enable this parameter, set **Area
characteristics** to ```
Different for each
flow path
```

and **Orifice
parameterization** to ```
Tabulated data -
Volumetric flow rate vs. spool travel and pressure
drop
```

.

`A-T orifice mass flow rate table, mdot(ds,dp)`

— Vector of mass flow rate for tabular parameterization - different flow paths

```
[1.7e-05, 2e-05, 2.6e-05; .0035, .0045,
.0053; .7, .9, 1.06; 1.96, 2.5, 3; 6, 7.7, 9.13]
kg/s
```

(default) | *M*-by-*N* matrix

*M*-by-*N* matrix of mass flow rates
based on independent values of pressure drop and spool travel distance.
*M* and *N* are the sizes of the
corresponding vectors:

*M*is the number of elements in the**A-T orifice pressure drop vector, dp**parameter.*N*is the number of elements in the**A-T orifice spool travel vector, s**parameter.

#### Dependencies

To enable this parameter, set **Area
characteristics** to ```
Different for each
flow path
```

and **Orifice
parameterization** to ```
Tabulated data -
Mass flow rate vs. spool travel and pressure
drop
```

.

### P-T Orifice

`Spool position at maximum P-T orifice area`

— Spool offset at maximum area between ports P and T

`2.5e-3 m`

(default) | scalar

Initial orifice opening distance between ports **P**
and **T**. The default represents a zero-lapped
system.

`P-T spool travel between closed and open orifice`

— Maximum stroke for the spool between ports P and T

`0.005 m`

(default) | positive scalar

Maximum distance of spool travel for the orifice between ports
**P** and **T**. This value
provides an upper limit to calculations so that simulations do not
return unphysical values.

#### Dependencies

To enable this parameter, set **Area
characteristics** type to ```
Different for
each flow path
```

.

`P-T maximum orifice area`

— Maximum area between ports P and T

`1e-4 m^2`

(default) | positive scalar

Cross-sectional area of the orifice between ports
**P** and **T** in its fully open
position.

#### Dependencies

To enable this parameter, set **Area
characteristics** to ```
Different for each
flow path
```

and **Orifice
parameterization** to ```
Linear - area vs.
spool travel
```

.

`P-T orifice spool travel vector`

— Vector of valve opening distances

```
[0, .002, .004, .007, .017]
m
```

(default) | 1-by-*n* vector

Vector of control member travel distances for the tabular
parameterization of valve area. The vector elements must correspond
one-to-one with the elements in the **P-T orifice area
vector** parameter. The values are listed in ascending
order and the first element must be 0. Linear interpolation is employed
between table data points.

#### Dependencies

To enable this parameter, set **Area
characteristics** to ```
Different for each
flow path
```

and **Orifice
parameterization** to ```
Tabulated data -
Area vs. spool travel
```

.

`P-T orifice area vector`

— Vector of valve opening areas

```
[1e-09, 2.0352e-07, 4.0736e-05, .00011438,
.00034356] m^2
```

(default) | 1-by-*n* vector

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

#### Dependencies

To enable this parameter, set **Area
characteristics** to ```
Different for each
flow path
```

and **Opening
parameterization** to ```
Tabulated data -
Area vs. spool travel
```

.

`P-T orifice spool travel vector, ds`

— Vector of valve opening distances

```
[0, .002, .004, .007, .017]
m
```

(default) | 1-by-*n* vector

Vector of control member travel distances for tabular parametrization
of volumetric flow rate. The spool travel vector forms an independent
axis with the **P-T orifice pressure drop vector, dp**
parameter for the 3-D dependent **P-T orifice volumetric flow
rate table, q(ds,dp)** or **Mass flow rate table,
mdot(ds,dp)** parameters. A positive displacement
corresponds to valve opening. The values are listed in ascending order
and the first element must be 0. Linear interpolation is employed
between table data points.

#### Dependencies

**Area
characteristics** to ```
Identical for all
flow paths
```

and **Orifice
parameterization** to ```
Volumetric flow rate
vs. spool travel and pressure drop
```

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

.

`P-T orifice pressure drop vector, dp`

— Vector of pressure drop values over the valve

`[.3, .5, .7] MPa`

(default) | 1-by-*n* vector

Vector of pressure drop values for tabular parametrization of
volumetric flow rate. The pressure drop vector forms an independent axis
with the **P-T orifice spool travel vector, ds**
parameter for the 3-D dependent **P-T orifice volumetric flow
rate table, q(ds,dp)** or **Mass flow rate table,
mdot(ds,dp)** parameters. The values are listed in
ascending order and must be greater than 0. Linear interpolation is
employed between table data points.

#### Dependencies

**Area
characteristics** to ```
Identical for all
flow paths
```

and **Orifice
parameterization** to ```
Volumetric flow rate
vs. spool travel and pressure drop
```

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

.

`P-T orifice volumetric flow rate table, q(ds,dp)`

— Vector of volumetric flow rate for tabular parameterization - different flow paths

```
[1.7e-05, 2e-05, 2.6e-05; .0035, .0045,
.0053; .7, .9, 1.06; 1.96, 2.5, 3; 6, 7.7, 9.13] .* 1e-3
m^3/s
```

(default) | *M*-by-*N* matrix

*M*-by-*N* matrix of volumetric flow
rates based on independent values of pressure drop and spool travel
distance. *M* and *N* are the sizes of
the corresponding vectors:

*M*is the number of elements in the**P-T orifice pressure drop vector, dp**parameter.*N*is the number of elements in the**P-T orifice spool travel vector, ds**parameter.

#### Dependencies

To enable this parameter, set **Area
characteristics** to ```
Different for each
flow path
```

and **Orifice
parameterization** to ```
Tabulated data -
Volumetric flow rate vs. spool travel and pressure
drop
```

.

`P-T orifice mass flow rate table, mdot(ds,dp)`

— Vector of mass flow rate for tabular parameterization - different flow paths

```
[1.7e-05, 2e-05, 2.6e-05; .0035, .0045,
.0053; .7, .9, 1.06; 1.96, 2.5, 3; 6, 7.7, 9.13]
kg/s
```

(default)

*M*-by-*N* matrix of mass flow rates
based on independent values of pressure drop and spool travel distance.
*M* and *N* are the sizes of the
corresponding vectors:

*M*is the number of elements in the**P-T orifice pressure drop vector, dp**parameter.*N*is the number of elements in the**P-T orifice spool travel vector, ds**parameter.

#### Dependencies

To enable this parameter, set **Area
characteristics** to ```
Different for each
flow path
```

and **Orifice
parameterization** to ```
Tabulated data -
Mass flow rate vs. spool travel and pressure
drop
```

.

## Model Examples

## Extended Capabilities

### C/C++ Code Generation

Generate C and C++ code using Simulink® Coder™.

## Version History

**Introduced in R2016a**

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