# Pressure-Reducing Valve (IL)

**Libraries:**

Simscape /
Fluids /
Isothermal Liquid /
Valves & Orifices /
Pressure Control Valves

## Description

The Pressure-Reducing Valve (IL) block represents a
pressure-reducing valve in an isothermal liquid network. The valve remains open when the
pressure at port **B** is less than a specified pressure. When the
pressure at port **B** meets or surpasses this pressure, the valve
closes. The block operates based on the differential between the set pressure and the
pressure at port **B**. The block contains a check valve portion that
functions identically to the Check Valve
(IL) block during flow reversals. For pressure control based on
another location in the fluid network, see the Pressure Compensator
Valve (IL) block.

### Set Pressure Control

The block regulates pressure between the set pressure and maximum pressure. When you set
**Set pressure control** to:

`Controlled`

— You can connect a pressure signal to port**Ps**. The block regulates pressure when the pressure at port**B**is greater than the reference set pressure,*P*, and below_{set}*P*. The pressure at port_{max}**B**acts as the control pressure,*P*, for this valve._{control}*P*is the sum of_{max}*P*and the pressure regulation range._{set}`Constant`

— The**Set pressure (gauge)**parameter defines a constant set pressure.

How the block determines the pressure regulation range depends on the
**Opening parameterization** parameter:

`Linear - Area vs. pressure`

— The**Pressure regulation range**parameter defines the pressure regulation range.`Tabulated data - Area vs. Pressure`

— The pressure regulation range is the difference between the last and first elements of the**Pressure at port B (gauge) vector**parameter.`Tabulated data - Volumetric flow rate vs. pressure`

— The pressure regulation range is the difference between the first and last elements of the**Reference pressure at port B (gauge) vector**parameter.

### Area vs. Pressure Parameterizations

When you set **Opening parameterization** to ```
Linear - Area
vs. pressure
```

, the block calculates the valve area as

$${A}_{valve}=\widehat{p}\left({A}_{leak}-{A}_{max}\right)+{A}_{max},$$

where the normalized pressure,$$\widehat{p}$$, is

$$\widehat{p}=\frac{{p}_{control}-{p}_{set}}{{p}_{max}-{p}_{set}}.$$

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 **Smoothing factor** parameter. If
the **Smoothing factor** parameter is nonzero, the block smoothly
saturates the control pressure between
*p _{set}* and

*p*. For more information, see Numerical Smoothing.

_{max}The figure demonstrates the opening characteristics of the valve when using the linear area
parameterization. The opening area,
*A _{valve}*, drops linearly with the outlet
pressure,

*p*. The opening area ranges from

_{B,gauge}*A*to

_{leak}*A*, and the pressure operating range starts at

_{Max}*p*and goes to

_{set}*p*.

_{max}When you set **Opening parameterization** to ```
Tabulated data -
Area vs. Pressure
```

, the block calculates the opening area as

$${A}_{valve}=tablelookup\left({p}_{control,TLU},{A}_{TLU},{p}_{control},interpolation=linear,extrapolation=nearest\right),$$

where:

*p*=_{control}*p*is the control pressure._{B,gauge}*p*=_{control,TLU}*p*+_{B,TLU}*p*._{offset}*p*is the_{B,TLU}**Pressure at port B (gauge) vector**parameter.*p*is an internal pressure offset that causes the valve to start closing when_{offset}*p*=_{B,Gauge}*p*, where_{set}*p*=_{offset}*p*-_{set}*p*._{B,TLU}(1)*A*is the_{TLU}**Opening area vector**parameter.

*A _{max}* and

*A*are the first and last parameters of the

_{leak}**Opening area vector**parameter, respectively. The figure demonstrates the opening characteristics of the valve when using the tabulated area parameterization.

**Conservation of Mass**

When you set **Opening parameterization** to
`Linear - Area vs. pressure`

or
`Tabulated data - Area vs. Pressure`

, the block
conserves mass such that:

$${\dot{m}}_{A}+{\dot{m}}_{B}=0.$$

The block calculates the mass flow rate as

$$\dot{m}=\frac{{C}_{d}{A}_{valve}\sqrt{2\overline{\rho}}}{\sqrt{P{R}_{loss}\left(1-{\left(\frac{{A}_{valve}}{{A}_{port}}\right)}^{2}\right)}}\frac{\Delta p}{{\left[\Delta {p}^{2}+\Delta {p}_{crit}^{2}\right]}^{1/4}},$$

where:

*C*is the_{d}**Discharge coefficient**parameter.*A*is the instantaneous valve open area._{valve}*A*is the_{port}**Cross-sectional area at ports A and B**parameter.$$\overline{\rho}$$ is the average fluid density.

*Δp*is the valve pressure difference*p*–_{A}*p*._{B}

The critical pressure difference,
*Δp _{crit}*, is the pressure
differential associated with the

**Critical Reynolds number**parameter,

*Re*, the flow regime transition point between laminar and turbulent flow:

_{crit}

$$\Delta {p}_{crit}=\frac{\pi \overline{\rho}}{8{A}_{valve}}{\left(\frac{\nu {\mathrm{Re}}_{crit}}{{C}_{d}}\right)}^{2}.$$

*Pressure loss* describes the reduction of pressure in the
valve due to a decrease in area. The block calculates
*PR _{loss}* as:

$$P{R}_{loss}=\frac{\sqrt{1-{\left(\frac{{A}_{valve}}{{A}_{port}}\right)}^{2}\left(1-{C}_{d}^{2}\right)}-{C}_{d}\frac{{A}_{valve}}{{A}_{port}}}{\sqrt{1-{\left(\frac{{A}_{valve}}{{A}_{port}}\right)}^{2}\left(1-{C}_{d}^{2}\right)}+{C}_{d}\frac{{A}_{valve}}{{A}_{port}}}.$$

*Pressure recovery* describes the positive pressure change in the valve
due to an increase in area. If you do not wish to capture this increase in
pressure, clear the **Pressure recovery** check box. In this
case, *PR _{loss}* is 1.

The block determines the opening area,
*A _{valve}*, using the valve opening
dynamics.

**Opening Dynamics**

For either area parameterization, you can choose to simulate the opening dynamics of the
valve response. If you select **Opening dynamics**, the block
adds a lag to the flow response when the valve opens, and
*A _{valve}* becomes the dynamic
opening area,

*A*. Otherwise,

_{dyn}*A*is the steady-state opening area. The block calculates the instantaneous change in the dynamic opening area based on the

_{valve}**Opening time constant**parameter,

*τ*:

$${\dot{p}}_{dyn}=\frac{{p}_{control}-{p}_{dyn}}{\tau}.$$

By default, the block ignores opening dynamics.

The block calculates the steady-state dynamics based on the control pressure,
*p _{control}*, and using the same
parameterization as the valve opening.

### Volumetric Flow Rate vs. Pressure Parameterization

The volumetric flow rate parameterization equations refer to these quantities:

*⩒*is the_{TLU,ref}**Reference volumetric flow rate vector**parameter.*P*and_{A,gauge,ref}*P*are the_{B,gauge,ref}**Reference pressure at port A (gauge) vector**and**Reference pressure at port B (gauge) vector**parameters, respectively.*p*is either the_{set,gauge}**Set pressure (gauge)**parameter or the signal at port**Ps**.*K*is the flow coefficient through the reducing stage, which the block calculates during the simulation.$$\overline{\rho}$$ is the average fluid density in the reducing valve.

*Δp*is the pressure drop across the valve for fluid flow.*Δp*is the critical pressure drop for fluid flow._{crit}*C*is the discharge coefficient, which the block sets internally for the volumetric flow rate parameterization._{d}*Re*is the critical Reynolds number, which the block sets internally._{crit}*ν*is the kinematic viscosity, which is constant for the isothermal liquid network.

When you set **Opening parameterization** to
`Tabulated data - Volumetric flow rate vs. pressure`

,
the block calculates the smoothed mass flow rate of the reducing valve such that

$$\begin{array}{l}{\dot{m}}_{valve}=\overline{\rho}K\frac{\Delta {p}_{}}{{\left(\Delta {p}_{}^{2}+\Delta {p}_{}^{2}\right)}^{{\scriptscriptstyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}}}\\ \Delta {p}_{}={p}_{A}-{p}_{B}\\ \Delta {p}_{crit}=\frac{\pi \sqrt{2\overline{\rho}}}{8{C}_{d}K}{\left(R{e}_{crit}\nu \right)}^{2}\end{array}$$

where the block computes *K* using a
`tablelookup`

function such that

$$\begin{array}{l}K=tablelookup(\Delta {p}_{control,TLU,Ref},{K}_{TLU,Ref},\Delta {p}_{control},interpolation=linear,extrapolation=nearest)\\ {K}_{TLU,Ref}=\frac{{\dot{V}}_{TLU,Ref}}{\sqrt{\Delta {p}_{TLU,Ref}}}\end{array}$$

The block calculates the control pressure as

$$\Delta {p}_{control}={p}_{B}-{p}_{drain},$$

where the block sets the drain pressure, *p _{drain}*, to 1 atm. The block calculates the reference control pressure
vector as

$$\Delta {p}_{control,TLU,Ref}={p}_{B,gauge,ref}+{p}_{offset},$$

where *p _{offset}* is an
internally computed pressure offset that causes the valve to start shutting when

*p*=

_{B,gauge,ref}*p*. Thus,

_{set,gauge}*p*=

_{offset}*p*-

_{set,gauge}*p*. The figure shows how the block controls pressure using the tabulated volumetric flow rate parameterization.

_{B,gauge,ref}### Faults

To model a fault, in the **Faults** section,
click the **Add fault** hyperlink next to the fault that you want to model. In
the Add Fault window, specify the fault properties. For more information about fault modeling,
see Introduction to Simscape Faults.

Three fault options are available for the reducing valve and check valve. For the
**Reducing valve opening when faulted** and **Check
valve opening when faulted** parameters, you can choose:

`Closed`

— The valve shuts to its smallest opening value, depending on the**Opening parameterization**parameter. When you set**Opening parameterization**to:`Linear - Area vs. pressure`

— The valve area reduces to the value of the**Leakage area**parameter.`Tabulated data - Area vs. pressure`

— The valve area reduces to the value of the last element in the**Opening area vector**parameter.`Tabulated data - Volumetric flow rate vs. pressure`

— The flow coefficient reduces to the value of the last element of the derived flow coefficient lookup table,*K*._{TLU,Ref}

`Open`

— The valve opens to its largest opening value, depending on the**Opening parameterization**parameter. When you set**Opening parameterization**to:`Linear - Area vs. pressure`

— The valve area opens to the value of the**Maximum opening area**.`Tabulated data - Area vs. pressure`

— The valve area opens to the value of the first element in the**Opening area vector**.`Tabulated data - Volumetric flow rate vs. pressure`

— The flow coefficient reduces to the value of the first element of the derived flow coefficient lookup table,*K*._{TLU,Ref}

`Maintain last value`

— The valve area remains at the valve opening area when the trigger occurred.

For the linear parameterization, numerical smoothing at the extremes
of the valve area causes the minimum area applied to be larger than the
**Leakage area** parameter, and the maximum is smaller than
the **Maximum orifice area** parameter.

After the fault triggers, the valve remains at the faulted area for the rest of the simulation.

### Predefined Parameterization

You can populate the block with pre-parameterized manufacturing data, which allows you to model a specific supplier component.

To load a predefined parameterization:

In the block dialog box, next to

**Selected part**, click the "<click to select>" hyperlink next to**Selected part**in the block dialogue box settings.The Block Parameterization Manager window opens. Select a part from the menu and click

**Apply all**. You can narrow the choices using the**Manufacturer**drop down menu.You can close the

**Block Parameterization Manager**menu. The block now has the parameterization that you specified.You can compare current parameter settings with a specific supplier component in the Block Parameterization Manager window by selecting a part and viewing the data in the

**Compare selected part with block**section.

**Note**

Predefined block parameterizations use available data sources to supply parameter values. The block substitutes engineering judgement and simplifying assumptions for missing data. As a result, expect some deviation between simulated and actual physical behavior. To ensure accuracy, validate the simulated behavior against experimental data and refine your component models as necessary.

To learn more, see List of Pre-Parameterized Components.

## Ports

### Input

### Conserving

## Parameters

## Extended Capabilities

## Version History

**Introduced in R2020a**