# Pressure Relief Valve (IL)

**Libraries:**

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

## Description

The Pressure Relief Valve (IL) block represents a pressure
relief valve in an isothermal liquid network. The valve remains closed when the pressure
is less than a specified value. When this pressure is met or surpassed, the valve opens.
This set pressure is either a threshold pressure differential over the valve, between
ports **A** and **B**, or between port
**A** and atmospheric pressure. For pressure control based on
another element in the fluid system, see the Pressure Compensator
Valve (IL) block.

### Pressure Control

For linear preparameterizations, the normalized pressure, $$\widehat{p}$$, which controls the valve opening area, depends on the value of
the **Set pressure control** parameter.

When you set **Set pressure control** to
`Constant`

and **Opening
parameterization** to ```
Linear - Area vs.
pressure
```

, the normalized pressure is

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

where:

*p*is the control pressure. When you set_{control}**Opening pressure specification**to`Pressure differential`

, the control pressure is*p*. When you set_{A}̶ p_{B}**Opening pressure specification**to`Pressure at port A`

, the control pressure is the difference between the pressure at port**A**and atmospheric pressure.*p*is the set pressure. When_{set}**Opening pressure specification**is`Pressure differential`

,*p*is the value of the_{set}**Set pressure differential**parameter. When**Opening pressure specification**is`Pressure at port A`

,*p*is the value of the_{set}**Set pressure (gauge)**parameter.*p*is the maximum of pressure regulation range,_{max}*p*, where_{max}= p_{set}+ p_{range}*p*is the value of the_{range}**Pressure regulation range**parameter.

When you set **Set pressure control** to
`Controlled`

, the normalized pressure is

$$\widehat{p}=\frac{{p}_{control}-{p}_{s}}{{p}_{max}-{p}_{s}},$$

where:

*p*is the value of the signal at port_{s}**Ps**.*p*, where_{max}= p_{s}+ p_{range}*p*is the value of the_{range}**Pressure regulation range**parameter.*p*is the pressure differential between ports_{control}**A**and**B**,*p*._{A}̶ p_{B}

### Opening Parameterization

The mass flow rate depends on the values of the **Set pressure
control** and **Opening parameterization**
parameters.

**Area vs. Pressure Parameterizations**

When you set **Set pressure control** to
`Controlled`

, or to
`Constant`

and **Opening
parameterization** to ```
Linear - Area vs.
pressure
```

or ```
Tabulated data - Area vs.
pressure
```

, the mass flow rate is

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

where:

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

*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.
*PR*_{loss} is calculated 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* is 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.

When you set **Set pressure control** to
`Controlled`

, or to
`Constant`

and **Opening
parameterization** to ```
Linear - Area vs.
pressure
```

, the opening area is

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

where:

*A*is the value of the_{leak}**Leakage area**parameter.*A*is the value of the_{max}**Maximum opening area**parameter.

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}When you set **Set pressure control** to
`Constant`

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

, the block interpolates
*A _{valve}* from the

**Opening area vector**parameter with respect to the

**Pressure differential vector**or

**Opening pressure (gauge) vector**parameter, depending on the value of the

**Pressure control specification**parameter. The block also uses the smoothed, normalized pressure when the smoothing factor is nonzero with linear interpolation and nearest extrapolation.

**Volumetric Flow Rate vs. Pressure Parameterization**

When you set **Set pressure control** to
`Constant`

and **Opening
parameterization** to ```
Tabulated data - Volumetric flow
rate vs. pressure
```

, the valve opens according to the
user-provided tabulated data of volumetric flow rate and pressure differential
between ports **A** and **B**.

The mass flow rate is

$$\dot{m}=\overline{\rho}K\frac{\Delta p}{{\left(\Delta {p}^{2}+\Delta {p}_{crit}{}^{2}\right)}^{1/4}},$$

where:

$$\overline{\rho}$$ is the average fluid density.

$$\Delta p={p}_{A}-{p}_{B}.$$

$$\Delta {p}_{crit}=\frac{\pi \sqrt{2\overline{\rho}}}{8{C}_{d}K}{\left({\mathrm{Re}}_{crit}v\right)}^{2},$$ where

*C*is the discharge coefficient,_{d}*Re*is the critical Reynolds number, and_{crit}*ν*is the kinematic viscosity. In this parameterization,*C*and_{d}*Re*are fixed at_{crit}`0.64`

and`150`

, respectively.

When the block operates in the limits of the tabulated data,

$$K=tablelookup\left(\Delta {p}_{TLU},{K}_{TLU},\Delta p,interpolation=linear,extrapolation=nearest\right),$$

where:

*Δp*is the_{TLU}**Pressure drop vector**parameter.$${\text{K}}_{TLU}=\frac{{\dot{V}}_{TLU}}{\sqrt{\Delta {p}_{TLU}}},$$ where

*$$\dot{V}$$*is the_{TLU}**Volumetric flow rate vector**parameter.

When the simulation pressure falls below the first element of the
**Pressure drop vector** parameter,
*K*`=`

*K _{Leak}*,

$${K}_{Leak}=\frac{{\dot{V}}_{TLU}(1)}{\sqrt{\left|\Delta {p}_{TLU}(1)\right|}},$$

where *$$\dot{V}$$ _{TLU}(1)* is the first
element of the

**Volumetric flow rate vector**parameter.

When the simulation pressure rises above the last element of the
**Pressure drop vector** parameter,
*K*`=`

*K _{Max}*,

$${K}_{Max}=\frac{{\dot{V}}_{TLU}(end)}{\sqrt{\left|\Delta {p}_{TLU}(end)\right|}},$$

where *$$\dot{V}$$ _{TLU}(end)* is the last
element of the

**Volumetric flow rate vector**parameter.

### Conservation of Mass

The block conserves mass through the valve such that

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

where $$\dot{m}$$ is the mass flow rate into the valve through the port indicated by
the **A** or **B**
subscript.

### Opening Dynamics

When you select **Opening dynamics**, the block introduces lag in the flow
response to the valve opening. *A _{valve}*
becomes the dynamic opening area,

*A*; otherwise,

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

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

*τ*:

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

By default, the block clears the **Opening
dynamics** check box.

Steady-state dynamics are set by the same parameterization as valve opening, and
are based on the control pressure,
*p*_{control}. A nonzero
**Smoothing factor** can provide additional numerical stability
when the orifice is in near-closed or near-open position.

### 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.

The **Opening area when faulted** parameter has three fault options:

`Closed`

— The valve freezes at its smallest value, depending on the**Opening parameterization**parameter:When you set

**Opening parameterization**to`Linear - Area vs. pressure`

, the valve area freezes at the**Leakage area**parameter.When you set

**Opening parameterization**to`Tabulated data - Area vs. pressure`

, the valve area freezes at the first element of the**Opening area vector**parameter.

`Open`

— The valve freezes at its largest value, depending on the**Opening parameterization**parameter:When you set

**Opening parameterization**to`Linear - Area vs. pressure`

, the valve area freezes at the**Maximum opening area**parameter.When you set

**Orifice parameterization**to`Tabulated data - Area vs. pressure`

, the valve area freezes at the last element of the**Opening area vector**parameter.

`Maintain last value`

— The valve area freezes at the valve open area when the trigger occurred.

Due to numerical smoothing at the extremes of the valve area, the
minimum area the block uses is larger than the **Leakage area**
parameter, and the maximum is smaller than the **Maximum orifice
area** parameter, in proportion to the **Smoothing
factor** parameter value.

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

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

,
the fault options are defined by the volumetric flow rate through the valve:

`Closed`

— The valve stops at the mass flow rate associated with the first elements of the**Volumetric flow rate vector**parameter and the**Pressure drop vector**parameter:$$\dot{m}={K}_{Leak}\overline{\rho}\sqrt{\Delta p}.$$

`Open`

— The valve stops at the mass flow rate associated with the last elements of the**Volumetric flow rate vector**parameter and the**Pressure drop vector**parameter:$$\dot{m}={K}_{Max}\overline{\rho}\sqrt{\Delta p}$$

`Maintain at last value`

— The valve stops at the mass flow rate and pressure differential when the trigger occurs:$$\dot{m}={K}_{Last}\overline{\rho}\sqrt{\Delta p},$$

where

$${K}_{Last}=\frac{\left|\dot{m}\right|}{\overline{\rho}\sqrt{\left|\Delta p\right|}}.$$

### 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

### Conserving

### Input

## Parameters

## Extended Capabilities

## Version History

**Introduced in R2020a**