# 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

You can use a constant value or a physical signal to control the set pressure:

When you set

**Set pressure control**to`Controlled`

, connect a pressure signal to port**Ps**and define the constant**Pressure regulation range**. The valve response will be triggered when*P*, the pressure differential between ports_{control}**A**and**B**, is greater than*P*and below_{set}*P*._{max}*P*is the sum of_{max}*P*and the pressure regulation range._{set}When you set

**Set pressure control**to`Constant`

, the valve opening is continuously regulated between*P*_{set}and*P*. There are two options for pressure regulation available in the_{max}**Opening pressure specification**parameter:*P*can be the pressure differential between ports_{control}**A**and**B**or the pressure differential between port**A**and atmospheric pressure. The opening area is then modeled by either linear or tabular parameterization. When the`Tabulated data`

option is selected,*P*and_{set}*P*are the first and last parameters of the_{max}**Pressure differential vector**, respectively.

### Conservation of Mass

The block conserves mass through the valve 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**.*A*is the instantaneous valve open area._{valve}*A*is 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* 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 opening area *A*_{valve} is determined by
the opening parameterization (for `Constant`

valves only)
and the valve opening dynamics.

### Opening Parameterization

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

, the block calculates the opening area as

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

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

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

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}When you set **Opening parameterization** to
`Tabulated data - Area vs. pressure`

,
*A _{leak}* and

*A*are the first and last parameters of the

_{max}**Opening area vector**, respectively. The smoothed, normalized pressure is also used when the smoothing factor is nonzero with linear interpolation and nearest extrapolation.

When you set **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**.

Within the limits of the tabulated data, the block calculates the mass flow rate as:

$$\dot{m}=\overline{\rho}\dot{V},$$

where:

$$\dot{V}$$ is the volumetric flow rate.

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

When the simulation pressure falls below the first element of the
**Pressure drop vector** parameter,
*Δp _{TLU}(1)*, the block calculates the
mass flow rate as:

$$\dot{m}={K}_{Leak}\overline{\rho}\sqrt{\Delta p}.$$

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

where *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,
*Δp _{TLU}(end)*, the block calculates
the mass flow rate as

$$\dot{m}={K}_{Max}\overline{\rho}\sqrt{\Delta p}$$

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

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

**Volumetric flow rate vector**parameter.

### 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

When faults are enabled, the valve open area becomes stuck at a specified value in response to one of these triggers:

Simulation time — Faulting occurs at a specified time.

Simulation behavior — Faulting occurs in response to an external trigger. This exposes port

**Tr**.

Three fault options are available in the **Opening area when
faulted** parameter:

`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 applied 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.

Once triggered, 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**