# Pressure Relief Valve (TL)

Pressure relief valve in a thermal liquid network

**Libraries:**

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

## Description

The Pressure Relief Valve (TL) block represents a valve
that relieves excess pressure in a thermal 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. A control pressure above the set
pressure causes the valve to gradually open, which allows the fluid network to relieve
excess pressure.

### Pressure Control

The normalized pressure, $$\widehat{p}$$, controls the valve opening area when **Opening
parameterization** is ```
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, which depends on the value of the_{control}**Pressure control specification**parameter.When you set

**Pressure control specification**to`Pressure differential`

, the control pressure is*p*._{A}̶ p_{B}When you set

**Pressure control 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, which depends on the value of the_{set}**Pressure control specification**parameter.When you set

**Pressure control specification**to`Pressure differential`

,*p*is the value of the_{set}**Set pressure differential**parameter.When you set

**Set pressure specification**to`Pressure at port A`

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

### Opening Parameterization

The mass flow rate depends on the value of the **Opening
parameterization** parameter.

**Area vs. Pressure Parameterizations**

When you set **Set pressure control** 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**parameter.*A*is the instantaneous valve open area._{valve}*A*is the value of 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**,

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

_{crit}

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

where *μ* is the dynamic viscosity of the thermal
liquid.

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

*PR*as

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

The pressure recovery describes the positive pressure change in the valve due
to an increase in area. When you clear the **Pressure
recovery** check box, the block sets
*PR _{loss}* to 1.

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

, the block calculates
the opening area as

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

where *A _{leak}* is the
value of the

**Leakage Area**parameter and

*A*is the value of the

_{max}**Maximum opening area**parameter.

This figure shows how the block controls the opening area using 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 **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`

, the block
calculates the opening area as

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

where:

*p*=_{control,TLU,ref}*p*+_{TLU}*p*._{offset}*p*is the_{TLU}**Pressure differential vector**or**Opening pressure (gauge) vector**parameter, depending on the value of the**Pressure control specification**parameter.*p*is an internal pressure offset that causes the valve to start closing when_{offset}*p*=_{control,TLU,ref}*p*._{set}*A*is the_{TLU}**Opening area vector**parameter.

This figure shows how the block controls the opening area when
**Opening parameterization** is ```
Tabulated data
- Area vs. pressure
```

.

**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 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.

The block calculates the relationship between the mass flow and pressure using

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

where

$$\text{K=}\frac{\dot{V}}{\sqrt{\left|\Delta p\right|}}.$$

**Controlled Pressure Regulation**

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 Dynamics

When you set **Opening dynamics** to
`On`

, the block introduces a control pressure lag where
*p _{control}* becomes the dynamic
control pressure,

*p*. The instantaneous change in dynamic opening area is calculated based on the

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

*τ*:

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

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

### Energy Balance

The energy conservation equation in the valve is

$${\varphi}_{A}+{\varphi}_{B}=0,$$

where:

*ϕ*_{A}is the energy flow rate into the valve through port**A**.*ϕ*_{B}is the energy flow rate into the valve through port**B**.

### Faults

To model a fault, in the **Faults** section,
click the **Add fault** hyperlink next to the fault that you want to model. Use
the fault parameters to 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:When you set

**Set pressure control**to`Constant`

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

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

**Set pressure control**to`Constant`

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

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

**Set pressure control**to`Controlled`

the valve area freezes at the**Leakage area**parameter.

`Open`

— The valve freezes at its largest value:When you set

**Set pressure control**to`Constant`

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

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

**Set pressure control**to`Constant`

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

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

**Set pressure control**to`Controlled`

the valve area freezes at the**Maximum opening area**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.

## Examples

## Ports

### Input

### Conserving

## Parameters

## Extended Capabilities

## Version History

**Introduced in R2016a**