# 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.

### Mass Balance

The mass conservation equation in the valve is

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

where:

$${\dot{m}}_{A}$$ is the mass flow rate into the valve through port

**A**.$${\dot{m}}_{B}$$ is the mass flow rate into the valve through port

**B**.

### Mass Flow Rate

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 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.

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

**Leakage Area**parameter and

*A*is the value of the

_{max}**Maximum opening area**parameter. The normalized pressure, $$\widehat{p}$$, is

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

where the expressions for
*p _{control}*,

*p*, and

_{set}*p*depend whether the setting of the

_{Max}**Pressure control specification**parameter is

`Pressure at port A`

or ```
Pressure
differential
```

. *p _{control}* is the valve control pressure:

$${p}_{control}=\{\begin{array}{ll}{p}_{A}-{p}_{Atm},\hfill & \text{PressureatportA}\hfill \\ {p}_{A}-{p}_{B},\hfill & \text{Pressuredifferential}\hfill \end{array}$$

where *p _{Atm}* is the
atmospheric pressure.

*p _{set}* is the set pressure:

$${p}_{set}=\{\begin{array}{ll}{p}_{set,gauge}+{p}_{Atm},\hfill & \text{Pressureatport}\text{\hspace{0.17em}}\text{A}\hfill \\ {p}_{set,diff},\hfill & \text{Pressuredifferential}\hfill \end{array}$$

*p _{Max}* is the maximum pressure:

$${p}_{max}=\{\begin{array}{ll}{p}_{set,gauge}+{p}_{range}+{p}_{Atm},\hfill & \text{PressureatportA}\hfill \\ {p}_{set,diff}+{p}_{range},\hfill & \text{Pressuredifferential}\hfill \end{array}$$

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**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
```

.

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**.

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

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

### 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**.

### 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

## Parameters

## Extended Capabilities

## Version History

**Introduced in R2016a**