# Pressure Relief Valve (TL)

Pressure relief valve in a thermal liquid network

**Library:**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 allows flow through
the networks and opens to relieve excess flow when the control pressure reaches the
value of the **Valve set pressure (gauge)** parameter. A control
pressure above the set pressure causes the valve to gradually open, which allows the
fluid network to relieve excess pressure.

A smoothing function allows the valve opening area to change smoothly between the fully closed and fully open positions. The smoothing function removes the abrupt opening area changes at the zero and maximum opening positions. The figure shows the effect of smoothing on the valve opening area curve.

### 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**.

### Momentum Balance

The momentum conservation equation in the valve is

$${p}_{A}-{p}_{B}=\frac{\dot{m}\sqrt{{\dot{m}}^{2}+{\dot{m}}_{cr}^{2}}}{2{\rho}_{Avg}{C}_{d}^{2}{S}^{2}}\left[1-{\left(\frac{{S}_{R}}{S}\right)}^{2}\right]P{R}_{Loss},$$

where:

*p*_{A}and*p*_{B}are the pressures at port**A**and port**B**.$$\dot{m}$$ is the mass flow rate.

$${\dot{m}}_{cr}$$ is the critical mass flow rate.

*ρ*_{Avg}is the average liquid density.*C*_{d}is the discharge coefficient.*S*_{R}is the valve opening area.*S*is the valve inlet area.*PR*_{Loss}is the pressure ratio:$$P{R}_{Loss}=\frac{\sqrt{1-{\left({S}_{R}/S\right)}^{2}\left(1-{C}_{d}^{2}\right)}-{C}_{d}\left({S}_{R}/S\right)}{\sqrt{1-{\left({S}_{R}/S\right)}^{2}\left(1-{C}_{d}^{2}\right)}+{C}_{d}\left({S}_{R}/S\right)}.$$

The block computes the valve opening as

$${S}_{R}={\widehat{p}}_{smoothed}\cdot \left({S}_{Max}-{S}_{Leak}\right)+{S}_{Leak}$$

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

where:

*S*is the valve leakage area._{Leak}*S*is the maximum valve opening area._{Max}*p*is the valve control pressure:_{control}$${p}_{control}=\{\begin{array}{ll}{p}_{A},\hfill & \text{PressureatportA}\hfill \\ {p}_{A}-{p}_{B},\hfill & \text{Pressuredifferential}\hfill \end{array}$$

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

*p*_{Max}is the maximum pressure:$${p}_{max}=\{\begin{array}{ll}{p}_{set,gauge}+{p}_{range}+{p}_{Atm},\hfill & \text{PressureatportA}\hfill \\ {p}_{set,diff}+{p}_{range},\hfill & \text{Pressuredifferential}\hfill \end{array}$$

where the two equations refer to the settings of the

**Pressure control specification**parameter.

The critical mass flow rate is

$${\dot{m}}_{cr}={\mathrm{Re}}_{cr}{\mu}_{Avg}\sqrt{\frac{\pi}{4}{S}_{R}}.$$

**Numerically-Smoothed Valve Area**

When the valve is in a near-open or
near-closed position, 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}### 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**.

## Ports

### Conserving

## Parameters

## Model Examples

## Extended Capabilities

## Version History

**Introduced in R2016a**