# Pressure Relief Valve (2P)

Pressure relief valve in a two-phase fluid network

**Library:**Simscape / Fluids / Two-Phase Fluid / Valves & Orifices / Pressure Control Valves

## Description

The Pressure Relief Valve (2P) block models a pressure-controlling relief valve in a
two-phase fluid network. The valve opens when the pressure exceeds the set pressure.
Specify the pressure differential that opens the valve in the **Set pressure
specification** parameter, which can be the pressure difference between
ports **A** and **B** or the gauge pressure at port
**A**. When you set **Set pressure control** to
`Controlled`

, the set pressure varies according to the
input signal at port **Ps**.

Fluid properties inside the valve are calculated from inlet conditions. There is no heat exchange between the fluid and the environment, and therefore phase change inside the valve only occurs due to a pressure drop or a propagated phase change from another part of the model.

A number of block parameters are based on nominal operating conditions, which correspond to the valve rated performance, such as a specification on a manufacturer datasheet.

### Pressure Control

The valve opens when the pressure in the valve,
*p _{control}*, exceeds the

**Set pressure differential**,

*p*. The valve is fully open when the control pressure reaches the end of the

_{set}**Pressure regulation range**,

*p*.

_{range}When you set **Set pressure control** to
`Constant`

, the opening fraction of the valve,
*λ*, is expressed as:

$$\lambda =\left(1-{f}_{leak}\right)\frac{\left({p}_{control}-{p}_{set}\right)}{{p}_{range}}+{f}_{leak},$$

where:

*f*is the_{leak}**Closed valve leakage as a fraction of nominal flow**.*p*is the control pressure, which depends on the_{control}**Set pressure specification**parameter.When you set

**Set pressure specification**to`Pressure differential`

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

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

, the control pressure is the difference between the pressure at port**A**and atmospheric pressure.

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

, the valve opening fraction is:

$$\lambda =\left(1-{f}_{leak}\right)\frac{\left({p}_{control}-{p}_{s}\right)}{{p}_{range}}+{f}_{leak},$$

where *p _{s}* is the signal
at port

**Ps**. If the control pressure exceeds the valve pressure regulation range, the valve opening fraction is 1.

**Mass Flow Rate**

The mass flow rate depends on the pressure differential, and therefore the open area of the valve. It is calculated as:

$${\dot{m}}_{A}=\lambda {\dot{m}}_{nom}\left[\sqrt{\frac{{v}_{nom}}{2\Delta {p}_{nom}}}\right]\sqrt{\frac{2}{{v}_{in}}}\frac{\Delta p}{{\left(\Delta {p}^{2}+\Delta {p}_{lam}^{2}\right)}^{0.25}},$$

where:

*Δp*is the pressure drop over the valve,*p*._{A}̶ p_{B}*Δp*is the pressure transition threshold between laminar and turbulent flow, which is calculated from the_{lam}**Laminar flow pressure ratio**,*B*:_{lam}$$\Delta {p}_{lam}=\frac{\left({p}_{A}+{p}_{B}\right)}{2}\left(1-{B}_{lam}\right).$$

$${\dot{m}}_{nom}$$ is the

**Nominal mass flow rate at maximum opening**.*Δp*is the_{nom}**Nominal pressure drop rate at maximum opening**.*v*is the nominal inlet specific volume. This value is determined from the fluid properties tabulated data based on the_{nom}**Nominal inlet specific enthalpy**and**Nominal inlet pressure**parameters.*v*is the inlet specific volume._{in}

### Fluid Specific Volume Dynamics

When the fluid at the valve inlet is a liquid-vapor mixture, the block calculates the specific volume as:

$${v}_{in}=\left(1-{x}_{dyn}\right){v}_{liq}+{x}_{dyn}{v}_{vap},$$

where:

*x*is the inlet vapor quality. The block applies a first-order lag to the inlet vapor quality of the mixture._{dyn}*v*is the liquid specific volume of the fluid._{liq}*v*is the vapor specific volume of the fluid._{vap}

If the inlet fluid is liquid or vapor,
*v _{in}* is the respective liquid or
vapor specific volume.

**Vapor Quality Lag**

If the inlet vapor quality is a liquid-vapor mixture, a first-order time lag is applied:

$$\frac{d{x}_{dyn}}{dt}=\frac{{x}_{in}-{x}_{dyn}}{\tau},$$

where:

*x*is the dynamic vapor quality._{dyn}*x*is the current inlet vapor quality._{in}*τ*is the**Inlet phase change time constant**.

If the inlet fluid is a subcooled liquid or superheated vapor,
*x _{dyn}* is equal to

*x*.

_{in}### Mass Balance

Mass is conserved in the valve:

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

where:

$${\dot{m}}_{A}$$ is the mass flow rate at port

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

**B**.

### Energy Balance

Energy is conserved in the valve:

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

where:

*Φ*is the energy flow at port_{A}**A**.*Φ*is the energy flow at port_{B}**B**.

### Assumptions and Limitations

The block does not model pressure recovery downstream of the valve.

There is no heat exchange between the valve and the environment.

The block does not model choked flow.

## Ports

### Conserving

### Input

## Parameters

## Version History

**Introduced in R2021a**