# Pressure Relief Valve (2P)

Pressure relief valve in a two-phase fluid network

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• 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, pcontrol, exceeds the Set pressure differential, pset. The valve is fully open when the control pressure reaches the end of the Pressure regulation range, prange.

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:

• fleak is the Closed valve leakage as a fraction of nominal flow.

• pcontrol is the control pressure, which depends on the Set pressure specification parameter.

When you set Set pressure specification to `Pressure differential`, the control pressure is PA ̶ pB.

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 ps 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:

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

where:

• Δp is the pressure drop over the valve, pA ̶ pB.

• Δplam is the pressure transition threshold between laminar and turbulent flow, which is calculated from the Laminar flow pressure ratio, Blam:

`$\Delta {p}_{lam}=\frac{\left({p}_{A}+{p}_{B}\right)}{2}\left(1-{B}_{lam}\right).$`

• ${\stackrel{˙}{m}}_{nom}$ is the Nominal mass flow rate at maximum opening.

• Δpnom is the Nominal pressure drop rate at maximum opening.

• vnom is the nominal inlet specific volume. This value is determined from the fluid properties tabulated data based on the Nominal inlet specific enthalpy and Nominal inlet pressure parameters.

• vin is the inlet specific volume.

### 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:

• xdyn is the inlet vapor quality. The block applies a first-order lag to the inlet vapor quality of the mixture.

• vliq is the liquid specific volume of the fluid.

• vvap is the vapor specific volume of the fluid.

If the inlet fluid is liquid or vapor, vin 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:

• xdyn is the dynamic vapor quality.

• xin is the current inlet vapor quality.

• τ is the Inlet phase change time constant.

If the inlet fluid is a subcooled liquid or superheated vapor, xdyn is equal to xin.

### Mass Balance

Mass is conserved in the valve:

`${\stackrel{˙}{m}}_{A}+{\stackrel{˙}{m}}_{B}=0,$`

where:

• ${\stackrel{˙}{m}}_{A}$ is the mass flow rate at port A.

• ${\stackrel{˙}{m}}_{B}$ is the mass flow rate at port B.

### Energy Balance

Energy is conserved in the valve:

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

where:

• ΦA is the energy flow at port A.

• ΦB is the energy flow at port 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

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Fluid entry or exit port.

Fluid entry or exit port.

### Input

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Input port for varying set pressure signal.

#### Dependencies

To enable this port, set Set pressure control to `Controlled`.

## Parameters

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Whether the pressure threshold is constant or variable. Setting this parameter to `Controlled` exposes the physical signal port Ps.

Control pressure specification:

• When set to `Pressure differential`, the valve opens when pA ̶ pB exceeds the Set pressure differential.

• When set to `Gauge pressure at port A`, the valve opens when pA ̶ patm exceeds the Set pressure (gauge).

Valve pressure threshold. When the control pressure, pA ̶ pB, exceeds the set pressure, the valve begins to open.

#### Dependencies

To enable this parameter, set Set pressure control to `Constant` and Set pressure specification to `Pressure differential`.

Valve pressure threshold. When the control pressure, pA ̶ patm, exceeds the set pressure, the valve begins to open.

#### Dependencies

To enable this parameter, set Set pressure control to `Constant` and Set pressure specification to `Gauge pressure at port A`.

Valve operational range. The valve begins to open at the set pressure value, and is fully open at pmax, the end of the pressure regulation range: pmax = pset + prange.

Mass flow rate through a fully open valve under typical, design, or rated conditions.

Pressure drop over a fully open valve under typical, design, or rated conditions.

Method of determining inlet fluid state. The valve inlet specific volume is determined from the fluid properties tabulated data based on the Nominal inlet pressure and the setting of the Nominal inlet condition specification parameters.

Inlet pressure to the valve in typical, design, or rated conditions. The valve inlet specific volume is determined from the fluid properties tabulated data based on the Nominal inlet pressure and the setting of the Nominal inlet condition specification parameters.

Inlet fluid temperature in nominal operating conditions.

#### Dependencies

To enable this parameter, set Nominal inlet condition specification to `Temperature`.

Inlet vapor quality of the mixture by mass fraction in nominal operating conditions. A value of `0` means that the inlet fluid is subcooled liquid. A value of `1` means that the inlet fluid is superheated vapor.

#### Dependencies

To enable this parameter, set Nominal inlet condition specification to ```Vapor quality```.

Inlet mixture by volume fraction in nominal operating conditions. A value of `0` means that the inlet fluid is subcooled liquid. A value of `1` means that the inlet fluid is superheated vapor.

#### Dependencies

To enable this parameter, set Nominal inlet condition specification to ```Vapor void fraction```.

Inlet specific enthalpy in nominal operating conditions.

#### Dependencies

To enable this parameter, set Nominal inlet condition specification to ```Specific enthalpy```.

Inlet specific internal energy in nominal operating conditions.

#### Dependencies

To enable this parameter, set Nominal inlet condition specification to ```Specific internal energy```.

Area of the valve ports A and B.

Fractional flow rate through the valve when it is fully closed. This parameter contributes to numerical stability by maintaining continuity in the fluid network.

Continuous smoothing factor that introduces a layer of gradual change to the flow response when the valve is in near-open or near-closed positions. Set this parameter to a nonzero value less than one to increase the stability of your simulation in these regimes.

Ratio of the valve outlet pressure to valve inlet pressure at which the fluid transitions between the laminar and turbulent regimes. The pressure loss corresponds to the mass flow rate linearly in laminar flows and quadratically in turbulent flows.

Time lag for liquid-vapor mixtures in computing the fluid specific volume. This parameter does not influence the specific volume when the inlet fluid is a fully supercooled liquid or fully superheated vapor.

## Version History

Introduced in R2021a