Pressure Relief Valve (2P)

Pressure relief valve in a two-phase fluid network

Since R2021a

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Libraries:
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_set. The valve is fully open when the control pressure reaches the end of the 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_leak is the Closed valve leakage as a fraction of nominal flow.

• p_control 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 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_lam is the pressure transition threshold between laminar and turbulent flow, which is calculated from the 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_nom is the Nominal pressure drop rate at maximum opening.

• v_nom 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.

• v_in 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:

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

• v_liq is the liquid specific volume of the fluid.

• v_vap is the vapor specific volume of the fluid.

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_dyn is the dynamic vapor quality.

• x_in 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, 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_A is the energy flow at port A.

• Φ_B 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

A — Fluid port

two-phase fluid

Fluid entry or exit port.

B — Fluid port

two-phase fluid

Fluid entry or exit port.

Input

Ps — Set pressure

physical signal

Input port for varying set pressure signal.

Dependencies

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

Parameters

Set pressure control — Variable or constant set pressure

Constant (default) | Controlled

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

Set pressure specification — Control pressure

Pressure differential (default) | Gauge pressure at port A

Control pressure specification:

• When set to Pressure differential, the valve opens when p_A ̶ p_B exceeds the Set pressure differential.

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

Set pressure differential — Set pressure

0.01 MPa (default) | positive scalar

Valve pressure threshold. When the control pressure, p_A ̶ p_B, 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.

Set pressure (gauge) — Set pressure

0.1 MPa (default) | positive scalar

Valve pressure threshold. When the control pressure, p_A ̶ p_atm, 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.

Pressure regulation range — Valve operational range

0.1 MPa (default) | positive scalar

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

Nominal mass flow rate at maximum opening — Rated mass flow rate

0.1 kg/s (default) | positive scalar

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

Nominal pressure drop at maximum opening — Rated pressure drop

0.001 MPa (default) | positive scalar

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

Nominal inlet condition specification — Method of determining inlet fluid state

Temperature (default) | Vapor quality | Vapor void fraction | Specific enthalpy | Specific internal energy

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.

Nominal inlet pressure — Pressure of fluid entering valve

0.101325 MPa (default) | positive scalar

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.

Nominal inlet temperature — Fluid temperature

293.15 K (default) | positive scalar

Inlet fluid temperature in nominal operating conditions.

Dependencies

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

Nominal inlet vapor quality — Inlet vapor quality by mass fraction

0.5 (default) | positive scalar in the range [0,1]

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.

Nominal inlet vapor void fraction — Inlet volume fraction

0.5 (default) | positive scalar in the range [0,1]

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.

Nominal inlet specific enthalpy — Inlet fluid specific enthalpy

1500 kJ/kg (default) | positive scalar

Inlet specific enthalpy in nominal operating conditions.

Dependencies

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

Nominal inlet specific internal energy — Inlet specific internal energy

1500 kJ/kg (default) | positive scalar

Inlet specific internal energy in nominal operating conditions.

Dependencies

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

Cross-sectional area at ports A and B — Valve port areas

0.01 m^2 (default) | positive scalar

Area of the valve ports A and B.

Closed valve leakage as a fraction of nominal flow — Fractional flow when valve is closed

1e-6 (default) | positive scalar

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

Smoothing factor — Numerical smoothing factor

0.01 (default) | positive scalar in the range [0,1]

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.

Laminar flow pressure ratio — Laminar-turbulent transition pressure ratio

0.999 (default) | positive scalar

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.

Inlet phase change time constant — Lag for mixture specific volume

0.1 s (default) | positive scalar

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.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2021a