Pressure Relief Valve (2P)

Pressure relief valve in a two-phase fluid network

Since R2021a

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.

The Modeling option parameter controls the parameterization options for a valve designed for modeling either vapor or liquid, but does not impact the fluid properties. The block calculates fluid properties inside the valve from inlet conditions. There is no heat exchange between the fluid and the environment, and therefore phase change inside the orifice only occurs due to a pressure drop or a propagated phase change from another part of the model.

Pressure Control

The valve opens when the pressure in the valve, p_control, exceeds the set pressure, p_set. The valve is fully open when the control pressure reaches p_set + p_range, where p_range is the value of the Pressure regulation range parameter.

For the linear parametrizations, the block calculates the opening fraction of the valve, λ. When you set Set pressure control to Constant, λ is

$λ = (1 - f_{l e a k}) \frac{(p_{c o n t r o l} - p_{s e t})}{p_{r a n g e}} + f_{l e a k},$

where:

f_leak is the value of the Leakage flow fraction parameter.
p_control is the control pressure, which depends on the value of 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.
p_set is the set pressure, which depends on the value of the Set pressure specification parameter.
When you set Set pressure specification to Pressure differential, p_set is the value of the Set pressure differential parameter.
When you set Set pressure specification to Gauge pressure at port A, p_set is the value of the Set pressure (gauge) parameter.

When you set Set pressure control to Controlled, the valve opening fraction is

$λ = (1 - f_{l e a k}) \frac{(p_{c o n t r o l} - p_{s})}{p_{r a n g e}} + f_{l e a k},$

where p_s is the value of the signal at port Ps. If the control pressure exceeds the valve pressure regulation range, the valve opening fraction is 1.

Liquid Valve

When Modeling option is Liquid operating condition, the block parameterizations depend on the value of the Valve parameterization parameter. The block calculates the pressure loss and pressure recovery in the same way for all liquid parameterization options.

The critical pressure difference, Δp_crit, is the pressure differential where the flow transitions between laminar and turbulent flow. For all liquid parameterizations, Δp_crit is

$Δ p_{c r i t} = \frac{(p_{A} + p_{B})}{2} (1 - B_{l a m}),$

where:

p_A and p_B are the pressure at port A and B, respectively.
B_lam is the value of the Laminar flow pressure ratio parameter.

The block accounts for pressure loss by using the ratio of the pressure loss across the whole valve to the pressure drop immediately across the valve restriction area. This ratio, PR_loss, is

$P R_{l o s s} = \frac{\sqrt{1 - {(\frac{A_{v a l v e}}{A_{p o r t}})}^{2} (1 - C_{d}^{2})} - C_{d} \frac{A_{v a l v e}}{A_{p o r t}}}{\sqrt{1 - {(\frac{A_{v a l v e}}{A_{p o r t}})}^{2} (1 - C_{d}^{2})} + C_{d} \frac{A_{v a l v e}}{A_{p o r t}}},$

where:

A_port is the value of the Cross-sectional area at ports A and B parameter.
C_d is the value of the Discharge coefficient parameter.
A_valve is the valve area.

The pressure recovery is the positive pressure change in the valve due to an increase in area after the orifice hole. If you do not want to capture this increase in pressure, clear the Pressure recovery check box. In this case, PR_loss is 1, which reduces the model complexity. Clear this setting if the orifice hole is quite small relative to the port area or if the next downstream component is close to the block and any jet does not have room to dissipate.

Linear - Nominal Mass Flow Rate vs. Pressure Parameterization

When you set Valve Parameterization to Nominal mass flow rate vs. pressure, the mass flow rate through the valve is

$\dot{m} = λ {\dot{m}}_{n o m} [\sqrt{\frac{v_{n o m}}{2 Δ p_{n o m}}}] \sqrt{\frac{2}{v_{i n}}} \frac{Δ p}{{(Δ p^{2} + Δ p_{c r i t}^{2})}^{0.25}},$

where:

Δp is the pressure drop over the valve, p_A ̶ p_B.
${\dot{m}}_{n o m}$ is the value of the Nominal mass flow rate at maximum valve opening parameter.
Δp_nom is the value of the Nominal pressure drop rate at maximum valve opening parameter.
v_nom is the nominal inlet specific volume. The block determines this value from the tabulated fluid properties data based on the Nominal inlet specific enthalpy and Nominal inlet pressure parameters.
v_in is the inlet specific volume.

Linear - Area vs. Pressure Parameterization

When you set Valve parameterization to Linear - area vs. pressure, the valve area is

$A_{v a l v e} = λ A_{m a x},$

where A_max is the value of the Maximum valve area parameter.

The mass flow rate is

$\dot{m} = \frac{C_{d} A_{v a l v e} \sqrt{\frac{2}{v_{i n}}}}{\sqrt{P R_{l o s s} (1 - {(\frac{A_{v a l v e}}{A_{p o r t}})}^{2})}} \frac{Δ p}{{[Δ p^{2} + Δ p_{c r i t}^{2}]}^{1 / 4}} .$

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 opening area between A_leak and A_max, where A_leak = f_leakA_max. For more information, see Numerical Smoothing.

Tabulated Data - Area vs. Pressure Parameterization

When you set Valve Parameterization to Tabulated data - area vs. pressure, the block interpolates the valve area from the Valve area vector and Opening pressure differential vector or Opening pressure (gauge) vector parameters.

The block uses the same equation as the Linear - Area vs. pressure setting to calculate the volumetric flow rate.

Fluid Specific Volume Dynamics

For all parameterizations, the block calculates the fluid specific volume during simulation based on the liquid state.

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

$v_{i n} = (1 - x_{d y n}) v_{l i q} + x_{d y n} v_{v a p},$

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.

If the inlet vapor quality is a liquid-vapor mixture, the block applies a first-order time lag,

$\frac{d x_{d y n}}{d t} = \frac{x_{i n} - x_{d y n}}{τ},$

where:

x_dyn is the dynamic vapor quality.
x_in is the current inlet vapor quality.
τ is the value of the Inlet phase change time constant parameter.

If the inlet fluid is a subcooled liquid, x_in = 0. If the inlet fluid is a superheated vapor, x_in = 1.

Vapor Valve

When Modeling option is Vapor operating condition, the block behavior depends on the Valve parameterization and Opening characteristic parameters.

The flow rate in the valve depends on the Opening characteristic parameter:

Linear — The block scales the measure of flow capacity by λ to account for the valve opening area.
Tabulated — The block interpolates the measure of flow capacity from either the Cv flow coefficient vector, Kv flow coefficient vector, or Orifice area vector parameters. This function uses a one-dimensional lookup table.

Cv Flow Coefficient Parameterization

When you set Valve parametrization to Cv flow coefficient, the mass flow rate is

$\dot{m} = C_{v} N_{6} Y \sqrt{\frac{(p_{i n} - p_{o u t})}{v_{i n}}},$

where:

C_v is the flow coefficient.
N₆ is a constant equal to 27.3 when mass flow rate is in kg/hr, pressure is in bar, and density is in kg/m³.
Y is the expansion factor.
p_in is the inlet pressure.
p_out is the outlet pressure.
v_in is the inlet specific volume.

The expansion factor is

$Y = 1 - \frac{p_{i n} - p_{o u t}}{3 p_{i n} F_{γ} x_{T}},$

where:

F_γ is the ratio of the isentropic exponent to 1.4.
x_T is the value of the xT pressure differential ratio factor at choked flow parameter.

The block smoothly transitions to a linearized form of the equation when the pressure ratio, $p_{o u t} / p_{i n}$ , rises above the value of the Laminar flow pressure ratio parameter, B_lam,

$\dot{m} = C_{v} N_{6} Y_{l a m} \sqrt{\frac{1}{p_{a v g} (1 - B_{l a m}) v_{a v g}}} (p_{i n} - p_{o u t}),$

where:

$Y_{l a m} = 1 - \frac{1 - B_{l a m}}{3 F_{γ} x_{T}} .$

When the pressure ratio, $p_{o u t} / p_{i n}$ , falls below $1 - F_{γ} x_{T}$ , the valve becomes choked and the block uses the equation

$\dot{m} = \frac{2}{3} C_{v} N_{6} \sqrt{\frac{F_{γ} x_{T} p_{i n}}{v_{i n}}} .$

Kv Flow Coefficient Parameterization

When you set Valve parametrization to Kv flow coefficient, the block uses the same equations as the Cv flow coefficient parametrization, but replaces C_v with K_v using the relation $K_{v} = 0.865 C_{v}$ .

Valve Area Parameterization

When you set Valve parametrization to Orifice area, the mass flow rate is

$\dot{m} = C_{d} A_{v a l v e} \sqrt{\frac{2 γ}{γ - 1} p_{i n} \frac{1}{v_{i n}} {(\frac{p_{o u t}}{p_{i n}})}^{\frac{2}{γ}} [\frac{1 - {(\frac{p_{o u t}}{p_{i n}})}^{\frac{γ - 1}{γ}}}{1 - {(\frac{A_{v a l v e}}{A_{p o r t}})}^{2} {(\frac{p_{o u t}}{p_{i n}})}^{\frac{2}{γ}}}]},$

where:

C_d is the value of the Discharge coefficient parameter.
γ is the isentropic exponent.

The block smoothly transitions to a linearized form of the equation when the pressure ratio, $p_{o u t} / p_{i n}$ , rises above the value of the Laminar flow pressure ratio parameter, B_lam,

$\dot{m} = C_{d} A_{v a l v e} \sqrt{\frac{2 γ}{γ - 1} p_{a v g}^{\frac{2 - γ}{γ}} \frac{1}{v_{a v g}} B_{l a m}^{\frac{2}{γ}} [\frac{1 - B_{l a m}^{\frac{γ - 1}{γ}}}{1 - {(\frac{A_{v a l v e}}{A_{p o r t}})}^{2} B_{l a m}^{\frac{2}{γ}}}]} (\frac{p_{i n}^{\frac{γ - 1}{γ}} - p_{o u t}^{\frac{γ - 1}{γ}}}{1 - B_{l a m}^{\frac{γ - 1}{γ}}}) .$

When the pressure ratio, $p_{o u t} / p_{i n}$ , falls below ${(\frac{2}{γ + 1})}^{\frac{γ}{γ - 1}}$ , the valve becomes choked and the block uses the equation

$\dot{m} = C_{d} A_{v a l v e} \sqrt{\frac{2 γ}{γ + 1} p_{i n} \frac{1}{v_{i n}} \frac{1}{{(\frac{γ + 1}{2})}^{\frac{2}{γ - 1}} - {(\frac{A_{v a l v e}}{A_{p o r t}})}^{2}}} .$

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,

$Φ_{A} + Φ_{B} = 0,$

where:

Φ_A is the energy flow at port A.
Φ_B is the energy flow at port B.

Assumptions and Limitations

There is no heat exchange between the valve and the environment.
When Modeling option is Liquid operating condition, the results may not be accurate outside of the subcooled liquid region. When Modeling option is Vapor operating condition, the results may not be accurate outside of the superheated vapor region. To model a valve in a liquid-vapor mixture, set Modeling option to Liquid operating condition.

Ports

Conserving

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A — Fluid entry or exit
two-phase fluid

Two-phase fluid conserving port associated with the fluid entry or exit port.

B — Fluid entry or exit
two-phase fluid

Two-phase fluid conserving port associated with the fluid entry or exit port.

Input

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Ps — Set pressure, Pa
physical signal

Input port for varying set pressure signal.

Dependencies

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

Parameters

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Modeling option — Modeling option for fluid phase
`Liquid operating condition` (default) | `Vapor operating condition`

Modeling option for the fluid phase at the valve. Set this parameter to Liquid operating condition if the two-phase fluid at the block location is in a liquid state. Set this parameter to Vapor operating condition if the two-phase fluid at the block location is in a vapor state.

Parameters

Valve parameterization — Model for valve parameterization
`Linear - Area vs. pressure` (default) | `Linear - Nominal mass flow rate vs. pressure` | `Tabulated data - Area vs. pressure` | `Cv flow coefficient` | `Kv flow coefficient` | `Orifice area`

Method the block uses to calculate the mass flow rate from the pressure difference across the valve or the pressure difference from the mass flow rate.

When Modeling option is Liquid operating condition, the choices for this parameter are:

Linear - Area vs. pressure
Linear - Nominal mass flow rate vs. pressure
Tabulated data - Area vs. pressure

When Modeling option is Vapor operating condition, the choices for this parameter are:

Cv flow coefficient
Kv flow coefficient
Orifice area

Opening pressure specification — Control pressure
`Pressure differential` (default) | `Gauge pressure at port A`

Control pressure specification:

When this parameter is Pressure differential, the valve opens when p_A ̶ p_B exceeds the Set pressure differential.
When this parameter is Gauge pressure at port A, the valve opens when p_A ̶ p_atm exceeds the Set pressure (gauge).

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 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 Opening pressure specification to Pressure differential, Set pressure control to Constant and either:

Modeling option to Liquid operating condition and Valve parameterization to Linear - Area vs. pressure or Linear - Nominal mass flow rate vs. pressure.
Modeling option to Vapor operating condition and Opening characteristic to Linear.

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 Opening pressure specification to Gauge pressure at port A, Set pressure control to Constant and either:

Modeling option to Liquid operating condition and Valve parameterization to Linear - Area vs. pressure or Linear - Nominal mass flow rate vs. pressure.
Modeling option to Vapor operating condition and Opening characteristic to Linear.

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, where p_max = p_set + p_range.

Dependencies

To enable this parameter, set either:

Modeling option to Liquid operating condition and Valve parameterization to Linear - Area vs. pressure or Linear - Nominal mass flow rate vs. pressure.
Modeling option to Vapor operating condition and Opening characteristic to Linear.

Nominal mass flow rate at maximum valve 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.

Dependencies

To enable this parameter, set Modeling option to Liquid operating condition and Valve parameterization to Linear - Nominal mass flow rate vs. pressure.

Nominal pressure drop at maximum valve opening — Rated pressure drop
`0.001` MPa (default) | positive scalar

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

Dependencies

To enable this parameter, set Modeling option to Liquid operating condition and Valve parameterization to Linear - Nominal mass flow rate vs. pressure.

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 the inlet fluid state. The block determines the orifice nominal inlet specific volume from the tabulated fluid properties data based on the value of the Nominal inlet pressure parameter and the setting of the Nominal inlet condition specification parameter.

Dependencies

To enable this parameter, set Modeling option to Liquid operating condition and Valve parameterization to Linear - Nominal mass flow rate vs. pressure.

Nominal inlet pressure — Inlet fluid pressure
`0.101325` MPa (default) | positive scalar

Inlet pressure in nominal conditions. The block determines the inlet specific volume from the tabulated fluid properties data based on the value of the Nominal inlet pressure parameter and the setting of the Nominal inlet condition specification parameter.

Dependencies

To enable this parameter, set Modeling option to Liquid operating condition and Valve parameterization to Linear - Nominal mass flow rate vs. pressure.

Nominal inlet temperature — Fluid temperature
`293.15` K (default) | positive scalar

Inlet fluid temperature in nominal operating conditions.

Dependencies

To enable this parameter, set Modeling option to Liquid operating condition, Valve parameterization to Linear - Nominal mass flow rate vs. pressure, and Nominal inlet condition specification to Temperature.

Nominal inlet vapor quality — Inlet vapor quality mass fraction
`0` (default) | positive scalar in the range [0,1]

Inlet mixture vapor quality 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

Nominal inlet vapor void fraction — Inlet volume fraction
`0` (default) | positive scalar in the range [0,1]

Inlet mixture 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

Nominal inlet specific enthalpy — Inlet fluid specific enthalpy
`400` kJ/kg (default) | positive scalar

Inlet specific enthalpy in nominal operating conditions.

Dependencies

Nominal inlet specific internal energy — Inlet specific internal energy
`400` kJ/kg (default) | positive scalar

Inlet specific internal energy in nominal operating conditions.

Dependencies

Maximum valve area — Maximum valve opening area
`1e-4 m^2` (default) | positive scalar

Maximum valve area when the valve is fully open.

Dependencies

To enable this parameter, set Modeling option to Liquid operating condition and Valve parameterization to Linear – Area vs. pressure.

Opening pressure differential vector — Vector of pressure differentials
`[0.2 : 0.2 : 1.2] MPa` (default) | 1-by-n vector

Vector of pressure differential values for the tabulated parameterization of valve area. The values in this vector correspond one-to-one with the elements in the Valve area vector, Orifice area vector, Cv flow coefficient vector, or Kv flow coefficient vector parameters.

Dependencies

To enable this parameter, set Opening pressure specification to Pressure differential and either:

Modeling option to Liquid operating condition and Valve parameterization to Tabulated data - Area vs. pressure
Modeling option to Vapor operating condition and Opening characteristic to Tabulated.

Opening pressure (gauge) vector — Vector of gauge pressures
`[0.2 : 0.2 : 1.2] MPa` (default) | 1-by-n vector

Vector of gauge pressure values for the tabulated parameterization of valve area. The values in this vector correspond one-to-one with the elements in the Valve area vector, Orifice area vector, Cv flow coefficient vector, or Kv flow coefficient vector parameters.

Dependencies

To enable this parameter, set Opening pressure specification to Gauge pressure at port A and either:

Modeling option to Liquid operating condition and Valve parameterization to Tabulated data - Area vs. pressure
Modeling option to Vapor operating condition, Valve parameterization to Orifice area, and Opening characteristic to Tabulated.

Valve area vector — Vector of valve opening area values
`[1e-10, 2e-06, 4e-06, 6e-06, 8e-06, 1e-05] m^2` (default) | 1-by-n vector

Vector of orifice area values for the tabulated parameterization of the valve area. The values in this vector correspond one-to-one with the elements in the Opening pressure differential vector or the Opening pressure (gauge) vector parameters.

Dependencies

To enable this parameter, set Modeling option to Liquid operating condition and Valve parameterization to Tabulated data - Area vs. pressure.

Discharge coefficient — Discharge coefficient
`0.64` (default) | positive scalar

Ratio of actual flow rate to ideal flow rate. This parameter accounts for real-world losses that are not captured in the orifice equation.

Dependencies

To enable this parameter, set either:

Modeling option to Liquid operating condition and Valve parameterization to Linear - Area vs. pressure or Tabulated data - Area vs. pressure.
Modeling option to Vapor operating condition and Valve parameterization to Orifice area.

Pressure recovery — Whether to account for pressure increase in area expansions
`off` (default) | `on`

Whether to account for the small rise in pressure after the pressure drop from the inlet to the orifice hole. When the fluid jet exits the orifice hole, it dissipates and expands to fill the port area, which causes this small pressure rise. The block does not model this pressure increase when you clear the Pressure recovery check box.

Dependencies

To enable this parameter, set Modeling option to Liquid operating condition and Valve parameterization to Linear - Area vs. pressure or Tabulated data - Area vs. pressure.

Opening characteristic — Method to parameterize measure of flow capacity
`Linear` (default) | `Tabulated`

Method by which to parameterize the vapor valve for the chosen measure of flow capacity.

Dependencies

To enable this parameter, set Modeling option to Vapor operating condition.

Maximum Cv flow coefficient — C_v coefficient that corresponds to maximally open component
`4` (default) | positive scalar

Value of the C_v flow coefficient when the restriction area available for flow is at a maximum. This parameter measures the ease with which the vapor traverses the resistive element when driven by a pressure differential.

Dependencies

To enable this parameter, set Modeling option to Vapor operating condition, Valve parameterization to Cv flow coefficient, and Opening characteristic to Linear.

Cv flow coefficient vector — C_v coefficients that correspond to values in member position vector
`[1e-06, .8, 1.6, 2.4, 3.2, 4]` (default) | 1-by-n vector

Vector of C_v flow coefficients. Each coefficient corresponds to a value in the Opening pressure differential vector or the Opening pressure (gauge) vector parameters. This parameter measures the ease with which the vapor traverses the resistive element when driven by a pressure differential.

Dependencies

To enable this parameter, set Modeling option to Vapor operating condition, Valve parameterization to Cv flow coefficient, and Opening characteristic to Tabulated.

Maximum Kv flow coefficient — K_v coefficient that corresponds to maximally open component
`3.6` (default) | positive scalar

Value of the K_v flow coefficient when the restriction area available for flow is at a maximum. This parameter measures the ease with which the vapor traverses the resistive element when driven by a pressure differential.

Dependencies

To enable this parameter, set Modeling option to Vapor operating condition, Valve parameterization to Kv flow coefficient, and Opening characteristic to Linear.

Kv flow coefficient vector — K_v coefficients that correspond to values in member position vector
`[1e-06, .72, 1.44, 2.16, 2.88, 3.6]` (default) | 1-by-n vector

Vector of K_v flow coefficients. Each coefficient corresponds to a value in the Opening pressure differential vector or the Opening pressure (gauge) vector parameters. This parameter measures the ease with which the vapor traverses the resistive element when driven by a pressure differential.

Dependencies

To enable this parameter, set Modeling option to Vapor operating condition, Valve parameterization to Kv flow coefficient, and Opening characteristic to Tabulated.

xT pressure differential ratio factor at choked flow — Ratio of pressure differentials
`0.7` (default) | positive scalar

Ratio between the inlet pressure, p_in, and the outlet pressure, p_out, defined as $(p_{i n} - p_{o u t}) / p_{i n}$ where choking first occurs.

Dependencies

To enable this parameter, Modeling option to Vapor operating condition and Valve parameterization to Cv flow coefficient or Kv flow coefficient.

Maximum orifice area — Maximum valve opening area
`1e-4 m^2` (default) | positive scalar

Maximum valve area when the valve is fully open.

Dependencies

To enable this parameter, set Modeling option to Vapor operating condition, Valve parameterization to Orifice area, and Opening characteristic to Linear.

Orifice area vector — Vector of valve opening area values
`[1e-10, 2e-05, 4e-05, 6e-05, 8e-05, .0001] m^2` (default) | 1-by-n vector

Vector of orifice area values for the tabulated parameterization of the vapor valve area. The values in this vector correspond one-to-one with the elements in the Opening pressure differential vector or the Opening pressure (gauge) vector parameters.

Dependencies

To enable this parameter, set Modeling option to Vapor operating condition, Valve parameterization to Orifice area, and Opening characteristic to Tabulated.

Leakage flow fraction — Ratio of flow rates
`1e-6` (default) | positive scalar

Ratio of the flow rate of the valve when it is closed to when it is open.

Dependencies

To enable this parameter, set either:

Modeling option to Liquid operating condition and Valve parameterization to Linear - Nominal mass flow rate vs. pressure or Linear - Area vs. pressure.
Modeling option to Vapor operating condition and Opening characteristic to Linear.

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 regions.

Dependencies

To enable this parameter, set either:

Modeling option to Liquid operating condition and Valve parameterization to Linear - Nominal mass flow rate vs. pressure or Linear - Area vs. pressure.
Modeling option to Vapor operating condition and Opening characteristic to Linear.

Inlet phase change time constant — Lag for liquid specific volume
`0.1` s (default) | positive scalar

Time lag for liquid-vapor mixtures in computing the fluid specific volume.

Dependencies

To enable this parameter, set Modeling option to Liquid operating condition.

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.

Cross-sectional area at ports A and B — Valve port areas
`0.01` m^2 (default) | positive scalar

Area of the ports A and B.

References

[1] ISO 6358-3. "Pneumatic fluid power – Determination of flow-rate characteristics of components using compressible fluids – Part 3: Method for calculating steady-state flow rate characteristics of systems". 2014.

[2] IEC 60534-2-3. "Industrial-process control valves – Part 2-3: Flow capacity – Test procedures". 2015.

[3] ANSI/ISA-75.01.01. "Industrial-Process Control Valves – Part 2-1: Flow capacity – Sizing equations for fluid flow underinstalled conditions". 2012.

[4] P. Beater. Pneumatic Drives. Springer-Verlag Berlin Heidelberg. 2007.

Extended Capabilities

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

Version History

Introduced in R2021a

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R2024a: Model vapor or liquid valves

You can now use the Modeling option parameter to specify an valve when the two-phase fluid is in a vapor or liquid state. Both modeling options also include new valve parameterizations.

When Modeling option is Liquid operating condition, you can now set Valve parameterization to:

Linear - Area vs. pressure
Tabulated data - Area vs. pressure

When Modeling option is Vapor operating condition, you can now set Valve parameterization to:

Cv flow coefficient
Kv flow coefficient
Orifice area

To preserve the block behavior from previous releases, set Modeling option to Liquid operating condition and Valve parameterization to Linear - Nominal mass flow rate vs. pressure.

Pressure Relief Valve (2P)

Description

Pressure Control

Liquid Valve

Vapor Valve

Mass Balance

Energy Balance

Assumptions and Limitations

Ports

Conserving

A — Fluid entry or exit two-phase fluid

B — Fluid entry or exit two-phase fluid

Input

Ps — Set pressure, Pa physical signal

Dependencies

Parameters

Modeling option — Modeling option for fluid phase Liquid operating condition (default) | Vapor operating condition

Parameters

Valve parameterization — Model for valve parameterization Linear - Area vs. pressure (default) | Linear - Nominal mass flow rate vs. pressure | Tabulated data - Area vs. pressure | Cv flow coefficient | Kv flow coefficient | Orifice area

Opening pressure specification — Control pressure Pressure differential (default) | Gauge pressure at port A

Set pressure control — Variable or constant set pressure Constant (default) | Controlled

Set pressure differential — Set pressure 0.01 MPa (default) | positive scalar

Dependencies

Set pressure (gauge) — Set pressure 0.1 MPa (default) | positive scalar

Dependencies

Pressure regulation range — Valve operational range 0.1 MPa (default) | positive scalar

Dependencies

Nominal mass flow rate at maximum valve opening — Rated mass flow rate 0.1 kg/s (default) | positive scalar

Dependencies

Nominal pressure drop at maximum valve opening — Rated pressure drop 0.001 MPa (default) | positive scalar

Dependencies

Nominal inlet condition specification — Method of determining inlet fluid state Temperature (default) | Vapor quality | Vapor void fraction | Specific enthalpy | Specific internal energy

Dependencies

Nominal inlet pressure — Inlet fluid pressure 0.101325 MPa (default) | positive scalar

Dependencies

Nominal inlet temperature — Fluid temperature 293.15 K (default) | positive scalar

Dependencies

Nominal inlet vapor quality — Inlet vapor quality mass fraction 0 (default) | positive scalar in the range [0,1]

Dependencies

Nominal inlet vapor void fraction — Inlet volume fraction 0 (default) | positive scalar in the range [0,1]

Dependencies

Nominal inlet specific enthalpy — Inlet fluid specific enthalpy 400 kJ/kg (default) | positive scalar

Dependencies

Nominal inlet specific internal energy — Inlet specific internal energy 400 kJ/kg (default) | positive scalar

Dependencies

Maximum valve area — Maximum valve opening area 1e-4 m^2 (default) | positive scalar

Dependencies

Opening pressure differential vector — Vector of pressure differentials [0.2 : 0.2 : 1.2] MPa (default) | 1-by-n vector

Dependencies

Opening pressure (gauge) vector — Vector of gauge pressures [0.2 : 0.2 : 1.2] MPa (default) | 1-by-n vector

Dependencies

Valve area vector — Vector of valve opening area values [1e-10, 2e-06, 4e-06, 6e-06, 8e-06, 1e-05] m^2 (default) | 1-by-n vector

Dependencies

Discharge coefficient — Discharge coefficient 0.64 (default) | positive scalar

Dependencies

Pressure recovery — Whether to account for pressure increase in area expansions off (default) | on

Dependencies

Opening characteristic — Method to parameterize measure of flow capacity Linear (default) | Tabulated

Dependencies

Maximum Cv flow coefficient — Cv coefficient that corresponds to maximally open component 4 (default) | positive scalar

Dependencies

Cv flow coefficient vector — Cv coefficients that correspond to values in member position vector [1e-06, .8, 1.6, 2.4, 3.2, 4] (default) | 1-by-n vector

Dependencies

Maximum Kv flow coefficient — Kv coefficient that corresponds to maximally open component 3.6 (default) | positive scalar

Dependencies

Kv flow coefficient vector — Kv coefficients that correspond to values in member position vector [1e-06, .72, 1.44, 2.16, 2.88, 3.6] (default) | 1-by-n vector

Dependencies

xT pressure differential ratio factor at choked flow — Ratio of pressure differentials 0.7 (default) | positive scalar

Dependencies

Maximum orifice area — Maximum valve opening area 1e-4 m^2 (default) | positive scalar

Dependencies

Orifice area vector — Vector of valve opening area values [1e-10, 2e-05, 4e-05, 6e-05, 8e-05, .0001] m^2 (default) | 1-by-n vector

Dependencies

Leakage flow fraction — Ratio of flow rates 1e-6 (default) | positive scalar

Dependencies

Smoothing factor — Numerical smoothing factor 0.01 (default) | positive scalar in the range [0,1]

Dependencies

Inlet phase change time constant — Lag for liquid specific volume 0.1 s (default) | positive scalar

Dependencies

Laminar flow pressure ratio — Laminar-turbulent transition pressure ratio 0.999 (default) | positive scalar

A — Fluid entry or exit
two-phase fluid

B — Fluid entry or exit
two-phase fluid

Ps — Set pressure, Pa
physical signal

Modeling option — Modeling option for fluid phase
`Liquid operating condition` (default) | `Vapor operating condition`

Valve parameterization — Model for valve parameterization
`Linear - Area vs. pressure` (default) | `Linear - Nominal mass flow rate vs. pressure` | `Tabulated data - Area vs. pressure` | `Cv flow coefficient` | `Kv flow coefficient` | `Orifice area`

Opening pressure specification — Control pressure
`Pressure differential` (default) | `Gauge pressure at port A`

Set pressure control — Variable or constant set pressure
`Constant` (default) | `Controlled`

Set pressure differential — Set pressure
`0.01` MPa (default) | positive scalar

Set pressure (gauge) — Set pressure
`0.1` MPa (default) | positive scalar

Pressure regulation range — Valve operational range
`0.1` MPa (default) | positive scalar

Nominal mass flow rate at maximum valve opening — Rated mass flow rate
`0.1` kg/s (default) | positive scalar

Nominal pressure drop at maximum valve opening — Rated pressure drop
`0.001` MPa (default) | positive scalar

Nominal inlet condition specification — Method of determining inlet fluid state
`Temperature` (default) | `Vapor quality` | `Vapor void fraction` | `Specific enthalpy` | `Specific internal energy`

Nominal inlet pressure — Inlet fluid pressure
`0.101325` MPa (default) | positive scalar

Nominal inlet temperature — Fluid temperature
`293.15` K (default) | positive scalar

Nominal inlet vapor quality — Inlet vapor quality mass fraction
`0` (default) | positive scalar in the range [0,1]

Nominal inlet vapor void fraction — Inlet volume fraction
`0` (default) | positive scalar in the range [0,1]

Nominal inlet specific enthalpy — Inlet fluid specific enthalpy
`400` kJ/kg (default) | positive scalar

Nominal inlet specific internal energy — Inlet specific internal energy
`400` kJ/kg (default) | positive scalar

Maximum valve area — Maximum valve opening area
`1e-4 m^2` (default) | positive scalar

Opening pressure differential vector — Vector of pressure differentials
`[0.2 : 0.2 : 1.2] MPa` (default) | 1-by-n vector

Opening pressure (gauge) vector — Vector of gauge pressures
`[0.2 : 0.2 : 1.2] MPa` (default) | 1-by-n vector

Valve area vector — Vector of valve opening area values
`[1e-10, 2e-06, 4e-06, 6e-06, 8e-06, 1e-05] m^2` (default) | 1-by-n vector

Discharge coefficient — Discharge coefficient
`0.64` (default) | positive scalar

Pressure recovery — Whether to account for pressure increase in area expansions
`off` (default) | `on`

Opening characteristic — Method to parameterize measure of flow capacity
`Linear` (default) | `Tabulated`

Maximum Cv flow coefficient — C_v coefficient that corresponds to maximally open component
`4` (default) | positive scalar

Cv flow coefficient vector — C_v coefficients that correspond to values in member position vector
`[1e-06, .8, 1.6, 2.4, 3.2, 4]` (default) | 1-by-n vector

Maximum Kv flow coefficient — K_v coefficient that corresponds to maximally open component
`3.6` (default) | positive scalar

Kv flow coefficient vector — K_v coefficients that correspond to values in member position vector
`[1e-06, .72, 1.44, 2.16, 2.88, 3.6]` (default) | 1-by-n vector

xT pressure differential ratio factor at choked flow — Ratio of pressure differentials
`0.7` (default) | positive scalar

Maximum orifice area — Maximum valve opening area
`1e-4 m^2` (default) | positive scalar

Orifice area vector — Vector of valve opening area values
`[1e-10, 2e-05, 4e-05, 6e-05, 8e-05, .0001] m^2` (default) | 1-by-n vector

Leakage flow fraction — Ratio of flow rates
`1e-6` (default) | positive scalar

Smoothing factor — Numerical smoothing factor
`0.01` (default) | positive scalar in the range [0,1]

Inlet phase change time constant — Lag for liquid specific volume
`0.1` s (default) | positive scalar

Laminar flow pressure ratio — Laminar-turbulent transition pressure ratio
`0.999` (default) | positive scalar

Cross-sectional area at ports A and B — Valve port areas
`0.01` m^2 (default) | positive scalar

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