Orifice (2P)

Constant- or variable-area orifice in a two-phase fluid network

Since R2021a

Libraries:
Simscape / Fluids / Two-Phase Fluid / Valves & Orifices

Description

The Orifice (2P) block models pressure loss due to a constant or variable area orifice in a two-phase fluid network. 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.

The orifice can be constant or variable. When Orifice type is Variable, the physical signal at port S sets the position of the control member, which opens and closes the orifice.

Liquid Orifice

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

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

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

where:

C_d is the value of the Discharge coefficient parameter.
A_orifice is the instantaneous orifice open area.
A_port is the value of the Cross-sectional area at ports A and B parameter.

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.

The critical pressure difference, Δp_crit, is the pressure differential where the flow transitions between laminar and turbulent flow,

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

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.

Nominal Mass Flow Rate Parameterization

When you set Orifice type to Constant and Orifice Parameterization to Nominal mass flow rate, the mass flow rate through the orifice is

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

where:

${\dot{m}}_{n o m}$ is the value of the Nominal mass flow rate parameter.
Δp_nom is the value of the Nominal pressure drop rate parameter.
v_nom is the nominal inlet specific volume. The block determines this value from the tabulated fluid properties data based on the value of the Nominal inlet condition specification parameter.
v_in is the inlet specific volume.

Liquid Orifice Area Parameterization

When you set Orifice type to Constant and Orifice Parameterization to Orifice area, the block calculates the mass flow rate as

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

where Δp is the pressure drop over the orifice, p_A ̶ p_B.

Linear - Nominal Mass Flow Rate vs. Control Member Position Parameterization

When you set Orifice type to Variable and Orifice Parameterization to Nominal mass flow rate vs. control member position, the mass flow rate through the variable-area orifice 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 λ is the orifice opening fraction, which is a fraction of the total orifice open area.

The block determines the orifice opening for all variable orifice parameterizations as

$λ = ε (1 - f_{l e a k}) \frac{(S - S_{\min})}{Δ S} + f_{l e a k},$

where:

ε is 1 when Opening orientation is Positive control member displacement opens orifice and -1 when Opening orientation is Negative control member displacement opens orifice.
f_leak is the value of the Leakage flow fraction parameter.
S is th value of the signal at port S.
S_min is the value of the Control member position at closed orifice parameter.
ΔS is the value of the Control member travel between closed and open orifice parameter.

Linear - Area vs. Control Member Position Parameterization

When you set Orifice type to Variable and Orifice Parameterization to Linear - Area vs. control member position, the orifice area is

$A_{o r i f i c e} = λ A_{\max},$

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

The mass flow rate is

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

When the orifice 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. Control Member Position Parameterization

When you set Orifice type to Variable and Orifice Parameterization to Tabulated data - Area vs. control member position, the block interpolates the orifice area, A_orifice, from the Orifice area vector and Control member position vector parameters. The signal at port S specifies the control member position. The block uses linear interpolation to query between the data points and nearest extrapolation for points beyond the table boundaries.

The block uses the same equation as the Linear - Area vs. control member position 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 orifice 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 Orifice

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

Variable Vapor Orifice

When you set Orifice type to Variable and Opening characteristic to Linear, the block uses the input at port S to calculate the orifice opening,

$λ = ε (1 - f_{l e a k}) \frac{(S - S_{\min})}{Δ S} + f_{l e a k},$

where S is the value of the signal at port S, and S_min and ΔS are the values of the Control member position at closed orifice and Control member travel between closed and open orifice parameters, respectively.

When you set Orifice type to Variable and Opening characteristic to Tabulated, the block interpolates the orifice characteristics from the Control member position vector parameter and the input at port S.

For a variable orifice, the flow rate in the orifice depends on the Opening characteristic parameter:

Linear — The measure of flow capacity is proportional to the control signal at port S. As the control signal increases, the measure of flow capacity scales from the specified minimum to the specified maximum.
When you set Orifice parameterization to Cv flow coefficient or Kv flow coefficient, the block treats the parameter xT pressure differential ratio factor at choked flow as a constant independent of the control signal.
Tabulated — The block calculates the measure of flow capacity as a function of the control signal at port S. This function uses a one-dimensional lookup table.
When you set Orifice parameterization to Cv flow coefficient or Kv flow coefficient, the block treats the parameter xT pressure differential ratio factor at choked flow as a function of the control signal.

Cv Flow Coefficient Parameterization

When you set Orifice 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 orifice 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 Orifice 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 $K_{v} = 0.865 C_{v}$ .

Vapor Orifice Area Parameterization

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

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

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,

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

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

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

Mass Balance

Mass is conserved in the orifice,

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

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 orifice,

$Φ_{A} + Φ_{B} = 0,$

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 an orifice in a liquid-vapor mixture, set Modeling option to Liquid operating condition.

Examples

Liquid Air Energy Storage System

Models a grid-scale energy storage system based on cryogenic liquid air. When there is excess power, the system liquefies ambient air based on a variation of the Claude cycle. The cold liquid air is stored in a low-pressure insulated tank until needed. When there is high power demand, the system expands the stored liquid air to produce power based on the Rankine cycle.

Open Model

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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S — Control member position, m
physical signal

Control member position that sets the orifice opening.

Dependencies

To enable this port, set Orifice type to Variable.

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 orifice. 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

Orifice type — Constant or variable orifice
`Variable` (default) | `Constant`

Type of orifice. When you set this parameter to Variable, the orifice area varies according to the input signal received at port S.

Orifice parameterization — Variable or constant orifice parameterization
`Linear - Area vs. control member position` (default) | `Orifice area` | `Nominal mass flow rate` | `Linear - Nominal mass flow rate vs. control member position` | `Tabulated data - Area vs. control member position` | `Cv flow coefficient` | `Kv flow coefficient`

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

When Modeling option is Liquid operating condition and Orifice type is Variable, the choices for this parameter are:

Linear - Area vs. control member position
Linear - Nominal mass flow rate vs. control member position
Tabulated data - Area vs. control member position

When Modeling option is Liquid operating condition and Orifice type is Constant, the choices for this parameter are:

Orifice area
Nominal mass flow rate

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

Cv flow coefficient
Kv flow coefficient
Orifice area

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

Typical, rated, or design mass flow rate through a constant orifice.

Dependencies

To enable this parameter, set Modeling option to Liquid operating condition, Orifice type to Constant, and Orifice parameterization to Nominal mass flow rate.

Nominal pressure drop — Rated pressure drop
`0.001` MPa (default) | positive scalar

Typical, rated, or design pressure drop through a constant orifice.

Dependencies

To enable this parameter, set Modeling option to Liquid operating condition, Orifice type to Constant, and Orifice parameterization to Nominal mass flow rate.

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 either:

Orifice type to Constant and Orifice parameterization to Nominal mass flow rate.
Orifice type to Variable and Orifice parameterization to Linear - Nominal mass flow rate vs. control member position.

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 either:

Orifice type to Constant and Orifice parameterization to Nominal mass flow rate.
Orifice type to Variable and Orifice parameterization to Linear - Nominal mass flow rate vs. control member position.

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 and either:

Orifice type to Constant, Orifice parameterization to Nominal mass flow rate, and Nominal inlet condition specification to Temperature.
Orifice type to Variable, Orifice parameterization to Linear - Nominal mass flow rate vs. control member position, 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

To enable this parameter, set Modeling option to Liquid operating condition and either:

Orifice type to Constant, Orifice parameterization to Nominal mass flow rate, and Nominal inlet condition specification to Vapor quality.
Orifice type to Variable, Orifice parameterization to Linear - Nominal mass flow rate vs. control member position, and Nominal inlet condition specification to Vapor quality.

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

To enable this parameter, set Modeling option to Liquid operating condition and either:

Orifice type to Constant, Orifice parameterization to Nominal mass flow rate, and Nominal inlet condition specification to Vapor void fraction.
Orifice type to Variable, Orifice parameterization to Linear - Nominal mass flow rate vs. control member position, and Nominal inlet condition specification to Vapor void fraction.

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

Inlet specific enthalpy in nominal operating conditions.

Dependencies

To enable this parameter, set Modeling option to Liquid operating condition and either:

Orifice type to Constant, Orifice parameterization to Nominal mass flow rate, and Nominal inlet condition specification to Specific enthalpy.
Orifice type to Variable, Orifice parameterization to Linear - Nominal mass flow rate vs. control member position, and Nominal inlet condition specification to Specific enthalpy.

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

Inlet specific internal energy in nominal operating conditions.

Dependencies

To enable this parameter, set Modeling option to Liquid operating condition and either:

Orifice type to Constant, Orifice parameterization to Nominal mass flow rate, and Nominal inlet condition specification to Specific internal energy.
Orifice type to Variable, Orifice parameterization to Linear - Nominal mass flow rate vs. control member position, and Nominal inlet condition specification to Specific internal energy.

Orifice area — Area of orifice opening
`1e-4` `m^2` (default) | positive scalar

Cross-sectional area of the orifice opening.

Dependencies

To enable this parameter, set Orifice type to Constant and Orifice parameterization to Orifice area.

Control member position at closed orifice — Control member offset
`0` m (default) | positive scalar

Control member offset, or the value at S when the orifice is fully closed.

Dependencies

To enable this parameter, set either:

Modeling option to Liquid operating condition, Orifice type to Variable, and Orifice parameterization to Linear – Nominal mass flow rate vs. control member position or Linear – Area vs. control member position.
Modeling option to Vapor operating condition, Orifice type to Variable, and Opening characteristic to Linear.

Control member travel between closed and open orifice — Control member stroke
`5e-3` m (default) | positive scalar

Distance the control member travels between a closed and open orifice. When you set Opening orientation to Positive control member displacement opens orifice, the orifice is fully open at the sum of the Control member position at closed orifice and Control member travel between closed and open orifice parameters. When you set Opening orientation to Negative control member displacement opens orifice, the orifice is fully open at the difference between the Control member position at closed orifice and Control member travel between closed and open orifice parameters.

Dependencies

To enable this parameter, set either:

Modeling option to Liquid operating condition, Orifice type to Variable, and Orifice parameterization to Linear – Nominal mass flow rate vs. control member position or Linear – Area vs. control member position.
Modeling option to Vapor operating condition, Orifice type to Variable, and Opening characteristic to Linear.

Opening orientation — Direction of displacement that opens the orifice
`Positive control member displacement opens orifice` (default) | `Negative control member displacement opens orifice`

Direction of the member displacement that opens the variable orifice. A positive orientation means that an increase in the signal at S opens the orifice. A negative orientation means that a decrease in the signal at S opens the orifice.

Dependencies

To enable this parameter, set either:

Modeling option to Liquid operating condition, Orifice type to Variable, and Orifice parameterization to Linear – Nominal mass flow rate vs. control member position or Linear – Area vs. control member position.
Modeling option to Vapor operating condition, Orifice type to Variable, and Opening characteristic to Linear.

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

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

Dependencies

To enable this parameter, set Modeling option to Liquid operating condition, Orifice type to Variable, and Orifice parameterization to Linear – Nominal mass flow rate vs. control member position.

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

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

Dependencies

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

Orifice area when it is fully open.

Dependencies

To enable this parameter, set either:

Modeling option to Liquid operating condition, Orifice type to Variable, and Orifice parameterization to Linear – Area vs. control member position.
Modeling option to Vapor operating condition, Orifice type to Variable, Orifice parameterization to Orifice area, and Opening characteristic to Linear.

Control member position vector — Vector of control member positions
`[0, .002, .004, .007, .017] m` (default) | 1-by-n vector

Vector of control member positions for the tabulated orifice parameterizations. The vector elements correspond one-to-one to the values in the Orifice area vector, Cv flow coefficient vector, or Kv flow coefficient vector parameters.

Dependencies

To enable this parameter, set Orifice type to Variable and either

Modeling option to Liquid operating condition and Orifice parameterization to Tabulated data - Area vs. control member position.
Modeling option to Vapor operating condition and Opening characteristic to Tabulated.

Orifice area vector — Vector of orifice 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 orifice area. The values in this vector correspond one-to-one with the elements in the Control member position vector parameter.

Dependencies

To enable this parameter, set either

Modeling option to Liquid operating condition, Orifice type to Variable, and Orifice parameterization to Tabulated data - Area vs. control member position.
Modeling option to Vapor operating condition, Orifice type to Variable, Orifice parameterization to Orifice area, and Opening characteristic to Tabulated.

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:

Orifice type to Constant and Orifice parameterization to Orifice area.
Modeling option to Liquid operating condition, Orifice type to Variable and Orifice parameterization to either Linear - Area vs. control member position or Tabulated data - Area vs. control member position.
Modeling option to Vapor operating condition, Orifice type to Variable and Orifice 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 either:

Orifice type to Variable and Orifice parameterization to either Linear - Area vs. control member position or Tabulated data - Area vs. control member position.
Orifice type to Constant and Orifice parameterization to Orifice area.

Opening characteristic — Method to convert from control signal to measure of flow capacity
`Linear` (default) | `Tabulated`

Method by which to convert the control signal specified at port S to the chosen measure of flow capacity.

Dependencies

To enable this parameter, set Modeling option to Vapor operating condition and Orifice type to Variable.

Cv flow coefficient — Flow coefficient
`4` (default) | positive scalar

Value of the constant C_v flow coefficient. 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, Orifice type to Constant, and Orifice parameterization to Cv flow coefficient.

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 orifice is fully open and the 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, Orifice type to Variable, Orifice 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 Control member position vector parameter. This parameter measures the ease with which the vapor traverses the resistive element when driven by a pressure differential. The size of the vector must be the same as the Control member position vector parameter.

Dependencies

Kv flow coefficient — Flow coefficient
`3.6` (default) | positive scalar

Value of the constant K_v flow coefficient. 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, Orifice type to Constant, and Orifice parameterization to Kv flow coefficient.

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 orifice is fully open and the 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, Orifice type to Variable, Orifice 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 Control member position vector parameter. This parameter measures the ease with which the vapor traverses the resistive element when driven by a pressure differential. The size of the vector must be the same as the Control member position vector parameter.

Dependencies

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 Orifice parameterization to Cv flow coefficient or Kv flow coefficient.

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

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

Dependencies

To enable this parameter, set Orifice type to Variable and any combination of other parameters, except when:

Modeling option is Liquid operating condition and Orifice parameterization is Tabulated data - Area vs. control member position.
Modeling option is Vapor operating condition and Opening characteristic is Tabulated.

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 orifice 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 Orifice type to Variable and any combination of other parameters, except when:

Modeling option is Liquid operating condition and Orifice parameterization is Tabulated data - Area vs. control member position.
Modeling option is Vapor operating condition and Opening characteristic is Tabulated.

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 orifice outlet pressure to orifice 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 orifice 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

expand all

R2024a: Model vapor or liquid valves

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

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

Linear - Area vs. control member position
Tabulated data - Area vs. control member position
Orifice area

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

Cv flow coefficient
Kv flow coefficient
Orifice area

To preserve the constant orifice behavior from previous releases, set Modeling option to Liquid operating condition and Orifice parameterization to Nominal mass flow rate. To preserve the variable orifice behavior from previous releases, set Modeling option to Liquid operating condition and Orifice parameterization to Linear – Nominal mass flow rate vs. control member position.

Orifice (2P)

Description

Liquid Orifice

Vapor Orifice

Mass Balance

Energy Balance

Assumptions and Limitations

Examples

Liquid Air Energy Storage System

Ports

Conserving

A — Fluid entry or exit two-phase fluid

B — Fluid entry or exit two-phase fluid

Input

S — Control member position, m physical signal

Dependencies

Parameters

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

Parameters

Orifice type — Constant or variable orifice Variable (default) | Constant

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

Dependencies

Nominal pressure drop — 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

Orifice area — Area of orifice opening 1e-4 m^2 (default) | positive scalar

Dependencies

Control member position at closed orifice — Control member offset 0 m (default) | positive scalar

Dependencies

Control member travel between closed and open orifice — Control member stroke 5e-3 m (default) | positive scalar

Dependencies

Opening orientation — Direction of displacement that opens the orifice Positive control member displacement opens orifice (default) | Negative control member displacement opens orifice

Dependencies

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

Dependencies

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

Dependencies

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

Dependencies

Control member position vector — Vector of control member positions [0, .002, .004, .007, .017] m (default) | 1-by-n vector

Dependencies

Orifice area vector — Vector of orifice opening area values [1e-10, 2e-05, 4e-05, 6e-05, 8e-05, .0001] 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 convert from control signal to measure of flow capacity Linear (default) | Tabulated

Dependencies

Cv flow coefficient — Flow coefficient 4 (default) | positive scalar

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

Kv flow coefficient — Flow coefficient 3.6 (default) | positive scalar

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

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

A — Fluid entry or exit
two-phase fluid

B — Fluid entry or exit
two-phase fluid

S — Control member position, m
physical signal

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

Orifice type — Constant or variable orifice
`Variable` (default) | `Constant`

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

Nominal pressure drop — 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

Orifice area — Area of orifice opening
`1e-4` `m^2` (default) | positive scalar

Control member position at closed orifice — Control member offset
`0` m (default) | positive scalar

Control member travel between closed and open orifice — Control member stroke
`5e-3` m (default) | positive scalar

Opening orientation — Direction of displacement that opens the orifice
`Positive control member displacement opens orifice` (default) | `Negative control member displacement opens orifice`

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

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

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

Control member position vector — Vector of control member positions
`[0, .002, .004, .007, .017] m` (default) | 1-by-n vector

Orifice area vector — Vector of orifice opening area values
`[1e-10, 2e-05, 4e-05, 6e-05, 8e-05, .0001] 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 convert from control signal to measure of flow capacity
`Linear` (default) | `Tabulated`

Cv flow coefficient — Flow coefficient
`4` (default) | positive scalar

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

Kv flow coefficient — Flow coefficient
`3.6` (default) | positive scalar

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

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

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