Orifice (MA)

Orifice in a moist air network

Since R2025a

• 

Libraries:
Simscape / Fluids / Moist Air / Valves & Orifices

Description

The Orifice (MA) block models pressure loss due to a constant or variable area orifice in a moist air network. 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 the Orifice type parameter is Variable, the physical signal at port S sets the position of the control member, which opens and closes the orifice.

Orifice Parameterizations

The block behavior depends on the Orifice parametrization parameter:

• Cv flow coefficient — The flow coefficient C_v determines the block parameterization. The flow coefficient measures the ease with which the moist air can flow when driven by a certain pressure differential.

• Kv flow coefficient — The flow coefficient K_v, where $$K_v=0.865C_v$$, determines the block parameterization. The flow coefficient measures the ease with which the moist air can flow when driven by a certain pressure differential.

• Sonic conductance — The sonic conductance of the resistive element at steady state determines the block parameterization. The sonic conductance measures the ease with which the moist air can flow when choked, which is a condition in which the flow velocity is at the local speed of sound. Choking occurs when the ratio between downstream and upstream pressures reaches a critical value known as the critical pressure ratio.

• Orifice area — The size of the flow restriction determines the block parametrization.

Variable 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,

$$\lambda =\epsilon \left(1-f_{leak}\right)\frac{\left(S-S_{\min }\right)}{\Delta S}+f_{leak},$$

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.

Momentum Balance

The block equations depend on the Orifice parametrization parameter.

Cv Flow Coefficient Parameterization

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

$$\dot{m}=C_v{N}_{6}Y\sqrt{\frac{(p_{in}-p_{out})}{v_{in}}},$$

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

$$Y=1-\frac{p_{in}-p_{out}}{3p_{in}{F}_{\gamma }{x}_T},$$

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, $$p_{out}/p_{in}$$, rises above the value of the Laminar flow pressure ratio parameter, B_lam,

$$\dot{m}=C_v{N}_6{Y}_{lam}\sqrt{\frac{1}{p_{avg}(1-B_{lam})v_{avg}}}(p_{in}-p_{out}),$$

where:

$$Y_{lam}=1-\frac{1-B_{lam}}{3F_{\gamma }{x}_T}.$$

When the pressure ratio, $$p_{out}/p_{in}$$, falls below $$1-F_{\gamma }{x}_T$$, the orifice becomes choked and the block uses the equation

$$\dot{m}=\frac{2}{3}{C}_v{N}_6\sqrt{\frac{F_{\gamma }{x}_T{p}_{in}}{v_{in}}}.$$

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 $$K_v=0.865C_v$$.

Sonic Conductance Parameterization

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

$$\dot{m}=C{\rho }_{ref}{p}_{in}\sqrt{\frac{T_{ref}}{T_{in}}}{\left[1-{\left(\frac{\frac{p_{out}}{p_{in}}-B_{crit}}{1-B_{crit}}\right)}^2\right]}^m,$$

where:

• C is the sonic conductance.

• B_crit is the critical pressure ratio.

• m is the value of the Subsonic index parameter.

• T_ref is the value of the ISO reference temperature parameter.

• ρ_ref is the value of the ISO reference density parameter.

• T_in is the inlet temperature.

The block smoothly transitions to a linearized form of the equation when the pressure ratio, $$p_{out}/p_{in}$$, rises above the value of the Laminar flow pressure ratio parameter B_lam,

$$\dot{m}=C{\rho }_{ref}\sqrt{\frac{T_{ref}}{T_{avg}}}{\left[1-{\left(\frac{B_{lam}-B_{crit}}{1-B_{crit}}\right)}^2\right]}^m\left(\frac{p_{in}-p_{out}}{1-B_{lam}}\right).$$

When the pressure ratio, $$p_{out}/p_{in}$$, falls below the critical pressure ratio, B_crit, the orifice becomes choked and the block switches to the equation

$$\dot{m}=C{\rho }_{ref}{p}_{in}\sqrt{\frac{T_{ref}}{T_{in}}}.$$

The Sonic conductance setting of the Orifice parameterization parameter is for pneumatic applications. If you use this setting for moist air with high levels of trace gasses or are modeling a fluid other than air, you may need to scale the sonic conductance by the square root of the mixture specific gravity.

Orifice Area Parameterization

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

$$\dot{m}=C_d{A}_{orifice}\sqrt{\frac{2\gamma }{\gamma -1}{p}_{in}\frac{1}{v_{in}}{\left(\frac{p_{out}}{p_{in}}\right)}^{\frac{2}{\gamma }}\left[\frac{1-{\left(\frac{p_{out}}{p_{in}}\right)}^{\frac{\gamma -1}{\gamma }}}{1-{\left(\frac{A_{orifice}}{A_{port}}\right)}^2{\left(\frac{p_{out}}{p_{in}}\right)}^{\frac{2}{\gamma }}}\right]},$$

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, $$p_{out}/p_{in}$$, rises above the value of the Laminar flow pressure ratio parameter, B_lam,

$$\dot{m}=C_d{A}_{orifice}\sqrt{\frac{2\gamma }{\gamma -1}{p}_{avg}^{\frac{2-\gamma }{\gamma }}\frac{1}{v_{avg}}{B}_{lam}^{\frac{2}{\gamma }}\left[\frac{1-B_{lam}^{\frac{\gamma -1}{\gamma }}}{1-{\left(\frac{A_{orifice}}{A_{port}}\right)}^2{B}_{lam}^{\frac{2}{\gamma }}}\right]}\left(\frac{p_{in}^{\frac{\gamma -1}{\gamma }}-p_{out}^{\frac{\gamma -1}{\gamma }}}{1-B_{lam}^{\frac{\gamma -1}{\gamma }}}\right).$$

When the pressure ratio, $$p_{out}/p_{in}$$, falls below$${\left(\frac{2}{\gamma +1}\right)}^{\frac{\gamma }{\gamma -1}}$$ , the orifice becomes choked and the block uses the equation

$$\dot{m}=C_d{A}_{orifice}\sqrt{\frac{2\gamma }{\gamma +1}{p}_{in}\frac{1}{v_{in}}\frac{1}{{\left(\frac{\gamma +1}{2}\right)}^{\frac{2}{\gamma -1}}-{\left(\frac{A_{orifice}}{A_{port}}\right)}^2}}.$$

Mass Balance

The block conserves mass through the valve

$$\begin{array}{l}{\dot{m}}_A+{\dot{m}}_B=0\\ {\dot{m}}_{wA}+{\dot{m}}_{wB}=0\\ {\dot{m}}_{gA}+{\dot{m}}_{gB}=0\\ {\dot{m}}_{dA}+{\dot{m}}_{dB}=0\end{array}$$

where ṁ is the mass flow rate and the subscript w denotes water vapor, the subscript g denotes trace gas, and the subscript d denotes water droplets.

Energy Balance

Energy is conserved in the orifice,

$${\Phi }_A+{\Phi }_B=0,$$

where:

• Φ_A is the energy flow at port A.

• Φ_B is the energy flow at port B.

Assumptions and Limitations

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

Ports

Conserving

A — Fluid entry or exit

moist air

Moist air conserving port associated with the fluid entry or exit port.

B — Fluid entry or exit

moist air

Moist air conserving port associated with the fluid entry or exit port.

Input

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

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

Cv flow coefficient (default) | Kv flow coefficient | Sonic conductance | Orifice area

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.

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 Orifice type to Variable.

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 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 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 Orifice type to Variable, and Opening characteristic to Linear.

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 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 Orifice type to Variable, Orifice parameterization to Cv flow coefficient, 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 Opening characteristic to Tabulated.

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

To enable this parameter, set Orifice type to Variable, Orifice parameterization to Cv 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 $$(p_{in}-p_{out})/p_{in}$$ where choking first occurs.

Dependencies

To enable this parameter, Orifice parameterization to Cv flow coefficient or Kv flow coefficient.

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 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 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

To enable this parameter, set Orifice type to Variable, Orifice parameterization to Kv flow coefficient, and Opening characteristic to Tabulated.

Sonic conductance — Measure of flow rate capacity in choked flow regime

12 l/(bar*s) (default) | positive scalar

Ratio, measured at the onset of choking, of the mass flow rate through the resistive element to the product of the upstream pressure and mass density at standard conditions as defined in ISO 8778. This parameter determines the maximum flow rate allowed at a given upstream pressure.

Dependencies

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

Maximum sonic conductance — Sonic conductance corresponding to maximally open component

12 l/(bar*s) (default) | positive scalar

Value of the sonic conductance when the control signal specified at port S is 1 and cross-sectional area available for flow is at a maximum.

Dependencies

To enable this parameter, set Orifice type to Variable, Orifice parameterization to Sonic conductance, and Opening characteristic to Linear.

Critical pressure ratio — Ratio of downstream and upstream pressures at which the flow first chokes

0.3 (default) | positive scalar

Pressure ratio at which flow first begins to choke and the flow velocity reaches its maximum, given by the local speed of sound. The pressure ratio is the outlet pressure divided by inlet pressure.

Dependencies

To enable this parameter, set either:

• Orifice type to Constant and Orifice parameterization to Sonic conductance.

• Orifice type to Variable, Orifice parameterization to Sonic conductance, and Opening characteristic to Linear.

Subsonic index — Exponent used to characterize mass flow in subsonic flow regime

0.5 (default) | positive scalar

Empirical value used to more accurately calculate the mass flow rate in the subsonic flow regime.

Dependencies

To enable this parameter, set Orifice parameterization to Sonic conductance.

ISO reference temperature — ISO 8778 reference temperature

293.15 K (default) | scalar

Temperature at standard reference atmosphere, defined as 293.15 K in ISO 8778.

You only need to adjust the ISO reference parameter values if you are using sonic conductance values that are obtained at difference reference values.

Dependencies

To enable this parameter, set Orifice parameterization to Sonic conductance.

ISO reference density — ISO 8778 reference density

1.185 kg/m^3 (default) | positive scalar

Density at standard reference atmosphere, defined as 1.185 kg/m3 in ISO 8778.

You only need to adjust the ISO reference parameter values if you are using sonic conductance values that are obtained at difference reference values.

Dependencies

To enable this parameter, set Orifice parameterization to Sonic conductance.

Sonic conductance vector — Sonic conductances corresponding to values in control member position vector

[1e-05, 2.4, 4.8, 7.2, 9.6, 12] l/(bar*s) (default) | vector of positive values

Vector of sonic conductances inside the resistive element. Each conductance corresponds to a value in the Control member position vector parameter. The size of the vector must be the same as the Control member position vector parameter.

Dependencies

To enable this parameter, set Orifice type to Variable, Orifice parameterization to Sonic conductance, and Opening characteristic to Tabulated.

Critical pressure ratio vector — Critical pressure ratios corresponding to values in control member position vector

0.3 * ones(1,6) (default) | vector of positive numbers

Vector of critical pressure ratios at which the flow first chokes, with each critical pressure ratio corresponding to a value in the Control member position vector parameter. The critical pressure ratio is the fraction of downstream-to-upstream pressures at which the flow velocity reaches the local speed of sound. The size of the vector must be the same as the Control member position vector parameter.

Dependencies

To enable this parameter, set Orifice type to Variable, Orifice parameterization to Sonic conductance, and Opening characteristic to Tabulated.

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.

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 Orifice type to Variable, Orifice parameterization to Orifice area, and Opening characteristic to Linear.

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 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 Orifice parameterization to Orifice area.

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 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 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 Opening characteristic to Linear.

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.

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Version History

Introduced in R2025a