Check Valve (MA)

Check valve in a moist air network

Since R2025a

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

Description

The Check Valve (MA) block models a directional control check valve in a moist air network. The valve maintains the fluid pressure by opening above a specified pressure and allowing flow from port A to port B, but not in the reverse direction. The pressure differential that opens the valve is specified in the Opening pressure specification parameter. This value can be either the pressure difference between ports A and B or the gauge pressure at port A.

Directional Control

The valve opens when the pressure in the valve, p_control, exceeds the cracking pressure, p_crack. The valve is fully open when the control pressure reaches the valve maximum pressure, p_max. For linear parameterizations, block calculates the opening fraction of the valve, λ, as

$$\lambda =\left(1-f_{leak}\right)\frac{\left(p_{control}-p_{crack}\right)}{\left(p_{\max }-p_{crack}\right)}+f_{leak},$$

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 Opening pressure specification parameter.

  When you set Opening pressure specification to Pressure differential, the control pressure is p_A ̶ p_B.

  When you set Opening pressure specification to Gauge pressure at port A, the control pressure is the difference between the pressure at port A and atmospheric pressure.

The cracking pressure and maximum pressure are specified as either a differential value or a gauge value, depending on the setting of the Opening pressure specification. If the control pressure exceeds the maximum pressure, the valve opening fraction is 1.

Momentum Balance

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, Orifice area vector, or Sonic conductance 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

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

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 valve 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 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 $$K_v=0.865C_v$$.

Valve Area Parameterization

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

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

where:

• 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,

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

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

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

Sonic Conductance Parameterization

When you set Valve parameterization 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 Valve 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.

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 valve,

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

where:

• Φ_A is the energy flow at port A.

• Φ_B is the energy flow at port B.

Assumptions and Limitations

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

Ports

Conserving

A — Fluid entry

moist air

Moist air conserving port associated with the fluid entry port.

B — Fluid exit

moist air

Moist air conserving port associated with the fluid exit port.

Parameters

Valve parameterization — Model for valve 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 valve 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 parameterize the chosen measure of flow capacity.

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 Cracking pressure differential.

• When this parameter is Gauge pressure at port A, the valve opens when p_A ̶ p_atm exceeds the Cracking pressure (gauge).

Cracking pressure (gauge) — Cracking pressure

0.1 MPa (default) | positive scalar

Valve pressure threshold. When the control pressure, p_A ̶ p_atm, exceeds the opening pressure, the valve begins to open.

Dependencies

To enable this parameter, set Opening pressure specification to Gauge pressure at port A and Opening characteristic to Linear.

Maximum opening pressure (gauge) — Pressure that fully opens the valve

0.2 MPa (default) | positive scalar

Valve operational pressure at which the valve is fully open. The valve begins to open at the cracking pressure value, and is fully open at p_max.

Dependencies

To enable this parameter, set Opening pressure specification to Gauge pressure at port A and Opening characteristic to Linear.

Cracking pressure differential — Cracking pressure

0.01 MPa (default) | positive scalar

Valve pressure threshold. When the control pressure, p_A ̶ p_B, exceeds the opening pressure, the valve begins to open.

Dependencies

To enable this parameter, set Opening pressure specification to Pressure differential and Opening characteristic to Linear.

Maximum opening pressure differential — Maximum valve operational pressure

0.1 MPa (default) | positive scalar

Maximum valve operational pressure. The valve begins to open at the cracking pressure value, and is fully open at p_max.

Dependencies

To enable this parameter, set Opening pressure specification to Pressure differential and Opening characteristic to Linear.

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.

Dependencies

To enable this parameter, set Opening pressure specification to Pressure differential 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.

Dependencies

To enable this parameter, set Opening pressure specification to Gauge pressure at port A 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 Valve parameterization to Orifice area.

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 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 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 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 Valve parameterization to Kv flow coefficient and Opening characteristic to Tabulated.

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 Valve 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 Valve 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 Valve 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 Valve 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 Valve 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. 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 Valve 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. The critical pressure ratio is the fraction of downstream-to-upstream pressures at which the flow velocity reaches the local speed of sound. 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 Valve parameterization to Sonic conductance 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, set 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 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 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 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 Opening characteristic to Linear.

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.

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Version History

Introduced in R2025a