Pressure Reducing Valve (MA)

Pressure reducing valve in a moist air network

Since R2025a

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

Description

The Pressure-Reducing Valve (MA) block models a pressure-controlling reducing valve in a moist air network. The valve is open when the pressure at port B is less than the set pressure, and closes when the pressure exceeds that value. The control pressure can be a constant, or, when you set Set pressure control to Controlled, the set pressure can vary according to the input signal at port Ps. For pressure control based on another location in the fluid network, see the Pressure Compensator Valve (MA) block.

Pressure Control

The valve closes when the pressure in the valve, p_control, exceeds the set pressure, p_set. The valve is fully closed 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

$$\lambda =1-\left(1-f_{leak}\right)\frac{\left(p_{control}-p_{set}\right)}{p_{range}},$$

where:

• f_leak is the value of the Leakage flow fraction parameter.

• p_control is the control pressure, which is the difference between the pressure at port B and atmospheric pressure.

• p_set is the value of the Set pressure (gauge) parameter.

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

$$\lambda =1-\left(1-f_{leak}\right)\frac{\left(p_{control}-p_s\right)}{p_{range}},$$

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

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:

• 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,

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

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 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 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.

Opening Dynamics

When you select Opening dynamics, the block introduces a control pressure lag and replaces p_control with the dynamic control pressure, p_dyn. The block calculates the dynamic control pressure based on the Opening time constant parameter, τ

$${\dot{p}}_{dyn}=\frac{p_{control}-p_{dyn}}{\tau }.$$

By default, the block clears the Opening dynamics check box.

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 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

Ps — Set pressure, Pa

physical signal

Input port for varying the set pressure signal.

Dependencies

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

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.

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 (gauge) — Set pressure

0.1 MPa (default) | positive scalar

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

Dependencies

To enable this parameter, set Set pressure control to Constant.

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 Opening characteristic to Linear.

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 characteristic to Tabulated.

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 (gauge) vector parameter. 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 (gauge) vector parameter. 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 (gauge) vector parameter.

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 Opening pressure (gauge) vector parameter.

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 (gauge) vector parameter.

Dependencies

To enable this parameter, set Valve 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 Valve parameterization to Orifice area.

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.

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.

Opening dynamics — Whether to account for flow response to valve opening

off (default) | on

Whether to account for transient effects to the fluid system due to the valve opening. Selecting this parameter approximates the opening conditions by introducing a first-order lag in the flow response.

Opening time constant — Valve opening time constant

0.1 s (default) | positive scalar

Time constant by which to compute the lag in the opening dynamics.

Dependencies

To enable this parameter, select Opening dynamics.

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