Pressure Source (MA)

Generate constant or time-varying pressure differential

Libraries:
Simscape / Foundation Library / Moist Air / Sources

Description

The Pressure Source (MA) block represents an ideal mechanical energy source in a moist air network. The source can maintain a constant pressure differential across its ports regardless of the flow rate through the source. There is no flow resistance and no heat exchange with the environment.

Ports A and B represent the source inlet and outlet. The input physical signal at port P specifies the pressure differential. Alternatively, you can specify a constant pressure differential as a block parameter. A positive pressure differential causes the pressure at port B to be greater than the pressure at port A.

The equations describing the source use these symbols.

c_p	Specific heat at constant pressure
h	Specific enthalpy
h_t	Specific total enthalpy
$\dot{m}$	Mass flow rate (flow rate associated with a port is positive when it flows into the block)
p	Pressure
ρ	Density
R	Specific gas constant
s	Specific entropy
T	Temperature
Φ_work	Power delivered to the moist air flow through the source

Subscripts A and B indicate the appropriate port. Subscripts a, w, d, and g indicate the properties of dry air, water vapor, water droplets, and trace gas, respectively.

Mass balance:

$\begin{array}{l} {\dot{m}}_{A} + {\dot{m}}_{B} = 0 \\ {\dot{m}}_{w A} + {\dot{m}}_{w B} = 0 \\ {\dot{m}}_{g A} + {\dot{m}}_{g B} = 0 \\ {\dot{m}}_{d A} + {\dot{m}}_{d B} = 0 \end{array}$

Energy balance:

$Φ_{A} + Φ_{B} + Φ_{w o r k} = 0$

If the source performs no work (Power added parameter is set to None), then $Φ_{w o r k} = 0$ .

If the source is isentropic (Power added parameter is set to Isentropic), then

$Φ_{w o r k} = {\dot{m}}_{A} (h_{t B} - h_{t A})$

where

$\begin{array}{l} h_{t A} = h_{A} + \frac{1}{2} {(\frac{{\dot{m}}_{A}}{ρ_{A} S_{A}})}^{2} \\ h_{t B} = h_{B} + \frac{1}{2} {(\frac{{\dot{m}}_{B}}{ρ_{B} S_{B}})}^{2} \end{array}$

The mixture-specific enthalpies, h_A = h(T_A) and h_B = h(T_B), are constrained by the isentropic relation, that is, there is no change in entropy:

$\int_{T_{A}}^{T_{B}} \frac{1}{T} d h (T) = R \ln (\frac{p_{B}}{p_{A}})$

The quantity specified by the Pressure differential parameter of the source is

$p_{B} - p_{A} = Δ p_{s p e c i f i e d}$

Assumptions and Limitations

There are no irreversible losses.
There is no heat exchange with the environment.

Examples

Pneumatic Actuator with Humidity

How the Simscape™ Foundation Library moist air components can be used to model a pneumatic actuator operating in a humid environment. The Directional Valve is a subsystem composed of four Variable Local Restriction (MA) blocks, and the Double-Acting Actuator is a subsystem composed of two Translational Mechanical Converter (MA) blocks in opposite mechanical orientation.

Open Model

Ports

Input

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P — Pressure differential control signal, Pa
physical signal

Input physical signal that specifies the pressure differential across the source.

Dependencies

To enable this port, set the Source type parameter to Controlled.

Conserving

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A — Source inlet
moist air

Moist air conserving port. A positive pressure differential causes the pressure at port B to be greater than the pressure at port A.

B — Source outlet
moist air

Moist air conserving port. A positive pressure differential causes the pressure at port B to be greater than the pressure at port A.

Parameters

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Source type — Select whether pressure differential can change during simulation
`Controlled` (default) | `Constant`

Select whether the pressure differential generated by the source can change during simulation:

Controlled — The pressure differential is variable, controlled by an input physical signal. Selecting this option exposes the input port P.
Constant — The pressure differential is constant during simulation, specified by a block parameter. Selecting this option enables the Pressure differential parameter.

Pressure differential — Constant pressure differential across the source
`0 MPa` (default) | scalar

Pressure differential of the moist air mixture across the ports of the source.

Dependencies

To enable this parameter, set Source type to Constant.

Power added — Select whether the source performs work
`Isentropic` (default) | `None`

Select whether the source performs work on the moist air flow:

Isentropic — The source performs isentropic work on the moist air to maintain the specified pressure differential. Use this option to represent an idealized pump or compressor and properly account for the energy input and output, especially in closed-loop systems.
None — The source performs no work on the flow, neither adding nor removing power, regardless of the pressure differential produced by the source. Use this option to set up the desired flow condition upstream of the system, without affecting the temperature of the flow.

Cross-sectional area at port A — Area normal to flow path at port A
`0.01 m^2` (default) | positive scalar

Area normal to flow path at port A.

Cross-sectional area at port B — Area normal to flow path at port B
`0.01 m^2` (default) | positive scalar

Area normal to flow path at port B.

Extended Capabilities

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

Version History

Introduced in R2018a

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R2024b: Model water droplets suspended in moist air flow

Blocks in the moist air domain can now model water droplets suspended in a moist air flow. To model water droplets, select Enable entrained water droplets in the Moist Air Properties (MA) block connected to your moist air network.

R2023b: Usability enhancement for moist air sources

In R2023b, separate Pressure Source (MA) and Controlled Pressure Source (MA) blocks have been combined into a single Pressure Source (MA) block that lets you select between generating constant or time-varying pressure differential.

This change has no compatibility impact when you use these Foundation library blocks in your models. When you open an existing model, the Controlled Pressure Source (MA) blocks are automatically replaced by Pressure Source (MA) blocks with exposed input port.

However, if you use these blocks in your custom composite components, you need to update the composite component code.

Source Block to Update	Old Syntax	New Syntax
Controlled Pressure Source (MA)	`source = foundation.moist_air.sources.controlled_pressure_source;`	`source = foundation.moist_air.sources.pressure_source;`
Pressure Source (MA)	`source = foundation.moist_air.sources.pressure_source;`	`source = foundation.moist_air.sources.pressure_source(source_type=foundation.enum.constant_controlled.constant);`

Pressure Source (MA)