Pressure Source (MA)

Generate constant 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 mass flow rate through the source. There is no flow resistance and no heat exchange with the environment. 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.

Mass balance:

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

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 power), 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

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

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

Isentropic power — 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.

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

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

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

Area normal to flow path at port A.

Pressure Source (MA)