# Controlled Pressure Source (MA)

Generate time-varying pressure differential

• Library:
• Simscape / Foundation Library / Moist Air / Sources

## Description

The Controlled Pressure Source (MA) block represents an ideal mechanical energy source in a moist air network. The pressure differential is controlled by the input physical signal at port P. The source can maintain the specified 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 signal at port P causes the pressure at port B to be greater than the pressure at port A.

The equations describing the source use these symbols.

 cp Specific heat at constant pressure h Specific enthalpy ht Specific total enthalpy $\stackrel{˙}{m}$ 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 Φwork Power delivered to the moist air flow through the source

Subscripts A and B indicate the appropriate port.

Mass balance:

`$\begin{array}{l}{\stackrel{˙}{m}}_{A}+{\stackrel{˙}{m}}_{B}=0\\ {\stackrel{˙}{m}}_{wA}+{\stackrel{˙}{m}}_{wB}=0\\ {\stackrel{˙}{m}}_{gA}+{\stackrel{˙}{m}}_{gB}=0\end{array}$`

Energy balance:

`${\Phi }_{A}+{\Phi }_{B}+{\Phi }_{work}=0$`

If the source performs no work (Power added parameter is set to `None`), then ${\Phi }_{work}=0$.

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

`${\Phi }_{work}={\stackrel{˙}{m}}_{A}\left({h}_{tB}-{h}_{tA}\right)$`

where

`$\begin{array}{l}{h}_{tA}={h}_{A}+\frac{1}{2}{\left(\frac{{\stackrel{˙}{m}}_{A}}{{\rho }_{A}{S}_{A}}\right)}^{2}\\ {h}_{tB}={h}_{B}+\frac{1}{2}{\left(\frac{{\stackrel{˙}{m}}_{B}}{{\rho }_{B}{S}_{B}}\right)}^{2}\end{array}$`

The mixture-specific enthalpies, hA = h(TA) and hB = h(TB), are constrained by the isentropic relation, that is, there is no change in entropy:

`${\int }_{{T}_{A}}^{{T}_{B}}\frac{1}{T}dh\left(T\right)=R\mathrm{ln}\left(\frac{{p}_{B}}{{p}_{A}}\right)$`

The quantity specified by the input signal of the source is

`${p}_{B}-{p}_{A}=\Delta {p}_{specified}$`

### Assumptions and Limitations

• There are no irreversible losses.

• There is no heat exchange with the environment.

## Ports

### Input

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Input physical signal that specifies the pressure differential of the moist air mixture across the source. A positive signal at port P causes the pressure at port B to be greater than the pressure at port A.

### Conserving

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

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

## Parameters

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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 mass flow rate, regardless of the 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 mass flow rate 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.

Area normal to flow path at port A.

Area normal to flow path at port B.