# Pressure Source (2P)

Generate constant or time-varying pressure differential

Libraries:
Simscape / Foundation Library / Two-Phase Fluid / Sources

## Description

The Pressure Source (2P) block represents an ideal mechanical energy source in a two-phase fluid 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.

### Mass Balance

The volume of fluid in the source is considered negligible and is ignored in a model. There is no fluid accumulation between the ports and the sum of all mass flow rates into the source must therefore equal zero:

`${\stackrel{˙}{m}}_{\text{A}}+\text{​}{\stackrel{˙}{m}}_{\text{B}}=0,$`

where $\stackrel{˙}{m}$ denotes the mass flow rate into the source through a port. The block accepts as input the mass flow rate at port A. The flow is directed from port A to port B when the specified value is positive.

### Energy Balance

By default, the source maintains the specified flow rate by performing isentropic work on the incoming fluid, though the block provides the option to ignore this term. The rate at which the source does work, if considered in the model, must equal the sum of the energy flow rates through the ports:

`${\varphi }_{\text{A}}+\text{​}{\varphi }_{\text{B}}+\text{​}{\varphi }_{\text{Work}}=0,$`

where ϕ denotes the energy flow rate into the source through a port or by means of work. The energy flow rate due to work is equal to the power generated by the source. Its value is calculated from the specific total enthalpies at the ports:

`${\varphi }_{\text{Work}}={\stackrel{˙}{m}}_{\text{A}}\left({h}_{\text{A}}-{h}_{\text{B}}\right).$`

The specific total enthalpy h is defined as:

`${h}_{*}={u}_{*}+{p}_{*}{v}_{*}+\frac{1}{2}{\left(\frac{{\stackrel{˙}{m}}_{*}{v}_{*}}{S}\right)}^{2},$`

where the asterisk denotes a port (A or B) and:

• u is specific internal energy.

• p is pressure.

• S is flow area.

The specific internal energy in the equation is obtained from the tabulated data of the Two-Phase Fluid Properties (2P) block. Its value is uniquely determined from the constraint that the work done by the source is isentropic. The specific entropy, a function of specific internal energy, must then have the same value at ports A and B:

`${s}_{\text{A}}\left({p}_{\text{A}},{u}_{\text{A}}\right)={s}_{\text{B}}\left({p}_{\text{B}},{u}_{\text{B}}\right),$`

where s is specific entropy. If the Power added parameter is set to `None`, the specific total enthalpies at the ports have the same value (${h}_{\text{A}}={h}_{\text{B}}$) and the work done by the source reduces to zero (${\varphi }_{\text{Work}}=0$).

### Assumptions and Limitations

• There are no irreversible losses.

• There is no heat exchange with the environment.

## Ports

### Input

expand all

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

#### Dependencies

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

### Conserving

expand all

Two-phase fluid conserving port. A positive flow rate causes fluid to flow from port A to port B.

Two-phase fluid conserving port. A positive flow rate causes fluid to flow from port A to port B.

## Parameters

expand all

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.

Desired pressure differential across the ports of the source.

#### Dependencies

To enable this parameter, set Source type to `Constant`.

Select whether the source performs work on the fluid flow:

• `Isentropic` — The source performs isentropic work on the fluid 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.

Area normal to flow path at port A.

Area normal to flow path at port B.

## Version History

Introduced in R2015b

expand all