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:

${\dot{m}}_{A} + {\dot{m}}_{B} = 0,$

where $\dot{m}$ 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:

$ϕ_{A} + ϕ_{B} + ϕ_{Work} = 0,$

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:

$ϕ_{Work} = {\dot{m}}_{A} (h_{A} - h_{B}) .$

The specific total enthalpy h is defined as:

$h_{*} = u_{*} + p_{*} v_{*} + \frac{1}{2} {(\frac{{\dot{m}}_{*} v_{*}}{S})}^{2},$

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:

$s_{A} (p_{A}, u_{A}) = s_{B} (p_{B}, u_{B}),$

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 ( $h_{A} = h_{B}$ ) and the work done by the source reduces to zero ( $ϕ_{Work} = 0$ ).

Assumptions and Limitations

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

Examples

Cavitation in Two-Phase Fluid

How two-phase fluid components can be used to simulate cavitation. The model is a translational mechanical converter driven by an oscillating pressure source. During the negative portion of the pressure source cycle, the fluid cavitates, reducing the force produced by the converter. As a result, the converter displacement drifts and does not return to the starting position.

Open Model

Ports

Input

expand all

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

expand all

A — Source inlet
two-phase fluid

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

B — Source outlet
two-phase fluid

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

Parameters

expand all

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 Pa` (default) | scalar

Desired pressure differential 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 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.

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 R2015b

expand all

R2023b: Usability enhancement for two-phase fluid sources

In R2023b, separate Pressure Source (2P) and Controlled Pressure Source (2P) blocks have been combined into a single Pressure Source (2P) 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 (2P) blocks are automatically replaced by Pressure Source (2P) 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 (2P)	`source = foundation.two_phase_fluid.sources.controlled_pressure_source;`	`source = foundation.two_phase_fluid.sources.pressure_source;`
Pressure Source (2P)	`source = foundation.two_phase_fluid.sources.pressure_source;`	`source = foundation.two_phase_fluid.sources.pressure_source(source_type=foundation.enum.constant_controlled.constant);`

Pressure Source (2P)

Description

Mass Balance

Energy Balance

Assumptions and Limitations

Examples

Cavitation in Two-Phase Fluid

Ports

Input

P — Pressure differential control signal, Pa physical signal

Dependencies

Conserving

A — Source inlet two-phase fluid

B — Source outlet two-phase fluid

Parameters

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

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

Dependencies

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

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

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

Extended Capabilities

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

Version History

R2023b: Usability enhancement for two-phase fluid sources

See Also

P — Pressure differential control signal, Pa
physical signal

A — Source inlet
two-phase fluid

B — Source outlet
two-phase fluid

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

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

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

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

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

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