Flow Rate Source (G)

Generate constant or time-varying mass flow rate or volumetric flow rate in gas network

Since R2023b

Libraries:
Simscape / Foundation Library / Gas / Sources

Description

The Flow Rate Source (G) block represents an ideal mechanical energy source in a gas network. The source can maintain the specified mass flow rate or volumetric flow rate regardless of the pressure differential. There is no flow resistance and no heat exchange with the environment. You specify the flow rate type by using the Flow rate type parameter.

The block icon changes depending on the values of the Source type and Flow rate type parameters.

Ports A and B represent the source inlet and outlet. The input physical signal at port M or V, depending on the flow rate type, specifies the flow rate. Alternatively, you can specify a fixed flow rate as a block parameter. A positive flow rate causes gas to flow from port A to port B.

The volumetric flow rate and mass flow rate are related through the expression

$\dot{m} = {\begin{array}{l} ρ_{B} \dot{V} & for \dot{V} \geq 0 \\ ρ_{A} \dot{V} & for \dot{V} < 0 \end{array}$

where:

$\dot{m}$ is the mass flow rate from port A to port B.
ρ_A and ρ_B are densities at ports A and B, respectively.
$\dot{V}$ is the volumetric flow rate.

You can choose whether the source performs work on the gas flow:

If the source is isentropic (Power added parameter is set to Isentropic), then the isentropic relation depends on the gas property model.
Gas Model Equations
Perfect gas $\frac{{(p_{A})}^{Z \cdot R / c_{p}}}{T_{A}} = \frac{{(p_{B})}^{Z \cdot R / c_{p}}}{T_{B}}$
Semiperfect gas $\int_{0}^{T_{A}} \frac{c_{p} (T)}{T} d T - Z \cdot R \cdot \ln (p_{A}) = \int_{0}^{T_{B}} \frac{c_{p} (T)}{T} d T - Z \cdot R \cdot \ln (p_{B})$
Real gas $s (T_{A}, p_{A}) = s (T_{B}, p_{B})$
The power delivered to the gas flow is based on the specific total enthalpy associated with the isentropic process.
$Φ_{w o r k} = - {\dot{m}}_{A} (h_{A} + \frac{w_{A}^{2}}{2}) - {\dot{m}}_{B} (h_{B} + \frac{w_{B}^{2}}{2})$
If the source performs no work (Power added parameter is set to None), then the defining equation states that the specific total enthalpy is equal on both sides of the source. It is the same for all three gas property models.
$h_{A} + \frac{w_{A}^{2}}{2} = h_{B} + \frac{w_{B}^{2}}{2}$
The power delivered to the gas flow Φ_work = 0.

Gas Model	Equations
Perfect gas	$\frac{{(p_{A})}^{Z \cdot R / c_{p}}}{T_{A}} = \frac{{(p_{B})}^{Z \cdot R / c_{p}}}{T_{B}}$
Semiperfect gas	$\int_{0}^{T_{A}} \frac{c_{p} (T)}{T} d T - Z \cdot R \cdot \ln (p_{A}) = \int_{0}^{T_{B}} \frac{c_{p} (T)}{T} d T - Z \cdot R \cdot \ln (p_{B})$
Real gas	$s (T_{A}, p_{A}) = s (T_{B}, p_{B})$

The equations use these symbols:

c_p	Specific heat at constant pressure
h	Specific enthalpy
$\dot{m}$	Mass flow rate (flow rate associated with a port is positive when it flows into the block)
p	Pressure
R	Specific gas constant
s	Specific entropy
T	Temperature
w	Flow velocity
Z	Compressibility factor
Φ_work	Power delivered to the gas flow through the source

Subscripts A and B indicate the appropriate port.

Assumptions and Limitations

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

Examples

Compressor Map with Scattered Lookup

Gas flow through a compressor which is modeled using a simple controlled mass flow rate source. The compressor map that governs this mass flow rate is modeled using the PS Scattered Lookup (2D) block whose data coordinates are the pressure ratio (Pa/Pa) and the engine RPM, and the output is the mass flow rate (kg/s). The scattered lookup block performs delaunay triangulation on the input data (which is shown in plots below), and uses this to interpolate and calculate the mass flow rate based on the input. Scattered lookup allows modeling of the compressor even if the data provided is in an unstructured format.

Open Model

Ports

Input

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M — Mass flow rate control signal, kg/s
physical signal

Input physical signal that specifies the mass flow rate of the gas through the source.

Dependencies

To enable this port, set the Source type parameter to Controlled and Flow rate type to Mass flow rate.

V — Volumetric flow rate control signal, m^3/s
physical signal

Input physical signal that specifies the volumetric flow rate of gas through the source.

Dependencies

To enable this port, set the Source type parameter to Controlled and Flow rate type to Volumetric flow rate.

Conserving

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A — Source inlet
gas

Gas conserving port. A positive flow rate causes gas to flow from port A to port B.

B — Source outlet
gas

Gas conserving port. A positive flow rate causes gas to flow from port A to port B.

Parameters

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

Select whether the flow rate generated by the source can change during simulation:

Controlled — The flow rate is variable, controlled by an input physical signal. Selecting this option exposes the input port M or V, depending on the value of the Flow rate type parameter.
Constant — The flow rate is constant during simulation, specified by a block parameter. Selecting this option enables the Mass flow rate or Volumetric flow rate parameter, depending on the value of the Flow rate type parameter.

Flow rate type — Select whether source generates mass or volumetric flow rate
`Mass flow rate` (default) | `Volumetric flow rate`

Select the type of flow rate, Mass flow rate or Volumetric flow rate.

Mass flow rate — Constant mass flow rate through the source
`0 kg/s` (default)

Desired mass flow rate of gas through the source.

Dependencies

To enable this parameter, set Source type to Constant and Flow rate type to Mass flow rate.

Volumetric flow rate — Constant volumetric flow rate through the source
`0 m^3/s` (default)

Desired volumetric flow rate of gas through the source.

Dependencies

To enable this parameter, set Source type to Constant and Flow rate type to Volumetric flow rate.

Specified flow rate conditions — Select whether to calculate volumetric flow rate at standard or actual working conditions
`Actual conditions` (default) | `Standard conditions`

Select whether the source calculates flow rate at actual working conditions or at a standard pressure and temperature:

Actual conditions — The source calculates the volumetric flow rate by using the gas density at the actual working conditions of the system.
Standard conditions — The source calculates the volumetric flow rate by using the gas density at standard conditions. When you select this option, additional parameters become available to let you specify the standard pressure and temperature.

Dependencies

To enable this parameter, set Flow rate type to Volumetric flow rate.

Standard pressure — Gas pressure at standard conditions
`0.10132 MPa` (default)

Gas pressure at standard conditions.

Dependencies

To enable this parameter, set Specified flow rate conditions to Standard conditions.

Standard temperature — Gas temperature at standard conditions
`20 degC` (default)

Gas temperature at standard conditions.

Dependencies

To enable this parameter, set Specified flow rate conditions to Standard conditions.

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

Select whether the source performs work on the gas flow:

Isentropic — The source performs isentropic work on the gas to maintain the specified mass flow rate. 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.

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.

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

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 R2023b

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R2023b: Usability enhancement for gas sources

In R2023b, separate Mass Flow Rate Source (G), Controlled Mass Flow Rate Source (G), Volumetric Flow Rate Source (G), and Controlled Volumetric Flow Rate Source (G) blocks have been combined into a single Flow Rate Source (G) block that lets you select between generating constant or time-varying mass flow rate or volumetric flow rate. The new block lets you use the block parameters to configure the block and expose only the input ports that you need in a particular model, which helps reduce clutter and improve the block diagram layout.

This change has no compatibility impact when you use these Foundation library blocks in your models. When you open an existing model, the old blocks are automatically replaced by Flow Rate Source (G) blocks with the appropriate configuration.

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 Mass Flow Rate Source (G)	`source = foundation.gas.sources.controlled_mass_flow_source;`	`source = foundation.gas.sources.flow_source;`
Mass Flow Rate Source (G)	`source = foundation.gas.sources.mass_flow_source;`	`source = foundation.gas.sources.flow_source(source_type=foundation.enum.constant_controlled.constant);`
Controlled Volumetric Flow Rate Source (G)	`source = foundation.gas.sources.controlled_volumetric_flow_source;`	`source = foundation.gas.sources.flow_source(flow_type=foundation.enum.mass_volumetric_flow.volumetric);`
Volumetric Flow Rate Source (G)	`source = foundation.gas.sources.volumetric_flow_source;`	`source = foundation.gas.sources.flow_source(source_type=foundation.enum.constant_controlled.constant,flow_type=foundation.enum.mass_volumetric_flow.volumetric);`

R2023a: Calculate volumetric flow rate by using density at standard pressure and temperature

When generating volumetric flow rate, the block lets you select whether to calculate the volumetric flow rate by using density at standard pressure and temperature or at the actual working conditions of the system. In previous releases, you could only use actual working conditions.

Flow Rate Source (G)