Volumetric Flow Rate Source (G)

Generate constant volumetric flow rate

Since R2019a

Libraries:
Simscape / Foundation Library / Gas / Sources

Description

The Volumetric Flow Rate Source (G) block represents an ideal mechanical energy source in a gas network. The source can maintain a constant volumetric flow rate regardless of the pressure differential. There is no flow resistance and no heat exchange with the environment. A positive volumetric 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 power), 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.

Ports

Conserving

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A — Source inlet
gas

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

B — Source outlet
gas

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

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 gas flow:

Isentropic power — The source performs isentropic work on the gas to maintain the specified volumetric 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 volumetric 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.

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

Desired volumetric flow rate of gas through the source.

Specified flow rate conditions — Select whether to calculate 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.

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.

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 R2019a

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

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.

Volumetric Flow Rate Source (G)