Controlled Volumetric Flow Rate Source (G)

Generate time-varying volumetric flow rate

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• Simscape / Foundation Library / Gas / Sources

Description

The Controlled Volumetric Flow Rate Source (G) block represents an ideal mechanical energy source in a gas network. The volumetric flow rate is controlled by the input physical signal at port V. The source can maintain the specified 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

where:

• $\stackrel{˙}{m}$ is the mass flow rate from port A to port B.

• ρA and ρB are densities at ports A and B, respectively.

• $\stackrel{˙}{V}$ 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 ModelEquations
Perfect gas$\frac{{\left({p}_{A}\right)}^{Z\cdot R/{c}_{p}}}{{T}_{A}}=\frac{{\left({p}_{B}\right)}^{Z\cdot R/{c}_{p}}}{{T}_{B}}$
Semiperfect gas${\int }_{0}^{{T}_{A}}\frac{{c}_{p}\left(T\right)}{T}dT-Z\cdot R\cdot \mathrm{ln}\left({p}_{A}\right)={\int }_{0}^{{T}_{B}}\frac{{c}_{p}\left(T\right)}{T}dT-Z\cdot R\cdot \mathrm{ln}\left({p}_{B}\right)$
Real gas$s\left({T}_{A},{p}_{A}\right)=s\left({T}_{B},{p}_{B}\right)$

The power delivered to the gas flow is based on the specific total enthalpy associated with the isentropic process.

`${\Phi }_{work}=-{\stackrel{˙}{m}}_{A}\left({h}_{A}+\frac{{w}_{A}^{2}}{2}\right)-{\stackrel{˙}{m}}_{B}\left({h}_{B}+\frac{{w}_{B}^{2}}{2}\right)$`
• 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 Φwork = 0.

The equations use these symbols:

 cp Specific heat at constant pressure h Specific enthalpy $\stackrel{˙}{m}$ 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 Φwork 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

Input

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

Conserving

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

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

Parameters

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Select whether the source performs work on the gas flow:

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