Volumetric Flow Rate Source (MA)

Generate constant volumetric flow rate

• Library:

• Simscape / Foundation Library / Moist Air / Sources

• 

Description

The Volumetric Flow Rate Source (MA) block represents an ideal mechanical energy source in a moist air 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 moist air to flow from port A to port B.

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

$$\dot{m}=\{\begin{array}{ll}{\rho }_B\dot{V}\hfill & \text{for }\dot{V}\ge 0\hfill \\ {\rho }_A\dot{V}\hfill & \text{for }\dot{V}<0\hfill \end{array}$$

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.

The equations describing the source use these symbols.

cp	Specific heat at constant pressure
h	Specific enthalpy
ht	Specific total enthalpy
$$\dot{m}$$	Mass flow rate (flow rate associated with a port is positive when it flows into the block)
p	Pressure
ρ	Density
R	Specific gas constant
s	Specific entropy
T	Temperature
Φwork	Power delivered to the moist air flow through the source

Subscripts A and B indicate the appropriate port.

Mass balance:

$$\begin{array}{l}{\dot{m}}_A+{\dot{m}}_B=0\\ {\dot{m}}_{wA}+{\dot{m}}_{wB}=0\\ {\dot{m}}_{gA}+{\dot{m}}_{gB}=0\end{array}$$

Energy balance:

$${\Phi }_A+{\Phi }_B+{\Phi }_{work}=0$$

If the source performs no work (Power added parameter is set to None), then $${\Phi }_{work}=0$$.

If the source is isentropic (Power added parameter is set to Isentropic power), then

$${\Phi }_{work}={\dot{m}}_A\left(h_{tB}-h_{tA}\right)$$

where

$$\begin{array}{l}{h}_{tA}=h_A+\frac{1}{2}{\left(\frac{{\dot{m}}_A}{{\rho }_A{S}_A}\right)}^2\\ h_{tB}=h_B+\frac{1}{2}{\left(\frac{{\dot{m}}_B}{{\rho }_B{S}_B}\right)}^2\end{array}$$

The mixture-specific enthalpies, h_A = h(T_A) and h_B = h(T_B), are constrained by the isentropic relation, that is, there is no change in entropy:

$${\displaystyle {\int }_{T_A}^{T_B}\frac{1}{T}}dh\left(T\right)=R\ln \left(\frac{p_B}{p_A}\right)$$

Assumptions and Limitations

• There are no irreversible losses.

• There is no heat exchange with the environment.

Ports

Conserving

A — Source inlet

moist air

Moist air conserving port. A positive volumetric flow rate causes moist air to flow from port A to port B.

B — Source outlet

moist air

Moist air conserving port. A positive volumetric flow rate causes moist air to flow from port A to port B.

Parameters

Power added — Select whether the source performs work

Isentropic power (default) | None

Select whether the source performs work on the moist air flow:

• Isentropic power — The source performs isentropic work on the moist air 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.

Mixture volumetric flow rate — Constant volumetric flow rate through the source

0 m^3/s (default)

Desired volumetric flow rate of the moist air through the source.

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 R2018a