Controlled Volumetric Flow Rate Source (MA)

Generate time-varying volumetric flow rate

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Libraries:
Simscape / Foundation Library / Moist Air / Sources

Description

The Controlled Volumetric Flow Rate Source (MA) block represents an ideal mechanical energy source in a moist air 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 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.

Examples

Medical Ventilator with Lung Model

Models a positive-pressure medical ventilator system. A preset flow rate is supplied to the patient. The lungs are modeled with the Translational Mechanical Converter (MA), which converts moist air pressure into translational motion. By setting the Interface cross-sectional area to unity, displacement in the mechanical translational network becomes a proxy for volume, force becomes a proxy for pressure, spring constant becomes a proxy for respiratory elastance, and damping coefficient becomes a proxy for respiratory resistance.

Open Model

Ports

Input

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

physical signal

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

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 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.

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, temperature, and relative humidity:

• Actual conditions — The source calculates the volumetric flow rate by using the moist air density at the actual working conditions of the system.

• Standard conditions — The source calculates the volumetric flow rate by using the moist air density at standard conditions. When you select this option, additional parameters become available to let you specify the standard pressure, temperature, and relative humidity.

Standard pressure — Moist air pressure at standard conditions

0.10132 MPa (default)

Moist air pressure at standard conditions.

Dependencies

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

Standard temperature — Moist air temperature at standard conditions

20 degC (default)

Moist air temperature at standard conditions.

Dependencies

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

Standard relative humidity — Moist air relative humidity at standard conditions

0.65 (default)

Moist air relative humidity 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 R2018a