Flow Resistance (MA)

General resistance in a moist air branch

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Libraries:
Simscape / Foundation Library / Moist Air / Elements

Description

The Flow Resistance (MA) block models a general pressure drop in a moist air network branch. The drop in pressure is proportional to the square of the mixture mass flow rate and inversely proportional to the mixture density. The constant of proportionality is determined from a nominal operating condition specified in the block dialog box. Set the Nominal mixture density parameter to zero to omit the density dependence.

Use this block when empirical data on the pressure losses and flow rates through a component is available, but detailed geometry information is unavailable.

The block equations use these symbols.

$$\dot{m}$$	Mass flow rate
Φ	Energy flow rate
p	Pressure
ρ	Density
R	Specific gas constant
S	Cross-sectional area
K	Proportionality constant
h	Specific enthalpy
T	Temperature

Subscripts a, w, d, and g indicate the properties of dry air, water vapor, water droplets, and trace gas, respectively. Subscripts A and B indicate the appropriate port.

Mass balance:

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

Energy balance:

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

If the Nominal mixture density parameter value, ρ_nom, is greater than zero, then the block computes the pressure drop as

$$p_A-p_B=K_1{\dot{m}}_A\sqrt{{\dot{m}}_A^2+{\left(f_{lam}{\dot{m}}_{nom}\right)}^2}\frac{R{T}_{in}}{p_{in}}$$

where:

• f_lam is the fraction of nominal mixture mass flow rate for laminar flow transition.

• p_in is the inlet pressure (p_A or p_B, depending on flow direction).

• T_in is the inlet temperature (T_A or T_B, depending on flow direction).

The proportionality constant is computed from the nominal flow conditions as

$$K_1=\frac{\Delta p_{nom}{\rho }_{nom}}{{\dot{m}}_{nom}^2}$$

If the Nominal mixture density parameter is set to zero, then the block computes the pressure drop as

$$p_A-p_B=K_2{\dot{m}}_A\sqrt{{\dot{m}}_A^2+{\left(f_{lam}{\dot{m}}_{nom}\right)}^2}$$

where the proportionality constant is computed from the nominal flow conditions as

$$K_2=\frac{\Delta p_{nom}}{{\dot{m}}_{nom}^2}$$

The flow resistance is assumed adiabatic, so the mixture specific total enthalpies are equal

$$h_A+\frac{1}{2}{\left(\frac{{\dot{m}}_{A}R{T}_A}{S{p}_A}\right)}^2=h_B+\frac{1}{2}{\left(\frac{{\dot{m}}_{B}R{T}_B}{S{p}_B}\right)}^2$$

Assumptions and Limitations

• The resistance is adiabatic. It does not exchange heat with the environment.

• The pressure drop is assumed to be proportional to the square of the mixture mass flow rate and inversely proportional to the mixture density.

Examples

Aircraft Environmental Control System

Models an aircraft environmental control system (ECS) that regulates pressure, temperature, humidity, and ozone (O3) to maintain a comfortable and safe cabin environment. Cooling and dehumidification are provided by the air cycle machine (ACM), which operates as an inverse Brayton cycle to remove heat from pressurized hot engine bleed air. Some hot bleed air is mixed directly with the output of the ACM to adjust the temperature. Pressurization is maintained by the outflow valve in the cabin. This model simulates the ECS operating from a hot ground condition to a cold cruise condition and back to a cold ground condition.

• Open Model

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

Conserving

A — Inlet or outlet

moist air

Moist air conserving port associated with the inlet or outlet of the flow resistance. This block has no intrinsic directionality.

B — Inlet or outlet

moist air

Moist air conserving port associated with the inlet or outlet of the flow resistance. This block has no intrinsic directionality.

Parameters

Nominal pressure drop — Pressure drop at a known operating condition

0.001 MPa (default)

Pressure drop from inlet to outlet at a known operating condition. The block uses the nominal parameters to calculate the constant of proportionality between the pressure drop and the mass flow rate.

Nominal mixture mass flow rate — Mass flow rate at a known operating condition

0.1 kg/s (default)

Mass flow rate of the air mixture through the block at a known operating condition. The block uses the nominal parameters to calculate the constant of proportionality between the pressure drop and the mass flow rate.

Nominal mixture density — Density at a known operating condition

0 kg/m^3 (default)

Mass density of the moist air mixture inside the flow resistance at a known operating condition. The block uses the nominal parameters to calculate the constant of proportionality between the pressure drop and the mass flow rate. Set this parameter to zero to ignore the dependence of the pressure drop on the air mixture density.

Cross-sectional area at ports A and B — Flow area at the ports of the flow resistance

0.01 m^2 (default)

Flow area at the ports of the flow resistance. The ports are assumed to be identical in size.

Fraction of nominal mixture mass flow rate for laminar flow transition — Ratio of threshold to nominal mass flow rates

1e-3 (default)

Ratio of the threshold mass flow rate to the nominal mass flow rate of the air mixture. The block uses this parameter to set the threshold for the linearization of the pressure drop.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2018a

R2024b: Model water droplets suspended in moist air flow

Blocks in the moist air domain can now model water droplets suspended in a moist air flow. To model water droplets, select Enable entrained water droplets in the Moist Air Properties (MA) block connected to your moist air network.