Area Change (MA)

R2026b

Area expansion or contraction in a moist air network

Since R2026b

• 

Area Change (MA) block

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Libraries:
Simscape / Fluids / Moist Air / Pipes & Fittings

Description

The Area Change (MA) block models a sudden or a gradual area change in a moist air network. When moist air flows from port A to port B, it experiences an area contraction. When moist air flows from port B to port A, it experiences an area expansion. You can use semi-empirical, tabular, or constant parameterizations to model losses. The component is assumed adiabatic. There is no heat exchange with the surroundings.

Semi-Empirical Parameterizations

If you set Local loss parameterization to either of the semi-empirical correlation settings, the hydraulic loss coefficient, K, characterizes losses in pressure and velocity based on the Contraction correction factor, C_contraction, and Expansion correction factor, C_expansion, parameters. The block calculates the area change coefficient from both expansion and contraction loss factors and based on the flow rate through the block.

When Local loss parameterization is Semi-empirical correlation - gradual area change, the loss factor depends on the value of the Cone angle parameter.

For area contractions where the value of the Cone angle parameter, θ, is between 0 and 45 degrees, the contraction loss factor is

$$K_{contraction}=0.8C_{contraction}\sin \left(\frac{\theta }{2}\right)\left(1-R\right),$$

where R is the port area ratio $$\frac{A_{smaller}}{A_{bigger}}.$$ For area contractions where the value of the Cone angle parameter is between 45 and 180 degrees, the contraction loss factor is

$$K_{contraction}=\frac{C_{contraction}}{2}\sqrt{\sin \left(\frac{\theta }{2}\right)}\left(1-R\right).$$

For area expansions where the value of the Cone angle parameter is between 0 and 45 degrees, the expansion loss factor is

$$K_{expansion}=2.6C_{expansion}\sin \left(\frac{\theta }{2}\right){\left(1-R\right)}^2,$$

and for expansions where the value of the Cone angle parameter is between 45 and 180 degrees, the expansion loss factor is

$$K_{expansion}=C_{expansion}{\left(1-R\right)}^2.$$

When Local loss parameterization is Semi-empirical correlation - sudden area change, the contraction loss factor is

$$K_{contraction}=\frac{C_{contraction}}{2}\left(1-R\right).$$

The expansion loss factor is

$$K_{expansion}=C_{expansion}{\left(1-R\right)}^2.$$

For both semi-empirical settings, the hydraulic loss coefficient is

$$K=K_{expansion}+\frac{K_{contraction}-K_{expansion}}{2}\left(\tanh \left(\frac{3{\dot{m}}_A}{{\dot{m}}_{th}}\right)+1\right),$$

where:

• $$\dot{m}$$_A is the mass flow rate through port A.

• $${\dot{m}}_{th}$$ is the threshold mass flow rate for flow reversal, which the block calculates from the Critical Reynolds number parameter, Re_c,

  $${\dot{m}}_{th}=\frac{{\mathrm{Re}}_c{A}_R\nu \overline{\rho }}{D_h},$$

  where:

  • A_R is the restriction area, which is the Cross-sectional area at port B parameter.

  • ν is the fluid kinematic viscosity.

  • $$\overline{\rho }$$ is the average fluid density.

  • D_h is the hydraulic diameter at the restriction area, $$D_h=\sqrt{\frac{4A_R}{\pi }}.$$

Constant Loss Parameterization

Set Local loss parameterization to Constant loss efficient to directly specify the loss coefficients with the Contraction loss coefficient and Expansion loss coefficient parameters.

Tabulated Data Parameterization

Set Local loss parameterization to Tabulated data - loss coefficient vs. Reynolds number to parameterize the loss factor by using data interpolated from the Reynolds number at the smallest area, which is a function of the Critical Reynolds number parameter,

$$K=TLU\left(\mathrm{Re}\right).$$

The block uses linear interpolation between data points, and nearest-neighbor extrapolation beyond the table boundaries.

Pressure Differential

The pressure differential over the area change is

$$p_A-p_B=\frac{{\dot{m}}^2}{2\rho A_R^2}\left(1-R^2\right)+\Delta p_{loss},$$

where ρ is the fluid density at the inlet.

The pressure loss is

$$\Delta p_{loss}=\frac{K}{2\rho A_R^2}{\dot{m}}_A\sqrt{{\dot{m}}_A^2+{\dot{m}}_{th}^2}.$$

Energy Balance

The energy conservation equation in the area change is

$${\varphi }_A+{\varphi }_B=0,$$

where:

• Φ_A and Φ_B are the energy flow rates into the block through ports A and B.

Assumptions and Limitations

• This component is adiabatic. It does not exchange heat with its surroundings.

• The cross-sectional area at port A must be greater than or equal to the cross-sectional area at port B.

• The flow is incompressible and the Mach number is small.

Ports

Conserving

A — Moist air entry or exit port

moist air

Moist air conserving port associated with the larger cross-sectional area.

Programmatic Use

Port: A

B — Moist air entry or exit port

moist air

Moist air conserving port associated with the smaller cross-sectional area.

Programmatic Use

Port: B

Parameters

Local loss parameterization — Method to use to model hydraulic losses

Semi-empirical correlation - sudden area change (default) | Semi-empirical correlation - gradual area change | Constant loss coefficient | Tabulated data - loss coefficient vs. Reynolds number

Method to use to model the hydraulic losses due to area change. You can choose from two semi-empirical formulations, provide your own tabulated data, or directly specify constant loss coefficients.

Programmatic Use

Parameter:	loss_spec
Values:	"fluids.moist_air.pipes_fittings.enum.AreaChangeLossSpec.SemiEmpiricalSudden" | "fluids.moist_air.pipes_fittings.enum.AreaChangeLossSpec.SemiEmpiricalGradual" | "fluids.moist_air.pipes_fittings.enum.AreaChangeLossSpec.ConstantLossCoefficient" | "fluids.moist_air.pipes_fittings.enum.AreaChangeLossSpec.Table1DRe"

Cone angle — Gradual area change angle

30 deg (default) | scalar between 0 and 180

Angle of expansion for a gradual area change. The block models the gradual area change as an increasing cone from the smaller port to the larger port.

Dependencies

To enable this parameter, set Local loss parameterization to Semi-empirical correlation - gradual area change.

Programmatic Use

Parameter: cone_angle

Cross-sectional area at port A — Area at port A

0.02 m^2 (default) | positive scalar

Area at port A. This value must be greater than the Cross-sectional area at port B parameter.

Programmatic Use

Parameter: area_A

Cross-sectional area at port B — Area at port B

0.01 m^2 (default) | positive scalar

Area at port B. This value must be less than the Cross-sectional area at port A parameter.

Programmatic Use

Parameter: area_B

Reynolds number vector — Reynolds number values for tabular parameterization

[10, 20, 30, 40, 50, 100, 200, 500, 1000, 2000] (default) | 1-by-n vector

Reynolds number values for the tabular parameterization of the area change. The elements must correspond one-to-one with the elements of the Contraction loss coefficient vector and the Expansion loss coefficient vector parameters. The vector values must be positive and in ascending order.

Dependencies

To enable this parameter, set Local loss parameterization to Tabulated data - loss coefficient vs. Reynolds number.

Programmatic Use

Parameter: Re_TLU

Contraction loss coefficient vector — Loss coefficients for area contraction

[5, 2.7, 1.8, 1.46, 1.3, .9, .65, .42, .3, .2] (default) | 1-by-n vector

Loss coefficients for an area contraction that correspond to the Reynolds number vector parameter. The elements must be greater than zero.

Dependencies

To enable this parameter, set Local loss parameterization to Tabulated data - loss coefficient vs. Reynolds number.

Programmatic Use

Parameter: loss_contraction_TLU

Expansion loss coefficient vector — Loss coefficients for area expansion

[3.1, 2.3, 1.65, 1.35, 1.15, .9, .75, .65, .9, .65] (default) | 1-by-n vector

Loss coefficients for an area expansion that correspond to the Reynolds number vector parameter. The elements must be greater than zero.

Dependencies

To enable this parameter, set Local loss parameterization to Tabulated data - loss coefficient vs. Reynolds number.

Programmatic Use

Parameter: loss_expansion_TLU

Contraction correction factor — Loss factor coefficient for area contraction

1 (default) | positive scalar

Coefficient that the block uses in the semi-empirical calculation of the area contraction loss factor.

Dependencies

To enable this parameter, set Local loss parameterization to either:

• Semi-empirical correlation - sudden area change

• Semi-empirical correlation - gradual area change

Programmatic Use

Parameter: k_contraction

Expansion correction factor — Loss factor coefficient for area expansion

1 (default) | positive scalar

Coefficient that the block uses in the semi-empirical calculation of the area expansion loss factor.

Dependencies

To enable this parameter, set Local loss parameterization to either:

• Semi-empirical correlation - sudden area change

• Semi-empirical correlation - gradual area change

Programmatic Use

Parameter: k_expansion

Contraction loss coefficient — Loss coefficient for area contraction

0.1 (default) | nonnegative scalar

Loss coefficient the block applies when moist air flows from port A to port B, experiencing an area contraction.

Dependencies

To enable this parameter, set Local loss parameterization to Constant loss coefficient.

Programmatic Use

Parameter: loss_coeff_contraction

Expansion loss coefficient — Loss coefficient for area expansion

0.05 (default) | nonnegative scalar

Loss coefficient the block applies when moist air flows from port B to port A, experiencing an area expansion.

Dependencies

To enable this parameter, set Local loss parameterization to Constant loss coefficient.

Programmatic Use

Parameter: loss_coeff_expansion

Critical Reynolds number — Upper Reynolds number limit for laminar flow

150 (default) | positive scalar

Upper Reynolds number limit for laminar flow through the area change. The block uses this parameter to calculate the threshold mass flow rate for smoothing the flow reversal transition.

Programmatic Use

Parameter: Re_c

References

[1] Crane Co, editor. Flow of Fluids: Through Valves, Fittings and Pipe. Repr, Crane, 2009.

[2] Idelʹchik, I. E., and A. S. Ginevskiĭ. Handbook of Hydraulic Resistance. 4th ed. rev. and Augmented, Begell House, 2007.

[3] Wessel, D. J. 2001. ASHRAE Fundamentals Handbook 2001 (SI Edition). American Society of Heating, Refrigerating and Air-Conditioning Engineers.

Extended Capabilities

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

Version History

Introduced in R2026b