Local Resistance (MA)

Pipe resistance in a moist air network

Since R2024a

• 

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

Description

The Local Resistance (MA) block models the pressure loss due to user-defined pipe resistance in a moist air network. You can specify different loss coefficients for forward and reversed flows through the pipe segment.

You can parameterize the loss factor as either a constant relationship based on the pipe pressure or by specifying tabular data for loss coefficients based on the Reynolds number.

Constant Loss Factor

When you set Local loss parameterization to Constant, the losses remain constant over the range of flow velocities. The loss factor is

$$k_{loss}=k_{loss,BA}+\frac{\left(k_{loss,AB}-k_{loss,BA}\right)}{2}\left[\tanh \left(\frac{3\Delta p}{\Delta p_{crit}}\right)+1\right],$$

where:

• k_loss,AB and k_loss,BA are the values of the Forward flow loss coefficient (from A to B) and Reverse flow loss coefficient (from B to A) parameters, respectively.

• Δp is the pressure difference, which is p_A – p_B.

The critical pressure difference, Δp_crit, is the pressure differential associated with the Critical Reynolds number parameter, Re_crit, which is the flow regime transition point between laminar and turbulent flow,

$$\Delta p_{crit}=\frac{\overline{\rho }}{2}{k}_{loss,crit}{\left(\frac{\nu {\mathrm{Re}}_{crit}}{D_h}\right)}^2,$$

where:

• k_loss,crit is the loss factor associated with the critical pressure. The value is based on an average of the forward and reverse loss coefficients.

• ν is the fluid kinematic viscosity.

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

• D_h is the segment hydraulic diameter, which is the equivalent diameter of a pipe with a non-circular cross-section, $$D_h=\sqrt{\frac{4}{\pi A_{flow}}}.$$, where A_flow is the value of the Flow area parameter.

Tabulated Loss Coefficient

When you set Local loss parameterization to Tabulated data - loss coefficient vs. Reynolds number, you can interpolate the loss coefficient from the Reynolds number and the loss coefficient data. The vector of Reynolds numbers can have both positive and negative values, which indicate forward and reverse flow, respectively: $$k_{loss}=TLU(\mathrm{Re}).$$

Mass Flow Rate

The block conserves mass such that

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

where:

• $$\dot{m}$$_B is the mixture mass flow rate at port B.

• $$\dot{m}$$_wA and $$\dot{m}$$_wB are the water vapor mass flow rates at ports A and B, respectively.

• $$\dot{m}$$_gA and $$\dot{m}$$_gB are the trace gas mass flow rates at ports A and B, respectively.

The mass flow rate through the valve is

$$\dot{m}=A_{flow}\frac{\sqrt{2\overline{\rho }}}{\sqrt{k_{loss}}}\frac{\Delta p}{{\left[\Delta p^2+\Delta p_{crit}^2\right]}^{1/4}},$$

where k_loss is the flow loss coefficient.

Energy Balance

The block balances energy such that

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

where:

• ϕ_A is the energy flow rate at port A.

• ϕ_B is the energy flow rate at port B.

Ports

Conserving

A — Liquid port

moist air

Moist air conserving port associated with the entry or exit port to the pipe segment. Flow is positive from port A to port B.

B — Liquid port

moist air

Moist air conserving port associated with the entry or exit port to the pipe segment. Flow is positive from port A to port B.

Parameters

Local loss parametrization — Loss factor calculation method

Constant (default) | Tabulated data - loss coefficient vs. Reynolds number

Method of calculating the pipe segment loss factor. You can parameterize the loss factor as either a linear relationship between the segment pressure drop and constant loss factor or by specifying the loss factor and Reynolds number data.

Forward flow loss coefficient (from A to B) — Loss coefficient for flow from port A to B

1 (default) | positive scalar

Loss coefficient associated with pressure loss for flows from port A to port B.

Dependencies

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

Reverse flow loss coefficient (from B to A) — Loss coefficient for flow from port B to A

1 (default) | positive scalar

Loss coefficient associated with pressure loss for flows from port B to port A.

Dependencies

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

Reynolds number vector — Reynolds numbers for tabular parameterization

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

Vector of Reynolds numbers for the tabular parameterization of the loss coefficient. The vector elements must correspond one-to-one with the elements in the Loss coefficient vector parameter. List the elements in ascending order.

Dependencies

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

Loss coefficient vector — Loss coefficients for tabular parameterization

[.65, .75, .9, 1.15, 1.35, 1.65, 2.3, 3.1, 4, 2.7, 1.8, 1.46, 1.3, .9, .65, .42, .3, .2] (default) | 1-by-n vector

Vector of loss coefficients for the tabular parameterization of the loss coefficient. The vector elements must correspond one-to-one with the elements in the Reynolds number vector parameter. The elements must be greater than 0.

Dependencies

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

Flow area — Segment cross-sectional area

1e-3 m^2 (default) | positive scalar

Cross-sectional area of the pipe segment.

Critical Reynolds number — Upper Reynolds number limit for laminar flow

150 (default) | positive scalar

Upper Reynolds number limit for laminar flow through the valve.

Extended Capabilities

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

Version History

Introduced in R2024a