Local Resistance (IL)

Pipe resistances in an isothermal liquid system

Since R2020a

• 

Libraries:
Simscape / Fluids / Isothermal Liquid / Pipes & Fittings

Description

The Local Resistance (IL) block models pressure loss due to user-defined pipe resistances in an isothermal liquid system. You can specify different loss coefficients for forward and reversed flows through the pipe segment. For pipe bends, you can also choose to use the Isothermal Liquid library blocks Pipe Bend (IL) and Elbow (IL) or, for area changes, the Area Change (IL) block.

The loss factor is parameterized by either a constant relationship based on the pipe pressure or by user-supplied tabular data for loss coefficients based on the Reynolds number.

Constant Loss Factor

Segments with loss factors that remain constant over a range of flow velocities are calculated as:

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

where:

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

• Δp is the pressure difference p_A – p_B.

The critical pressure difference, Δp_crit, is the pressure differential associated with the Critical Reynolds number, 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, and 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 Flow area.

Tabulated Loss Coefficient

The loss coefficient can alternatively be interpolated from user-provided Reynolds number and loss coefficient data. The vector of Reynolds numbers can have both positive and negative values, indicating forward and reverse flow, respectively: $$k_{loss}=TLU(\mathrm{Re}).$$

Mass Flow Rate

Mass is conserved through the valve:

$${\dot{m}}_A+{\dot{m}}_B=0.$$

The mass flow rate through the valve is calculated as:

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

where k_loss is the flow loss coefficient, which is selected between the Forward flow loss coefficient (from A to B) and Reverse flow loss coefficient (from B to A) based on the block flow direction.

Examples

Lubrication System

A simplified version of a lubrication system fed with the centrifugal pump. The system consists of five major units: Pump Unit, Scavenge Unit, Heat Exchanger Manifold, Nozzle Manifold, and Control Unit. Both the pump and the scavenge unit are built around the centrifugal pump. The Scavenge Unit collects fluid discharged by nozzles and pumps it back into the reservoir of the Pump Unit. The Control Unit generates commands to bypass either the heat exchanger, represented as a local resistance, or the nozzles block. In a real system, these commands are generated by temperature sensors installed in lubrication cavities.

• Open Model

Ports

Conserving

A — Liquid port

isothermal liquid

Liquid entry or exit port to the pipe segment. Flow is positive from port A to port B.

B — Liquid port

isothermal liquid

Liquid 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. The loss factor is parameterized by either a linear relationship between the segment pressure drop and constant loss factor or by interpolation of user-provided loss factor and Reynolds number data.

Forward flow loss coefficient (from A to B) — Loss coefficient for flow from 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 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 — Vector of 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. The elements are listed in ascending order.

Dependencies

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

Loss coefficient vector — Vector of 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 R2020a