Annular Leakage (IL)

Models annular leakage between a circular tube and a round insert in an isothermal flow

Since R2020a

• 

Libraries:
Simscape / Fluids / Isothermal Liquid / Valves & Orifices / Orifices

Description

The Annular Leakage (IL) block models annular leakage between a circular tube and a round insert in an isothermal liquid network. The insert can be located off-center from the tube and can have varying lengthwise overlap with the tube.

Ports A and B correspond with the orifice inlet and outlet. The input ports L and E are optional physical signal ports that model variable overlap length (L) and variable eccentricity (E).

The Mass Flow Rate Equation

The leakage mass flow rate is calculated from the pressure-flow rate equation

$$\dot{m}=\frac{\pi {\left(R-r\right)}^3\left(R+r\right)}{12v}\frac{\left(p_A-p_B\right)}{l}\left[1+3{\epsilon }_{{}_{sat}}^2\frac{R}{\left(R+r\right)}+\frac{3}{8}{\epsilon }^4\frac{\left(R-r\right)}{\left(R+r\right)}\right],$$

where:

• R is the annulus outer radius.

• r is the annulus inner radius.

• p_A is the pressure at port A.

• p_B is the pressure at port B.

• ν is the fluid kinematic viscosity.

• l is the overlap length.

• ε is the eccentricity ratio, $$\epsilon =\frac{e}{R-r}$$, where e is the eccentricity, which can be defined as a physical signal or constant value.

• ε_sat is the saturated eccentricity ratio, which is ε for constant orifices, or the physical signal connected to port L for variable orifices. The eccentricity ratio is always between 0 and 1.

When modeling a variable overlap length, the user-defined minimum overlap length is used if the physical signal falls below the value of the Minimum overlap length parameter.

Assumptions and Limitations

The pressure-flow equation is valid only for fully-developed, laminar flows. The flow Reynolds number can be determined using $$\mathrm{Re}=\frac{\dot{m}{D}_h}{\mu \pi \left(R^2-r^2\right)}$$ or by checking the simulation log in the Results Explorer or the Simulation Data Inspector. For more information, see Data Logging.

Ports

Conserving

A — Liquid port

isothermal liquid

Entry or exit port of the liquid to or from the orifice.

B — Liquid port

isothermal liquid

Entry or exit port of the liquid to or from the orifice.

Input

L — Variable overlap length

physical signal

Optional physical signal port that provides the variable overlap length between the sleeve and annular insert.

Dependencies

To expose this port, set Overlap length specification to Variable.

E — Variable eccentricity

physical signal

Optional physical signal port that provides variable eccentricity of the annular insert to the sleeve.

Dependencies

To expose this port, set Eccentricity specification to Variable.

Parameters

Overlap length specification — Type of insert-sleeve overlap

Constant (default) | Variable

Whether the length-wise sleeve-insert overlap is constant or variable.

Overlap length — Overlap between tube and insert

1e-3 m (default) | positive scalar

Length-wise overlap between the insert and tube.

Dependencies

To enable this parameter, set Overlap length specification to Constant.

Minimum overlap length — Minimum overlap between tube and insert

1e-6 m (default) | positive scalar

Lower limit to the length-wise overlap between the insert and tube. Any length shorter than this value will be set to the specified minimum.

Dependencies

To enable this parameter, set Overlap length specification to Variable.

Eccentricity specification — Eccentricity variability

Constant (default) | Variable

Whether the orifice eccentricity changes or remains at a set value.

Eccentricity — Center of insert offset with respect to sleeve center

0 m (default) | positive scalar

The distance between the center of the orifice and the center of the insert.

Dependencies

To enable this parameter, set Eccentricity specification to Constant.

Inner radius — Radius of insert

9.8e-3 m (default) | positive scalar

Insert radius r.

Outer radius — Radius of tube

1e-2 m (default) | positive scalar

Tube radius R, measured from the tube center to the inner wall.

Extended Capabilities

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

Version History

Introduced in R2020a