Annular Leakage (IL)

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

• Library:
• 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

$\stackrel{˙}{m}=\frac{\pi {\left(R-r\right)}^{3}\left(R+r\right)}{12v}\frac{\left({p}_{A}-{p}_{B}\right)}{l}\left[1+3{\epsilon }_{{}_{sat}}^{2}\frac{R}{\left(R+r\right)}+\frac{3}{8}{\epsilon }^{4}\frac{\left(R-r\right)}{\left(R+r\right)}\right],$

where:

• R is the annulus outer radius.

• r is the annulus inner radius.

• pA is the pressure at port A.

• pB 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.

• εsat 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 $\mathrm{Re}=\frac{\stackrel{˙}{m}{D}_{h}}{\mu \pi \left({R}^{2}-{r}^{2}\right)}$ or by checking the simulation log in the Results Explorer or the Simulation Data Inspector. For more information, see Data Logging.

Ports

Conserving

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

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

Input

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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.

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

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

Length-wise overlap between the insert and tube.

Dependencies

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

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.

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

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

Dependencies

To enable this parameter, set Eccentricity specification to Constant.

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