Laminar Leakage (IL)
A block modelling laminar flow through sections of different geometries in an isothermal liquid network.
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Description
The Laminar Leakage (IL) block simulates laminar flow in isothermal liquid networks. The block includes several common cross-sectional geometries as well as a custom geometry. Select a value for the Cross-sectional geometry parameter, and then specify values for other element parameters based on the selected parameter:
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`Circular' for diameter and length.
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The
Annularis the inner diameter, outer diameter and length. -
The `Rectangular' is the width, height and length.
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Elliptical - major axis, minor axis and length.
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The `Equilateral triangular' is the side of the triangle and the length.
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Custom- specify the value of hydraulic resistance, i.e. the ratio of pressure loss to mass flow. In this configuration the block simulates linear hydraulic resistance.
Flow calculations are based on the Hagen-Poiseuille equation, which is valid for laminar flow:
Where:
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- is the mass flow rate through the port A.
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and are pressures at ports A and B respectively.
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- coefficient calculated on the basis of cross-sectional geometry.
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- diameter of the circular cross-section.
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- outer diameter of the circular cross-section.
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- inner diameter of the annular section.
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- width of the rectangular section.
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- height of the rectangular section.
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- major axis of the elliptical section.
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- minor axis of the elliptical section.
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- side length of the triangular section.
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- length.
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- linear hydraulic resistance for custom geometry.
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- kinematic viscosity of the fluid at atmospheric pressure; global parameter defined by the block Isothermal Liquid Properties (IL) connected to the model.
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- average density of the fluid mixture.
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and - values of liquid mixture density at ports A and B, respectively. The equations used to calculate the liquid mixture density depend on the selected isothermal liquid model.
Ports
Non-directional
A - inlet or outlet port
isothermal liquid
The isothermal liquid port corresponds to the laminar leakage inlet or outlet. This unit has no internal directionality.
B - inlet or outlet port
isothermal liquid
The isothermal liquid port corresponds to the laminar leakage inlet or outlet. This unit has no internal directionality.
Parameters
Cross-sectional geometry - cross-sectional shape of the leakage cross section
Circular (by default) | Annular | Rectangular | Elliptical | Equilateral triangular | Custom
Select the cross-sectional shape, and then set the values of the other parameters based on the selected option.
Diameter - diameter of the circular cross section
`1e-3 m (by default)
Diameter of circular cross section.
Dependencies
Enabled when the Cross-sectional geometry parameter is set to Circular.
Inner diameter - inner diameter of the circular section
5e-4 m (by default).
Inner diameter of the annular section.
Dependencies
Available when the Cross-sectional geometry parameter is set to Annular.
Outer diameter - outer diameter of the annular section
1e-3 m (by default).
Outer diameter of the annular section.
Dependencies
Available when the Cross-sectional geometry parameter is set to Annular.
Width - width of the rectangular section
1e-3 m (by default).
Width of rectangular section.
Dependencies
Available when the Cross-sectional geometry parameter is set to Rectangular.
Height - height of rectangular section
0.1 m (by default).
Height of rectangular section.
Dependencies
Available when the Cross-sectional geometry parameter is set to Rectangular.
Major axis is the major axis of the elliptical cross-sectional geometry
1e-3 m (by default).
Major axis of the elliptical cross section.
Dependencies
Available when the Cross-sectional geometry parameter is set to Elliptical.
Minor axis - minor axis of elliptical cross-sectional geometry
5e-4 m (by default).
Minor axis of the elliptical cross section.
Dependencies
Available when the Cross-sectional geometry parameter is set to Elliptical.
Side length - triangle side length for an equilateral triangular section
1e-3 m (by default).
Triangle side length for equilateral triangular section.
Dependencies
Available when the Cross-sectional geometry parameter is set to Equilateral triangular.
Longitudinal length - length
`5 m (by default)'.
Leakage channel length.
Linear pressure-flow resistance - ratio of pressure loss to volumetric flow rate
1e3 s-MPa/m³ (by default)
Ratio of pressure loss to volumetric flow rate. If the cross-sectional geometry is unknown, the block acts as a linear pressure-flow resistance.
Dependencies
Available when the Cross-sectional geometry parameter is set to `Custom'.