Annular Leakage (IL)

Leakage through an annular gap between a circular tube and a cylindrical rod in an isothermal liquid network.

annular leakage il

Description

The Annular Leakage (IL) block simulates leakage through an annular gap between a circular tube and a cylindrical rod in an isothermal liquid network. The position of the rod in the pipe is not necessarily concentric and its immersion depth can be varied.

annular leakage 1

Ports A and B correspond to the inlet and outlet to the block. The input ports L and E are additional ports that adjust the rod immersion depth ( ) and eccentricity ( ).

Mass flow equation

Leakage mass flow rate is calculated from the equation relating flow rate to pressure:

where

- is the outer radius of the annular gap;
- is the inner radius of the annular gap;
- pressure in port A;
- pressure in port B;
- kinematic viscosity of the fluid;
- rod immersion depth;
- relative eccentricity , where is the eccentricity, which, depending on the mode, is a constant value or equal to the value at port E;
- relative eccentricity of saturation, which is equal to for constant holes or to the value at port E for variable holes. The relative eccentricity is always between 0 and 1.

If the rod immersion depth in the tube is controlled by the L port, its value is limited from below by the Minimum overlap length parameter.

Assumptions and limitations

The pressure-flow equation used in the block is valid only for fully developed, laminar flows. The Reynolds number of the flow can be defined as .

Ports

Conserving

# A — isothermal liquid port
isothermal liquid

Details

isothermal liquid port, corresponds to the inlet or outlet of the unit.

Program usage name

port_a

# B — isothermal liquid port
isothermal liquid

Details

isothermal liquid port, corresponds to the inlet or outlet of the unit.

Program usage name

port_b

Input

# L — adjustable rod immersion depth
scalar

Details

Optional port that sets the depth of the rod immersion in the pipe.

Dependencies

To use this parameter, select the Variable overlap length checkbox.

Data types	`Float64`.
Complex numbers support	No

# E — variable eccentricity
scalar

Details

Additional port that sets the eccentricity between the pipe and the rod.

Dependencies

To use this port, select the Variable eccentricity checkbox.

Data types	`Float64`.
Complex numbers support	No

Parameters

# Variable overlap length — adjustable rod plunging depth

Details

If this box is checked, the rod plunging depth is equal to the value on the L port.

If unchecked, the rod plunge depth is constant and equal to the Overlap length parameter.

Default value	`false (switched off)`
Program usage name	`variable_overlap_length`
Evaluatable	No

# Overlap length — rod immersion depth in the pipe
m | cm | ft | in | km | mi | mm | um | yd

Details

The depth to which the rod is immersed in the pipe.

Dependencies

To use this parameter, uncheck the Variable overlap length box.

Values	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`0.001 m`
Program usage name	`overlap_length`
Evaluatable	Yes

# Minimum overlap length — minimum plunging depth of the rod
m | cm | ft | in | km | mi | mm | um | yd

Details

The minimum value of the rod immersion depth in the pipe. Anything less than this value will be equated to the specified minimum.

Dependencies

To use this parameter, select the Variable overlap length checkbox.

Values	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`1e-06 m`
Program usage name	`min_overlap_length`
Evaluatable	Yes

# Variable eccentricity — variable eccentricity

Details

If this check box is selected, the eccentricity value is equal to the value from port E.

When unchecked, the eccentricity value of is constant and equal to the Eccentricity parameter.

Default value	`false (switched off)`
Program usage name	`variable_eccentricity`
Evaluatable	No

# Eccentricity — displacement of the rod axis with respect to the pipe axis
m | cm | ft | in | km | mi | mm | um | yd

Details

Distance between the axis of the rod and the pipe.

Dependencies

To use this parameter, uncheck the Variable eccentricity box.

Values	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`0.0 m`
Program usage name	`eccentricity`
Evaluatable	Yes

# Inner radius — rod radius
m | cm | ft | in | km | mi | mm | um | yd

Details

Rod radius, .

Values	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`0.0098 m`
Program usage name	`inner_radius`
Evaluatable	Yes

# Outer radius — pipe radius
m | cm | ft | in | km | mi | mm | um | yd

Details

Pipe radius , measured from the centre of the pipe to its inner wall.

Values	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`0.01 m`
Program usage name	`outer_radius`
Evaluatable	Yes