Partially Filled Pipe (IL)

A pipe with a variable volume of liquid in an isothermal fluid network.

blockType: EngeeFluids.IsothermalLiquid.Pipes.PartiallyFilled

Path in the library:

/Physical Modeling/Fluids/Isothermal Liquid/Pipes & Fittings/Partially Filled Pipe (IL)

Description

Block Partially Filled Pipe (IL) simulates a pipe with the ability to vary the liquid level inside. The pipe may also become completely empty during simulation.

In addition to the isothermal fluid ports A and B, the unit has an input port AL, which receives the liquid level value in the form of a scalar from the connected units. If the value on port AL is greater than zero, then port A is immersed in liquid. If the value on AL is less than or equal to zero, then the port is open. The liquid level in the pipe is transmitted as a scalar to the connected units via the L port.

Port A is always higher than port B. If port A becomes open, the pipe can be filled through port B. When liquid enters the pipe through port B, the mass flow rate through port A is 0 until the pipe is completely filled, and then .

Block Partially Filled Pipe (IL) can be used together with the block Tank (IL) when the liquid level is expected to drop below the tank inlet. Multiple blocks Partially Filled Pipe (IL) They can also be connected in series or in parallel. It should be borne in mind that the pipe can only be filled through port B. Therefore, if port A of one block in the parallel configuration turns out to be open, then it will be impossible to fill this pipe if it is not possible to fill the pipe through port B.

Pressure loss in the pipe

Pressure drop in the pipe, , includes losses due to wall friction and the difference in hydrostatic pressure between the height of the liquid surface and the height of the liquid in the port A:

Friction losses depend on the flow regime in the pipe. If the flow is laminar, then the friction losses are:

where

— kinematic viscosity of the liquid;
— parameter value Laminar friction constant for Darcy friction factor;
— the sum of the pipe length and the value Aggregate equivalent length of local resistances proportional to the filling level of the pipe: ;
, — liquid level and parameter value Elevation drop from port A to port B accordingly;
— the hydraulic diameter of the pipe. If the pipe section is not circular, then the hydraulic diameter is equal to the equivalent round diameter.

If the flow is turbulent, the friction losses are:

where — the Darcy coefficient of friction for turbulent flow, which is determined by the empirical Haaland equation:

where — parameter value Internal surface absolute roughness.

The Reynolds number depends on the mass flow rate in port B and the hydraulic diameter of the pipe.

The difference in hydrostatic pressure is

Mass consumption

The flow rate in the pipe is determined by the internal liquid level and the conditions in port B. The pipe can be filled or empty in B if the entire pipe is partially empty. If the pipe is completely filled, then , and the mass is preserved:

The mass of liquid in the pipe is determined by the relative filling level of the pipe:

Assumptions and limitations

This unit does not take into account the dynamic compressibility or inertia of the liquid, nor does it simulate the dynamics of air (or a second liquid) in the pipe.

Ports

Conserving

# A — inlet or outlet
Isothermal liquid

Details

The inlet or outlet for the liquid in the pipe. Port A is always higher than port B. When port A is immersed in liquid: . When port A is open: .

Program usage name

inlet

# B — inlet or outlet
Isothermal liquid

Details

The inlet or outlet for the liquid in the pipe. Port A is always higher than port B. When port A is immersed in liquid: . When port A is open, any flow into or out of port B changes the fluid level in the pipe. An empty or partially empty pipe can only be filled through port B.

Program usage name

outlet

Input

# AL — relative liquid level in the connected unit, m
scalar

Details

The relative level of the liquid in the connected unit in m, given as a scalar. If the value on the AL port is positive, then the end of the pipe is immersed in liquid. Otherwise the port is open.

Data types	`Float64`
Complex numbers support	I don’t

Output

# L — liquid level in the pipe, m
scalar

Details

The liquid level in the pipe in m, returned as a scalar.

Data types	`Float64`
Complex numbers support	I don’t

Parameters

Geometry

# Pipe length — pipe length
m | cm | ft | in | km | mi | mm | um | yd

Details

Pipe length.

Units	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`5.0 m`
Program usage name	`pipe_length`
Evaluatable	Yes

# Cross-sectional area — the cross-sectional area of the hole
m^2 | cm^2 | ft^2 | in^2 | km^2 | mi^2 | mm^2 | um^2 | yd^2

Details

The cross-sectional area of the pipe opening.

Units	`m^2` \| `cm^2` \| `ft^2` \| `in^2` \| `km^2` \| `mi^2` \| `mm^2` \| `um^2` \| `yd^2`
Default value	`0.01 m^2`
Program usage name	`area`
Evaluatable	Yes

# Hydraulic diameter — hydraulic diameter
m | cm | ft | in | km | mi | mm | um | yd

Details

The hydraulic diameter used in calculating the Reynolds number in a pipe. For non—circular pipes, the hydraulic diameter is the diameter of an equivalent cylindrical pipe with the same cross-sectional area. For round pipes, the hydraulic diameter and the pipe diameter are the same.

Units	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`0.1128 m`
Program usage name	`hydraulic_diameter`
Evaluatable	Yes

# Elevation drop from port A to port B — pipe lifting height between ports A and B
m | cm | ft | in | km | mi | mm | um | yd

Details

Changing the height of the pipe vertically. Port A is always higher than port B.

Units	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`5.0 m`
Program usage name	`elevation_drop`
Evaluatable	Yes

# Initial liquid level — initial liquid level
m | cm | ft | in | km | mi | mm | um | yd

Details

The liquid level in the pipe at the beginning of the simulation.

Units	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`5.0 m`
Program usage name	`level_start`
Evaluatable	Yes

# Liquid level below zero — notification of the absence of liquid in the pipe
None | Error

Details

Do I need to notify if there is no liquid in the pipe? Set this parameter to None if you do not want to receive an error message if there is no liquid in the pipe. Set the value Error if you want the simulation to stop when this happens.

Values	`None` \| `Error`
Default value	`Error`
Program usage name	`zero_level_assert_action`
Evaluatable	Yes

# Gravitational acceleration — acceleration of free fall
gee | m/s^2 | cm/s^2 | ft/s^2 | in/s^2 | km/s^2 | mi/s^2 | mm/s^2

Details

Constant acceleration of free fall.

Units	`gee` \| `m/s^2` \| `cm/s^2` \| `ft/s^2` \| `in/s^2` \| `km/s^2` \| `mi/s^2` \| `mm/s^2`
Default value	`9.81 m/s^2`
Program usage name	`g_const`
Evaluatable	Yes

Friction

# Aggregate equivalent length of local resistances — pipe length for calculating equivalent losses
m | cm | ft | in | km | mi | mm | um | yd

Details

The length of the pipe that will result in equivalent hydraulic losses, as will a pipe with bends, area changes, or other non-uniform characteristics.

Units	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`1.0 m`
Program usage name	`length_add`
Evaluatable	Yes

# Internal surface absolute roughness — roughness of the pipe walls
m | cm | ft | in | km | mi | mm | um | yd

Details

The absolute roughness of the pipe walls. This parameter is used to determine the Darcy coefficient of friction, which contributes to the pressure loss in the pipe.

Units	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`1.5e-5 m`
Program usage name	`roughness`
Evaluatable	Yes

# Laminar flow upper Reynolds number limit — the upper limit of the Reynolds number in the laminar flow regime

Details

The upper limit of the Reynolds number in the laminar flow regime. Beyond this number, the flow regime becomes transitional, approaches the turbulent regime, and becomes completely turbulent at the level of Turbulent flow lower Reynolds number limit.

Default value	`2000.0`
Program usage name	`Re_laminar`
Evaluatable	Yes

# Turbulent flow lower Reynolds number limit — the lower limit of the Reynolds number in the turbulent flow regime

Details

The maximum lower value of the Reynolds number in the turbulent flow regime. Below this number, the flow regime is transitional, approaching laminar and becoming completely laminar at the level of Laminar flow upper Reynolds number limit.

Default value	`4000.0`
Program usage name	`Re_turbulent`
Evaluatable	Yes

# Laminar friction constant for Darcy friction factor — loss coefficient for calculating local resistances (Darcy coefficient) in the laminar flow regime

Details

The loss coefficient for calculating the Darcy coefficient in the laminar flow regime. The Darcy friction coefficient takes into account the contribution of wall friction to pressure loss calculations.

Default value	`64.0`
Program usage name	`shape_factor`
Evaluatable	Yes