Y-Junction (IL)

A Y-shaped connection in a system with an isothermal liquid.

blockType: EngeeFluids.IsothermalLiquid.Fittings.YJunction

Path in the library:

/Physical Modeling/Fluids/Isothermal Liquid/Pipes & Fittings/Y-Junction (IL)

Description

Block Y-Junction (IL) simulates a connection consisting of a forward passage and a side branch in an isothermal fluid network. The path between ports A and B is a direct route. The path between ports A and C or between ports B and C is a side branch.

Flow direction

A tee is considered to be extensive if the flows of the forward course and the lateral branch merge. A tee is considered to be flowing if the flow in the lateral branch is separated from the forward flow.

The unit uses a hybrid automaton to determine each resistance coefficient for a given flow configuration. This table describes the conditions and coefficients when for the parameter Loss coefficient model the value is set Custom.

Flow Configuration

Motionless

—

1 or the last acceptable value

Separation from port A

0

Separation from port B

0

Merge to port A

0

Merge to port B

0

Merge to port C (branch)

0

Separation from port C (branch)

0

This table describes the conditions and coefficients when for the parameter Loss coefficient model the value is set Idel’chik correlation.

Flow Configuration

Flow Configuration
Motionless	—	—	—	`1` or the last acceptable value	`1` or the last acceptable value	`1` or the last acceptable value
Separation from port A is invalid				`0`	`1`	`1`
Separation from port B					`0`
Merging to port A is invalid				`0`	`1`	`1`
Merge to port B					`0`
Merging to port C (branch) is invalid				`1`	`1`	`0`
Separation from port C (branch) is invalid				`1`	`1`	`0`

Motionless

—

1 or the last acceptable value

Separation from port A is invalid

0

1

Separation from port B

0

Merging to port A is invalid

0

1

Merge to port B

0

Merging to port C (branch) is invalid

1

0

Separation from port C (branch) is invalid

1

0

In a stationary flow, the mass flow conditions do not correspond to any given flow configuration. A stationary flow is allowed at the beginning of the simulation, but the block does not return to this state after reaching another mode. The threshold value of the mass flow, that is, the point at which the flow in the pipe begins to change direction, is defined as

where

— the critical Reynolds number, when exceeded, the transient flow mode begins;
— viscosity of the liquid;
— the average density of the liquid;
— the smallest cross-sectional area at the pipe junction.

Idelchik coefficient

If for the parameter Loss coefficient model the value is set Idel’chik correlation, the block calculates the resistance coefficients in the tee according to [1].

configuration of the stream

The unit supports two flow configurations between a direct flow from ports A and B and a side branch from port C. The lateral branch is rotated relative to the forward course by an angle , which is the value of the parameter Junction angle between (A-C).

In the exhaust tee, the flow enters ports A and C and exits port B.

y junction il 1

In the intake tee, the flow enters port B and exits ports A and C.

y junction il 2

You can control the behavior of a block in a prohibited flow configuration using the parameter Report when flow configuration is invalid. If for the parameter Report when flow configuration is invalid the value is set None, The model will continue to work in the forbidden flow configuration, but the results may be incorrect.

Extension tee

For the exhaust tee, the unit calculates the resistance coefficient in the lateral branch between ports C and B using a simplified version of the Idelchik formula, assuming a constant forward running area. The coefficient of resistance in the lateral branch is equal to

where

, , — mass expenses on ports A, B, C respectively;
, , — the area of ports A, B, C, respectively.

The unit calculates the resistance coefficient of the forward stroke between ports A and B using a simplified version of the Idelchik formula, assuming that the forward stroke area is constant, and , where — volume flow through the specified port. The resistance coefficient of the forward stroke is

_ Supply tee_

For the intake tee, the unit calculates the resistance coefficient in the lateral branch between ports C and B as

where

and

The unit calculates the forward travel resistance coefficient between ports A and B as

User Coefficient

If for the parameter Loss coefficient model the value is set Custom, the block calculates the resistance coefficient in the pipe for each port, based on custom resistance parameters for the exhaust and intake tees, as well as the mass flow rate for each port. It is necessary to set , , and as parameter values Main branch converging loss coefficient, Main branch diverging loss coefficient, Side branch converging loss coefficient and Side branch diverging loss coefficient accordingly. The behavior of the custom resistance coefficient model for the Y-shaped joint is similar to the behavior for the custom T-tee model.

Conservation of mass and momentum

The block retains mass in the joint, so that

The unit calculates the flow through the pipe connection using the momentum conservation equations between ports A, B and C:

where represents the inertia of the fluid, and

where — parameter Main branch area (A,B), and — parameter Side branch area (C).

Ports

Conserving

# A — liquid port
isothermal liquid

Details

A non-directional port connected to the inlet or outlet of liquid from the tee.

Program usage name

port_a

# B — liquid port
isothermal liquid

Details

A non-directional port connected to the inlet or outlet of liquid from the tee.

Program usage name

port_b

# C — liquid port
isothermal liquid

Details

A non-directional port connected to the inlet or outlet of liquid from the tee.

Program usage name

port_c

Parameters

# Junction angle between (A-C) — the angle between the side branch and the straight line
rad | deg | rev | mrad | arcsec | arcmin | gon

Details

The angle between the side branch and the straight line.

Units	`rad` \| `deg` \| `rev` \| `mrad` \| `arcsec` \| `arcmin` \| `gon`
Default value	`45.0 deg`
Program usage name	`angle`
Evaluatable	Yes

# Main branch area (A,B) — the cross-sectional area of the forward stroke
m^2 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac

Details

The cross-sectional area of the straight pipe passage between ports A and B.

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

# Side branch area (C) — cross-sectional area of the lateral branch
m^2 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac

Details

The area of the connecting pipe between port C and the direct passage.

Units	`m^2` \| `um^2` \| `mm^2` \| `cm^2` \| `km^2` \| `in^2` \| `ft^2` \| `yd^2` \| `mi^2` \| `ha` \| `ac`
Default value	`0.004 m^2`
Program usage name	`side_area`
Evaluatable	Yes

# Loss coefficient model — type of resistance coefficient
Idel’chik correlation | Custom

Details

The model of the coefficient of resistance in the connection. Set this parameter to Custom to set separate resistance coefficients for each segment of the exhaust and intake tees.

Values	`Idel’chik correlation` \| `Custom`
Default value	`Idel'chik correlation`
Program usage name	`loss_coefficient_parameterization`
Evaluatable	No

# Report when flow configuration is invalid — warning mode for invalid flow configurations
None | Error

Details

The mode warns the user about operating conditions that exceed the limits of acceptable flow configurations. If this parameter is set to Error. the simulation will be stopped under conditions outside the acceptable flow configurations.

Dependencies

To use this parameter, set for the parameter Loss coefficient model meaning Idel’chik correlation.

Values	`None` \| `Error`
Default value	`None`
Program usage name	`flow_configuration_assert_action`
Evaluatable	No

# Critical Reynolds number — the upper limit of the Reynolds number for laminar flow

Details

The upper limit of the Reynolds number for laminar flow through a joint.

Default value	`150.0`
Program usage name	`Re_critical`
Evaluatable	Yes

# Main branch converging loss coefficient — drag coefficient at flow fusion between ports A and B

Details

The resistance coefficient for calculating the pressure loss between ports A and B at the confluence of the flow.

Dependencies

To use this parameter, set for the parameter Loss coefficient model meaning Custom.

Default value	`1.12`
Program usage name	`main_converging_loss_coefficient`
Evaluatable	Yes

# Main branch diverging loss coefficient — flow separation resistance coefficient between ports A and B

Details

The resistance coefficient for calculating the pressure loss between ports A and B during flow separation.

Dependencies

To use this parameter, set for the parameter Loss coefficient model meaning Custom.

Default value	`1.12`
Program usage name	`main_diverging_loss_coefficient`
Evaluatable	Yes

# Side branch converging loss coefficient — drag coefficient at flow confluence between port C and direct flow

Details

The resistance coefficient for calculating the pressure loss between port C and the forward flow at the confluence of the flow.

Dependencies

To use this parameter, set for the parameter Loss coefficient model meaning Custom.

Default value	`1.12`
Program usage name	`side_converging_loss_coefficient`
Evaluatable	Yes

# Side branch diverging loss coefficient — resistance coefficient for flow separation between port C and direct flow

Details

The resistance coefficient for calculating the pressure loss between port C and the forward flow during flow separation.

Dependencies

To use this parameter, set for the parameter Loss coefficient model meaning Custom.

Default value	`1.12`
Program usage name	`side_diverging_loss_coefficient`
Evaluatable	Yes

Literature

Idelchik I. E. Handbook of hydraulic resistance / Edited by M. O. Steinberg. — 3rd ed., reprint. and add. — M.: Mechanical Engineering, 1997. — 672 p.: ill. — ISBN 5-217-00393-6.