Cross-Junction (IL)

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Cross-coupling in a system with an isothermal liquid.

blockType: EngeeFluids.IsothermalLiquid.Fittings.CrossJunction

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

Description

Block Cross-Junction (IL) It is a four-way connection in an isothermal fluid network. The block simulates the interaction of liquids depending on the flow direction in each port, where the path between ports A and C is a straight line, and ports B and D are side branches.

Conservation of mass and momentum

The block keeps the mass in the joint:

where — mass flow rate for a given port .

The unit determines which coefficient and vector element to use, and then calculates the pressure difference to conserve momentum in such a way that

where

— the average density of the liquid;
— pressure for a given port ;
— pressure in node 1;
— the flow rate that the unit assigns to this port . Parameter Loss coefficient model defines the method used by the block for calculation ;
— fluid inertia for a given port .

The block calculates inertia for each port as

where — parameter value Main line area (A,C), and — parameter value Branch line area (B,D).

Idelchik coefficient

If for the parameter Loss coefficient model the value is set Idel’chik correlation, the block calculates the resistance coefficients in the pipe according to [1]. The Idelchik model supports merging streams to port C, or splitting from port C. To obtain correct results, it is necessary to orient the block in accordance with the expected flow configuration in the model’s fluid network.

The block considers the connection as symmetrical with respect to the horizontal and vertical planes, so that — parameter value Main line area (A,C), and — parameter value Branch line area (B,D), where — the area of the corresponding port.

cross junction il 1 en

If the flow geometry is invalid, the block behavior can be controlled 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 continues to run in an invalid flow configuration, but the results may be incorrect.

Fluence of streams

When merging streams, the resistance coefficients for ports A and C:

The resistance coefficients for ports B and D are

dividing the stream

With divergent flow from port C, the resistance coefficients for ports A and C are

The resistance coefficients for ports B and D are

where by or , and by or . The block smooths out the transition between and using the hyperbolic tangent function.

According to [1], these resistance coefficients are applicable only when the ratio of the diameter of the lateral branch to the diameter of the forward stroke is less than or equal to 2/3. However, the expected margin of error for the relationship is higher 2/3 It is usually small enough for the block to continue using the specified resistance coefficients.

User Coefficient

If for the parameter Loss coefficient model the value is set Custom The block uses user-defined loss parameters to describe the resistance coefficient in the pipe for each port.

For the user ratio, the block allows four configurations: confluence of flows, flow separation, perpendicular flows and counter flows:

flow merging — the flow enters nodes 1, 2 and 4 and exits node 3;
flow separation — the flow enters node 1 and exits nodes 2, 3 and 4;
perpendicular flows — the flow enters nodes 1 and 2 and exits nodes 3 and 4;
oncoming flows — the flow enters nodes 1 and 3 and exits nodes 2 and 4.

The figure shows the configuration data.

cross junction il 2 en

The block considers the connection as symmetrical with respect to the horizontal and vertical planes, so that and , where — the area of the corresponding port in the drawing. Using this symmetry, the block assumes that the resistance coefficients from 1 to 2 and from 1 to 4 are the same for merging, separation and oncoming flows.

During the simulation, the unit continuously checks the flow direction at each port and compares the result with four possible flow configurations. When the block determines the flow configuration, it adjusts the node corresponding to each port. For example, if the unit detects a separating flow in which liquid enters port A and exits ports B, C, and D, it assigns node 1 to port A, as shown in the first figure. Other figures show the designated nodes for the split stream entering ports other than A.

cross junction il 3

For a user factor, all four flow configurations can be implemented in a single block during simulation. You only need to set the parameters for each condition. When using two-element vectors to set flow coefficients, the block uses the first or second element, depending on whether node 1 coincides with a straight line or with a side branch. The first element corresponds to node 1 in port A or C, and the second element corresponds to node 1 in port B or D.

This table describes the conditions for each operating mode used to determine the resistance coefficients.

Flow Configuration

Separation from port A

0

Separation from port B

0

Separation from port C

0

Separation from port D

0

Merge to port A

0

Merge to port B

0

Merge to port C

0

Merge to port D

0

Perpendicular to the direct entrance A

0

Perpendicular to the direct entrance B

0

Perpendicular to the direct entrance C

0

Perpendicular to the direct entrance D

0

Oncoming traffic from the forward passage to the branch

0

Oncoming traffic from a branch line to a straight line

0

Motionless

—

1 or the last acceptable value

The flow is considered stationary if the mass flow conditions do not correspond to any given flow configuration. The block uses the following parameters to calculate the flow coefficients:

and — the first and second elements of the parameter Diverging flow straight loss coefficient accordingly;
and — the first and second elements of the parameter Diverging flow turning loss coefficient accordingly;
and — the first and second elements of the parameter Converging flow straight loss coefficient accordingly;
and — the first and second elements of the parameter Converging flow turning loss coefficient accordingly;
and — the first and second elements of the parameter Perpendicular flow straight loss coefficient accordingly;
and — the first and second elements of the parameter Perpendicular flow straight loss coefficient accordingly;
and — the first and second elements of the parameter Perpendicular flow straight loss coefficient accordingly;
and — the first and second elements of the parameter Colliding flow straight loss coefficient accordingly;
and — the first and second elements of the parameter Colliding flow turning loss coefficient accordingly.

Ports

Conserving

# A — liquid port
isothermal liquid

Details

Non-directional port, liquid inlet or outlet.

Program usage name

port_a

# B — liquid port
isothermal liquid

Details

Non-directional port, liquid inlet or outlet.

Program usage name

port_b

# C — liquid port
isothermal liquid

Details

Non-directional port, liquid inlet or outlet.

Program usage name

port_c

# D — liquid port
isothermal liquid

Details

Non-directional port, liquid inlet or outlet.

Program usage name

port_d

Parameters

Junction Properties

# Main line area (A,C) — 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 forward flow from port A to port C.

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

# Branch line area (B,D) — cross-sectional area of the lateral branches
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 lateral branches of the flow from port B to port D.

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	`side_area`
Evaluatable	Yes

# Critical Reynolds number — 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

# 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 diverging and converging flow.

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 thread configurations that exceed the acceptable limits. 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

# Diverging flow loss coefficients — the ability to specify resistance coefficients for flow separation

Details

Whether to specify resistance coefficients for flow separation.

Dependencies

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

Default value	`true (switched on)`
Program usage name	`enable_diverging_loss_coefficients`
Evaluatable	No

# Converging flow loss coefficients — the ability to specify resistance coefficients for merging flows

Details

Whether to specify resistance coefficients for merging flows.

Dependencies

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

Default value	`true (switched on)`
Program usage name	`enable_converging_loss_coefficients`
Evaluatable	No

# Perpendicular flow loss coefficients — the ability to specify resistance coefficients for perpendicular flows

Details

Whether to specify resistance coefficients for perpendicular flows.

Dependencies

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

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

# Colliding flow loss coefficients — the ability to specify resistance coefficients for oncoming flows

Details

Whether to specify resistance coefficients for oncoming flows.

Dependencies

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

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

Diverging Flow Coefficients

# Diverging flow straight loss coefficient — forward running resistance coefficient for flow separation

Details

Forward running resistance coefficient for flow separation. When setting this parameter as a vector, the first element represents the resistance coefficient when ports A or C coincide with node 1. The second element represents the resistance coefficient when ports B or D coincide with node 1. When using a scalar, the block behaves the same for all orientations.

Dependencies

To use this parameter, set for the parameter Loss coefficient model meaning Custom and check the box Diverging flow loss coefficients.

Default value	`[1.12, 1.12]`
Program usage name	`straight_diverging_loss_coefficient`
Evaluatable	Yes

# Diverging flow turning loss coefficient — coefficient of resistance of lateral branches for flow separation

Details

The coefficient of resistance of the lateral branches for flow separation. When setting this parameter as a vector, the first element represents the resistance coefficient when ports A or C coincide with node 1. The second element represents the resistance coefficient when ports B or D coincide with node 1. When using a scalar, the block behaves the same for all orientations.

Dependencies

To use this parameter, set for the parameter Loss coefficient model meaning Custom and check the box Diverging flow loss coefficients.

Default value	`[1.12, 1.12]`
Program usage name	`turning_diverging_loss_coefficient`
Evaluatable	Yes

Converging Flow Coefficients

# Converging flow straight loss coefficient — forward running resistance coefficient for flow fusion

Details

The coefficient of resistance of the forward stroke for merging flows. When setting this parameter as a vector, the first element represents the resistance coefficient when ports A or C coincide with node 1. The second element represents the resistance coefficient when ports B or D coincide with node 1. When using a scalar, the block behaves the same for all orientations.

Dependencies

To use this parameter, set for the parameter Loss coefficient model meaning Custom and check the box Converging flow loss coefficients.

Default value	`[1.12, 1.12]`
Program usage name	`straight_converging_loss_coefficient`
Evaluatable	Yes

# Converging flow turning loss coefficient — coefficient of resistance of lateral branches for merging flows

Details

The coefficient of resistance of the lateral branches for merging flows. When setting this parameter as a vector, the first element represents the resistance coefficient when ports A or C coincide with node 1. The second element represents the resistance coefficient when ports B or D coincide with node 1. When using a scalar, the block behaves the same for all orientations.

Dependencies

To use this parameter, set for the parameter Loss coefficient model meaning Custom and check the box Converging flow loss coefficients.

Default value	`[1.12, 1.12]`
Program usage name	`turning_converging_loss_coefficient`
Evaluatable	Yes

Perpendicular Flow Coefficients

# Perpendicular flow straight loss coefficient — forward running resistance coefficient for perpendicular flows

Details

The coefficient of resistance of the forward stroke for perpendicular flows. When setting this parameter as a vector, the first element represents the resistance coefficient when ports A or C coincide with node 1. The second element represents the resistance coefficient when ports B or D coincide with node 1. When using a scalar, the block behaves the same for all orientations.

Dependencies

To use this parameter, set for the parameter Loss coefficient model meaning Custom and check the box Perpendicular flow loss coefficients.

Default value	`[1.12, 1.12]`
Program usage name	`perpendicular_straight_loss_coefficient`
Evaluatable	Yes

# Perpendicular flow turning to inflow loss coefficient — coefficient of resistance of lateral branches with flowing perpendicular flows

Details

The coefficient of resistance when the flow is rotated perpendicular to the inflow. When setting this parameter as a vector, the first element represents the resistance coefficient when ports A or C coincide with node 1. The second element represents the resistance coefficient when ports B or D coincide with node 1. When using a scalar, the block behaves the same for all orientations.

Dependencies

To use this parameter, set for the parameter Loss coefficient model meaning Custom and check the box Perpendicular flow loss coefficients.

Default value	`[1.12, 1.12]`
Program usage name	`perpendicular_turning_in_loss_coefficient`
Evaluatable	Yes

# Perpendicular flow turning to outflow loss coefficient — coefficient of resistance of lateral branches with flowing perpendicular flows

Details

The coefficient of resistance for perpendicular rotation of the flow to the outflow. When setting this parameter as a vector, the first element represents the coefficient of resistance when ports A or C are adjacent to node 1. The second element represents the coefficient of resistance when ports B or D coincide with node 1. When using a scalar, the block behaves the same for all orientations.

Dependencies

To use this parameter, set for the parameter Loss coefficient model meaning Custom and check the box Perpendicular flow loss coefficients.

Default value	`[1.12, 1.12]`
Program usage name	`perpendicular_turning_out_loss_coefficient`
Evaluatable	Yes

Colliding Flow Coefficients

# Colliding flow straight loss coefficient — forward running resistance coefficient for oncoming flows

Details

Forward running resistance coefficient for oncoming flows. When setting this parameter as a vector, the first element represents the resistance coefficient when ports A or C coincide with node 1. The second element represents the resistance coefficient when ports B or D coincide with node 1. When using a scalar, the block behaves the same for all orientations.

Dependencies

To use this parameter, set for the parameter Loss coefficient model meaning Custom and check the box Colliding flow loss coefficients.

Default value	`[1.12, 1.12]`
Program usage name	`colliding_straight_loss_coefficient`
Evaluatable	Yes

# Colliding flow turning loss coefficient — coefficient of resistance of side branches for oncoming flows

Details

The coefficient of resistance of lateral branches for oncoming flows. When setting this parameter as a vector, the first element represents the resistance coefficient when ports A or C coincide with node 1. The second element represents the resistance coefficient when ports B or D coincide with node 1. When using a scalar, the block behaves the same for all orientations.

Dependencies

To use this parameter, set for the parameter Loss coefficient model meaning Custom and check the box Colliding flow loss coefficients.

Default value	`[1.12, 1.12]`
Program usage name	`colliding_turning_loss_coefficient`
Evaluatable	Yes

Literature

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