Cross-Junction (IL)

Cross-junction in an isothermal liquid network

Since R2022b

• 

Libraries:
Simscape / Fluids / Isothermal Liquid / Pipes & Fittings

Description

The Cross-Junction (IL) block represents a four-way junction in an isothermal liquid network. The block abstracts the fluid interactions depending on the direction of flow at each port, where ports A and C are the main line and ports B and D are the branch line. The block defines four unique flow configurations: diverging flow, converging flow, perpendicular flow, and colliding flow. All four configurations can occur in the same block during a simulation. You only need to supply parameters for each condition that the block experiences. The block conserves mass such that

$${\dot{m}}_A+{\dot{m}}_B+{\dot{m}}_C+{\dot{m}}_D=0,$$

where ṁ_i is the mass flow rate for a given port, i.

The possible flow configurations are:

• Diverging flow — Flow enters at node 1 and exits at nodes 2, 3, and 4.

• Converging flow — Flow enters at nodes 1, 2, and 4 and exits at node 3.

• Perpendicular flow — Flow enters at nodes 1 and 2 and exits at nodes 3 and 4.

• Colliding flow — Flow enters at nodes 1 and 3 and exits at nodes 2 and 4.

This figure demonstrates these configurations.

The block takes advantage of simplifying assumptions to reduce the total number of parameters that you need to provide. The block treats the junction as symmetrical about both the horizontal and vertical planes such that A₁ = A₃, and A₂ = A₄, where A_1,2,3,4 is the area of the corresponding port in the figure. Using this symmetry, the block assumes the loss coefficients from 1 to 2 and from 1 to 4 are identical during diverging, converging, and colliding flow.

During simulation, the block continually checks the direction of flow at each port and compares the result to the four possible flow configurations. When the block determines the flow configuration, it adjusts the node that each port corresponds to. For example, when the block experiences diverging flow where the fluid enters at port C and exits at ports A, B, and D, it assigns node 1 to port C as in the figure.

If you use two-element vectors to specify the flow coefficients, the block uses the first or second element depending on whether node 1 aligns with the main line or the branch line. The first element corresponds to node 1 at port A or C, and the second element corresponds to node 1 at port B or D. The block determines which coefficient and which vector element to use, then computes the pressure difference to conserve momentum such that

$$p_i-p_1=I_i+\frac{\raisebox{1ex}{$k_i$}\!\left/ \!\raisebox{-1ex}{$2$}\right.{\dot{m}}_i\sqrt{{\dot{m}}_i^2+{\dot{m}}_{threshold}^2}}{\overline{\rho }{A}_i^2},$$

where:

• $$\overline{\rho }$$ is the average fluid density.

• p_i is the pressure for a given port, i.

• p₁ is the pressure at node 1.

• k_i is the flow coefficient that the block assigns to a given port, i. This value can be either the turning flow or straight flow coefficient, depending on the port.

• I_i is the fluid inertia for a given port, i.

The block calculates the inertia for each port as

$$\begin{array}{l}{I}_A={\ddot{m}}_A\frac{\sqrt{\pi A_{side}}}{A_{main}}\\ I_B={\ddot{m}}_B\frac{\sqrt{\pi A_{main}}}{A_{side}}\\ I_C={\ddot{m}}_C\frac{\sqrt{\pi A_{side}}}{A_{main}}\\ I_D={\ddot{m}}_D\frac{\sqrt{\pi A_{main}}}{A_{side}}\end{array}$$

The block uses mode charts to determine the value of k_i. This table describes the conditions and coefficients for each operational mode.

Flow Scenario	ṁA	ṁB	ṁC	ṁD	kA	kB	kC	kD
Diverging from node A	>ṁthresh	<-ṁthresh	<-ṁthresh	<-ṁthresh	0	kdiv,turning,main	kdiv,straight,main	kdiv,turning,main
Diverging from node B	<-ṁthresh	>ṁthresh	<-ṁthresh	<-ṁthresh	kdiv,turning,side	0	kdiv,turning,side	kdiv,straight,side
Diverging from node C	<-ṁthresh	<-ṁthresh	>ṁthresh	<-ṁthresh	kdiv,straight,main	kdiv,turning,main	0	kdiv,turning,main
Diverging from node D	<-ṁthresh	<-ṁthresh	<-ṁthresh	>ṁthresh	kdiv,turning,side	kdiv,straight,side	kdiv,turning,side	0
Converging to node A	<-ṁthresh	>ṁthresh	>ṁthresh	>ṁthresh	0	kconv,turning,main	kconv,straight,main	kconv,turning,main
Converging to node B	>ṁthresh	<-ṁthresh	>ṁthresh	>ṁthresh	kconv,turing,side	0	kconv,turing,side	kconv,straight,side
Converging to node C	>ṁthresh	>ṁthresh	<-ṁthresh	>ṁthresh	kconv,straight,main	kconv,turning,main	0	kconv,turning,main
Converging to node D	>ṁthresh	>ṁthresh	>ṁthresh	<-ṁthresh	kconv,turing,side	kconv,straight,side	kconv,turing,side	0
Perpendicular with main entry A	>ṁthresh	>ṁthresh	<-ṁthresh	<-ṁthresh	0	kperp,turning in,main	kperp,straight,main	kperp,turning out,main
Perpendicular with main entry B	<-ṁthresh	>ṁthresh	>ṁthresh	<-ṁthresh	kperp,turning out,side	0	kperp,turning in,side	kperp,turning straight,side
Perpendicular with main entry C	<-ṁthresh	<-ṁthresh	>ṁthresh	>ṁthresh	kperp,straight,main	kperp,turning out,main	0	kperp,turning in,main
Perpendicular with main entry D	>ṁthresh	<-ṁthresh	<-ṁthresh	>ṁthresh	kperp,turning in,side	kperp,turning straight,side	kperp,turning out,side	0
Colliding from main to branch	>ṁthresh	<-ṁthresh	>ṁthresh	<-ṁthresh	0	kcoll,turning,main	kcoll,straight,main	kcoll,turning,main
Colliding from branch to main	<-ṁthresh	>ṁthresh	<-ṁthresh	>ṁthresh	kcoll,turning,side	0	kcoll,turning,side	kcoll,straight,side
Stagnant	–	–	–	–	1 or last valid	1 or last valid	1 or last valid	1 or last valid

The flow is stagnant when the mass flow rate conditions do not match any defined flow scenario. The block uses these parameters to calculate the flow coefficients.

• k_{div,straight,main} and k_{div,straight,side} are the first and second elements Diverging flow straight loss coefficient parameter, respectively.

• k_{div,turning,main} and k_{div,turning,side} are the first and second elements Diverging flow turning loss coefficient parameter, respectively.

• k_{conv,straight,main} and k_{conv,straight,side} are the first and second elements Converging flow straight loss coefficient parameter, respectively.

• k_{conv,turning,main} and k_{conv,turning,side} are the first and second elements Converging flow turning loss coefficient parameter, respectively.

• k_{perp,straight,main} and k_{perp,straight,side} are the first and second elements Perpendicular flow straight loss coefficient parameter, respectively.

• k_{perp,turning in,main} and k_{perp,turning in,side} are the first and second elements Perpendicular flow straight loss coefficient parameter, respectively.

• k_{perp,turning out,main} and k_{perp,turning out,side} are the first and second elements Perpendicular flow straight loss coefficient parameter, respectively.

• k_{coll,straight,main} and k_{coll,straight,side} are the first and second elements Colliding flow straight loss coefficient parameter, respectively.

• k_{coll,turning,main} and k_{coll,turning,side} are the first and second elements Colliding flow turning loss coefficient parameter, respectively.

Ports

Conserving

A — Liquid port

isothermal liquid

Isothermal liquid conserving port.

B — Liquid port

isothermal liquid

Isothermal liquid conserving port.

C — Liquid port

isothermal liquid

Isothermal liquid conserving port.

D — Liquid port

isothermal liquid

Isothermal liquid conserving port.

Parameters

Junction Properties

Main line area (A,C) — Area of main path

0.01 m^2 (default) | positive scalar

Cross-sectional area of the main flow path from port A to port C.

Branch line area (B,D) — Area of branch path

0.01 m^2 (default) | positive scalar

Cross-sectional area of the branch flow path from port B to port D.

Critical Reynolds number — Upper Reynolds number limit for laminar flow

150 (default) | positive scalar

Upper Reynolds number limit for laminar flow through the junction.

Diverging flow loss coefficients — Option to specify loss coefficients for diverging flow

On (default) | Off

Whether to specify loss coefficients for diverging flow.

Converging flow loss coefficients — Option to specify loss coefficients for converging flow

On (default) | Off

Whether to specify loss coefficients for converging flow.

Perpendicular flow loss coefficients — Option to specify loss coefficients for perpendicular flow

Off (default) | On

Whether to specify loss coefficients for perpendicular flow.

Colliding flow loss coefficients — Option to specify loss coefficients for colliding flow

Off (default) | On

Whether to specify loss coefficients for colliding flow.

Diverging Flow Coefficients

Diverging flow straight loss coefficient — Diverging flow straight loss coefficient

[1.12, 1.12] (default) | positive scalar or vector

Loss coefficient for the straight portion of the diverging flow. When you specify this parameter as a vector, the first element represents the loss coefficient when ports A or C align to reference node 1. The second element represents when ports B or D align to reference node 1. The block behaves the same for all orientations when you use a scalar.

Dependencies

To enable this parameter, select the Diverging flow loss coefficients parameter.

Diverging flow turning loss coefficient — Diverging flow turning loss coefficient

[1.12, 1.12] (default) | positive scalar or vector

Loss coefficient for the turning portions of the diverging flow. When you specify this parameter as a vector, the first element represents the loss coefficient when ports A or C align to reference node 1. The second element represents when ports B or D align to reference node 1. The block behaves the same for all orientations when you use a scalar.

Dependencies

To enable this parameter, select the Diverging flow loss coefficients parameter.

Converging Flow Coefficients

Converging flow straight loss coefficient — Converging flow straight loss coefficient

[1.12, 1.12] (default) | positive scalar or vector

Loss coefficient for the straight portion of the converging flow. When you specify this parameter as a vector, the first element represents the loss coefficient when ports A or C align to reference node 1. The second element represents when ports B or D align to reference node 1. The block behaves the same for all orientations when you use a scalar.

Dependencies

To enable this parameter, select the Converging flow loss coefficients parameter.

Converging flow turning loss coefficient — Converging flow turning loss coefficient

[1.12, 1.12] (default) | positive scalar or vector

Loss coefficient for the turning portions of the converging flow. When you specify this parameter as a vector, the first element represents the loss coefficient when ports A or C align to reference node 1. The second element represents when ports B or D align to reference node 1. The block behaves the same for all orientations when you use a scalar.

Dependencies

To enable this parameter, select the Converging flow loss coefficients parameter.

Perpendicular Flow Coefficients

Perpendicular flow turning to inflow loss coefficient — Perpendicular flow turning to inflow loss coefficient

[1.12, 1.12] (default) | positive scalar or vector

Loss coefficient for the flow turning to inflow in the perpendicular flow. When you specify this parameter as a vector, the first element represents the loss coefficient when ports A or C align to reference node 1. The second element represents when ports B or D align to reference node 1. The block behaves the same for all orientations when you use a scalar.

Dependencies

To enable this parameter, select the Perpendicular flow loss coefficients parameter.

Perpendicular flow turning to outflow loss coefficient — Perpendicular flow turning to outflow loss coefficient

[1.12, 1.12] (default) | positive scalar or vector

Loss coefficient for the flow turning to outflow in the perpendicular flow. When you specify this parameter as a vector, the first element represents the loss coefficient when ports A or C align to reference node 1. The second element represents when ports B or D align to reference node 1. The block behaves the same for all orientations when you use a scalar.

Dependencies

To enable this parameter, select the Perpendicular flow loss coefficients parameter.

Perpendicular flow straight loss coefficient — Perpendicular flow straight loss coefficient

[1.12, 1.12] (default) | positive scalar or vector

Loss coefficient for the straight portion of the perpendicular flow. When you specify this parameter as a vector, the first element represents the loss coefficient when ports A or C align to reference node 1. The second element represents when ports B or D align to reference node 1. The block behaves the same for all orientations when you use a scalar.

Dependencies

To enable this parameter, select the Perpendicular flow loss coefficients parameter.

Colliding Flow Coefficients

Colliding flow turning loss coefficient — Colliding flow turning loss coefficient

[1.12, 1.12] (default) | positive scalar or vector

Loss coefficient for the turning portion of the colliding flow. When you specify this parameter as a vector, the first element represents the loss coefficient when ports A or C align to reference node 1. The second element represents when ports B or D align to reference node 1. The block behaves the same for all orientations when you use a scalar.

Dependencies

To enable this parameter, select the Colliding flow loss coefficients parameter.

Colliding flow straight loss coefficient — Colliding flow straight loss coefficient

[1.12, 1.12] (default) | positive scalar or vector

Loss coefficient for the turning portion of the colliding flow. When you specify this parameter as a vector, the first element represents the loss coefficient when ports A or C align to reference node 1. The second element represents when ports B or D align to reference node 1. The block behaves the same for all orientations when you use a scalar.

Dependencies

To enable this parameter, select the Colliding flow loss coefficients parameter.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2022b