# Cross-Junction (TL)

Cross-junction in a thermal liquid network

• Library:
• Simscape / Fluids / Thermal Liquid / Pipes & Fittings

## Description

The Cross-Junction (TL) block represents a four-way junction in an thermal 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

`${\stackrel{˙}{m}}_{A}+{\stackrel{˙}{m}}_{B}+{\stackrel{˙}{m}}_{C}+{\stackrel{˙}{m}}_{D}=0,$`

where 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 A1,2,3,4 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

`${p}_{i}-{p}_{1}={I}_{i}+\frac{{k}_{i}}{2}{\stackrel{˙}{m}}_{i}\sqrt{{\stackrel{˙}{m}}_{i}^{2}+{\stackrel{˙}{m}}_{threshold}^{2}}}{\overline{\rho }{A}_{i}^{2}},$`

where:

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

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

• p1 is the pressure at node 1.

• ki 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.

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

The block calculates the inertia for each port as

`$\begin{array}{l}{I}_{A}={\stackrel{¨}{m}}_{A}\frac{\sqrt{\pi {A}_{side}}}{{A}_{main}}\\ {I}_{B}={\stackrel{¨}{m}}_{B}\frac{\sqrt{\pi {A}_{main}}}{{A}_{side}}\\ {I}_{C}={\stackrel{¨}{m}}_{C}\frac{\sqrt{\pi {A}_{side}}}{{A}_{main}}\\ {I}_{D}={\stackrel{¨}{m}}_{D}\frac{\sqrt{\pi {A}_{main}}}{{A}_{side}}\end{array}$`

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

Flow ScenarioABCDkAkBkCkD
Diverging from node A>thresh<-ṁthresh<-ṁthresh<-ṁthresh0kdiv,turning,mainkdiv,straight,mainkdiv,turning,main
Diverging from node B<-ṁthresh>thresh<-ṁthresh<-ṁthreshkdiv,turning,side0kdiv,turning,sidekdiv,straight,side
Diverging from node C<-ṁthresh<-ṁthresh>thresh<-ṁthreshkdiv,straight,mainkdiv,turning,main0kdiv,turning,main
Diverging from node D<-ṁthresh<-ṁthresh<-ṁthresh>threshkdiv,turning,sidekdiv,straight,sidekdiv,turning,side0
Converging to node A<-ṁthresh>thresh>thresh>thresh0kconv,turning,mainkconv,straight,mainkconv,turning,main
Converging to node B>thresh<-ṁthresh>thresh>threshkconv,turing,side0kconv,turing,sidekconv,straight,side
Converging to node C>thresh>thresh<-ṁthresh>threshkconv,straight,mainkconv,turning,main0kconv,turning,main
Converging to node D>thresh>thresh>thresh<-ṁthreshkconv,turing,sidekconv,straight,sidekconv,turing,side0
Perpendicular with main entry A>thresh>thresh<-ṁthresh<-ṁthresh0kperp,turning in,mainkperp,straight,mainkperp,turning out,main
Perpendicular with main entry B<-ṁthresh>thresh>thresh<-ṁthreshkperp,turning out,side0kperp,turning in,sidekperp,turning straight,side
Perpendicular with main entry C<-ṁthresh<-ṁthresh>thresh>threshkperp,straight,mainkperp,turning out,main0kperp,turning in,main
Perpendicular with main entry D>thresh<-ṁthresh<-ṁthresh>threshkperp,turning in,sidekperp,turning straight,sidekperp,turning out,side0
Colliding from main to branch >thresh<-ṁthresh>thresh<-ṁthresh0kcoll,turning,mainkcoll,straight,mainkcoll,turning,main
Colliding from branch to main<-ṁthresh>thresh<-ṁthresh>threshkcoll,turning,side0kcoll,turning,sidekcoll,straight,side
Stagnant1 or last valid1 or last valid1 or last valid1 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.

• kdiv,straight,main and kdiv,straight,side are the first and second elements Diverging flow straight loss coefficient parameter, respectively.

• kdiv,turning,main and kdiv,turning,side are the first and second elements Diverging flow turning loss coefficient parameter, respectively.

• kconv,straight,main and kconv,straight,side are the first and second elements Converging flow straight loss coefficient parameter, respectively.

• kconv,turning,main and kconv,turning,side are the first and second elements Converging flow turning loss coefficient parameter, respectively.

• kperp,straight,main and kperp,straight,side are the first and second elements Perpendicular flow straight loss coefficient parameter, respectively.

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

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

• kcoll,straight,main and kcoll,straight,side are the first and second elements Colliding flow straight loss coefficient parameter, respectively.

• kcoll,turning,main and kcoll,turning,side are the first and second elements Colliding flow turning loss coefficient parameter, respectively.

The block conserves energy such that

`${\phi }_{A}+{\phi }_{B}+{\phi }_{C}+{\phi }_{D}=0.$`

## Ports

### Conserving

expand all

Thermal liquid conserving port.

Thermal liquid conserving port.

Thermal liquid conserving port.

Thermal liquid conserving port.

## Parameters

expand all

### Junction Properties

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

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

Upper Reynolds number limit for laminar flow through the junction.

Whether to specify loss coefficients for diverging flow.

Whether to specify loss coefficients for converging flow.

Whether to specify loss coefficients for perpendicular flow.

Whether to specify loss coefficients for colliding flow.

### Diverging Flow Coefficients

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.

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

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.

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

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.

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.

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

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.

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.

## Version History

Introduced in R2022b