Y-junction (IH)#

The Y-junction (IH) block simulates the junction of three branches of the hydraulic network at an arbitrary angle. To calculate the loss coefficients at the junction of flows, one can choose one of three correlation options in accordance with the values of Loss coefficient model property:

According to Idelchik;
Custom.

Branch and flow type symbols:

Hint

The AIB branch is the main one, the CI branch is the side one.

1. Idelchik’s Loss Calculation#

The loss coefficients for converging and diverging flows are equal and are defined for the main and side branches as follows (1), (2), (3), (6):

(1)#\[K_{side,conv}=(1+(\frac{\dot{m_C}}{\dot{m_B}}\cdot \frac{A_B}{A_C})^2-2 \cdot(\frac{A_B}{A_A})\cdot (1-\frac{\dot{m_C}}{\dot{m_B}})^2-2 \cdot cos \alpha \cdot \frac{A_B}{A_C}\cdot (\frac{\dot{m_C}}{\dot{m_B}})^2)\cdot (\frac{\dot{m_C}}{\dot{m_B}}\cdot \frac{A_C}{A_B})^{-2}\]

(2)#\[K_{main,conv}=(1-(1-\frac{\dot{m_C}}{\dot{m_B}})^2-2 \cdot cos \alpha \cdot \frac{A_B}{A_C}\cdot (\frac{\dot{m_C}}{\dot{m_B}})^2)\cdot (1-(\frac{\dot{m_C}}{\dot{m_B}})^2)^{-1}\]

(3)#\[K_{side,div}=A'\cdot(1+(\frac{\dot{m_C}}{\dot{m_B}}\cdot \frac{A_B}{A_C})^2-2 \cdot cos \alpha \cdot \frac{A_B}{A_C}\cdot \frac{\dot{m_C}}{\dot{m_B}})\cdot (\frac{\dot{m_C}}{\dot{m_B}}\cdot \frac{A_C}{A_B})^{-2}\]

where \(A'\) coefficient is defined as (4) :

(4)#\[A'=\frac{1}{2}\cdot (1+tanh(\frac{4\cdot (R_{A'}-0.8)}{0.8}))+\frac{0.9}{2}\cdot (1-tanh(\frac{4\cdot (R_{A'}-0.8)}{0.8}))\]

where \(R_{A'}\) coefficient is defined as (5) :

(5)#\[R_{A'}=\frac{\sqrt{\dot{m^2_C}+\dot{m^2_{thresh}}}}{\sqrt{\dot{m^2_B}+\dot{m^2_{thresh}}}}\]

(6)#\[K_{main,div}=0.4 \cdot (1-\frac{\dot{m_A}}{\dot{m_B}}\cdot\frac{A_B}{A_A})^2\cdot (\frac{\dot{m_A}}{\dot{m_B}})^{-2}\]

User Loss Factors:

With this setting, the user directly sets dimensionless loss coefficients for converging and diverging flows on the main and side branches:

\(K_{main,conv}\) – divergent flow on the main branch;

\(K_{main,div}\) – converging flow on the main branch;

\(K_{side,conv}\) – divergent flow on the side branch;

\(K_{side,div}\) – converging flow on the side branch.

Mass conservation equation (7) :

(7)#\[m_A+m_B+m_C=0\]

Pressure drop calculation (8), (9), (10) :

(8)#\[p_A-p_I=I_A+\frac{K_A}{2\cdot \bar \rho \cdot A^2_{main}}\cdot \dot{m_A} \cdot \sqrt{\dot{m_A}^2+\dot{m_{thresh}}^2}\]

(9)#\[p_B-p_I=I_B+\frac{K_B}{2\cdot \bar \rho \cdot A^2_{main}}\cdot \dot{m_B} \cdot \sqrt{\dot{m_B}^2+\dot{m_{thresh}}^2}\]

(10)#\[p_C-p_I=I_C+\frac{K_C}{2\cdot \bar \rho \cdot A^2_{side}}\cdot \dot{m_C} \cdot \sqrt{\dot{m_C}^2+\dot{m_{thresh}}^2}\]

where:

\(A_{main}\) – main branch cross-sectional area, [m\(^2\)];

\(A_{side}\) – side branch cross-sectional area, [m\(^2\)];

\(K_A, K_B, K_C\) – dimensionless loss coefficients on branches AI, BI, CI respectively;

\(I_A, I_B, I_C\) – liquid inertia on branches AI, BI, CI respectively;

\(m_A, m_B, m_C\) – mass flow rate of liquid through ports A, B, C, respectively, [kg/s].

\(m_{thresh}\) – threshold flow rate, below which the flow is considered stagnant and cannot be defined as converging or diverging. Calculated using the following formula (11) :

(11)#\[\dot{m_{thresh}}=Re_{crit} \cdot \nu \cdot \bar \rho \cdot \sqrt{\frac{\pi}{4}\cdot A_{min}}\]

where:

\(A_{min}\) – minimum area of the side and main branches, [m\(^2\)];

\( ho\) – liquid density, [kg/m\(^3\)];

\( u\) – liquid kinematic viscosity, [mm\(^2\)/s].

Calculation of inertia (12), (13), (14) :

(12)#\[I_A=\ddot{m_A}\cdot \frac{\sqrt{\pi \cdot A_{side}}}{A_{main}}\]

(13)#\[I_B=\ddot{m_B}\cdot \frac{\sqrt{\pi \cdot A_{side}}}{A_{main}}\]

(14)#\[I_C=\ddot{m_C}\cdot \frac{\sqrt{\pi \cdot A_{main}}}{A_{side}}\]

2. Properties#

Property	Default Value	Description	Units of measurement
Loss coefficient model: Idelchik; Custom	Idelchik	-	-
Main branch area	0.01	-	m\(^2\)
Side branch area	0.01	-	m\(^2\)
Junction angle, available when selecting `Loss coefficient model` - `Idelchik`	45.0	-	\(^о\)
Critical Reynolds number	150.0	-	-
Loss coefficient for main branch (convergence flow), available when selecting `Loss coefficient model` - `Custom`	1.12	-	-
Loss coefficient for main branch (divergence flow), available when selecting `Loss coefficient model` - `Custom`	1.12	-	-
Loss coefficient for side branch (convergence flow), available when selecting `Loss coefficient model` - `Custom`	1.12	-	-
Loss coefficient for side branch (divergence flow), available when selecting `Loss coefficient model` - `Custom`	1.12	-	-

3. Inputs and outputs#

Parameters	Input/Output	Description	Units of measurement	Port type
Port A	Input	-	-	Isothermal Hydraulics
Port B	Input	-	-	Isothermal Hydraulics
Port C	Input	-	-	Isothermal Hydraulics

In order to see the connection capabilities of the block, you need to go to page Description of block ports