X-junction (P)#

The X-junction (P) block models the intersection of four branches of a pneumatic network at an angle of 90\(^o\).

Branch and flow type symbols:

Hint

The AC branch is the main one, the BD branch is the side one.

1. Calculation of loss coefficients#

With this setting, the user directly sets dimensionless loss coefficients for converging and diverging, perpendicular and counter flows:

divLossCoef – when three flows making part of an assembly merge into one common flow in the direction of the fourth vertex of the junction :

Fig. 3 Three flows making part of an assembly merge into one common flow in the direction of the fourth junction vertex#

convLossCoef – when an incoming flow on one of the vertices diverges into three flows towards the other three vertices :

Fig. 4 The incoming flow on one of the vertices diverges into three flows towards the other three vertices#

perpLossCoef - when the two flows entering the assembly are perpendicular and the two outgoing flows are perpendicular to the incoming ones and each other :

Fig. 5 The two flows entering the assembly are perpendicular and the two outgoing flows are perpendicular to the incoming ones and each other#

collLossCoef - for the case when two flows entering the assembly are opposite, and two outgoing flows form an angle of 90\(^о\):

Fig. 6 The two flows entering the assembly are opposite, and the two outgoing flows form an angle of 90° with the incoming flow#

Mass conservation equation(1) :

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

Pressure drop calculation (2) :

(2)#\[p_i-p_I=I_i+\frac{K_i/2 \cdot \dot{m_i}\cdot \sqrt{\dot{m_i}^2+\dot{m_{threshold}}^2}}{\bar \rho \cdot A^2_i} \]

where:

\(I=A, B, C, D\);

\(A_i\) – cross-sectional area of branch I, [m\(^2\)];

\(K_i\) – dimensionless loss factors on branch I;

\(I_i\) – gas inertia on branch I;

\(m_i\) – mass flow rate of gas through port I, [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 (3) :

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

where:

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

\( ho\) – gas density, [kg/m\(^3\)];

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

Calculation of inertia (4), (5), (6), (7) :

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

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

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

(7)#\[I_D=\ddot{m_D}\cdot \frac{\sqrt{\pi \cdot A_{main}}}{A_{side}}\]

2. Properties#

Property	Default Value	Description	Units of measurement
Main branch AC area	0.01	-	m\(^2\)
Side branch BD area	0.01	-	m\(^2\)
Critical Reynolds number	150.0	-	-
Loss coefficient for divergence flows (from 1 to 3)	1.12	-	-
Loss coefficient for convergence flows (from 3 to 1)	1.12	-	-
Loss coefficient for perpendicular flows (from 2 to 2)	1.12	-	-
Loss coefficient for colliding flows (from 2 to 2)	1.12	-	-

3. Inputs and outputs#

Parameters	Input/Output	Description	Units of measurement	Port type
Port A	Input	-	-	Pneumatics
Port B	Input	-	-	Pneumatics
Port С	Input	-	-	Pneumatics
Port D	Input	-	-	Pneumatics

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