4.27. Splitter

Fig. 4.27.1 Splitter

type label	description	active
2-splitter	Three-node junction which splits up a combined flow into 2 separate branch flows. Cross section can be circular or rectangular.	no

The splitter differs from the Y-junctions (Section 4.40) because there is no straight main flow. The area of the three legs may be different.

The Splitter component acts as a Merger component (Section 4.16) in the case of negative flow.

4.27.1. Mathematical model

4.27.1.1. Positive flow definition

The definition for the positive direction of flow (and velocity) together with the location of the connect point numbers is important to understand the results in the property window. Notice that the connect point numbering of the Splitter differs from that of the Merger (Section 4.16).

The positive flow definition and the numbers of the connect points are defined in the figure below for the Splitter-junction.

Fig. 4.27.2 Positive flow direction

4.27.1.2. Flow regimes

The Splitter supports only the positive dividing flow and for negative flow the merging variant. The other flow regimes are not supported and for these circumstances the local losses are ignored, that means the splitter becomes frictionless.

In the table below the different flow regimes are explained with a scheme with corresponding actual flow arrows.

Table 1: definition of different flow regimes

Splitting flow (Positive flow)

Merging flow (Negative flow)

Not supported flow regimes

Not supported flow regimes

4.27.1.3. Equations

The head loss over a 3-node component depends on the distribution of the discharges and the area of the connected legs. The Splitter supports only the user specified resistance coefficient Xi (ξ) depending on discharge ratio’s for a fixed area ratio.

The head loss in 3-node components is a function of the combined flow in leg 1. Including the continuity equation (no production or loss of mass in the component) the general set of the three equations of the Y-junction is:

(4.27.1)\[f_{1}=Q_{1}-Q_{2}-Q_{3}=0\]

Where:

Qi = total discharge in leg i	[m3/s]
Hi = energy head in connect point i	[m]
Ai = pipe area leg i (leg with total flow)	[m2]
ξij = loss coefficient between point i and j	[-]

The subscripts (1), (2) and (3) correspond to the different legs.

For negative merging flow the formulas of the Merger component (Section 4.16) will be used with Q₁ taken into account instead of Q₃.

For the not supported flow regimes the head loss equation becomes H1-H2 = 0 and H1-H3 = 0

4.27.2. Splitter properties

The input and output properties for both types are specified below.

Input properties

Description	input	unit	range	default	Remarks
Cross section	Circular Rectangular			Circular
Diameter combined leg	Real	[mm]			If Cross section = Circular
Diameter split branch 1	Real	[mm]			If Cross section = Circular
Diameter split branch 2	Real	[mm]			If Cross section = Circular
Width combined leg	Real	[mm]			If Cross section = Rectangular
Height combined leg	Real	[mm]			If Cross section = Rectangular
Width split branch 1	Real	[mm]			If Cross section = Rectangular
Height split branch 1	Real	[mm]			If Cross section = Rectangular
Width split branch 2	Real	[mm]			If Cross section = Rectangular
Height split branch 2	Real	[mm]			If Cross section = Rectangular
Xi method	Formula Table

If Xi method = Formula, the following input should be defined:

Description	input	unit	range	default	Remarks
Angle	15 30 45

De definition of the angle is shown in Fig. 4.27.3.

Fig. 4.27.3 Definition of the angle

If Xi method = Table, the following input should be defined:

Description	input	unit	range	default	Remarks
Xi tables valid for	Splitting Merging Both
Xi splitting branch 1	Table (ξ12)				if Xi tables = Splitting or Both
Xi splitting branch 2	Table (ξ13)				if Xi tables = Splitting or Both
Xi merging branch 1	Table (ξ21)				if Xi tables = Merging or Both
Xi merging branch 2	Table (ξ31)				if Xi tables = Merging or Both

Example of a Xi table (valid for Area ratio = 0.5); splitting branch 1 (ξ₁₂)

Discharge ratio	Xi
[-]	[-]
0.0	0.90
0.2	0.12
0.4	0.39
0.6	0.92
0.8	1.48
1.0	2.08

Component specific output properties

Loss coefficient branch 1 [-]	The ξ12 for positive flow and ξ21 for negative flow
Loss coefficient branch 2 [-]	The ξ13 for positive flow and ξ31 for negative flow
Head loss branch 1 [m]	The ΔH12 for positive flow and ΔH21 for negative flow
Head loss branch 2 [m]	The ΔH13 for positive flow and ΔH31 for negative flow

Component messages

Message	Type	Explanation
Splitting flow	Info
Merging flow	Info
Not supported flow regime - no resistance used	Info	or