4.16. Merger

Fig. 4.16.1 Schematic wanda component merger

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

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

Instead of negative flow the Merger component acts as a Splitter component (Section 4.27).

4.16.1. Mathematical model

4.16.1.1. Positive flow definition

The positive flow definition and the numbers of the connect points is important to understand the results in the property window. Notice that the connect point numbering of the Merger differs from that of the Splitter (Section 4.27).

For the Merger-junction the positive flow definition and connect point numbers are defined in the figure below.

Fig. 4.16.2 Merger-junction positive flow direction and connection points.

4.16.1.2. Flow regimes

The Merger supports only the positive merging flow and for negative flow the splitting variant. The other flow regimes are not supported and for these circumstances the local losses are ignored, that means the Merger 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

Merging flow (Positive flow)

Splitting flow (Negative flow)

Not supported flow regimes

Not supported flow regimes

4.16.1.3. Equations

The head loss over a 3-node component depends on the distribution of the discharges and the area of the connected legs. The Merger 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 the combined leg. 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:

(4.16.1)$$f_1=Q_1+Q_2-Q_3=0$$

Where:

Q i = 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 splitting flow the formulas of the Splitter component (Section 4.27) will be used with Q₁ taken into account instead of Q₃.

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

4.16.2. Merger 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 merge branch 1	Real	[mm]			If Cross section = Circular
Diameter merge 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 merge branch 1	Real	[mm]			If Cross section = Rectangular
Height merge branch 1	Real	[mm]			If Cross section = Rectangular
Width merge branch 2	Real	[mm]			If Cross section = Rectangular
Height merge 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. 4.16.3.

Fig. 4.16.3 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 Xi table (valid for Area ratio = 0.5); Merging branch 1 (ξ13)

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 ξ13 for positive flow and ξ31 for negative flow
Loss coefficient branch 2 [-]	The ξ23 for positive flow and ξ32 for negative flow
Head loss branch 1 [m]	The ΔH13 for positive flow and ΔH31 for negative flow
Head loss branch 2 [m]	The ΔH23 for positive flow and ΔH32 for negative flow

Component messages

Message	Type	Explanation
Merging flow	Info
Splitting flow	Info
Not supported flow regime	Info	or