.. _chap_merger: Merger ------ .. figure:: ../media/image582.png :figwidth: 1.77083in :align: center Schematic wanda component merger +------------+--------------------------------------------------------------------------------+--------+ | type label | description | active | +============+================================================================================+========+ | 2-merger | Three-node junction which merges 2 separate branch flows into a combined flow. | no | | | | | | | Cross section can be circular or rectangular. | | +------------+--------------------------------------------------------------------------------+--------+ The merger differs from the Y-junctions (:numref:`chap_y-junction`) 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 (:numref:`chap_splitter`). .. _mathematical-model-19: Mathematical model ^^^^^^^^^^^^^^^^^^ .. _positive-flow-definition-3: 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 (:numref:`chap_splitter`). For the Merger\ **-junction** the positive flow definition and connect point numbers are defined in the figure below. .. figure:: ../media/image583.png :figwidth: 2.21875in :align: center Merger\ **-junction** positive flow direction and connection points. .. _flow-regimes-3: 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) .. image:: ../media/image584.png :width: 1.3125in :height: 1.08333in ============================== ============================== ============================== ============================= Splitting flow (Negative flow) .. image:: ../media/image585.png :width: 1.3125in :height: 1.08333in ============================== ============================= ============================== ============================= Not supported flow regimes .. image:: ../media/image586.png :width: 1.3125in :height: 1.08333in ============================== ============================= ============================== ============================= Not supported flow regimes .. image:: ../media/image587.png :width: 1.3125in :height: 1.08333in ============================== ============================= .. _equations-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: .. math:: f_{1}=Q_{1}+Q_{2}-Q_{3}=0 Where: ===================================================== =============== Q :sub:`i` = total discharge in leg i [m\ :sup:`3`/s] ===================================================== =============== H\ :sub:`i` = energy head in connect point i [m] A\ :sub:`i` = pipe area leg i (leg with total flow) [m\ :sup:`2`] ξ\ :sub:`ij` = 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 (:numref:`chap_splitter`) will be used with Q\ :sub:`1` taken into account instead of Q\ :sub:`3`. For the not supported flow regimes the head loss equation becomes *H\ 1-H\ 3 = 0* and *H\ 2-H\ 3 = 0* Merger properties ^^^^^^^^^^^^^^^^^ The input and output properties for both types are specified below. Input properties +-------------------------+----------------+------+-------+----------+----------------------------------+ | Description | input | unit | range | default | Remarks | +=========================+================+======+=======+==========+==================================+ | Cross section | Circular | | | Circular | | | | | | | | | | | Rectangular | | | | | +-------------------------+----------------+------+-------+----------+----------------------------------+ | 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 :numref:`fig_merger_angle`. .. _fig_merger_angle: .. figure:: ../liquid/media/merger1248.png :figwidth: 2.85417in :align: center 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 | | | | if Xi tables = Splitting or Both | | | | | | | | | | (ξ\ :sub:`12`) | | | | | +-------------------------+----------------+------+-------+----------+----------------------------------+ | Xi splitting branch 2 | Table | | | | if Xi tables = Splitting or Both | | | | | | | | | | (ξ\ :sub:`13`) | | | | | +-------------------------+----------------+------+-------+----------+----------------------------------+ | Xi merging branch 1 | Table | | | | if Xi tables = Merging or Both | | | | | | | | | | (ξ\ :sub:`21`) | | | | | +-------------------------+----------------+------+-------+----------+----------------------------------+ | Xi merging branch 2 | Table | | | | if Xi tables = Merging or Both | | | | | | | | | | (ξ\ :sub:`31`) | | | | | +-------------------------+----------------+------+-------+----------+----------------------------------+ 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 ξ\ :sub:`13` for positive flow and ξ\ :sub:`31` for negative flow | +===============================+=========================================================================+ | Loss coefficient branch 2 [-] | The ξ\ :sub:`23` for positive flow and ξ\ :sub:`32` for negative flow | +-------------------------------+-------------------------------------------------------------------------+ | Head loss branch 1 [m] | The ΔH\ :sub:`13` for positive flow and ΔH\ :sub:`31` for negative flow | +-------------------------------+-------------------------------------------------------------------------+ | Head loss branch 2 [m] | The ΔH\ :sub:`23` for positive flow and ΔH\ :sub:`32` for negative flow | +-------------------------------+-------------------------------------------------------------------------+ Component messages ========================= ==== ========================= Message Type Explanation ========================= ==== ========================= Merging flow Info |image114| Splitting flow Info |image115| Not supported flow regime Info |image116| or\ |image117| ========================= ==== ========================= .. include:: substitutions_liquid.rst