.. _chap_splitter: Splitter -------- .. figure:: ../media/image714.png :figwidth: 1.85417in :align: center Splitter +--------------+-----------------------------------------------------------------------------------+--------+ | type label | description | active | +==============+===================================================================================+========+ | 2-splitter | Three-node junction which splits up a combined flow into 2 separate branch flows. | no | | | | | | | Cross section can be circular or rectangular. | | +--------------+-----------------------------------------------------------------------------------+--------+ The splitter 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. The Splitter component acts as a Merger component (:numref:`chap_merger`) in the case of negative flow. .. _mathematical-model-32: Mathematical model ^^^^^^^^^^^^^^^^^^ .. _positive-flow-definition-4: 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 (:numref:`chap_merger`). The positive flow definition and the numbers of the connect points are defined in the figure below for the Splitter\ **-junction**. .. figure:: ../media/image715.png :figwidth: 3.28125in :align: center Positive flow direction .. _flow-regimes-4: 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) .. image:: ../media/image716.png :width: 1.3125in :height: 1.08333in ============================== ============================== ============================== ============================= Merging flow (Negative flow) .. image:: ../media/image717.png :width: 1.3125in :height: 1.08333in ============================== ============================= ============================== ============================= Not supported flow regimes .. image:: ../media/image718.png :width: 1.3125in :height: 1.08333in ============================== ============================= ============================== ============================= Not supported flow regimes .. image:: ../media/image719.png :width: 1.3125in :height: 1.08333in ============================== ============================= .. _equations-4: 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: .. 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 merging flow the formulas of the Merger component (:numref:`chap_merger`) 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\ 2 = 0* and *H\ 1-H\ 3 = 0* Splitter 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 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 :numref:`fig_splitter_angle`. .. _fig_splitter_angle: .. figure:: ../liquid/media/splitter1248.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 a Xi table (valid for Area ratio = 0.5); splitting branch 1 (ξ\ :sub:`12`) =============== ==== 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:`12` for positive flow and ξ\ :sub:`21` for negative flow | +===============================+=========================================================================+ | Loss coefficient branch 2 [-] | The ξ\ :sub:`13` for positive flow and ξ\ :sub:`31` for negative flow | +-------------------------------+-------------------------------------------------------------------------+ | Head loss branch 1 [m] | The ΔH\ :sub:`12` for positive flow and ΔH\ :sub:`21` for negative flow | +-------------------------------+-------------------------------------------------------------------------+ | Head loss branch 2 [m] | The ΔH\ :sub:`13` for positive flow and ΔH\ :sub:`31` for negative flow | +-------------------------------+-------------------------------------------------------------------------+ Component messages +------------------------------------------------+------+---------------------------+ | Message | Type | Explanation | +================================================+======+===========================+ | Splitting flow | Info | |image136| | +------------------------------------------------+------+---------------------------+ | Merging flow | Info | |image137| | +------------------------------------------------+------+---------------------------+ | Not supported flow regime - no resistance used | Info | |image138| or\ |image139| | +------------------------------------------------+------+---------------------------+ .. include:: substitutions_liquid.rst