.. _chap_y-junction: Y-JUNCTION ---------- .. figure:: ../media/image543.png :figwidth: 3.30208in :align: center Schematic overview of Wanda Y-junctions +----------------------+-------------------------------------------------------------------------------------------------------------------------+--------+ | type label | description | active | +======================+=========================================================================================================================+========+ | Y-junction combining | Three-node junction with a non right angle branched leg and a combining flow. Both straight legs have the same diameter | no | +----------------------+-------------------------------------------------------------------------------------------------------------------------+--------+ | Y-junction dividing | Three-node junction with a non right angle branched leg and a dividing flow. Both straight legs have the same diameter | no | +----------------------+-------------------------------------------------------------------------------------------------------------------------+--------+ Both components can be used for all kind of flow regimes in a Y‑junction with several angles. The supported angles for the formula based types are 30, 45 and 60 degrees. The difference between the two Y-junctions has to do with the flow regime in the branched legs, combining either dividing. The arrows in the symbol specify the positive direction of the flow (and the velocity). .. _mathematical-model-17: Mathematical model ^^^^^^^^^^^^^^^^^^ .. _positive-flow-definition-1: Positive flow definition """""""""""""""""""""""" The definition for the positive direction of flow (and velocity) is important to understand the results in the property window. Each Y-junction type has his own definition. For the **Y-junction combining** component the positive flow definition is defined in the left figure below. For the **Y-junction dividing** component (right figure) the positive flow definition for the branch leg is opposite to that of the Y-junction combining. The positive flow definitions in the straight legs are the same for both types. .. figure:: ../media/image544.png :figwidth: 5.16667in :align: center Flow definitions for both types of Y-junction. .. _flow-regimes-1: Flow regimes """""""""""" In the table below all different flow regimes which can occur are listed and explained with a scheme with corresponding actual flow arrows. It is called straight flow if the total flow (in some literature also called: combined flow) is in one of the straight legs, branch flow means that the total flow is in the branch. .. _table_y_junction_properties: .. table:: definition of flow regimes for both types +---------------------------+----------------------------------+----------------------------------+ | | Y-junction combining type | Y-junction dividing type | +===========================+==================================+==================================+ | 1 Combining straight flow | .. image:: ../media/image545.png | .. image:: ../media/image546.png | | | :width: 1.03125in | :width: 1.03125in | | | :height: 0.5625in | :height: 0.55208in | | | | | | | Positive straight flow | Negative straight flow | +---------------------------+----------------------------------+----------------------------------+ | 2 Dividing straight flow | .. image:: ../media/image547.png | .. image:: ../media/image548.png | | | :width: 1.03125in | :width: 1.03125in | | | :height: 0.5625in | :height: 0.55208in | | | | | | | Negative straight flow | Positive straight flow | +---------------------------+----------------------------------+----------------------------------+ | 3 Combining straight flow | .. image:: ../media/image549.png | .. image:: ../media/image550.png | | | :width: 1.03125in | :width: 1.03125in | | | :height: 0.5625in | :height: 0.55208in | | | | | | | Negative straight flow | Positive straight flow | +---------------------------+----------------------------------+----------------------------------+ | 4 Dividing straight flow | .. image:: ../media/image551.png | .. image:: ../media/image552.png | | | :width: 1.03125in | :width: 1.03125in | | | :height: 0.5625in | :height: 0.55208in | | | | | | | Positive straight flow | Negative straight flow | +---------------------------+----------------------------------+----------------------------------+ | 5 Combining branch flow | .. image:: ../media/image553.png | .. image:: ../media/image554.png | | | :width: 1.03125in | :width: 1.03125in | | | :height: 0.5625in | :height: 0.55208in | | | | | | | Negative branch flow | Positive branch flow | +---------------------------+----------------------------------+----------------------------------+ | 6 Dividing branch flow | .. image:: ../media/image555.png | .. image:: ../media/image556.png | | | :width: 1.03125in | :width: 1.03125in | | | :height: 0.5625in | :height: 0.55208in | | | | | | | Positive branch flow | Negative branch flow | +---------------------------+----------------------------------+----------------------------------+ .. _equations-1: Equations """"""""" The head loss over a 3-node component depends on the distribution of the discharges and the area of the connected legs. The Y-junction supports two different ways for retrieving the resistance coefficient Xi (*ξ*). 1. the head loss functions according to Idelchik’s Handbook [ref. 1] for angles of 30, 45 and 60 degree 2. user specified table with Xi depending on discharge ratio. These table values belong to a fixed area ratio. Please note that the loss coefficients according to the handbooks apply to junctions with a certain minimum pipe length interval in between multiple junctions. The head loss in 3-node components is a function of the combined flow in the *combined* leg, which is either one leg (1 or 2) of the straight part or the branch (leg 3). 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 ΔH Y-junction combining, combined flow in leg 2 .. math:: f_{2}=H_{1}-H_{2}-\xi_{12} \frac{Q_{2}\left|Q_{2}\right|}{2 g A_{2}^{2}} ΔH Y-junction dividing, combined flow in leg 1 .. math:: f_{2}=H_{1}-H_{2}-\xi_{12} \frac{Q_{1}\left|Q_{1}\right|}{2 g A_{1}^{2}} ΔH Y-junction, combined flow in branch .. math:: f_{2}=H_{3}-H_{1}-\xi_{31} \frac{Q_{3}\left|Q_{3}\right|}{2 g A_{3}^{2}} 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. The subscript x at the discharge Q\ :sub:`x` refers always to the leg in which the combined (total) flow Q occurs. For positive straight dividing flow and negative straight combining flow, Q\ :sub:`1` will be taken into account. For positive straight combining flow and negative straight dividing flow, Q\ :sub:`2` will be taken into account. .. _resistance-coefficients-based-on-formulas-1: Resistance coefficients based on formulas """"""""""""""""""""""""""""""""""""""""" The resistance coefficients based of formulas are taken from the Idelchik Handbook with the following restriction to the section areas: .. math:: \begin{array}{l} A_{1}+A_{3}>A_{2} \\ A_{1}=A_{2} \end{array} The formulas are only valid for the normal flow regimes 1 and 2, as explained in :numref:`table_y_junction_properties`. For each formula the *ξ*\ ‑values for various area and discharge ratios are collected in a table. **Note** that all indices used in the formulas are based on positive flow. For the other flow regimes where one of the flow direction is around the acute angle there are no formulas available. For those situations a fixed value of ξ = 2,0 will be used. **Straight flow combining** For the **straight** leg, the resistance coefficient ξ\ :sub:`12` is calculated according to: .. math:: \xi_{12} \approx 1-\left(1-\frac{Q_{3}}{Q_{2}}\right)^{2}-C_{\alpha} \frac{A_{2}}{A_{3}}\left(\frac{Q_{3}}{Q_{2}}\right)^{2} *C\ α* is a coefficient, which depends on the angle *α*. In WANDA three fixed *α*.values are included: - α = 30°: *C\ α* = 1,74; - α = 45°: *C\ α* = 1,41; - α = 60°: *C\ α* = 1,00. Table :numref:`table_straight_flow_combinig_30deg`, :numref:`table_straight_flow_combinig_45deg`, and :numref:`table_values_straight_flow_combining_60deg` shows the ξ\ :sub:`12` values according the formula above for various ratios of discharge and areas for the supported angles, respectively 30, 45 and 60 degrees. .. _table_straight_flow_combinig_30deg: .. table:: Values of ξ\ :sub:`12` for α=30° straight flow combining +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | | **A\ 3/A\ 2** | | | | | | | | | | +===============+=========+===============+=========+=========+=========+=========+=========+=========+=========+=========+=========+ | |   | **0.1** | **0.2** | **0.3** | **0.4** | **0.5** | **0.6** | **0.7** | **0.8** | **0.9** | **1.0** | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | **Q\ 3/Q\ 2** | **0.0** | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.1** | 0.02 | 0.10 | 0.13 | 0.15 | 0.16 | 0.16 | 0.17 | 0.17 | 0.17 | 0.17 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.2** | -0.34 | 0.01 | 0.13 | 0.19 | 0.22 | 0.24 | 0.26 | 0.27 | 0.28 | 0.29 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.3** | -1.06 | -0.27 | -0.01 | 0.12 | 0.20 | 0.25 | 0.29 | 0.31 | 0.34 | 0.35 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.4** | -2.14 | -0.75 | -0.29 | -0.06 | 0.08 | 0.18 | 0.24 | 0.29 | 0.33 | 0.36 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.5** | -3.60 | -1.42 | -0.70 | -0.34 | -0.12 | 0.03 | 0.13 | 0.21 | 0.27 | 0.31 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.6** | -5.42 | -2.29 | -1.25 | -0.73 | -0.41 | -0.20 | -0.05 | 0.06 | 0.14 | 0.21 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.7** | -7.62 | -3.35 | -1.93 | -1.22 | -0.80 | -0.51 | -0.31 | -0.16 | -0.04 | 0.06 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.8** | -10.18 | -4.61 | -2.75 | -1.82 | -1.27 | -0.90 | -0.63 | -0.43 | -0.28 | -0.15 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.9** | -13.10 | -6.06 | -3.71 | -2.53 | -1.83 | -1.36 | -1.02 | -0.77 | -0.58 | -0.42 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **1.0** | -16.40 | -7.70 | -4.80 | -3.35 | -2.48 | -1.90 | -1.49 | -1.17 | -0.93 | -0.74 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ .. _table_straight_flow_combinig_45deg: .. table:: Values of ξ\ :sub:`12` for α=45° straight flow combining +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | | **A\ 3/A\ 2** | | | | | | | | | | +===============+=========+===============+=========+=========+=========+=========+=========+=========+=========+=========+=========+ | |   | **0.1** | **0.2** | **0.3** | **0.4** | **0.5** | **0.6** | **0.7** | **0.8** | **0.9** | **1.0** | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | **Q\ 3/Q\ 2** | **0.0** | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.1** | 0.05 | 0.12 | 0.14 | 0.15 | 0.16 | 0.17 | 0.17 | 0.17 | 0.17 | 0.18 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.2** | -0.20 | 0.08 | 0.17 | 0.22 | 0.25 | 0.27 | 0.28 | 0.29 | 0.30 | 0.30 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.3** | -0.76 | -0.12 | 0.09 | 0.19 | 0.26 | 0.30 | 0.33 | 0.35 | 0.37 | 0.38 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.4** | -1.62 | -0.49 | -0.11 | 0.08 | 0.19 | 0.26 | 0.32 | 0.36 | 0.39 | 0.41 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.5** | -2.77 | -1.01 | -0.42 | -0.13 | 0.05 | 0.16 | 0.25 | 0.31 | 0.36 | 0.40 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.6** | -4.24 | -1.70 | -0.85 | -0.43 | -0.18 | -0.01 | 0.11 | 0.21 | 0.28 | 0.33 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.7** | -6.00 | -2.54 | -1.39 | -0.82 | -0.47 | -0.24 | -0.08 | 0.05 | 0.14 | 0.22 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.8** | -8.06 | -3.55 | -2.05 | -1.30 | -0.84 | -0.54 | -0.33 | -0.17 | -0.04 | 0.06 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.9** | -10.43 | -4.72 | -2.82 | -1.87 | -1.29 | -0.91 | -0.64 | -0.44 | -0.28 | -0.15 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **1.0** | -13.10 | -6.05 | -3.70 | -2.52 | -1.82 | -1.35 | -1.01 | -0.76 | -0.57 | -0.41 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ .. _table_values_straight_flow_combining_60deg: .. table:: Values of ξ\ :sub:`12` for α=60° straight flow combining +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | | **A\ 3/A\ 2** | | | | | | | | | | +===============+=========+===============+=========+=========+=========+=========+=========+=========+=========+=========+=========+ | |   | **0.1** | **0.2** | **0.3** | **0.4** | **0.5** | **0.6** | **0.7** | **0.8** | **0.9** | **1.0** | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | **Q\ 3/Q\ 2** | **0.0** | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.1** | 0.09 | 0.14 | 0.16 | 0.17 | 0.17 | 0.17 | 0.18 | 0.18 | 0.18 | 0.18 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.2** | -0.04 | 0.16 | 0.23 | 0.26 | 0.28 | 0.29 | 0.30 | 0.31 | 0.32 | 0.32 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.3** | -0.39 | 0.06 | 0.21 | 0.28 | 0.33 | 0.36 | 0.38 | 0.40 | 0.41 | 0.42 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.4** | -0.96 | -0.16 | 0.11 | 0.24 | 0.32 | 0.37 | 0.41 | 0.44 | 0.46 | 0.48 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.5** | -1.75 | -0.50 | -0.08 | 0.12 | 0.25 | 0.33 | 0.39 | 0.44 | 0.47 | 0.50 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.6** | -2.76 | -0.96 | -0.36 | -0.06 | 0.12 | 0.24 | 0.33 | 0.39 | 0.44 | 0.48 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.7** | -3.99 | -1.54 | -0.72 | -0.31 | -0.07 | 0.09 | 0.21 | 0.30 | 0.37 | 0.42 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.8** | -5.44 | -2.24 | -1.17 | -0.64 | -0.32 | -0.11 | 0.05 | 0.16 | 0.25 | 0.32 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.9** | -7.11 | -3.06 | -1.71 | -1.03 | -0.63 | -0.36 | -0.17 | -0.02 | 0.09 | 0.18 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **1.0** | -9.00 | -4.00 | -2.33 | -1.50 | -1.00 | -0.67 | -0.43 | -0.25 | -0.11 | 0.00 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ For the **branch** leg. the resistance coefficient is calculated according to: .. math:: \xi_{32}=A\left[1+\left(\frac{Q_{3}}{Q_{2}} \frac{A_{2}}{A_{3}}\right)^{2}-2\left(1-\frac{Q_{3}}{Q_{2}}\right)^{2}-C_{\alpha} \frac{A_{2}}{A_{3}}\left(\frac{Q_{3}}{Q_{2}}\right)^{2}\right] The coefficient *A* depends on the area and discharge ratios again. :numref:`table_a_values_y_junction` shows the values: .. _table_a_values_y_junction: .. table:: Values of the variable *A*. +-------------------------+-----------+-----------------------------------------------+-------+ | A\ :sub:`3`/A\ :sub:`2` | ≤ 0.35 | > 0.35 | | +-------------------------+-----------+-----------------------------------------------+-------+ | Q\ :sub:`3`/Q\ :sub:`2` | 0.0 – 1.0 | ≤ 0.4 | > 0.4 | +-------------------------+-----------+-----------------------------------------------+-------+ | A | 1.0 | :math:`0.9\left(1-\frac{Q_{3}}{Q_{2}}\right)` | 0.55 | +-------------------------+-----------+-----------------------------------------------+-------+ *C\ α* is a coefficient, which depends on the angle *α*. In WANDA three fixed *α*.values are included: - α = 30°: *C\ α* = 1.74; - α = 45°: *C\ α* = 1.41; - α = 60°: *C\ α* = 1.00. Table :numref:`tabel_y_junction_30deg_combining`, :numref:`tabel_y_junction_45deg_combining`, and :numref:`tabel_y_junction_60deg_combining` shows the ξ\ :sub:`32` values according the formula above for various ratios of discharge and areas for the supported angles, respectively 30, 45 and 60 degrees. .. _tabel_y_junction_30deg_combining: .. table:: Values of ξ\ :sub:`32` for α=30° branch flow combining +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | | **A\ 3/A\ 2** | | | | | | | | | | +===============+=========+===============+=========+=========+=========+=========+=========+=========+=========+=========+=========+ | |   | **0.1** | **0.2** | **0.3** | **0.4** | **0.5** | **0.6** | **0.7** | **0.8** | **0.9** | **1.0** | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | **Q\ 3/Q\ 2** | **0.0** | -1.00 | -1.00 | -1.00 | -0.90 | -0.90 | -0.90 | -0.90 | -0.90 | -0.90 | -0.90 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.1** | 0.21 | -0.46 | -0.57 | -0.49 | -0.50 | -0.50 | -0.51 | -0.51 | -0.51 | -0.51 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.2** | 3.02 | 0.37 | -0.07 | -0.15 | -0.19 | -0.21 | -0.21 | -0.22 | -0.22 | -0.22 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.3** | 7.45 | 1.49 | 0.50 | 0.12 | 0.04 | 0.01 | -0.01 | -0.02 | -0.03 | -0.03 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.4** | 13.50 | 2.89 | 1.13 | 0.32 | 0.20 | 0.14 | 0.11 | 0.10 | 0.09 | 0.09 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.5** | 21.15 | 4.57 | 1.83 | 0.54 | 0.35 | 0.26 | 0.21 | 0.19 | 0.18 | 0.17 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.6** | 30.42 | 6.55 | 2.59 | 0.75 | 0.48 | 0.35 | 0.29 | 0.25 | 0.24 | 0.23 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.7** | 41.29 | 8.81 | 3.42 | 0.96 | 0.59 | 0.42 | 0.33 | 0.29 | 0.26 | 0.25 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.8** | 53.78 | 11.35 | 4.32 | 1.17 | 0.69 | 0.46 | 0.35 | 0.29 | 0.26 | 0.25 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.9** | 67.89 | 14.18 | 5.28 | 1.39 | 0.77 | 0.48 | 0.34 | 0.27 | 0.23 | 0.21 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **1.0** | 83.60 | 17.30 | 6.31 | 1.60 | 0.84 | 0.48 | 0.31 | 0.21 | 0.17 | 0.14 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ .. _tabel_y_junction_45deg_combining: .. table:: Values of ξ\ :sub:`32` for α=45° branch flow combining +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | | **A\ 3/A\ 2** | | | | | | | | | | +===============+=========+===============+=========+=========+=========+=========+=========+=========+=========+=========+=========+ | |   | **0.1** | **0.2** | **0.3** | **0.4** | **0.5** | **0.6** | **0.7** | **0.8** | **0.9** | **1.0** | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | **Q\ 3/Q\ 2** | **0.0** | -1.00 | -1.00 | -1.00 | -0.90 | -0.90 | -0.90 | -0.90 | -0.90 | -0.90 | -0.90 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.1** | 0.24 | -0.44 | -0.56 | -0.48 | -0.49 | -0.50 | -0.50 | -0.50 | -0.50 | -0.51 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.2** | 3.16 | 0.44 | -0.02 | -0.12 | -0.17 | -0.19 | -0.20 | -0.21 | -0.21 | -0.21 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.3** | 7.75 | 1.64 | 0.60 | 0.17 | 0.08 | 0.04 | 0.01 | 0.00 | -0.01 | -0.01 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.4** | 14.02 | 3.15 | 1.31 | 0.39 | 0.25 | 0.19 | 0.15 | 0.13 | 0.12 | 0.12 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.5** | 21.98 | 4.99 | 2.10 | 0.65 | 0.44 | 0.33 | 0.28 | 0.25 | 0.23 | 0.22 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.6** | 31.60 | 7.14 | 2.99 | 0.91 | 0.61 | 0.46 | 0.38 | 0.33 | 0.31 | 0.29 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.7** | 42.91 | 9.62 | 3.96 | 1.19 | 0.77 | 0.57 | 0.46 | 0.40 | 0.36 | 0.34 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.8** | 55.90 | 12.41 | 5.02 | 1.47 | 0.92 | 0.66 | 0.52 | 0.44 | 0.39 | 0.36 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.9** | 70.56 | 15.52 | 6.17 | 1.75 | 1.06 | 0.73 | 0.55 | 0.45 | 0.39 | 0.36 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **1.0** | 86.90 | 18.95 | 7.41 | 2.05 | 1.20 | 0.79 | 0.56 | 0.44 | 0.37 | 0.32 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ .. _tabel_y_junction_60deg_combining: .. table:: Values of ξ\ :sub:`32` for α=60° branch flow combining +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | | **A\ 3/A\ 2** | | | | | | | | | | +===============+=========+===============+=========+=========+=========+=========+=========+=========+=========+=========+=========+ | |   | **0.1** | **0.2** | **0.3** | **0.4** | **0.5** | **0.6** | **0.7** | **0.8** | **0.9** | **1.0** | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | **Q\ 3/Q\ 2** | **0** | -1.00 | -1.00 | -1.00 | -0.90 | -0.90 | -0.90 | -0.90 | -0.90 | -0.90 | -0.90 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.1** | 0.28 | -0.42 | -0.54 | -0.47 | -0.49 | -0.49 | -0.50 | -0.50 | -0.50 | -0.50 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.2** | 3.32 | 0.52 | 0.03 | -0.09 | -0.14 | -0.17 | -0.18 | -0.19 | -0.20 | -0.20 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.3** | 8.12 | 1.82 | 0.72 | 0.23 | 0.13 | 0.08 | 0.05 | 0.03 | 0.02 | 0.01 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.4** | 14.68 | 3.48 | 1.52 | 0.48 | 0.32 | 0.25 | 0.20 | 0.18 | 0.16 | 0.15 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.5** | 23.00 | 5.50 | 2.44 | 0.79 | 0.55 | 0.43 | 0.36 | 0.32 | 0.29 | 0.28 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.6** | 33.08 | 7.88 | 3.48 | 1.12 | 0.77 | 0.59 | 0.50 | 0.44 | 0.40 | 0.37 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.7** | 44.92 | 10.62 | 4.63 | 1.46 | 0.99 | 0.75 | 0.62 | 0.54 | 0.48 | 0.45 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.8** | 58.52 | 13.72 | 5.90 | 1.83 | 1.21 | 0.90 | 0.72 | 0.62 | 0.55 | 0.51 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.9** | 73.88 | 17.18 | 7.28 | 2.21 | 1.43 | 1.03 | 0.81 | 0.68 | 0.59 | 0.54 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **1.0** | 91.00 | 21.00 | 8.78 | 2.61 | 1.65 | 1.16 | 0.89 | 0.72 | 0.62 | 0.55 | +---------------+---------+---------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ **Straight flow dividing** For the straight leg the resistance coefficient is given using the following formula: .. math:: \xi_{12}=\tau_{12} \frac{Q_{3}}{Q_{1}} where *τ*\ :sub:`12` depends on the area and discharge ratios as given in table :numref:`table_y_junction_t12`. .. _table_y_junction_t12: .. table:: Values of τ12 +-------------------------+-------------------------------+-----------------------------------+-----------------------------------+ | A\ :sub:`3`/A\ :sub:`1` | ≤ 0.4 | 0.4 | | +-------------------------+-------------------------------+-----------------------------------+-----------------------------------+ | Q\ :sub:`3`/Q\ :sub:`1` | 0-1.0 | ≤ 0.5 | >0.5 | +-------------------------+-------------------------------+-----------------------------------+-----------------------------------+ | τ\ :sub:`12` | 0.4 (Q\ :sub:`3`/Q\ :sub:`1`) | 0.2(2Q\ :sub:`3`/Q\ :sub:`1` – 1) | 0.3(2Q\ :sub:`3`/Q\ :sub:`1` – 1) | +-------------------------+-------------------------------+-----------------------------------+-----------------------------------+ :numref:`table_y_junction_x12` shows the *ξ\ 12* values according to the formula above for various values of discharge ratios. .. _table_y_junction_x12: .. table:: ξ\ :sub:`12` values for dividing flow +-------------------------+-----+-------------------------+------+------+------+-------+-------+-------+-------+-------+-------+ | | | A\ :sub:`3`/A\ :sub:`1` | | | | | | | | | | +=========================+=====+=========================+======+======+======+=======+=======+=======+=======+=======+=======+ | | | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 | 0.9 | 1.0 | +-------------------------+-----+-------------------------+------+------+------+-------+-------+-------+-------+-------+-------+ | Q\ :sub:`3`/Q\ :sub:`1` | 0.0 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | +-------------------------+-----+-------------------------+------+------+------+-------+-------+-------+-------+-------+-------+ | | 0.1 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 | -0.02 | -0.02 | -0.02 | -0.02 | -0.02 | +-------------------------+-----+-------------------------+------+------+------+-------+-------+-------+-------+-------+-------+ | | 0.2 | 0.02 | 0.02 | 0.02 | 0.02 | -0.02 | -0.02 | -0.02 | -0.02 | -0.02 | -0.02 | +-------------------------+-----+-------------------------+------+------+------+-------+-------+-------+-------+-------+-------+ | | 0.3 | 0.04 | 0.04 | 0.04 | 0.04 | -0.02 | -0.02 | -0.02 | -0.02 | -0.02 | -0.02 | +-------------------------+-----+-------------------------+------+------+------+-------+-------+-------+-------+-------+-------+ | | 0.4 | 0.06 | 0.06 | 0.06 | 0.06 | -0.02 | -0.02 | -0.02 | -0.02 | -0.02 | -0.02 | +-------------------------+-----+-------------------------+------+------+------+-------+-------+-------+-------+-------+-------+ | | 0.5 | 0.10 | 0.10 | 0.10 | 0.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | +-------------------------+-----+-------------------------+------+------+------+-------+-------+-------+-------+-------+-------+ | | 0.6 | 0.14 | 0.14 | 0.14 | 0.14 | 0.04 | 0.04 | 0.04 | 0.04 | 0.04 | 0.04 | +-------------------------+-----+-------------------------+------+------+------+-------+-------+-------+-------+-------+-------+ | | 0.7 | 0.20 | 0.20 | 0.20 | 0.20 | 0.08 | 0.08 | 0.08 | 0.08 | 0.08 | 0.08 | +-------------------------+-----+-------------------------+------+------+------+-------+-------+-------+-------+-------+-------+ | | 0.8 | 0.26 | 0.26 | 0.26 | 0.26 | 0.14 | 0.14 | 0.14 | 0.14 | 0.14 | 0.14 | +-------------------------+-----+-------------------------+------+------+------+-------+-------+-------+-------+-------+-------+ | | 0.9 | 0.32 | 0.32 | 0.32 | 0.32 | 0.22 | 0.22 | 0.22 | 0.22 | 0.22 | 0.22 | +-------------------------+-----+-------------------------+------+------+------+-------+-------+-------+-------+-------+-------+ | | 1.0 | 0.40 | 0.40 | 0.40 | 0.40 | 0.30 | 0.30 | 0.30 | 0.30 | 0.30 | 0.30 | +-------------------------+-----+-------------------------+------+------+------+-------+-------+-------+-------+-------+-------+ The resistance coefficient *ξ\ 13*\ for the branch is calculated using the following formula: .. math:: \xi_{13}=A^{\prime}\left[1+\left(\frac{Q_{3}}{Q_{1}} \frac{A_{1}}{A_{3}}\right)^{2}-2\left(\frac{Q_{3}}{Q_{1}} \frac{A_{1}}{A_{3}}\right) \cos \alpha\right] The values of A’ are given in :numref:`table_y_junction_a_values`. .. _table_y_junction_a_values: .. table:: :math:`A'` values for dividing flow +-------------------------+-----------------------+--------+------------------------+-------+ | A\ :sub:`3`/A\ :sub:`1` | ≤ 0.35 | > 0.35 | | | +-------------------------+-----------------------+--------+------------------------+-------+ | Q\ :sub:`3`/Q\ :sub:`1` | ≤ 0.4 | > 0.4 | ≤ 0.6 | > 0.6 | +-------------------------+-----------------------+--------+------------------------+-------+ | A’ | 1.1 – 0.7 *Q\ 3/Q\ 1* | 0.85 | 1.0 – 0.65 *Q\ 3/Q\ 1* | 0.6 | +-------------------------+-----------------------+--------+------------------------+-------+ Table :numref:`tabel_y_junction_30deg_dividing`. :numref:`tabel_y_junction_45deg_dividing`, and :numref:`tabel_y_junction_60deg_dividing` shows the *ξ\ 13* values according to the formulas above for various values of discharge and area ratio for the supported angles of 30, 45, and 60 degrees. .. _tabel_y_junction_30deg_dividing: .. table:: Values of ξ\ :sub:`13` for α=30° branch flow dividing +-------------------------+---------+-------------------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | | A\ :sub:`3`/A\ :sub:`1` | | | | | | | | | | +=========================+=========+=========================+=========+=========+=========+=========+=========+=========+=========+=========+=========+ | |   | **0.1** | **0.2** | **0.3** | **0.4** | **0.5** | **0.6** | **0.7** | **0.8** | **0.9** | **1.0** | +-------------------------+---------+-------------------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | Q\ :sub:`3`/Q\ :sub:`1` | **0.0** | 1.10 | 1.10 | 1.10 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | +-------------------------+---------+-------------------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.1** | 0.28 | 0.40 | 0.55 | 0.59 | 0.65 | 0.69 | 0.72 | 0.75 | 0.77 | 0.78 | +-------------------------+---------+-------------------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.2** | 1.47 | 0.26 | 0.28 | 0.33 | 0.41 | 0.46 | 0.51 | 0.55 | 0.58 | 0.60 | +-------------------------+---------+-------------------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.3** | 4.28 | 0.58 | 0.24 | 0.21 | 0.26 | 0.31 | 0.36 | 0.40 | 0.43 | 0.46 | +-------------------------+---------+-------------------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.4** | 8.26 | 1.26 | 0.38 | 0.20 | 0.19 | 0.21 | 0.25 | 0.28 | 0.32 | 0.35 | +-------------------------+---------+-------------------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.5** | 14.74 | 2.48 | 0.76 | 0.27 | 0.18 | 0.17 | 0.18 | 0.21 | 0.23 | 0.26 | +-------------------------+---------+-------------------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.6** | 22.62 | 4.08 | 1.31 | 0.40 | 0.22 | 0.16 | 0.15 | 0.16 | 0.18 | 0.20 | +-------------------------+---------+-------------------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.7** | 32.19 | 6.11 | 2.04 | 0.62 | 0.32 | 0.20 | 0.16 | 0.15 | 0.15 | 0.17 | +-------------------------+---------+-------------------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.8** | 43.47 | 8.56 | 2.97 | 0.92 | 0.47 | 0.28 | 0.20 | 0.16 | 0.15 | 0.15 | +-------------------------+---------+-------------------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.9** | 56.45 | 11.44 | 4.08 | 1.30 | 0.67 | 0.39 | 0.26 | 0.19 | 0.16 | 0.15 | +-------------------------+---------+-------------------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **1.0** | 71.13 | 14.74 | 5.39 | 1.75 | 0.92 | 0.53 | 0.34 | 0.24 | 0.19 | 0.16 | +-------------------------+---------+-------------------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ .. _tabel_y_junction_45deg_dividing: .. table:: Values of ξ\ :sub:`13` for α=45° branch flow dividing +-------------------------+---------+-------------------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | | A\ :sub:`3`/A\ :sub:`1` | | | | | | | | | | +=========================+=========+=========================+=========+=========+=========+=========+=========+=========+=========+=========+=========+ | |   | **0.1** | **0.2** | **0.3** | **0.4** | **0.5** | **0.6** | **0.7** | **0.8** | **0.9** | **1.0** | +-------------------------+---------+-------------------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | Q\ :sub:`3`/Q\ :sub:`1` | **0.0** | 1.10 | 1.10 | 1.10 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | +-------------------------+---------+-------------------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.1** | 0.60 | 0.56 | 0.66 | 0.66 | 0.71 | 0.74 | 0.77 | 0.78 | 0.80 | 0.81 | +-------------------------+---------+-------------------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.2** | 2.08 | 0.56 | 0.48 | 0.47 | 0.52 | 0.56 | 0.59 | 0.62 | 0.64 | 0.66 | +-------------------------+---------+-------------------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.3** | 5.12 | 1.00 | 0.52 | 0.40 | 0.41 | 0.44 | 0.46 | 0.49 | 0.51 | 0.54 | +-------------------------+---------+-------------------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.4** | 9.30 | 1.78 | 0.73 | 0.43 | 0.38 | 0.37 | 0.38 | 0.40 | 0.42 | 0.44 | +-------------------------+---------+-------------------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.5** | 16.09 | 3.16 | 1.21 | 0.54 | 0.40 | 0.35 | 0.34 | 0.34 | 0.35 | 0.37 | +-------------------------+---------+-------------------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.6** | 24.24 | 4.89 | 1.85 | 0.69 | 0.45 | 0.36 | 0.32 | 0.31 | 0.31 | 0.31 | +-------------------------+---------+-------------------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.7** | 34.09 | 7.06 | 2.67 | 0.95 | 0.59 | 0.43 | 0.35 | 0.32 | 0.30 | 0.30 | +-------------------------+---------+-------------------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.8** | 45.63 | 9.64 | 3.69 | 1.30 | 0.78 | 0.54 | 0.41 | 0.35 | 0.32 | 0.31 | +-------------------------+---------+-------------------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.9** | 58.88 | 12.65 | 4.89 | 1.73 | 1.02 | 0.68 | 0.50 | 0.40 | 0.35 | 0.32 | +-------------------------+---------+-------------------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **1.0** | 73.83 | 16.09 | 6.29 | 2.23 | 1.30 | 0.85 | 0.61 | 0.48 | 0.40 | 0.35 | +-------------------------+---------+-------------------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ .. _tabel_y_junction_60deg_dividing: .. table:: Values of ξ\ :sub:`13` for α=60° branch flow dividing +-------------------------+---------+-------------------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | | A\ :sub:`3`/A\ :sub:`1` | | | | | | | | | | +=========================+=========+=========================+=========+=========+=========+=========+=========+=========+=========+=========+=========+ | |   | **0.1** | **0.2** | **0.3** | **0.4** | **0.5** | **0.6** | **0.7** | **0.8** | **0.9** | **1.0** | +-------------------------+---------+-------------------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | Q\ :sub:`3`/Q\ :sub:`1` | **0.0** | 1.10 | 1.10 | 1.10 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | +-------------------------+---------+-------------------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.1** | 1.03 | 0.77 | 0.80 | 0.76 | 0.79 | 0.81 | 0.82 | 0.83 | 0.84 | 0.85 | +-------------------------+---------+-------------------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.2** | 2.88 | 0.96 | 0.75 | 0.65 | 0.66 | 0.68 | 0.69 | 0.71 | 0.72 | 0.73 | +-------------------------+---------+-------------------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.3** | 6.23 | 1.56 | 0.89 | 0.65 | 0.61 | 0.60 | 0.61 | 0.62 | 0.63 | 0.64 | +-------------------------+---------+-------------------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.4** | 10.66 | 2.46 | 1.18 | 0.74 | 0.62 | 0.58 | 0.56 | 0.56 | 0.56 | 0.56 | +-------------------------+---------+-------------------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.5** | 17.85 | 4.04 | 1.79 | 0.89 | 0.68 | 0.58 | 0.54 | 0.52 | 0.51 | 0.51 | +-------------------------+---------+-------------------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.6** | 26.35 | 5.95 | 2.55 | 1.07 | 0.76 | 0.61 | 0.54 | 0.50 | 0.47 | 0.46 | +-------------------------+---------+-------------------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.7** | 36.55 | 8.29 | 3.49 | 1.39 | 0.94 | 0.72 | 0.60 | 0.53 | 0.50 | 0.47 | +-------------------------+---------+-------------------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.8** | 48.45 | 11.05 | 4.63 | 1.80 | 1.18 | 0.87 | 0.70 | 0.60 | 0.54 | 0.50 | +-------------------------+---------+-------------------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **0.9** | 62.05 | 14.24 | 5.95 | 2.29 | 1.46 | 1.05 | 0.82 | 0.68 | 0.60 | 0.55 | +-------------------------+---------+-------------------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ | | **1.0** | 77.35 | 17.85 | 7.46 | 2.85 | 1.80 | 1.27 | 0.97 | 0.79 | 0.67 | 0.60 | +-------------------------+---------+-------------------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+ Y-Junction properties ^^^^^^^^^^^^^^^^^^^^^ The input properties of both Y-junction are exactly the same. The input and output properties for both types are specified below. Properties Y-junction (combining and dividing type) """"""""""""""""""""""""""""""""""""""""""""""""""" Input properties T-junction straight +-----------------------+----------------+------+-------+---------+----------------------------------+ | Description | input | unit | range | default | Remarks | +=======================+================+======+=======+=========+==================================+ | Diameter straight leg | Real | [mm] | | | | +-----------------------+----------------+------+-------+---------+----------------------------------+ | Diameter branch leg | Real | [mm] | | | | +-----------------------+----------------+------+-------+---------+----------------------------------+ | Xi method | Formula | | | Formula | | | | | | | | | | | Tables | | | | | +-----------------------+----------------+------+-------+---------+----------------------------------+ | Xi tables valid for | Combining | | | | Only when Xi method = Tables | | | | | | | | | | Dividing | | | | | | | | | | | | | | Both | | | | | +-----------------------+----------------+------+-------+---------+----------------------------------+ | Xi combining straight | Table | | | | if Xi tables = Combining or Both | | | | | | | | | | (ξ\ :sub:`12`) | | | | | +-----------------------+----------------+------+-------+---------+----------------------------------+ | Xi combining branch | Table | | | | if Xi tables = Combining or Both | | | | | | | | | | (ξ\ :sub:`32`) | | | | | +-----------------------+----------------+------+-------+---------+----------------------------------+ | Xi dividing straight | Table | | | | if Xi tables = Dividing or Both | | | | | | | | | | (ξ\ :sub:`12`) | | | | | +-----------------------+----------------+------+-------+---------+----------------------------------+ | Xi dividing branch | Table | | | | if Xi tables = Dividing or Both | | | | | | | | | | (ξ\ :sub:`13`) | | | | | +-----------------------+----------------+------+-------+---------+----------------------------------+ With the tables for the Xi-values it is possible to choose user-defined loss coefficients. for instance for a certain kind of Y-junction with rounded angles. The user has to specify a set of *loss coefficient values* related to the *discharge ratio* between the branch leg and the straight combined flow leg. If the user does not specify both combining and dividing Xi-tables, WANDA uses the formulas according to the Idelchik handbook for the unspecified flow regimes. **Example of Xi table**; straight flow combining, branch leg (ξ\ :sub:`32`) valid for Area ratio = 0.5 =================== ======= 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 Y-junction straight +-------------------------------+-----------------------------------------------------------------------------------------------------------+ | Loss coefficient straight [-] | The ξ\ :sub:`12` for positive flow and ξ\ :sub:`21` for negative flow | | | | | | In case of branch flow regime this is the ξ\ :sub:`31` coefficient | +-------------------------------+-----------------------------------------------------------------------------------------------------------+ | Loss coefficient branch [-] | The ξ\ :sub:`13` for positive flow and ξ\ :sub:`31` for negative flow | | | | | | In case of branch flow regime this is the ξ\ :sub:`32` coefficient | +-------------------------------+-----------------------------------------------------------------------------------------------------------+ | Head loss straight [m] | The ΔH\ :sub:`12` for positive flow and ΔH\ :sub:`21` for negative flow | | | | | | In case of branch flow regime this is the ΔH\ :sub:`13` for combining and ΔH\ :sub:`31` for dividing flow | +-------------------------------+-----------------------------------------------------------------------------------------------------------+ | Head loss branch [m] | The ΔH\ :sub:`13` for positive flow and ΔH\ :sub:`31` for negative flow | | | | | | In case of branch flow regime this is the ΔH\ :sub:`23` for combining and ΔH\ :sub:`32` for dividing flow | +-------------------------------+-----------------------------------------------------------------------------------------------------------+ Component messages Y-junction straight ================ ==== ====================== ====================== Message Type Explanation ================ ==== ====================== ====================== Combining Info Positive straight flow Negative straight flow \ |image96| |image97| Dividing Info Positive straight flow Negative straight flow \ |image98| |image99| Branch combining Info Positive branch flow Negative branch flow \ |image100| |image101| Branch dividing Info Positive branch flow Negative branch flow \ |image102| |image103| ================ ==== ====================== ====================== With the tables for the Xi-values it is possible to choose user-defined loss coefficients, for instance for a certain kind of T-junction with rounded angles. The user has to specify a set of *loss coefficients values* related to the *discharge ratio* between the side and combined branch. If the user does not specify both combining and dividing Xi-tables, WANDA uses the formulas according to the Idelchik handbook for the unspecified flow regimes. **NOTE:** The numbering of the branches in the literature is not always consistent with the WANDA definition as given under ‘Mathematical Model’ above. The Miller Handbook for instance indicates the side branch with *1*, the straight branch with *2* and the combined one as *3*. .. include:: substitutions_liquid.rst