VALVE ----- Valve (class) ^^^^^^^^^^^^^ .. figure:: ../media/image787.png :figwidth: 0.95833in :align: center Control valve, block valve **Fall type** +------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------+ | type label | description | active | +============+==============================================================================================================================================================================================================+========+ | Valve | Control or block valve with choice out of four predefined Deltares standard head loss characteristics or user specified characteristics; several initial settings can be used for flow or pressure balancing | Yes | +------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------+ .. _mathematical-model-37: Mathematical model """""""""""""""""" The discharge characteristic indicates the relation between the flow Q through the valve and the pressure ∆p across the valve as a function of the valve position. This relation is expressed in a discharge coefficient K\ :sub:`v` or C\ :sub:`v` and a loss coefficient ξ. The coefficients are derived from the general equation for a Newtonian flow through a restriction in a pipeline under cavitation free circumstances: .. math:: \Delta p=\xi \frac{\rho v^{2}}{2} in which: == = ======================================== ================ ∆p = net pressure difference across the valve [N/m\ :sup:`2`] ξ = loss coefficient of the valve [-] ρ = density of the fluid [kg/m\ :sup:`3`] v = velocity [m/s] == = ======================================== ================ or .. math:: \Delta H=\xi \frac{v^{2}}{2 g} in which: == = ========================================= =============== ∆H = pressure head difference across the valve [m] ξ = loss coefficient of the valve [-] v = velocity [m/s] g = gravitational acceleration [m/s\ :sup:`2`] == = ========================================= =============== In practice the discharge coefficients K\ :sub:`v` is used. .. math:: K_{v}=\frac{Q}{\sqrt{\Delta p}} with: +-------------+---+------------------------------------------+----------------------+ | K\ :sub:`v` | = | discharge coefficient | [m\ :sup:`3`/h/√bar] | +-------------+---+------------------------------------------+----------------------+ | Q | = | flow | [m\ :sup:`3`/h] | +-------------+---+------------------------------------------+----------------------+ | ∆p | = | net pressure difference across the valve | [bar] | +-------------+---+------------------------------------------+----------------------+ In words: the discharge coefficient K\ :sub:`v` denotes the flow in m\ :sup:`3`/h which flows through a valve at a pressure difference of 1 bar. Apart from Kv, Cv is also defined as a discharge coefficients for American units. .. math:: C_{v}=\frac{Q}{\sqrt{\Delta p}} with =========== = ======================================== ================ C\ :sub:`v` = discharge coefficient [USGPM/√psi] Q = flow [US gallons/min] ∆p = net pressure difference across the valve [psi] =========== = ======================================== ================ The relation between ξ, Kv and Cv is as follows: .. math:: \xi=1.6 \cdot 10^{9} \frac{1}{K_{v}^{2}} \cdot D^{4} .. math:: K_{v}=0.865 C_{v} A valve is characterised by *ξ* = f (*θ*) or K\ :sub:`v` = f (*θ*) or C\ :sub:`v` = f (*θ*). *θ* denotes the dimensionless valve opening. *θ* ranges from 0 to 1 (in SI-units, or 0 = 100 % in percentage annotation) - *θ* = 0, valve is closed. - *θ* = 1, valve is completely open. The different discharge characteristic are always translated to the following equation: .. math:: \Delta H=a \xi Q_{1}\left|Q_{1}\right| in which: +---------------+---+----------------------------------------------------------+---------------------------+ | *∆H* | = | *H*\ :sub:`1` ‑ *H*\ :sub:`2` in positive flow direction | [m] | +---------------+---+----------------------------------------------------------+---------------------------+ | *H*\ :sub:`1` | = | upstream head | [m] | +---------------+---+----------------------------------------------------------+---------------------------+ | *H*\ :sub:`2` | = | downstream head | [m] | +---------------+---+----------------------------------------------------------+---------------------------+ | *a* | = | 1 / (2 g A\ :sub:`f`\ :sup:`2`) | [s\ :sup:`2`/m\ :sup:`5`] | +---------------+---+----------------------------------------------------------+---------------------------+ | *ξ* | = | loss coefficient | [‑] | +---------------+---+----------------------------------------------------------+---------------------------+ | *Q*\ :sub:`1` | = | discharge upstream | [m\ :sup:`3`/s] | +---------------+---+----------------------------------------------------------+---------------------------+ | *A*\ :sub:`f` | = | discharge area valve | [m\ :sup:`2`] | +---------------+---+----------------------------------------------------------+---------------------------+ The discharge characteristic may be defined by one of Deltares’ standard characteristics (See Hydraulic specifications) or by a user-defined discharge characteristic. If the valve position does not coincide with a tabulated position, interpolation must be performed to obtain the discharge coefficient for intermediate valve positions. The standard characteristics and the user-defined *ξ* characteristic are interpolated logarithmically according to the following equation: .. math:: {\theta(z) = z \cdot \theta_{1} + \left( 1 - z \right) \cdot \theta_{2} }{\xi\left( \theta(z) \right) = \xi_{1}^{z} \cdot \xi_{2}^{1 - z}} The user-defined K\ :sub:`v` and C\ :sub:`v` characteristics are interpolated such that K\ :sub:`v` or C\ :sub:`v` values are interpolated linearly: .. math:: \frac{1}{\sqrt{\xi(\theta(z))}}=\frac{z}{\sqrt{\xi_{1}}}+\frac{1-z}{\sqrt{\xi_{2}}} in which: +--------------+---+-----------------------------------------------------------------+-----+ | *θ\ 1, θ\ 2* | = | tabulated valve positions | [-] | +--------------+---+-----------------------------------------------------------------+-----+ | *z* | = | fraction, which defines intermediate valve position (0 < z < 1) | [-] | +--------------+---+-----------------------------------------------------------------+-----+ | *θ(z)* | = | intermediate valve position | [-] | +--------------+---+-----------------------------------------------------------------+-----+ | *ξ* | = | loss coefficient at *θ\ 1, θ\ 2* | [‑] | +--------------+---+-----------------------------------------------------------------+-----+ | *ξ ( θ(z))* | = | interpolated loss coefficient | [‑] | +--------------+---+-----------------------------------------------------------------+-----+ If the valve is fully closed the governing equations is: .. math:: Q_{1}=0 **Cavitation** Cavitation depends on the pressure conditions around the valve. Usually these pressure conditions are defined by a pressure relation. Several different definitions are use in the industrial standards. In WANDA the factor Xf is used, according the German VDMA standard. .. math:: X_{f}=\frac{\Delta p}{p_{1}-p_{v}} in which: =========== = ======================================== =============== X\ :sub:`f` = pressure ratio [-] ∆p = net pressure difference across the valve [N/m\ :sup:`2`] p\ :sub:`1` = absolute pressure upstream of the valve [N/m\ :sup:`2`] p\ :sub:`v` = vapour pressure of the fluid [N/m\ :sup:`2`] =========== = ======================================== =============== The pressure ratio depends of the valve opening: X\ :sub:`f` = f (θ) The pressure ratio X\ :sub:`f` is only calculated for positive flow; for negative flow X\ :sub:`f` = 0. If the cavitation characteristic is specified, the program calculates the pressure ratio in the system and warns the user if it exceeds the available value as defined in the characteristic. **Note**: In other standards (ISA, BS, IEC) the pressure ratio :math:`X_{T}` is used: .. math:: X_{T}=\frac{p_{1}-p_{2}}{p_{1}}=\frac{\Delta p}{p_{1}} In some standards (e.g. ISA) the Thoma number σ is used. :math:`\sigma=\frac{p_{1}-p_{v}}{\Delta p}` in which: =========== = ======================================== =============== σ = pressure ratio [-] ∆p = net pressure difference across the valve [N/m\ :sup:`2`] P\ :sub:`1` = absolute pressure upstream of the valve [N/m\ :sup:`2`] p\ :sub:`v` = vapour pressure of the fluid [N/m\ :sup:`2`] =========== = ======================================== =============== The relationship between *X\ f* and σ is: :math:`\sigma=\frac{1}{X_{f}}` Another definition for the Thoma number is based on the downstream pressure *p\ 2*: .. math:: \sigma_{2}=\frac{p_{2}-p_{v}}{\Delta p} where :math:`\sigma=1+\sigma_{2}` and :math:`\sigma_{2}=\frac{1}{X f}-1` Valve properties ^^^^^^^^^^^^^^^^ .. _hydraulic-specifications-44: Hydraulic specifications """""""""""""""""""""""" +-----------------------------+------------+-----------------+--------------------------------+----------+--------------------------+ | Description | input | Unit | range | default | remarks | +-----------------------------+------------+-----------------+--------------------------------+----------+--------------------------+ | Characteristic type | Standard/ | | | | | | | | | | | | | | Kv/ | | | | | | | | | | | | | | Cv/ | | | | | | | | | | | | | | Xi | | | | | +-----------------------------+------------+-----------------+--------------------------------+----------+--------------------------+ | Standard type | Buttrfly/ | | | Buttrfly | if char.type = Standard | | | | | | | | | | Ball/ | | | | | | | | | | | | | | Gate/ | | | | | | | | | | | | | | Gate_sqr | | | | | +-----------------------------+------------+-----------------+--------------------------------+----------+--------------------------+ | Kv characteristic | Table | | | | if char.type = Kv | +-----------------------------+------------+-----------------+--------------------------------+----------+--------------------------+ | Cv characteristic | Table | | | | if char.type = Cv | +-----------------------------+------------+-----------------+--------------------------------+----------+--------------------------+ | Xi characteristic | Table | | | | if char.type = Xi | +-----------------------------+------------+-----------------+--------------------------------+----------+--------------------------+ | Inner diameter | Real | [m] | (0-1000] | | | +-----------------------------+------------+-----------------+--------------------------------+----------+--------------------------+ | Initial setting | Position/ | | | | | | | | | | | | | | H_upstream | | | | | | | | | | | | | | H_downstr | | | | | | | | | | | | | | Discharge | | | | | | | | | | | | | | P_upstream | | | | | | | | | | | | | | P_downstr | | | | | +-----------------------------+------------+-----------------+--------------------------------+----------+--------------------------+ | Initial position (open) | Real | [-] | [0-1] | | | 0 = closed | | | | | | | | 1= open | | | | | | | | | | | | | | If init_set = Position | +-----------------------------+------------+-----------------+--------------------------------+----------+--------------------------+ | Initial upstream head | Real | [m] | [-1000 – 1000] | | If init_set = H_upstream | +-----------------------------+------------+-----------------+--------------------------------+----------+--------------------------+ | Initial downstream head | Real | [m] | [-1000 – 1000] | | If init_set = H_downstr | +-----------------------------+------------+-----------------+--------------------------------+----------+--------------------------+ | Initial discharge | Real | [m\ :sup:`3`/s] | (0, 10) | | If init_set = Discharge | +-----------------------------+------------+-----------------+--------------------------------+----------+--------------------------+ | Initial upstream pressure | Real | [N/m\ :sup:`2`] | [-10\ :sup:`5` – 10\ :sup:`7`] | | If init_set = P_upstream | +-----------------------------+------------+-----------------+--------------------------------+----------+--------------------------+ | Initial downstream pressure | Real | [N/m\ :sup:`2`] | [-10\ :sup:`5` – 10\ :sup:`7`] | | If init_set = P_downstr | +-----------------------------+------------+-----------------+--------------------------------+----------+--------------------------+ | Check cavitation | Yes/No | | | | | +-----------------------------+------------+-----------------+--------------------------------+----------+--------------------------+ | Cavitation table | Table | | | | If check cavitation=Yes | +-----------------------------+------------+-----------------+--------------------------------+----------+--------------------------+ Deltares standard characteristics =============== ======== ========== ===== ======= Butterfly valve Ball valve θ ξ θ ξ 0.000 1.0E+10 0.000 1.0E+10 0.010 10000000 0.015 900000 0.025 1700000 0.025 350000 0.050 140000 0.050 40000 0.075 23000 0.075 9500 0.100 6000 0.100 2750 0.125 2400 0.150 650 0.150 1150 0.200 270 0.200 440 0.300 79.5 0.250 195 0.400 30.0 0.300 97.5 0.500 13.8 0.400 31.0 0.600 6.1 0.500 13.8 0.700 2.7 0.600 5.80 0.800 1.03 0.700 2.40 0.900 0.14 0.800 1.00 1.000 0.01 0.900 .420 1.000 0.150 =============== ======== ========== ===== ======= ========== ======= ================= ====== ======= Gate valve Square gate valve θ ξ θ ξ 0.000 1.0E+10 0.000 1.0E+10 0.0025 270000 0.0025 249000 0.025 2850 0.050 850 0.050 625 0.075 370 0.075 270 0.100 195 0.100 140 0.150 82 0.150 58 0.200 45 0.200 31 0.300 17.8 0.300 11.5 0.400 8.2 0.400 5.35 0.500 4.0 0.500 2.55 0.600 2.1 0.600 1.27 0.700 0.95 0.700 0.67 0.800 0.39 0.800 0.355 0.900 0.09 0.900 0.188 1.000 0.001 1.000 0.100 ========== ======= ================= ====== ======= .. _component-specific-output-42: Component specific output """"""""""""""""""""""""" Valve position (open) [-] Pressure ratio X\ :sub:`f` system [-] .. _h-actions-40: H-actions """"""""" A valve can be opened or closed. To do that the valve must be activated. How the valve opens or closes is arranged via a *θ*-time relation in tabular form (menu 'actions' in model). An example: ====================================== ============ Input of table valve type VALVE ACTION Time (s) Position (-) 0 1. 0.5 0. 10.0 0. 12.0 1. 14.0 0.5 18.0 0.5 ====================================== ============ Note: the position unit depends on the setting made in menu Units The valve closes linearly in 0.5 s. It remains closed until 10 s. Then the valve opens again in 2 s and starts to close directly until theta = 0.5 at 14.0 s. From then on the valve remains in that position. .. _component-messages-39: Component messages """""""""""""""""" +-----------------------------------------+-------+------------------------------------------------+ | Message | Type | Explanation | +-----------------------------------------+-------+------------------------------------------------+ | starts in open phase | Info | | +-----------------------------------------+-------+------------------------------------------------+ | Opens | Info | | +-----------------------------------------+-------+------------------------------------------------+ | starts in closed phase | Info | | +-----------------------------------------+-------+------------------------------------------------+ | Closes | Info | | +-----------------------------------------+-------+------------------------------------------------+ | Xf valve exceeded, valve may be choking | Info | Only if “Check Cavitation” = “Yes” | | | | | | | | Current pressure ratio exceeds the table value | +-----------------------------------------+-------+------------------------------------------------+ | Inconsistent valve position valve | Error | The action table input for the valve position | | position between steady state results | | does not match with the Initial setting. | | and action table; modify input | | The user should verify that the required | | | | Initial setting corresponds with the valve | | | | position of the action table. The values in | | | | the action table are allowed to deviate | | | | slightly from the Initial setting. | +-----------------------------------------+-------+------------------------------------------------+ .. include:: substitutions_liquid.rst