.. _sec_H_valve: Valve ----- .. _fig_heat_valve: .. figure:: ../media/heat/image1256.svg :width: 200in :align: center Schematic of a Heat valve. **Fall type** +------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------+ | Type label | Description | Active | +============+==============================================================================================================================================================================================================+========+ | Heat 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-62: Mathematical model ^^^^^^^^^^^^^^^^^^ Pressure loss coefficients """""""""""""""""""""""""" The discharge characteristic indicates the relation between the flow :math:`Q` through the valve and the pressure loss :math:`\Delta p` across the valve as a function of the valve position. This relation is expressed in a discharge coefficient :math:`K_v` or :math:`C_v` and a loss coefficient :math:`\xi`. 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_{1}v_{1}^{2}}{2} with: ============================= ====================================================================== ======================== Variable Description Units ============================= ====================================================================== ======================== :math:`\Delta p` Pressure difference over the valve Pa :math:`\xi` Loss coefficient of the valve \- :math:`\rho_1` Density of the fluid (upstream) kg/m\ :sup:`3` :math:`v_1` Velocity of the fluid (upstream) m/s ============================= ====================================================================== ======================== In practice the discharge coefficients :math:`K_v` is often used: .. math:: K_{v}=\frac{Q}{\sqrt{\Delta p}} with: ============================= ====================================================================== ========================================== Variable Description Units ============================= ====================================================================== ========================================== :math:`K_v` Discharge coefficient m\ :sup:`3` /h/:math:`\sqrt{\text{bar}}` :math:`Q` Flowrate m\ :sup:`3`/h :math:`\Delta p` Pressure difference over 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 :math:`K_v`, :math:`C_v` is also defined as a discharge coefficients for American units. .. math:: C_{v}=\frac{Q}{\sqrt{\Delta p}} with ============================= ====================================================================== ========================================== Variable Description Units ============================= ====================================================================== ========================================== :math:`C_v` Discharge coefficient USGM/ :math:`\sqrt{\text{psi}}` :math:`Q` Flowrate USGM :math:`\Delta p` Pressure difference over 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}|Q_{1}| with: ============================= ====================================================================== ========================================== Variable Description Units ============================= ====================================================================== ========================================== :math:`\Delta H` :math:`H_1 - H_2` in the positive flow direction m :math:`H_1 / H_2` Upstream and downstream head m :math:`a` :math:`1 / \left(2 g A_f^2 \right)` s\ :sup:`2`/m\ :sup:`5` :math:`\xi` Loss coefficient \- :math:`Q_1` Upstream discharge m\ :sup:`3`/s ============================= ====================================================================== ========================================== 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 \theta_1 + \left( 1 - z \right) \theta_2 .. math:: \xi\left( \theta (z) \right) = \xi_1^z \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\left( \theta (z) \right)}} = \frac{z}{\sqrt{\xi_{1}}} + \frac{1 - z}{\sqrt{\xi_{2}}} with: ============================= ====================================================================== ========================================== Variable Description Units ============================= ====================================================================== ========================================== :math:`\theta_1, \theta_2` Tabulated valve opening positions \- :math:`z` Fraction defining intermediate valve position (:math:`0 < z < 1`) \- :math:`\theta (z)` Intermediate valve position loss coefficient \- :math:`\xi ( \theta (z))` Interpolated loss coefficient \- ============================= ====================================================================== ========================================== If the valve is closed the governing equations is: .. math:: Q_{1} = 0 To calculate the temperature the following equation is used: .. math:: \dot{m}c_{p, 1}T_{1} - \dot{m}c_{p, 2}T_{2} + fr Q_{\text{gen}} = 0 with: ============================= ====================================================================== ========================================== Variable Description Units ============================= ====================================================================== ========================================== :math:`\dot{m}` Mass flow rate kg/s :math:`c_{p, i}` Specific heat at connection point :math:`i` J/kg/K :math:`T_{i}` Temperature at connection point :math:`i` K :math:`fr` Fraction generated heat supplied to fluid \- :math:`Q_{gen}` Heat generated by friction W ============================= ====================================================================== ========================================== The generated heat is given by: .. math:: Q_{gen} = \xi \frac{\dot{m}^3}{2 \rho^2 A^2} ============================= ====================================================================== ========================================== Variable Description Units ============================= ====================================================================== ========================================== :math:`A` Area of the valve m\ :sup:`2` ============================= ====================================================================== ========================================== .. _cavitation-1: Cavitation """""""""" Cavitation depends on the pressure conditions around the valve. Usually these pressure conditions are defined by a pressure relation. Several different definitions are used in industrial standards. In WANDA the factor :math:`X_f` is used, according the German VDMA standard. .. math:: X_{f} = \frac{\Delta p}{p_1 - p_v} with: ============================= ====================================================================== ========================================== Variable Description Units ============================= ====================================================================== ========================================== :math:`X_f` Pressure ratio \- :math:`\Delta p` Pressure difference over valve Pa :math:`p_1` Absolute pressure upstream of the valve Pa abs :math:`p_v` Vapour pressure of the fluid Pa ============================= ====================================================================== ========================================== 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 (:math:`\sigma`) is used. .. math:: \sigma_{} = \frac{p_1 - p_v}{\Delta p} with: ============================= ====================================================================== ========================================== Variable Description Units ============================= ====================================================================== ========================================== :math:`X_f` Pressure ratio - :math:`\Delta p` Pressure difference over valve Pa :math:`p_1` Absolute pressure upstream of the valve Pa abs :math:`p_v` Vapour pressure of the fluid Pa ============================= ====================================================================== ========================================== 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-1: Valve properties ^^^^^^^^^^^^^^^^ .. _hydraulic-specifications-71: Hydraulic specifications """""""""""""""""""""""" +-----------------------------+--------------+----------------------+---------------------------------------------+ | Description | input | SI-units | Remarks | +=============================+==============+======================+=============================================+ | Characteristic type | Standard | | | | | | | | | | Kv | | | | | | | | | | Cv | | | | | | | | | | Xi | | | +-----------------------------+--------------+----------------------+---------------------------------------------+ | Standard type | Buttrfly | | if char.type = Standard, default = Buttrfly | | | | | | | | Ball | | | | | | | | | | Gate | | | | | | | | | | Gate_sqr | | | +-----------------------------+--------------+----------------------+---------------------------------------------+ | Kv characteristic | table | [m\ :sup:`3`/h/√bar] | if char.type = Kv | +-----------------------------+--------------+----------------------+---------------------------------------------+ | Cv characteristic | table | [USGM/√psi] | if char.type = Cv | +-----------------------------+--------------+----------------------+---------------------------------------------+ | Xi characteristic | table | [-] | if char.type = Xi | +-----------------------------+--------------+----------------------+---------------------------------------------+ | Inner diameter | real | [m] | | +-----------------------------+--------------+----------------------+---------------------------------------------+ | Initial setting | Position | | | | | | | | | | P_upstream | | | | | | | | | | P_downstr | | | | | | | | | | Mass flow | | | | | T_downstream | | | +-----------------------------+--------------+----------------------+---------------------------------------------+ | Initial position (open) | real | [-] | | 0 = closed | | | | | | 1= open | | | | | | | | | | If init_set = Position | +-----------------------------+--------------+----------------------+---------------------------------------------+ | Initial upstream pressure | real | [N/m²] | If init_set = P_upstream | +-----------------------------+--------------+----------------------+---------------------------------------------+ | Initial downstream pressure | real | [N/m²] | If init_set = P_downstr | +-----------------------------+--------------+----------------------+---------------------------------------------+ | Initial mass flow | real | [kg/s] | If init_set = Mass flow | +-----------------------------+--------------+----------------------+---------------------------------------------+ | Check cavitation | Yes/No | | | +-----------------------------+--------------+----------------------+---------------------------------------------+ | Cavitation table | table | | If check cavitation=Yes | +-----------------------------+--------------+----------------------+---------------------------------------------+ | Fraction gen. heat to fluid | real | [-] | Default = 1 (100%) | +-----------------------------+--------------+----------------------+---------------------------------------------+ Deltares standard characteristics **Butterfly valve** =============== ================= :math:`\theta` :math:`\xi` =============== ================= 0.000 1.0E+10 0.010 10000000 0.025 1700000 0.050 140000 0.075 23000 0.100 6000 0.125 2400 0.150 1150 0.200 440 0.250 195 0.300 97.5 0.400 31.0 0.500 13.8 0.600 5.80 0.700 2.40 0.800 1.00 0.900 .420 1.000 0.150 =============== ================= **Ball valve** =============== ================= :math:`\theta` :math:`\xi` =============== ================= 0.000 1.0E+10 0.015 900000 0.025 350000 0.050 40000 0.075 9500 0.100 2750 0.150 650 0.200 270 0.300 79.5 0.400 30.0 0.500 13.8 0.600 6.1 0.700 2.7 0.800 1.03 0.900 0.14 1.000 0.01 =============== ================= **Gate valve** =============== ================= :math:`\theta` :math:`\xi` =============== ================= 0.000 1.0E+10 0.0025 270000 0.025 2850 0.050 625 0.075 270 0.100 140 0.150 58 0.200 31 0.300 11.5 0.400 5.35 0.500 2.55 0.600 1.27 0.700 0.67 0.800 0.355 0.900 0.188 1.000 0.100 =============== ================= **Square gate valve** =============== ================= :math:`\theta` :math:`\xi` =============== ================= 0.000 1.0E+10 0.0025 249000 0.050 850 0.075 370 0.100 195 0.150 82 0.200 45 0.300 17.8 0.400 8.2 0.500 4.0 0.600 2.1 0.700 0.95 0.800 0.39 0.900 0.09 1.000 0.001 =============== ================= .. _component-specific-output-65: Component specific output """"""""""""""""""""""""" - Valve position (open) [-] - Pressure ratio X\ :sub:`f` system [-] - Generated Heat flux [W] .. _actions-10: Actions """"""" An activated valve can be opened or closed. How the valve opens or closes is arranged via a *θ*-time relation in tabular form. An example: **Valve action table** ================== ============ 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-62: Component messages """""""""""""""""" +----------------------------------------------------------------------------------+---------+--------------------------------------------------------------------------------------+ | Message | Type | Explanation | +==================================================================================+=========+======================================================================================+ | starts in open phase | Info | | +----------------------------------------------------------------------------------+---------+--------------------------------------------------------------------------------------+ | starts in closed phase | Info | | +----------------------------------------------------------------------------------+---------+--------------------------------------------------------------------------------------+ | Opens | Info | | +----------------------------------------------------------------------------------+---------+--------------------------------------------------------------------------------------+ | Closes | Info | | +----------------------------------------------------------------------------------+---------+--------------------------------------------------------------------------------------+ | | | | +----------------------------------------------------------------------------------+---------+--------------------------------------------------------------------------------------+ | Initial valve position below minimum position; minimum table value used | Warning | | +----------------------------------------------------------------------------------+---------+--------------------------------------------------------------------------------------+ | Initial valve position above maximum position; maximum table value used | Warning | | +----------------------------------------------------------------------------------+---------+--------------------------------------------------------------------------------------+ | Valve position truncated to input range | Warning | | +----------------------------------------------------------------------------------+---------+--------------------------------------------------------------------------------------+ | Indifferent valve position (zero discharge and zero dH) max. open position taken | Warning | | +----------------------------------------------------------------------------------+---------+--------------------------------------------------------------------------------------+ | Valve characteristic table entries not in between [0-1] | Error | The input table is not correct | +----------------------------------------------------------------------------------+---------+--------------------------------------------------------------------------------------+ | Valve resistance in max. open position too large to obtain prescribed state | Error | The desired flow rate is too large for this valve with the calculated pressure drop. | +----------------------------------------------------------------------------------+---------+--------------------------------------------------------------------------------------+ | Valve resistance in min. open position too small to obtain prescribed state | Error | | +----------------------------------------------------------------------------------+---------+--------------------------------------------------------------------------------------+ | Initial setting not physically realistic Discharge opposite to pressure drop | Error | Check your model or chose different settings. | +----------------------------------------------------------------------------------+---------+--------------------------------------------------------------------------------------+ | Cavitation in steady state not allowed' | Error | | +----------------------------------------------------------------------------------+---------+--------------------------------------------------------------------------------------+ | Inconsistent valve position valve position between steady state results | Error | The action table input for the valve position does not match with the Initial | | and action table; modify input | | setting. 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. | +----------------------------------------------------------------------------------+---------+--------------------------------------------------------------------------------------+