Pressure relief valve --------------------- PRV (class) ^^^^^^^^^^^ .. figure:: ../media/image616.png :figwidth: 0.94792in :align: center Pressure relief valve, safety valve **Fall type** +------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------+ | Type label | description | active | +========================+========================================================================================================================================================================+========+ | PRV (Ideal) | This prv monitors the system pressure and opens upon exceedance of a set pressure. Opening time, friction, choking flow and valve dynamics are not taken into account. | No | +------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------+ | PRV (simplified char.) | The opening pressure, as well as the full lift pressure and discharge, must be specified. (accumulation is taken into account). | No | +------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------+ .. _mathematical-model-23: Mathematical model """""""""""""""""" The PRV is always closed in the steady state. In steady state and closed state the governing equation of the prv component is very simple: .. math:: Q_{1}=0 in which: ============= ================== =============== Variable Description Units ============= ================== =============== *Q*\ :sub:`1` upstream discharge m\ :sup:`3`/s ============= ================== =============== The PRV has been implemented as a Fall type (up- and downstream head and flow) to allow a downstream pressure that is different from atmospheric pressure. Only the PRV (simpl. char.) is influenced by the downstream pressure head. If the system pressure (measured at the upstream H-node: H\ :sub:`1`) exceeds the set pressure (gauge pressure) the prv opens, maintains the set pressure, P\ :sub:`set`, and the governing equation of the ideal PRV becomes: .. math:: H_{1}=\frac{P_{s e t}}{\rho_{f} g}+h in which: ============= ========================== =============== Variable Description Units ============= ========================== =============== :math:`H1` pstream pressure head m :math:`Pset` set pressure (gauge) N/m\ :sup:`2` :math:`P_{f}` fluid density kg/m\ :sup:`3` :math:`g` gravitational acceleration m/s\ :sup:`2` :math:`h` elevation of PRV m ============= ========================== =============== The ideal PRV is not influenced by the downstream head, because it maintains the set pressure ideally. In practice, however the PRV will not act ideally. The non-ideal behaviour can be modelled with a simplified characteristic of the PRV. After exceeding the set pressure the valve body will lift and gradually open upon increasing pressure and discharge. If the internal pressure keeps rising, the valve body will eventually hit a stop and the full lift condition is entered. From then on, the PRV will act as a resistance with constant loss coefficient. The simplified characteristic PRV is influenced by the downstream head so that the user may specify a boundary condition that is different from atmospheric pressure. One could think of a pressurised tank at the downstream side of the PRV. In the partial lift phase ( 0 Q1 Qfull ) the governing equations are: .. math:: \Delta P=\Delta P_{\mathrm{set}}+\left(\Delta P_{\mathrm{full}}-\Delta P_{\mathrm{set}}\right) \frac{Q_{1}}{Q_{\text {full }}} .. math:: Q_{1}=Q_{2} in which: +----------------------+------------------------------------------------------------------------+-----------------+ | Variable | Description | Units | +======================+========================================================================+=================+ | :math:`\Delta` P | pressure difference over PRV: ρ\ *g* ( *H*\ :sub:`1` - *H*\ :sub:`2` ) | [N/m\ :sup:`2`] | +----------------------+------------------------------------------------------------------------+-----------------+ | :math:`\Delta` Pset | set pressure difference | [N/m\ :sup:`2`] | +----------------------+------------------------------------------------------------------------+-----------------+ | :math:`\Delta` Pfull | full lift pressure difference | [N/m\ :sup:`2`] | +----------------------+------------------------------------------------------------------------+-----------------+ | Qfull | full lift discharge | [m\ :sup:`3`/s] | +----------------------+------------------------------------------------------------------------+-----------------+ In the full lift phase ( Q1 Qfull ) the governing equations are: .. math:: \Delta P=\frac{\Delta P_{\text {full }}}{Q_{\text {full }}^{2}} Q_{1}^{2} The Q P relation is shown in the figure below: .. figure:: ../media/image626.png :figwidth: 3.47917in :align: center Q-P relation for pressure relief valve (PRV) The prv closes again if *Q*\ :sub:`1` < 0. PRV (simplified char.) ^^^^^^^^^^^^^^^^^^^^^^ .. _hydraulic-specifications-24: Hydraulic specifications """""""""""""""""""""""" +-------------------------+-------+------------------+------------------+---------+---------+ | Description | input | unit | range | default | remarks | +=========================+=======+==================+==================+=========+=========+ | set pressure (∆P) | real | [N/m\ :sup:`2`] | (0-10\ :sup:`8`) | | | +-------------------------+-------+------------------+------------------+---------+---------+ | full lift pressure (∆P) | real | [N/m\ :sup:`2`] | (0-10\ :sup:`8`) | | | +-------------------------+-------+------------------+------------------+---------+---------+ | full lift discharge | real | [m] | (0-10\ :sup:`8`) | | | +-------------------------+-------+------------------+------------------+---------+---------+ See also "Mathematical model" (:numref:`mathematical-model-23`). **Tip**: The downstream head of the PRV should be set to the elevation level of the PRV if you want to model an atmospheric pressure at the downstream side. .. _component-specific-output-23: Component specific output """"""""""""""""""""""""" None .. _h-actions-21: H-actions """"""""" None .. _component-messages-20: Component messages """""""""""""""""" ============== ==== =========== Message Type Explanation ============== ==== =========== closes Info partially open Info fully open Info ============== ==== =========== PRV (Ideal) ^^^^^^^^^^^ .. _hydraulic-specifications-25: Hydraulic specifications """""""""""""""""""""""" +-------------------------+-------+------------------+------------------+---------+---------+ | Description | Input | unit | range | default | remarks | +=========================+=======+==================+==================+=========+=========+ | set pressure (P upstr.) | Real | N/m\ :sup:`2` | (0-10\ :sup:`8`) | | | +-------------------------+-------+------------------+------------------+---------+---------+ | Elevation | Real | m | | | | +-------------------------+-------+------------------+------------------+---------+---------+ See also "Mathematical model" (:numref:`mathematical-model-23`). | **Tip**: | The downstream head of the PRV should be set to the elevation level of the PRV if you want to model an atmospheric pressure at the downstream side. .. _component-specific-output-24: Component specific output """"""""""""""""""""""""" None .. _h-actions-22: H-actions """"""""" None .. _component-messages-21: Component messages """""""""""""""""" +----------------------------------------------------+---------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Message | Message | explanation | +====================================================+=========+=======================================================================================================================================================================================================================================================================================+ | Closes | Info | | +----------------------------------------------------+---------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Opens | Info | | +----------------------------------------------------+---------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Not valid (H2>H1), down­stre­am capacity exceed­ed | Warning | *H*\ :sub:`2` does not play a role in the current mathematical model of the ideal prv. If however *H*\ :sub:`2` becomes greater than *H*\ :sub:`1` the prv "drowns" and effectively the computation loses physical relevance. This is a useful aid to design the downstream capacity. | +----------------------------------------------------+---------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ .. include:: substitutions_liquid.rst