Checkvalve
----------

CHECKV (class)
^^^^^^^^^^^^^^

.. figure:: ../media/image394.png
	:figwidth: 0.94792in
	:align: center
	
	Check valve / Non-return valve

**Fall type**

+-----------------------------------+-------------------------------------------------------------------------+--------+
| type label                        | description                                                             | active |
+===================================+=========================================================================+========+
| Checkvalve (ideal)                | ideal check valve;                                                      | No     |
|                                   |                                                                         |        |
|                                   | closes if Q < 0.0, opens if H1 > H2                                     |        |
+-----------------------------------+-------------------------------------------------------------------------+--------+
| Checkvalve (deltaP for reopen)    | ideal check valve;                                                      | No     |
|                                   |                                                                         |        |
|                                   | closes if Q < 0.0, opens if P1-P2 > ∆P                                  |        |
+-----------------------------------+-------------------------------------------------------------------------+--------+
| CHECKV - undamped                 | Check valve using the undamped dynamic characteristic (with dimensions) | No     |
+-----------------------------------+-------------------------------------------------------------------------+--------+
| CHECKV - undamped (dimensionless) | Check valve using the undamped dynamic characteristic, dimensionless    | No     |
+-----------------------------------+-------------------------------------------------------------------------+--------+

Within the component **checkv** four check valves models are avail­able. 
The choice of the model will often depend on the informa­tion (data) which is available and on the degree of accuracy desired. 
If no data are available at all, one may be forced to model the check valve as an **ideal** check valve, which closes without reverse flow. 
However, in practice a check valve does not behave ideally, but closes after flow reversal. The closure is accom­panied with a certain amount of reverse flow and pressure surges, depending on the valve type. 
A better way to model **undamped** as well as **damped** check valves is by means of so‑called dynamic characteris­tics. At this moment WANDA supports only the undamped dynamic characteristic. 
For several valve types these characteristics (dimensionless only) are available in the check valve property templates.

Alternatively, the closure behaviour of check valves may be modelled with the component **valve**. The valve position is then prescribed as function of (closure) time. 
In the case of damped check valves the valve may be closed in two stages: A stage of passive and a stage of active damping.

The initial state of the check valve (i.e., open or closed) is automatically corrected. 
A warning message is shown to the user if the initial state of the check valve is altered.

.. _math_model_checkv_class:

Mathematical models
"""""""""""""""""""

w. Ideal check valve

An open check valve is modelled as a resistance by the following equations:

.. math::

	H_{1}-H_{2}=a \xi Q_{1}\left|Q_{1}\right|

============================= ================================================================================ ============================
variable                      Description                                                                      Units
============================= ================================================================================ ============================
:math:`H_1/H_2`               Head (upstream or downstream)                                                    m
:math:`Q_1/Q_2`               Discharge (upstream or downstream)                                               m\ :sup:`3`/s
:math:`a`                     coefficient (i.e., :math:`\frac{1}{2 g A}`)                                      s\ :sup:`2`/m\ :sup:`5`
:math:`g`                     Gravitational acceleration                                                       m/s\ :sup:`2`
:math:`A`                     Valve discharge area                                                             m\ :sup:`2`
============================= ================================================================================ ============================


The discharge area of the check valve may differ from the cross sectional area of the adjacent pipes. The area is calculated from the check valve inlet diameter *D* according to:

.. math::

	A=\pi D^{2} / 4

Once the check valve is closed, the valve is modelled by:

.. math::

	Q_{1}=0


Now the criteria for opening and closure must be defined.

**Closure criteria**

An ideal check valve closes when:

.. math::

	Q_{1}<0

**Opening criteria**

A closed valve (re)opens when the pressure difference across the valve exceeds a specified value:

.. math::

	\mathrm{P} 1-\mathrm{P} 2>\Delta \mathrm{P}

The default value of :math:`\Delta P = 0`. For the "Check valve (:math:`\Delta p_{\text{reopen}}`)", the `\Delta P` is specified by the user. 
*Note:*  The :math:`\Delta p_{\text{reopen}}` may not correspond with the results of :math:`\Delta p`, because of discretization errors. 
The :math:`\Delta p_{\text{reopen}}` approaches :math:`\Delta p` for small :math:`\Delta t`.

1. Undamped check valve (standard)

An open check valve is modelled as a resistance by:

.. math::

	H_{1}-H_{2}=a \xi Q_{1}\left|Q_{1}\right|

with:

============= ====================== =========================
Variable      Description            Units
============= ====================== =========================
*H*\ :sub:`1` upstream head          m
*H*\ :sub:`2` downstream head        m
a             1/(2\ *gA*\ :sup:`2`)  s\ :sup:`2`/m\ :sup:`5`
:math:`\xi`   valve loss coefficient ‑
*Q*\ :sub:`1` upstream discharge     m\ :sup:`3`/s
*Q*\ :sub:`2` downstream discharge   m\ :sup:`3`/s
A             valve inlet area       m\ :sup:`2`
============= ====================== =========================

Once the check valve is closed, the valve is modelled by:

.. math::

	Q_{1}=0


Now the criteria for opening and closure must be defined.

**Closure criteria**

The check valve (re)closes when:

.. math::

	Q_{1}<Q_{R}=\frac{\pi}{4} D^{2} v_{R}

.. math:: 

   v_{R}=f_{1}\left(\theta_{i}\right) \cdot f_{2}\left(\frac{d v}{d t}\right)


Where:

.. math::

	f_{1}\left(\theta_{i}\right)=\frac{v_{i}}{v_{o}}

.. math::

	\frac{d v}{d t}=\frac{v-v_{i}}{t-t_{i}}

If: :math:`v_i \geq v_o` then :math:`v_i = v_o` and :math:`t_i = t_o`

If: :math:`v_i < v_o` then :math:`v_i = v_i` and :math:`t_i = t_i`

with:

============================= ================================================================================ ============================
variable                      Description                                                                      Units
============================= ================================================================================ ============================
:math:`D`                     Valve inlet diameter                                                             m
:math:`v_r`                   Maximum reverse flow velocity                                                    m/s
:math:`v_o`                   critical velocity (valve just 100% open)                                         m/s
:math:`v_i`                   initial (steady) velocity before (re)closure                                     m/s
:math:`dv/dt`                 (mean) flow deceleration                                                         m/s\ :sup:`2`
============================= ================================================================================ ============================


The function *f\ 1* accounts for the effect of an initially, partly opened valve on the maximum reverse flow velocity. The function *f\ 2* represents the dynamic characteristic for undamped check valves, for the initially, fully opened valve.

For several valve types dynamic characteristics are available in the check valve property templates

**Opening criteria**

A closed valve (re)opens when the pressure difference across the valve exceeds a specified value:

.. math::

	P_{1}-P_{2}>\Delta P

The default value of :math:`\Delta P=0` .

1. Undamped check valve (dimensionless)

An open check valve is modelled as a resistance by:

.. math::

	H_{1}-H_{2}=a \xi Q_{1}\left|Q_{1}\right|


with:

=========== ====================== =========================
Variable    Description            Units
=========== ====================== =========================
H\ :sub:`1` upstream head          m
H\ :sub:`2` downstream head        m
a           1/(2gA\ :sup:`2`)      s\ :sup:`2`/m\ :sup:`5`
ξ           valve loss coefficient ‑
Q\ :sub:`1` upstream discharge     m\ :sup:`3`/s
Q\ :sub:`2` downstream discharge   m\ :sup:`3`/s
A           valve inlet area       m\ :sup:`2`
=========== ====================== =========================

Once the check valve is closed, the valve is modelled by:

.. math::

	Q_{1}=0


Now the criteria for opening and closure must be defined.

**Closure criteria**

The check valve (re)closes when:

.. math::

	Q_{1}<Q_{R}=\frac{\pi}{4} D^{2} v_{R}

The maximum reverse flow *Q\ R* (< 0) is determined from:


.. math::
   
   \frac{v_{R}}{v_{o}}=f_{1}\left(\frac{\theta_{i}-\theta_{c}}{\theta_{o}-\theta_{c}}\right) \cdot f_{2}\left(\frac{D}{v_{o}^{2}} \frac{d v}{d t}\right)


Where:


.. math:: 
   
   f_{1}\left(\frac{\theta_{i}-\theta_{c}}{\theta_{o}-\theta_{c}}\right)=\frac{v_{i}}{v_{o}}


.. math::

	\frac{d v}{d t}=\frac{v-v_{i}}{t-t_{i}}

If: *v\ i* ≥ *v\ o* then *v\ i* = *v\ o*\ and *t\ i* = *t\ o*

If: *v\ i* < *v\ o*\ then *v\ i* = *v\ i* and *t\ i* = *t\ i*

with:

============================= ================================================================================ ============================
variable                      Description                                                                      Units
============================= ================================================================================ ============================
:math:`D`                     Valve inlet diameter                                                             m
:math:`v_r`                   Maximum reverse flow velocity                                                    m/s
:math:`v_o`                   critical velocity (valve just 100% open)                                         m/s
:math:`v_i`                   initial (steady) velocity before (re)closure                                     m/s
:math:`dv/dt`                 (mean) flow deceleration                                                         m/s\ :sup:`2`
============================= ================================================================================ ============================

The function *f\ 1* accounts for the effect of an initially, partly opened valve on the maximum reverse flow velocity. The function *f\ 2* represents the dynamic characteristic for undamped check valves, for the initially, fully opened valve.

For several valve types dimensionless dynamic characteristics are available in the property template files.

**Opening criteria**

A closed valve (re)opens when the pressure difference across the valve exceeds a specified value:

.. math::

	P_{1}-P_{2}>\Delta P

The default value of :math:`\Delta P=0`.

**Anchor forces**

The anchor forces on a check valve are directly related to the pressure difference over the check valve. The pressure difference both upstream (:math:`\Delta H_u`) and downstream (:math:`\Delta H_d`) can be calculated as:


.. math::
	
	\Delta H_u = + \frac{c\nu_r}{g}

.. math::
	
	\Delta H_d = - \frac{c\nu_r}{g}


with 

+--------------------+-------------------------------------------------------------------+---------------+
| Variable           | Description                                                       | Units         |
+====================+===================================================================+===============+
| :math:`\Delta H_u` | Upstream pressure difference due to valve closure                 | m             |
+--------------------+-------------------------------------------------------------------+---------------+
| :math:`\Delta H_d` | Downstream pressure difference due to valve closure               | m             |
+--------------------+-------------------------------------------------------------------+---------------+
| :math:`c`          | Speed of sound in the connected pipe.                             | m/s           |
+--------------------+-------------------------------------------------------------------+---------------+
| :math:`\nu_r`      | Maximum return speed over the checkvalve.                         | m/s           |
+--------------------+-------------------------------------------------------------------+---------------+

The anchor forces are directly related to the pressure difference over the check valve. Therefore, the anchor force can be derived as:

.. math::
	
	F = \Delta p(x)A = \rho g (\Delta H_u - \Delta H_d)A


where :math:`A` is the valve area.


Checkvalve (ideal)
^^^^^^^^^^^^^^^^^^

.. _hydraulic-specifications-9:

Hydraulic specifications
""""""""""""""""""""""""

================ ===================== ==== ====== ========= =======
description      input                 unit range  default   remarks
================ ===================== ==== ====== ========= =======
inner diameter   real                  [m]  (0-10)         
loss coefficient real                  [-]  [0-10]           
initial state    open/closed/automatic             automatic    
================ ===================== ==== ====== ========= =======

See also “Mathematical models” (:numref:`math_model_checkv_class`).
The check valve will automaticly determine if it is open or closed when it is in the initial state automatic.
To determine the position it will first try the calculation with open check valve. If this results in return flow, it will retry with a closed check valve.
If it cannot find a solution  general message that the solution is unstable will be given. The user is then advised to set the state manual.

.. _component-specific-output-8:

Component specific output
"""""""""""""""""""""""""

None

.. _h-actions-8:

H-actions
"""""""""

None

.. _component-messages-9:

Component messages
""""""""""""""""""

====================== ==== ===========
Message                Type Explanation
====================== ==== ===========
Starts in closed phase Info 
Starts in open phase   Info 
Closes                 Info 
Opens                  Info 
====================== ==== ===========

Checkvalve (deltaP for reopen)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.. _hydraulic-specifications-10:

Hydraulic specifications
""""""""""""""""""""""""

+--------------------+-------------+-----------------+------------------+---------+---------+
| description        | input       | unit            | range            | default | remarks |
+====================+=============+=================+==================+=========+=========+
| inner diameter     | real        | [m]             | (0-10)           |         |         |
+--------------------+-------------+-----------------+------------------+---------+---------+
| loss coefficient   | real        | [-]             | [0-10]           |         |         |
+--------------------+-------------+-----------------+------------------+---------+---------+
| delta_p for reopen | real        | [N/m\ :sup:`2`] | (0-10\ :sup:`6`) |         |         |
+--------------------+-------------+-----------------+------------------+---------+---------+
| initial state      | open/closed/|                 |                  |automatic|         |
|                    | automatic   |                 |                  |         |         |
+--------------------+-------------+-----------------+------------------+---------+---------+

See also “Mathematical models” (:numref:`math_model_checkv_class`).
The check valve will automaticly determine if it is open or closed when it is in the initial state automatic.
To determine the position it will first try the calcualtion with open check valve. If this results in return flow, it will retry with a closed check valve.
If it cannot find a solution the user will be informed and need to select either the open or closed state self. 

.. _component-specific-output-9:

Component specific output
"""""""""""""""""""""""""

None

.. _h-actions-9:

H-actions
"""""""""

None

.. _component-messages-10:

Component messages
""""""""""""""""""

====================== ==== ===========
Message                Type Explanation
====================== ==== ===========
Starts in closed phase Info 
Starts in open phase   Info 
Closes                 Info 
Opens                  Info 
====================== ==== ===========

CHECKV - undamped
^^^^^^^^^^^^^^^^^

.. _hydraulic-specifications-11:

Hydraulic specifications
""""""""""""""""""""""""

+------------------------+-------------+-----------------+------------------+---------+---------+
| description            | input       | unit            | range            | default | remarks |
+========================+=============+=================+==================+=========+=========+
| inner diameter         | real        | [m]             | (0-10)           |         |         |
+------------------------+-------------+-----------------+------------------+---------+---------+
| loss coefficient       | real        | [-]             | [0-10]           |         |         |
+------------------------+-------------+-----------------+------------------+---------+---------+
| delta_p for reopen     | real        | [N/m\ :sup:`2`] | (0-10\ :sup:`6`) |         |         |
+------------------------+-------------+-----------------+------------------+---------+---------+
| Dynamic characteristic | table       |                 |                  |         |         |
+------------------------+-------------+-----------------+------------------+---------+---------+
| Critical velocity      | real        | [m/s]           | (0-10)           |         |         |
+------------------------+-------------+-----------------+------------------+---------+---------+
| initial state          | open/closed |                 |                  |automatic|         |
|                        | automatic   |                 |                  |         |         |
+------------------------+-------------+-----------------+------------------+---------+---------+

See also “Mathematical models” (:numref:`math_model_checkv_class`).
The check valve will automaticly determine if it is open or closed when it is in the initial state automatic.
To determine the position it will first try the calcualtion with open check valve. If this results in return flow, it will retry with a closed check valve.
If it cannot find a solution the user will be informed and need to select either the open or closed state self. 

.. _component-specific-output-10:

Component specific output
"""""""""""""""""""""""""

Dv/dt: [m/s\ :sup:`2`]

Anchor force: [N]

.. _h-actions-10:

H-actions
"""""""""

None

.. _component-messages-11:

Component messages
""""""""""""""""""

====================== ==== ===========
Message                Type Explanation
====================== ==== ===========
starts in closed phase Info 
starts in open phase   Info 
closes                 Info 
opens                  Info 
====================== ==== ===========

.. _example-3:

Example
"""""""

=========================================== =====================
Type                                        Checkvalve (undamped)
=========================================== =====================
Comment: horizontal position; spring loaded 
Model name                                  Split disc
Inner diameter (mm)                         200.0
Loss coefficient (-)                        2.400
Delta_p for reopen (kPa)                    5.000
Critical velocity Vo (m/s)                  1.750
=========================================== =====================

.. figure:: ../media/image424.png
	:figwidth: 4.4375in
	:align: center
	
	Consult your manufacturer for the dynamic characteristic of his product.



CHECKV - undamped (dimensionless)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.. _hydraulic-specifications-12:

Hydraulic specifications
""""""""""""""""""""""""

+--------------------------------------+-------------+-----------------+------------------+---------+---------+
| description                          | input       | unit            | range            | default | remarks |
+======================================+=============+=================+==================+=========+=========+
| inner diameter                       | real        | [m]             | (0-10)           |         |         |
+--------------------------------------+-------------+-----------------+------------------+---------+---------+
| loss coefficient                     | real        | [-]             | [0-10]           |         |         |
+--------------------------------------+-------------+-----------------+------------------+---------+---------+
| delta_p for reopen                   | real        | [N/m\ :sup:`2`] | (0-10\ :sup:`6`) |         |         |
+--------------------------------------+-------------+-----------------+------------------+---------+---------+
| Dimensionless dynamic characteristic | table       |                 |                  |         |         |
+--------------------------------------+-------------+-----------------+------------------+---------+---------+
| Critical velocity                    | real        | [m/s]           | (0-10)           |         |         |
+--------------------------------------+-------------+-----------------+------------------+---------+---------+
| initial state                        | open/closed |                 |                  |automatic|         |
|                                      | automatic   |                 |                  |         |         |
+--------------------------------------+-------------+-----------------+------------------+---------+---------+

See also “Mathematical models” (:numref:`math_model_checkv_class`).
The check valve will automaticly determine if it is open or closed when it is in the initial state automatic.
To determine the position it will first try the calcualtion with open check valve. If this results in return flow, it will retry with a closed check valve.
If it cannot find a solution the user will be informed and need to select either the open or closed state self. 

.. _component-specific-output-11:

Component specific output
"""""""""""""""""""""""""

Dv/dt: [m/s\ :sup:`2`]

Anchor force: [N]

.. _h-actions-11:

H-actions
"""""""""

None

.. _component-messages-12:

Component messages
""""""""""""""""""

====================== ==== ===========
Message                Type Explanation
====================== ==== ===========
starts in closed phase Info 
starts in open phase   Info 
closes                 Info 
opens                  Info 
====================== ==== ===========

.. _example-4:

Example
"""""""

+---------------------------------------------+---------------------------------+
| Type                                        | Checkvalve (undamped, dimless ) |
+=============================================+=================================+
| Comment: horizontal position; spring loaded |                                 |
+---------------------------------------------+---------------------------------+
| Model name                                  | Nozzle type                     |
+---------------------------------------------+---------------------------------+
| Inner diameter (mm)                         | 800.0                           |
+---------------------------------------------+---------------------------------+
| Loss coefficient (-)                        | 4.500                           |
+---------------------------------------------+---------------------------------+
| Delta_p for reopen (kPa)                    | 10.000                          |
+---------------------------------------------+---------------------------------+
| Critical velocity Vo (m/s)                  | 2.50                            |
+---------------------------------------------+---------------------------------+

.. figure:: ../media/image425.png
	:figwidth: 4.4375in
	:align: center
	
	A sample characteristic of a check-valve showing :math:`dv/dt` versus :math:`v_r`

Some typical dimensionless dynamic characteristics are shown in the picture below. These characteristics are for reference only.

.. figure:: ../media/image426.png
	:figwidth: 5.40625in
	:align: center
	
	Consult your check valve manufacturer for the real dynamic characteristics of his product.



.. include:: substitutions_liquid.rst