# DynamicCheckValve


## Copyright © EDF 2002 - 2026   
## ThermoSysPro Version 4.2  
This component model is documented in Sect. 13.12 of the ThermoSysPro book.   
# Dynamic check valve   

The dynamic check valve is modeled as a control valve which position is controlled by the flow through the clapper aperture.  
The inertia of the movement of the clapper is taken into account, contrary to the [check valve](ThermoSysPro.WaterSteam.PressureLosses.CheckValve).  
The model presented here only accounts for clapper check valves.  


## Modelica component model  

The equations mentioned below are implemented in the component *DynamicCheckValve*, located in the *WaterSteam.PressureLosses* sub-library.   
This component has 2 connectors:  
- C1: fluid inlet,  
- C2: fluid outlet.  
   
![ThermoSysPro.WaterSteam.PressureLosses.DynamicCheckValve.svg](./icons/ThermoSysPro.WaterSteam.PressureLosses.DynamicCheckValve.svg)  

## Nomenclature  

| Symbol| Description| Unit| Definition| Modelica name |  
| :----------------------------------------------- | :------------------------------------------------------------------------------------- | :------------------------------- | :-------------------------------- | :----------- |  
| $A$| Clapper hydraulic area| $\mathrm{m}^{2}$|| A |  
| $C_{\mathrm{f}}$| Friction torque acting on the clapper| $\mathrm{N} \mathrm{m}$|| Cf |  
| $C_{\mathrm{h}}$| Hydraulic torque acting on the clapper| $\mathrm{N} \mathrm{m}$|| Ch |  
| $C_{\mathrm{s}}$| Spring torque acting on the clapper| $\mathrm{N} \mathrm{m}$|| - |  
| $C_{\mathrm{t}}$| Total torque acting on the clapper| $\mathrm{N} \mathrm{m}$|| Ct |  
| $C_{\mathrm{v}}$| Flow coefficient of the valve| U.S. [USG/min]|| Cv |  
| $C_{\mathrm{w}}$| Weight torque acting on the clapper| $\mathrm{N} \mathrm{m}$|| Cp |  
| $g$| Gravity constant| $\mathrm{m} / \mathrm{s}^{2}$|| g_n |  
| $h$| Fluid specific enthalpy | $\mathrm{J} / \mathrm{kg}$|| h |  
| $J$| Clapper moment of inertia| $\mathrm{kg} \mathrm{m}^{2}$|| J |  
| $K_{1}$| Clapper friction law coefficient| $-$|| Kf1 |  
| $K_{2}$| Clapper friction law coefficient| $-$|| Kf2 |  
| $m$| Fluid mass flow rate through the valve| $\mathrm{kg} / \mathrm{s}$|| Q |  
| $M$| Clapper mass| $\mathrm{kg}$|| m |  
| $n$| Clapper friction law exponent| $-$|| n |  
| $P_{\mathrm{i}}$| Fluid pressure at the valve inlet| $\mathrm{Pa}$|| C1.P |  
| $P_{\mathrm{o}}$| Fluid pressure at the valve outlet| $\mathrm{Pa}$|| C2.P |  
| $r$| Clapper radius| $\mathrm{m}$| $\frac{A}{\pi}$| r |  
| $\Delta P$| Fluid pressure loss between the inlet and the outlet| $\mathrm{Pa}$| $P_{\mathrm{i}}-P_{\mathrm{o}}$ | deltaP |  
| $\theta$| Clapper aperture angle| $\mathrm{rad}$|| theta |  
| $\theta_{\min }$| Minimum clapper aperture angle \(valve fully closed\)| $\mathrm{rad}$|| theta_min |  
| $\theta_{\max }$| Maximum clapper aperture angle \(valve fully open\)| $\mathrm{rad}$|| theta_max |  
| $\rho$| Fluid density| $\mathrm{kg} / \mathrm{m}^{3}$ || rho |  
| $\rho_{\text {water, } 60^{\circ} \mathrm{F}}$ | Density of water at $60^{\circ} \mathrm{F}\left(15.5556^{\circ} \mathrm{C}\right) .$ | $\mathrm{kg} / \mathrm{m}^{3}$ || - |  
| $\omega$| Clapper angular velocity| $\mathrm{rad} / \mathrm{s}$|| omega |  
| $\Omega$| Valve position| $-$| $1-\cos (\theta)$| Ouv |  



## Governing equations  

### Static momentum balance equation  


- Validity domain:   
   
 $\forall \dot{m}$ and $C_{\mathrm{v}} \geq 0$. For $C_{\mathrm{v}}=0, \Delta P$ must be defined.  

- Mathematical formulation:   
   
 $$\Delta P \cdot C_{\mathrm{v}} \cdot \lvert C_{\mathrm{v}} \rvert  
=1.732189 \times 10^{12} \cdot \frac{\dot{m} \cdot \lvert \dot{m} \rvert  
}{\rho \cdot \rho_{\text {water,60 }^{\circ} F}}$$  

- Comments:   
   
 This equation is the same as the control valve’s  $C_{\mathrm{v}}=f_{v}(\Omega)$ where $f_{v}$ is the valve characteristic.  


###  Clapper equation  

- Validity domain:  

$ \theta_{\min} \leq \theta \leq \theta_{\max} $  

- Mathematical formulation:   

$$   J \cdot \frac{\mathrm{d} \omega}{\mathrm{d}t}=\left\{\begin{array}{l} C_{\mathrm{t}} \text{ if } \theta_{\min }<\theta<\theta_{\max } \   C_{\mathrm{t}} \text{ if } \theta \leq \theta_{\min } \text{ and } C_{\mathrm{t}}>0 \   C_{\mathrm{t}} \text{ if } \theta \geq \theta_{\max } \text{ and } C_{\mathrm{t}}<0 \   0  \text{ else }\end{array}\right.$$ 
 $$   \omega=\left\{\begin{array}{l}\frac{\mathrm{d} \theta}{\mathrm{d} t}    \text{ when } \theta_{\min }<\theta<\theta_{\max } \   0 \text{ when } \theta \leq \theta_{\min } \text{ or } \theta \geq \theta_{\max }\end{array}\right.$$ 
 $$   C_{\mathrm{t}} = C_{\mathrm{w}}+C_{\mathrm{s}} +C_{\mathrm{f}}+ C_{\mathrm{h}} \   C_{\mathrm{w}} = -M \cdot g \cdot r \cdot \sin(\theta) \   C_{\mathrm{f}} = -\operatorname{sign}(\omega) \cdot \left(K_{1}+K_{2} \cdot \lvert\omega \rvert^{n}\right) \   C_{\mathrm{h}} = \Delta P \cdot A \cdot r \cdot \cos(\theta)$$  

- Comments:  

The angular velocity and acceleration are set to zero when the clapper hits  
the mechanical stops. The equal sign is replaced by $\leq$ or $\geq$ in the transition conditions $\theta=\theta_{\min }$ and $\theta=\theta_{\max }$ because equal signs are not recognized by solvers to compare real values.  

## References   
   
El Hefni, Baligh and Bouskela, Daniel (2019). [Modeling and Simulation of Thermal Power Plants with ThermoSysPro](https://link.springer.com/book/10.1007/978-3-030-05105-1), sect. 13.1. Springer Nature Switzerland AG.