.ThermoSysPro.WaterSteam.PressureLosses.DynamicCheckValve

Information

## 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](modelica://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.  
   
![modelica://ThermoSysPro/UsersGuide/Documentation/ThermoSysPro.WaterSteam.PressureLosses.DynamicCheckValve.svg](modelica://ThermoSysPro/UsersGuide/Documentation/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.  
    

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