modelDiaphragm

Information

## Copyright © EDF 2002 - 2026  
## ThermoSysPro Version 4.2  
This component model is documented in Sect. 13.7 of the ThermoSysPro book.   

# Diaphragm   
   
A diaphragm measures pressure losses to compute mass flow rates.  
For water/steam, the flow regime can be single-phase or homogeneous two-phase flow. This model accounts for friction pressure losses only.  

Following assumptions are made:  
- the diaphragm aperture relies on sharp ridges.  

The friction pressure loss coefficient is calculated using the geometry of the diaphragm. The diaphragm component thus completes the [singular pressure loss](modelica://ThermoSysPro.WaterSteam.PressureLosses.SingularPressureLoss), in which the pressure loss coefficient is a single parameter.  

## Modelica component model  

The equations mentioned below are implemented in the component *Diaphragm*, 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.Diaphragm.svg](modelica://ThermoSysPro/UsersGuide/Documentation/ThermoSysPro.WaterSteam.PressureLosses.Diaphragm.svg)  

## Nomenclature  

| Symbol| Description| Unit| Definition| Modelica name |  
| :----------------- | :----------------------------------- | :------------------------------- | :--------------------------------------------------------------------------- | :----------- |  
| \\(D\\)| Diaphragm diameter| \\(\mathrm{m}\\)|| D |  
| \\(h\\)| Fluid specific enthalpy | \\(\mathrm{J} / \mathrm{kg}\\)|| h |  
| \\(m\\)| Fluid mass flow rate| \\(\mathrm{kg} / \mathrm{s}\\)|| Q |  
| \\(P\_{\mathrm{i}}\\) | Fluid pressure at the inlet| \\(\mathrm{Pa}\\)|| C1.P |  
| \\(P\_{\mathrm{o}}\\) | Fluid pressure at the outlet| \\(\mathrm{Pa}\\)| \\(-\\)| C2.P |  
| \\(Re\\)| Reynolds number|| \\(\frac{4 \cdot \lvert \dot{m} \rvert}{\pi \cdot D \cdot \mu \cdot \Omega}\\) | Re |  
| \\(Re\_{\lim }\\)| Limiting Reynolds number| \\(-\\)| \\(10^{5}\\)| Relim |  
| \\(\zeta\_{\zeta}\\)| Fluid pressure loss| \\(\mathrm{Pa}\\)| \\(P\_{\mathrm{i}}-P\_{\mathrm{o}}\\)| deltaP |  
| \\(\mu\\)| Friction pressure loss coefficient| \\(-\\)|| khi |  
| \\(\rho\\)| Fluid dynamic viscosity| \\(\mathrm{Pa} \mathrm{s}\\)|| mu |  
| \\(\Omega\\)| Fluid density| \\(\mathrm{kg} / \mathrm{m}^{3}\\) || rho |  



## Governing equations  

### Static momentum balance equation  


    
    

- Validity domain:   
   
 \\(\forall \dot{m}\\)  

- Mathematical formulation:   
   
 $$\Delta P=8 \cdot \zeta\_{f} \cdot \frac{\dot{m} \cdot \lvert \dot{m} \rvert}{\pi^{2} \cdot D^{4} \cdot \rho}$$  

- Comments:   
   



### Friction pressure loss coefficient  


    
    

- Validity domain:   
   
 \\(\forall \dot{m}\\) with \\(Re>Re\_{lim}\\) and \\(\Omega>0\\)  

- Mathematical formulation:   
   
 $$\zeta\_{f}=\left\(\frac{1.707-\Omega}{\Omega}\right\)^{2}$$   

- Comments:   
   


## 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. 13.7. Springer Nature Switzerland AG.

Parameters

Connectors

Components

Revisions

Author  

Daniel Bouskela