.ThermoSysPro.WaterSteam.Junctions.Splitter3

Information

## Copyright © EDF 2002 - 2026   
## ThermoSysPro Version 4.2  
This component model is documented in Sect. 14.8 of the ThermoSysPro book.   
# Splitter3   
   
The static splitter is a cavity splitting an incoming flow into two or more exiting flows of adiabatic single-phase or homogeneous two-phase fluid.  


## Modelica component model  

The equations mentioned below are implemented in the component *Splitter3*, located in the *WaterSteam.Junctions* sub-library.   
This component has 8 connectors:  
- Ce: fluid inlet,  
- Cs1: first fluid outlet,  
- Cs2: second fluid outlet,  
- Cs3: third fluid outlet,  
- Ialpha1: extraction coefficient  imposing the fraction Ce1.Q/Cs.Q,  
- Ialpha2: extraction coefficient imposing the fraction Ce2.Q/Cs.Q,  
- Oalpha1: value of Ce1.Q/Cs.Q,  
- Oalpha2: value of Ce2.Q/Cs.Q.  

If the connector Ialpha.*x* is not connected, then the fraction Ce*x*.Q/Cs.q is not imposed.  
If the connector Ialpha.*x* is connected, then Oalpha*x*=Ialpha*x*.  
   
![modelica://ThermoSysPro/UsersGuide/Documentation/ThermoSysPro.WaterSteam.Junctions.Splitter3.svg](modelica://ThermoSysPro/UsersGuide/Documentation/ThermoSysPro.WaterSteam.Junctions.Splitter3.svg)  

## Nomenclature  

| Symbol| Description| Unit| Definition| Modelica name |  
| :--------------------------- | :---------------------------------------------------------- | :--------------------------- | :-------------------------------------------------------- | :----------- |  
| \\(h\_{\mathrm{i}}\\)| Specific enthalpy of the fluid at the inlet of the splitter | \\(\mathrm{J} / \mathrm{kg}\\) || Ce.h |  
| \\(h\_{\mathrm{o}\_{1}}\\)| Specific enthalpy of the fluid at outlet 1| \\(\mathrm{J} / \mathrm{kg}\\) || Cs1.h |  
| \\(h\_{\mathrm{o}\_{2}}\\)| Specific enthalpy of the fluid at outlet 2| \\(\mathrm{J} / \mathrm{kg}\\) || Cs2.h |  
| \\(h\_{\mathrm{o} 3}\\)| Specific enthalpy of the fluid at outlet 3| \\(\mathrm{J} / \mathrm{kg}\\) || Cs3.h |  
| \\(\dot{m}\_{\mathrm{i}}\\)| Fluid mass flow rate at the inlet| \\(\mathrm{kg} / \mathrm{s}\\) || Ce.Q |  
| \\(\dot{m}\_{\mathrm{o}\_{1}}\\) | Fluid mass flow rate at outlet 1| \\(\mathrm{kg} / \mathrm{s}\\) || Cs1.Q |  
| \\(\dot{m}\_{\mathrm{o}\_2}\\)| Fluid mass flow rate at outlet 2| \\(\mathrm{kg} / \mathrm{s}\\) || Cs2.Q |  
| \\(\dot{m}\_{\mathrm{o}\_{3}}\\) | Fluid mass flow rate at outlet 3| \\(\mathrm{kg} / \mathrm{s}\\) || Cs3.Q |  
| \\(\alpha\_{1}\\)| Extraction coefficient for outlet 1 \(output of the model\)| \\(-\\)| \\(\frac{\dot{m}\_{\mathrm{o}\_{1}}}{\dot{m}\_{\mathrm{i}}}\\) | alpha1 |  
| \\(\alpha\_{2}\\)| Extraction coefficient for outlet 2 \(output of the model\)| \\(-\\)| \\(\frac{\dot{m}\_{\mathrm{o}\_{2}}}{\dot{m}\_{\mathrm{i}}}\\) | alpha2 |  
| \\(\alpha\_{\mathrm{o}\_{1}}\\)| Mass fraction coefficient for outlet 1||| Ialpha1.signal |  
| \\(\alpha\_{\mathrm{o}\_{2}}\\)| Mass fraction coefficient for outlet 2| \\(-\\)|| Ialpha2.signal |  


## Governing equations  

### Static mass balance equation  


    
    

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

- Mathematical formulation:   
   
 $$0=\dot{m}\_{\mathrm{i}}-\dot{m}\_{\mathrm{o}\_{1}}-\dot{m}\_{\mathrm{o}\_{2}}-\dot{m}\_{\mathrm{o} 3}$$  

- Comments:   
   
 The value of \\(\dot{m}\_{\mathrm{o}\_{1}}\\) and \\(\dot{m}\_{\mathrm{o}\_{2}}\\) can be defined as a fraction of the input mass flow rate:  
$$   \dot{m}_{\mathrm{o}_{1}}  =\alpha_{\mathrm{o}_{1}} \cdot \dot{m}_{\mathrm{i}} \\   \dot{m}_{\mathrm{o}\_{2}}  =\alpha_{\mathrm{o}_{2}} \cdot \dot{m}_{\mathrm{i}}$$  

This option enables to compute the mass flow rates at the outlets knowing the mass flow rate at the inlet.  


### Static energy balance equation  


    
    

- Validity domain:   
   
 \\(\exists \dot{m}\\) such that \\(\dot{m} \neq 0\\)  

- Mathematical formulation:   
   
 $$0=\dot{m}\_{\mathrm{i}} \cdot h\_{\mathrm{i}}-\dot{m}\_{\mathrm{o}\_{1}} \cdot h\_{\mathrm{o}\_{1}}-\dot{m}\_{\mathrm{o}\_{2}} \cdot h\_{\mathrm{o}\_{2}}-\dot{m}\_{\mathrm{o}\_{3}} \cdot h\_{\mathrm{o}\_{3}}$$  

- Comments:   
   
 This equation is valid if at least one mass flow rate is nonzero. Otherwise, the mixing specific enthalpy inside the splitter is undefined.  

## 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. 14.8. Springer Nature Switzerland AG.  
    

Revisions