# Splitter3


## 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*.  
   
![ThermoSysPro.WaterSteam.Junctions.Splitter3.svg](./icons/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.