# Mixer3


## Copyright © EDF 2002 - 2026   
## ThermoSysPro Version 4.2  
This component model is documented in Sect. 14.7 of the ThermoSysPro book.   
# Mixer3   
   
This static model describes the mixing of an adiabatic single-phase fluid or two-phase fluid with homogeneous flow in the mixer volume.  

## Modelica component model  

The equations mentioned below are implemented in the component *Mixer3*, located in the *WaterSteam.Junctions* sub-library.   
This component has 8 connectors:  
- Ce1: first fluid inlet,  
- Ce2: second fluid inlet,  
- Ce3: third fluid inlet,  
- Cs: 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.Mixer3.svg](./icons/ThermoSysPro.WaterSteam.Junctions.Mixer3.svg)  

## Nomenclature  

|Symbol | Description | Unit | Definition | Modelica name |  
| :--------------------------------------- | :---------------------------------------------------------------------------------------- | :--------------------------- | :---------------------- | :----------- |  
|$h_{\mathrm{i}_{1}}$ | Specific enthalpy of the fluid at inlet 1 | $\mathrm{J} / \mathrm{kg}$ || Ce1.h |  
|$h_{\mathrm{i}_{2}}$ | Specific enthalpy of the fluid at inlet 2 | $\mathrm{J} / \mathrm{kg}$ || Ce2.h |  
|$h_{\mathrm{i}_{3}}$ | Specific enthalpy of the fluid at inlet 3 | $\mathrm{J} / \mathrm{kg}$ || Ce3.h |  
|$h_{\mathrm{o}}$ | Specific enthalpy of the fluid at the outlet of the mixer | $\mathrm{J} / \mathrm{kg}$ || Cs.h |  
|$m_{\mathrm{i}_{1}}$ | Mass flow rate of the fluid at inlet 1 | $\mathrm{kg} / \mathrm{s}$ || Ce1.Q |  
|$\dot{m}_{\mathrm{i}_{2}}$ | Mass flow rate of the fluid at inlet 2 | $\mathrm{kg} / \mathrm{s}$ || Ce2.Q |  
|$\dot{m}_{\mathrm{i}_{3}}$ | Mass flow rate of the fluid at inlet 3 | $\mathrm{kg} / \mathrm{s}$ || Ce3.Q |  
|$\dot{m}_{\mathrm{o}}$ | Mass flow rate of the fluid at the outlet | $\mathrm{kg} / \mathrm{s}$ || Cs.Q |  
| $\alpha_{1}$ | Extraction coefficient for inlet 1 \(output of the model\) | $-$ |$\frac{\dot{m}_{\mathrm{i}_{l}}}{\dot{m}_{\mathrm{o}}}$ || alpha1 |  
|$\alpha_{2}$ | Extraction coefficient for inlet 2 \(output of the model\) | $-$ | $\frac{\dot{m}_{\mathrm{i}_{2}}}{\dot{m}_{\mathrm{o}}}$|| alpha2 |  
|$\alpha_{\mathrm{i}_{1}}$ | Mass fraction coefficient for inlet 1 | $-$ || Ialpha1.signal |  
|$\alpha_{\mathrm{i}_{2}}$ | Mass fraction coefficient for inlet 2 | $-$ || Ialpha2.signal |  


## Governing equations  

### Static mass balance equation  


    
    

- Validity domain:   
   
 $\forall \dot{m}$  

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

- Comments:   
   
$\dot{m}_{\mathrm{i}_{l}}$ and $\dot{m}_{\mathrm{i} 2}$ can be defined as a fraction of the output mass flow rate:  
$$\dot{m}_{\mathrm{i}_{l}}=\alpha_{\mathrm{i}_{l}} \cdot \dot{m}_{\mathrm{o}} \quad \text{and} \quad \dot{m}_{\mathrm{i}_{2}}=\alpha_{\mathrm{i}_{2}} \cdot \dot{m}_{\mathrm{o}}$$  
This enables the computation of the mass flow rates at the inlets from the outlet mass flow rate.   


### Static energy balance equation  


    
    

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

- Mathematical formulation:   
   
 $$0=\dot{m}_{\mathrm{i}_{l}} \cdot h_{\mathrm{i}_{l}}+\dot{m}_{\mathrm{i}_{2}} \cdot h_{\mathrm{i}_{2}}+\dot{m}_{\mathrm{i}_{3}} \cdot h_{\mathrm{i}_{3}}-\dot{m}_{\mathrm{o}} \cdot h_{\mathrm{o}}$$  

- Comments:   
   
 This equation is valid if some mass flow rates are non-zero. Otherwise, the mixing specific enthalpy 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. 14.7. Springer Nature Switzerland AG.