# CombustionTurbine


## Copyright © EDF 2002 - 2026  
## ThermoSysPro Version 4.2  
This component model is documented in Sect. 11.4 of the ThermoSysPro book.   

# Combustion turbine   

A combustion turbine, also called gas turbine, is a type of internal combustion engine. The main elements common to all gas turbines are an upstream rotating gas compressor, a combustor and a downstream turbine on the same shaft as the compressor.  
In this model, the hot fluid flow is assumed steady-state and supersonic.  

## Modelica component model  

The equations mentioned below are implemented in the component *CombustionTurbine*, located in the *FlueGases.Machines* sub-library.  
The component has 4 connectors:  
- Ce: flue gases at the inlet,  
- Cs: flue gases at the outlet,  
- CompressorPower: compressor power input,  
- MechPower: mechanical power output.  
   
![ThermoSysPro.FlueGases.Machines.CombustionTurbine.svg](./icons/ThermoSysPro.FlueGases.Machines.CombustionTurbine.svg)  

## Nomenclature  

| Symbol| Description| Unit| Definition| Modelica name|  
| :------------------------- | :----------------------------------------------------- | :--------------------------- | :---------------------------------- | :-------------------------------|  
| $h_{\mathrm{i}}$| Fluid specific enthalpy at the inlet| $\mathrm{J} / \mathrm{kg}$ ||He|  
| $h_{\mathrm{is}}$| Fluid specific enthalpy after the isentropic expansion | $\mathrm{J} / \mathrm{kg}$ ||His|  
| $h_{\mathrm{o}}$| Fluid specific enthalpy at the outlet| $\mathrm{J} / \mathrm{kg}$ ||Hs|  
| $\dot{m}$| Fluid mass flow rate| $\mathrm{kg} / \mathrm{s}$ ||Q|  
| $\dot{m}_{\mathrm{cor}}$ | Corrected mass flow rate \(mass flow rate parameter\)| $-$||Qred|  
| $P_{\mathrm{i}}$| Fluid pressure at the inlet| $\mathrm{Pa}$||Pe|  
| $P_{\mathrm{o}}$| Fluid pressure at the outlet| $\mathrm{Pa}$||Ps|  
| $W_{\mathrm{c}}$| Compressor power \(negative value\)| $\mathrm{W}$||Wcp|  
| $W_{\mathrm{m}}$| Mechanical power| $\mathrm{W}$||Wmech|  
| $W_{\mathrm{t}}$| Turbine power \(total power\)| $\mathrm{W}$||Wturb|  
| $X$| Ratio between the actual and nominal expansion rate| $-$| $\pi / \pi_{n}$|Xtau|  
| $\eta_{\mathrm{is}}$| Isentropic efficiency| $-$||is_eff|  
| $\eta_{\mathrm{n}}$| Nominal isentropic efficiency| $-$||is_eff_n|  
| $\pi$| Expansion rate| $-$| $P_{\mathrm{o}} / P_{\mathrm{i}}$|tau|  
| $\pi_{\mathrm{n}}$| Nominal expansion rate| $-$||tau_n|  

## Governing equations  

### Fluid specific enthalpy at the outlet  


    
    

- Validity domain:   
   
 $\forall h_{\mathrm{i}}$  

- Mathematical formulation:   
   
 $$h_{\mathrm{o}}=h_{\mathrm{i}}+\eta_{\mathrm{is}} \cdot\left(h_{\mathrm{is}}-h_{\mathrm{i}}\right)$$  

- Comments:   
   



### Isentropic efficiency  


    
    

- Validity domain:   
   
 $X>0$  

- Mathematical formulation:   
   
 $$\eta_{\mathrm{is}}=f_{\eta_{\mathrm{is}}}(X) \cdot \eta_{n}$$  

- Comments:   
   
 $f_{\eta_{\mathrm{is}}}(X)$ is the turbine map expressed as a polynomial function of $X$.   


### Total turbine power  


    
    

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

- Mathematical formulation:   
   
 $$W_{\mathrm{t}}=\dot{m} \cdot\left(h_{\mathrm{i}}-h_{\mathrm{o}}\right)$$  

- Comments:   
   



### Mechanical power  


    
    

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

- Mathematical formulation:   
   
 $$W_{\mathrm{m}}=W_{\mathrm{t}}+W_{\mathrm{c}}$$  

- Comments:   
   
 The mechanical power produced by the shaft of the electricity generator is the total turbine power minus the power used by the compressor (counted negatively).   


### Mass flow rate  


    
    

- Validity domain:   
   
 $\forall P_{i}$ and $\forall T_{\mathrm{i}}$  

- Mathematical formulation:   
   
 $$\dot{m}_{\mathrm{cor}}=\frac{\dot{m} \cdot \sqrt{T_{\mathrm{i}}}}{P_{\mathrm{i}}}$$  

- Comments:   
   
 This equation calculates the mass flow rate from the corrected mass flow rate provided by the user.   

## 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. 11.4. Springer Nature Switzerland AG.