Gas turbine combustion chamber
## Copyright © EDF 2002 - 2026
## ThermoSysPro Version 4.2
This component model is documented in Sect. 8.1 of the ThermoSysPro book.
# GT combustion chamber
This component is a combustion chamber for a gas turbine.
A gas turbine is a type of internal combustion engine.
It is composed of an upstream compressor, a combustion chamber and a downstream turbine.
At the inlet, air is compressed, up to 30 times the atmospheric pressure.
In the combustion chamber, it is mixed with fuel, which launches the combustion.
The expansion of hot gases bring the turbine in rotation, producing electricity.
## Modelica component model
The equations mentioned below are implemented in the component *GTCombustionChamber*, located in the *Combustion.CombustionChambers* sub-library.
The component has 4 connectors:
- Cws: water/steam at the inlet,
- Ca: air at the inlet,
- Cfuel: fuel at the inlet,
- Cfg: flue gases at the outlet.
## Nomenclature
| Symbol | Description | Unit | Definition | Modelica name |
|------------------- |---------------------------------------------------------- |---------------------------|------------------------------------- |-------------------------|
| A | Average cross-sectional area of the combustion chamber | \\( \mathrm{m}^2 \\) || Acham |
| \\( c_{p, f} \\) | Fuel specific heat capacity | \\( \mathrm{J/kg/K} \\) | | Cpfuel |
| \\(E_x \\) | Dry air stoichiometry necessary for 1kg fuel combustion | - | Proportion of oxygen in the air at the inlet required to burn 1kg fuel | - |
| \\(E_{X,a} \\) | Excess air | \\(\% \\) | \\( 100 \cdot \left(\frac{\dot{m}\_a \cdot (1 - X_{h_2O, a})}{\dot{m}\_f \cdot E_X} - 1 \right) \\) | - |
| \\( h\_{a, i} \\) | Air specific enthalpy at the inlet | \\(\mathrm{J/kg} \\) | | Hea |
| \\(\tilde{h}_{a, r} \\) | Air reference specific enthalpy | \\(\mathrm{J/kg} \\) | \\(2501569 \cdot X_{h_2O, a} \\) | Hrair |
| \\( h\_{at,i} \\) | Air specific enthalpy at the inlet of the atomization compressor | \\( \mathrm{J/kg} \\) | | Hecpat |
| \\( h\_{at,o} \\) | Air specific enthalpy at the outlet of the atomization compressor | \\( \mathrm{J/kg} \\) | | - |
| \\( h_{f} \\) | Fuel specific enthalpy at the inlet | \\(\mathrm{J/kg} \\) | \\(c_{p, f} \cdot (T_f - 273.16) \\) | Hfuel |
| \\( \tilde{h}_{f, r} \\) | Fuel reference specific enthalpy | \\(\mathrm{J/kg} \\) | 0 | Hrfuel |
| \\( h_{g, o} \\) | Flue gases specific enthalpy at the outlet | \\(\mathrm{J/kg} \\) | | Hsf |
| \\( \tilde{h}_{g, r} \\) | Flue gases reference specific enthalpy | \\(\mathrm{J/kg} \\) |\\(2501569 \cdot X_{h_2O, g} \\) | Hrfg |
| \\( h_{ws, i} \\) | Water/steam specific enthalpy at the inlet | \\(\mathrm{J/kg} \\) | | Hews |
| \\( h_{ws, r} \\) | Water/steam reference specific enthalpy | \\(\mathrm{J/kg} \\) |2501569 | Hrws |
| LHV | Fuel lower heating value | \\(\mathrm{J/kg} \\) | | LHVfuel |
| \\(\dot{m}\_a \\) | Air mass flow rate | \\(\mathrm{kg/s} \\) | | Qea |
| \\(\\dot{m}\_f \\) | Fuel mass flow rate | \\(\mathrm{kg/s} \\) | | Qfuel |
| \\(\dot{m}\_g \\) | Flue gases mass flow rate | \\(\mathrm{kg/s} \\) | | Qsf |
| \\(\dot{m}\_m \\) | Average mass flow rate in the combustion chamber| \\(\mathrm{kg/s} \\) | \\(\dot{m}\_a + \frac{\\dot{m}\_f + \\dot{m}\_{ws}}{2} \\)| Qm |
| \\(\\dot{m}\_{ws} \\) | Water/steam mass flow rate | \\(\mathrm{kg/s} \\) | | Qews |
| \\( M_C \\) | Carbon atomic mass | \\(\mathrm{kg/kmol} \\) | 12.01115 | amC |
| \\( M_H \\) | Hydrogen atomic mass | \\(\mathrm{kg/kmol} \\) | 1.00797 | amH |
| \\( M_O \\) | Oxygen atomic mass | \\(\mathrm{kg/kmol} \\) | 15.9994 | amO |
| \\( M_S \\) | Sulfur atomic mass | \\(\mathrm{kg/kmol} \\) | 32.064 | amS |
| \\( M_{CO_2} \\) | \\(CO_2\\) molar mass | \\(\mathrm{kg/kmol} \\) | \\(M_C + 2 \cdot M_O \\) | amCO2 |
| \\( M_{H_2O} \\) | \\(H_2O\\) molar mass | \\(\mathrm{kg/kmol} \\) | \\(M_O + 2 \cdot M_H \\) | amH2O |
| \\( M_{SO_2} \\) | \\(SO_2\\) molar mass | \\(\mathrm{kg/kmol} \\) | \\(M_S + 2 \cdot M_O \\) | amSO2 |
| \\( P_{at,i} \\) | Pressure at the inlet of the atomization compressor | \\( \mathrm{Pa} \\) | With air atomization: \\( P_{at,i} = P_i \cdot (1 - \Lambda_{at}) \\), else: \\( P_{at,i} = P_i \\). | Pecpat |
| \\( P_{at,o} \\) | Pressure at the outlet of the atomization compressor | \\( \mathrm{Pa} \\) | With air atomization: \\( P_{at,i} = P_i \cdot (1 + XP_{at}) \\), else: \\( P_{at,i} = P_i \\). | Pscpat |
| \\( P_i \\) | Fluid pressure at the inlet | \\(\mathrm{Pa} \\) | | Pea |
| \\( P_o \\) | Fluid pressure at the outlet | \\(\mathrm{Pa} \\) | | Psf |
| \\( S_{at,i} \\) | Entropy at the inlet of the atomization compressor | \\( \mathrm{J/kg/K} \\)| | Secpat |
| \\( T_{a,i} \\) | Air temperature at the inlet | \\(\mathrm{K} \\) | | Tea |
| \\( T_{at} \\) | Temperature at the inlet of the atomization compressor | \\(\mathrm{K} \\) | | Tecpat |
| \\( T_{f} \\) | Fuel temperature at the inlet | \\(\mathrm{K} \\) | | Tfuel |
| \\( T_{g,o} \\) | Flue gases temperature at the outlet | \\(\mathrm{K} \\) | | Tsf |
| \\( \nu \\) | Flue gases velocity in the combustion chamber | \\( \mathrm{m/s} \\) | \\( \frac{\\dot{m}\_m}{A \cdot \rho_m} \\) | v |
| \\( W_{at} \\) | Power of the atomization compressor | \\( \mathrm{W} \\) | | Wcpat |
| \\( W_{at,o} \\) | Thermal power extracted by the atomization refrigerant | \\( \mathrm{W} \\) | | Wrfat |
| \\( W_f \\) | LHV power available in the fuel | \\( \mathrm{W} \\) | \\( \\dot{m}\_f \cdot LHV \\) | Wfuel |
| \\( W_l \\) | Thermal losses | \\(\mathrm{W} \\) | | Wpth |
| \\( X_{C,f} \\) | Carbon mass fraction in the fuel | \\(\mathrm{-} \\) | | XCfuel |
| \\( X_{H,f} \\) | Hydrogen mass fraction in the fuel | \\(\mathrm{-} \\) | | XHfuel |
| \\( X_{O,f} \\) | Oxygen mass fraction in the fuel | \\(\mathrm{-} \\) | | XOfuel |
| \\( X_{S,f} \\) | Sulfur mass fraction in the fuel | \\(\mathrm{-} \\) | | XSfuel |
| \\( X_{CO_2,a} \\) | \\( CO_2 \\) mass fraction in the air at the inlet | \\(\mathrm{-} \\) || XeaCO2 |
| \\( X_{CO_2,g} \\) | \\( CO_2 \\) mass fraction in the flue gasess | \\(\mathrm{-} \\) | | XsfCO2 |
| \\( X_{H_2O,a} \\) | \\( H_2O \\) mass fraction in the air at the inlet | \\(\mathrm{-} \\) || XeaH2O |
| \\( X_{H_2O,g} \\) | \\( H_2O \\) mass fraction in the flue gases | \\(\mathrm{-} \\) || XsfH2O |
| \\( X_{O_2,a} \\) | \\( O_2 \\) mass fraction in the air at the inlet | \\(\mathrm{-} \\) || XeaO2 |
| \\( X_{O_2,g} \\) | \\( O_2 \\) mass fraction in the flue gases | \\(\mathrm{-} \\) || XsfO2 |
| \\( XM_{at} \\) | Atomization air mass flow rate coefficient | \\(\mathrm{-} \\) || XQat |
| \\( XP_{at} \\) | Atomization overpressure coefficient | \\(\mathrm{-} \\) || Xspat |
| \\( \Delta P \\) | Pressure loss in the combustion chamber | \\(\mathrm{Pa} \\) | \\( P_i - P_o \\) | deltaPccb |
| \\( \eta_{at} \\) | Atomization compressor isentropic efficiency | \\(\mathrm{-} \\) | | eta_is |
| \\( \eta_c \\) | Combustion efficiency \\( 0 < \eta_c \le 1 \\) | \\(\mathrm{-} \\) | Burnt fuel mass divided by the input fuel mass | eta_comb |
| \\( \Lambda \\) | Pressure loss coefficient in the combustion chamber | \\(\mathrm{m}^{-4} \\) | | kcham |
| \\( \Lambda_{at} \\) | Atomization pressure loss coefficient | \\(\mathrm{m}^{-4} \\) | | kat |
| \\( \rho_i \\) | Air density at the inlet | \\(\mathrm{kg/m}^3 \\) | | rhoea |
| \\( \rho_o \\) | Flue gases density at the outlet | \\(\mathrm{kg/m}^3 \\) | | rhosf |
| \\( \rho_m \\) | Fluid average density | \\(\mathrm{kg/m}^3 \\) | \\( \frac{\rho_i + \rho_o}{2} \\) | - |
## Governing equations
The *GTCombustionChamber* model is based on the following mass and energy balance equations.
The dry air stoichiometry and the resulting mass fractions are the same for the [boiler](modelica://ThermoSysPro.MultiFluids.Boilers.FossilFuelBoiler) component.
This set of equations must be completed by the state equations involving \\( h_{a,i}, \\, h_{at,i}, \\, h_{at,o}, \\ S_{at,i}, \\, T_{g,o}, \\, \rho_i \\; \text{and} \\; \rho_o \\).
### Mass balance equation
- Validity formulation:
\\( \forall \dot{m}\_g \\, , \dot{m}\_a \\, , \dot{m}\_f \\; \\text{and} \\; \dot{m}\_{ws} \\)
- Mathematical formulation:
$$ \quad \dot{m}\_g = \\dot{m}\_a + \dot{m}\_f + \dot{m}\_{ws} $$
- Comments:
Flue gases result from the combustion of fuel with air. The incoming vapor is vaporized and mixed with the flue gases in the combustion chamber.
### Energy balance equation
- Validity formulation:
\\( \forall \\dot{m}\_a \\, , \dot{m}\_f \\, , \dot{m}\_{ws} \\; \text{and} \\; \dot{m}\_g>0 \\)
- Mathematical formulation:
$$ \dot{m}\_g \cdot h_{g,o} + W_{at,o} + W_l- \\dot{m}\_a \cdot h_{a,i} - \dot{m}\_f \cdot (h_f + \eta_c \cdot LHV) - \dot{m}\_{ws} \cdot h_{ws,i} - W_{at} = 0 $$
- Comments:
This equation is used to compute the flue gases specific enthalpy after combustion \\( h_{g,o} \\).
The combustion efficiency \\(\eta_c \\) and the fuel lower heating value LHV are model inputs.
The specific enthalpies \\( h_f \\) and \\( h_{a,i} \\) are computed using properties tables from the known temperatures \\(T_f \\) and \\(T_{a,i} \\).
### Energy balance equation (without air atomization)
- Validity formulation:
\\( \forall \\dot{m}\_a \\, , \dot{m}\_f \\, , \dot{m}\_{ws} \\; \\text{and} \\; \dot{m}\_g \neq 0 \\)
- Mathematical formulation:
$$ \\dot{m}\_a \cdot h_{a,i} + \dot{m}\_f \cdot (h_f + \eta_c \cdot LHV) - W_l - \dot{m}\_g \cdot h_{g,o} + \dot{m}\_{ws} \cdot h_{ws,i} = 0 $$
- Comments:
This equation computes the specific enthalpy \\( h_{g,o} \\).
### Power of the atomization compressor
- Validity formulation:
\\( \eta_{isc} > 0 \\; \text{and} \\; \forall \dot{m}\_a \geq 0 \\)
- Mathematical formulation:
With air atomization: \\( W_{at} = \\dot{m}\_a \cdot XM_{at} \cdot \eta_{isc} \cdot (h_{at,o} - h_{at,i}) \\)
Without air atomization: \\( W_{at} = 0 \\)
### Thermal power extracted by the atomization refrigerant
- Validity formulation:
\\( \forall \dot{m}\_a \geq 0 \\)
- Mathematical formulation:
With air atomization: \\( W_{at} = \\dot{m}\_a \cdot XM_{at} \cdot \eta_{isc} \cdot (h_{a,i} - h_{at,i}) \\)
Without air atomization: \\( W_{at} = 0 \\)
### Momentum balance equation for the fluid
- Validity formulation:
\\( \forall \nu \\)
- Mathematical formulation:
$$ P_o = P_i - \Lambda \cdot \frac{\rho_m \cdot \nu \cdot | \nu |}{2} $$
### Dry air stoichiometry for the combustion of 1 kg fuel
- Validity formulation:
\\( X_{H_20,a} < 1 \\; \\text{and} \\;\\ X_{O_2,a} > 0) \\)
- Mathematical formulation:
$$ E_X = M_O \cdot \frac{\frac{2 \cdot X_{C,f}}{M_C} + \frac{X_{H,f}}{2 \cdot M_H} + \frac{2 \cdot X_{S,f}}{M_S} - \frac{X_{O,f}}{M_O}}{\frac{X_{0_2,a}}{1 - X_{H_2O,a}}} $$
- Comments:
This formulation arises from the chemical reactions considered in the combustion:
$$ C + O_2 \longrightarrow CO_2 $$
$$ H + \frac{1}{4} 0_2 \longrightarrow H_2O $$
$$ S + O_2 \longrightarrow SO_2 $$
### \\( CO_2 \\) mass fraction in the flue gases
- Validity formulation:
\\( \dot{m}\_g \neq 0 \\)
- Mathematical formulation:
$$ X_{CO_2,g} = \frac{\\dot{m}\_a}{\dot{m}\_g} \cdot X_{CO_2,a} + \frac{\dot{m}\_f}{\dot{m}\_g} \cdot X_{C,f} \cdot \frac{M_{CO_2}}{M_C} $$
- Comments:
This formulation arises from the chemical reaction considered in the combustion:
$$ C + O_2 \longrightarrow CO_2 $$.
### \\( H_2O \\) mass fraction in the flue gases
- Validity formulation:
\\( \dot{m}\_g \neq 0 \\)
- Mathematical formulation:
$$ X_{H_2O,g} = \frac{\\dot{m}\_a}{\dot{m}\_g} \cdot X_{H_2O,a} + \frac{\dot{m}\_f}{\dot{m}\_g} \cdot X_{H,f} \cdot \frac{M_{H_2O}}{2 \cdot M_H} $$
- Comments:
This formulation arises from the chemical reaction considered in the combustion:
$$ H + \frac{1}{4} O_2 \longrightarrow H_2O $$
### \\( O_2 \\) mass fraction in the flue gases
- Validity formulation:
\\( \dot{m}\_g \neq 0 \\)
- Mathematical formulation:
$$ X_{O_2,g} = \frac{\\dot{m}\_a}{\dot{m}\_g} \cdot X_{O_2,a} - M_O \cdot \frac{\dot{m}\_f}{\dot{m}\_g} \cdot \left( \frac{2 \cdot X_{HC,f}}{M_C} + \frac{X_{H,f}}{2 \cdot M_H} + \frac{2 \cdot X_{S,f}}{M_S} \right) + \frac{\dot{m}\_f}{\dot{m}\_g} \cdot X_{O,f} $$
- Comments:
This formulation arises from the three chemical reactions mentioned in the dry air stoichiometry equation.
### \\( SO_2 \\) mass fraction in the flue gases
- Validity formulation:
\\( \dot{m}\_g \neq 0 \\)
- Mathematical formulation:
$$ X_{SO_2,g} = \frac{\\dot{m}\_a}{\dot{m}\_g} \cdot X_{SO_2,a} + \frac{\dot{m}\_f}{\dot{m}\_g} \cdot X_{S,f} \cdot \frac{M_{SO_2}}{M_S}$$
- Comments:
This formulation arises from the three chemical reactions mentioned in the dry air stoichiometry equation.
## 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. 8.1. Springer Nature Switzerland AG.
Author Baligh El Hefni
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