Generic combustion chamber 1D
## Copyright © EDF 2002 - 2026
## ThermoSysPro Version 4.2
This component model is documented in Sect. 8.2 of the ThermoSysPro book.
# Generic combustion 1D
This component is a combustion chamber for boiler furnace.
In thermal power plants, the combustion takes place in the furnace.
The combustion generates high-temperature flue gases, which circulate outside the membrane of the furnace that wraps the tubes where water vaporizes.
## Modelica component model
The equations mentioned below are implemented in the component *GenericCombustion1D*, located
in the *Combustion.CombustionChambers* sub-library.
The component has 5 connectors:
- Cws: water/steam at the inlet,
- Ca: air at the inlet,
- Cfuel: fuel at the inlet,
- Cfg: flue gases at the outlet,
- Cth: thermal flow created through the membrane of the furnace.
## Nomenclature
| Symbol | Description | Unit | Definition | Modelica name |
|------------------- |---------------------------------------------------------- |---------------------------|------------------------------------- |----------------------------------|
| A | Average cross-sectional area of the combustion chamber | \\( \mathrm{m}^2 \\) || Acham |
| \\( c_{p,cd} \\) | Ashes specific heat capacity | \\(\mathrm{J/kg/K} \\) || Cpcd |
| \\( 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_{bf} \\)| Low furnace ashes specific enthalpy at the outlet | \\( \mathrm{J/kg} \\) | \\( c_{p,cd} \cdot (T_{bf} - 273.16) \\)| Hbf |
\\( h_c \\) | Convective/conductive (+fouling) heat exchange coefficient| \\(\mathrm{W/m^2/K} \\) || Kec |
\\( h_{c,r} \\) | Ashes reference specific enthalpy | \\(\mathrm{J/kg} \\) |0 | -|
\\( h_{cv} \\) | Volatile ashes specific enthalpy at the outlet | \\(\mathrm{J/kg} \\) | \\(c_{p,cd} \cdot (T_{g,o} - 273.16) \\) | Hcv |
| \\( 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 |
| \\( \text{HHV}_c \\) | Unburnt carbon higher heating value | \\(\mathrm{J/kg} \\) | \\( 32.8 \times 10^6 \\)| HHVcarbone |
| \\(I_{CV} \\) | Unburnt particles ratio in the volatile ashes | - | \\( 0 \leq I_{CV} \leq 1 \\) | ImbCV |
| \\(I_{BF} \\) | Unburnt particles ration in the low furnace ashes | - | \\( 0 \leq I_{BF} \leq 1 \\) | ImbBF |
| \\( \text{LHV}_d \\) | Fuel lower heating value of the dry matter | \\(\mathrm{J/kg} \\) || LHVfuel |
| LHV | Fuel lower heating value (effective value or crude) | \\(\mathrm{J/kg} \\) | \\( \text{LHV}\_d \cdot (1-X\_{W,f})\\) \\(- 25.1 \times 10^5 \cdot X\_{W,f} \\) |
| \\(\dot{m}\_a \\) | Air mass flow rate | \\(\mathrm{kg/s} \\) || Qea |
| \\(\dot{m}\_{bf} \\) | Low furnace ashes mass flow rate | \\(\mathrm{kg/s} \\) | \\( \\dot{m}\_f \cdot X\_{CD,f} \cdot X\_{bf}\\) \\(\cdot (1-I\_{BF}) \\) | Qbf |
| \\(\dot{m}\_{bf} \\) | Volatile ashes mass flow rate | \\(\mathrm{kg/s} \\) | \\( \frac{\dot{m}\_f \cdot X\_{CD,f} \cdot (1-X\_{bf})}{1-I\_{BF}} \\) | Qcv |
| \\(\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 |
| n | Number of segments in the combustion chamber | - || NCEL |
| \\( P_i \\) | Fluid pressure at the inlet | \\(\mathrm{Pa} \\) || Pea |
| \\( P_o \\) | Fluid pressure at the outlet | \\(\mathrm{Pa} \\) || Psf |
| \\( R_{S,i} \\) | Corrective coefficient for heat exchange area of cell *i* | - || RSURF[i] |
| \\( S_i \\) | Heat exchange area for cell *i* | \\( \mathrm{m}^2 \\)|| SM[i] |
| \\( T_{a,i} \\) | Air temperature at the inlet | \\(\mathrm{K} \\) || Tea |
| \\( T_{bf} \\) | Ashes temperature at the outlet of low furnace | \\(\mathrm{K} \\) || Tbf |
| \\( T_f \\) | Fuel temperature at the inlet | \\(\mathrm{K} \\) || Tfuel |
| \\( T_{g,o} \\) | Flue gases temperature at the outlet | \\(\mathrm{K} \\) || Tsf |
| \\( T_{w,i} \\) | Furnace wall temperature for cell *i* | \\(\mathrm{K} \\) || Tpi[i] |
| \\( \nu \\) | Flue gases velocity in the combustion chamber | \\( \mathrm{m/s} \\) | \\( \frac{\dot{m}_m}{A \cdot \rho_m} \\) | v |
| \\( W_l \\) | Thermal power loss | \\( \mathrm{W} \\) | \\( \dot{m}\_f \cdot \text{LHV} \cdot x\_{w,l} \\)| Wpth |
| \\( W_{s,i} \\) | Thermal power exchanged between flue gases and furnace wall for cell *i* | \\( \mathrm{W} \\) || Ws[i] |
| \\( W_s \\) | Total thermal power exchanged between flue gases and furnace wall | \\( \mathrm{W} \\) | \\( \sum_i W\_{s,i} \\) | Wst |
| \\( 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_{W,f} \\) | \\( H_2O \\) mass fraction in the fuel | \\(\mathrm{-} \\) || XeaH2O |
| \\( X_{CD,f} \\) | Ashes mass fraction in the fuel | \\(\mathrm{-} \\) || XCDfuel |
| \\( 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 |
| \\( X_{SO_2,a} \\) | \\( SO_2 \\) mass fraction in the air at the inlet | \\(\mathrm{-} \\) || XeaSO2 |
| \\( X_{SO_2,g} \\) | \\( SO_2 \\) mass fraction in the flue gases | \\(\mathrm{-} \\) || XSfuel |
| \\(x_{W,l} \\) | Thermal loss fraction in the body of the combustion chamber | - | \\( 0 \leq x_{W,l} \leq 1 \\) | Xpth |
| \\( \Delta P \\) | Pressure loss in the combustion chamber | \\(\mathrm{Pa} \\) | \\( P_i - P_o \\) | deltaPccb |
| \\( \epsilon \\) | Wall emissivity | \\(\mathrm{-} \\) || EPSPAR |
| \\( \Lambda \\) | Pressure loss coefficient in the combustion chamber | \\(\mathrm{m}^{-4} \\) || kcham |
| \\( \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} \\) | - |
| \\( \sigma \\) | Stefan-Boltzmann constant | \\(\mathrm{W/m^2/K^4} \\) | \\( 5.67 \times 10^{-8} \\) | SIGMA |
## Governing equations
The modeling of the combustion chamber for boiler furnace is based on the mass, energy and momentum balance equations.
This set of equations must be completed by the state equations involving \\( h_{a,i}, \\, T_{g,o}, \\, \rho_i \\; \text{and} \\; \rho_o \\).
### Mass balance equation
- Validity domain:
\\( \forall \dot{m}\_g \\, , \dot{m}\_a \\, , \dot{m}\_f \\; \\text{and} \\; \dot{m}\_{ws} \\)
- Mathematical formulation:
$$ \quad \dot{m}\_g = \\dot{m}\_a + \dot{m}\_{ws} + \dot{m}\_f (1 - X\_{CD,f} - \dot{m}\_{cv} \cdot I\_{cv} - \dot{m}\_{bf} \cdot I\_{BF}) $$
### Energy balance equation
- Validity domain:
\\( \forall \\dot{m}\_a > 0 \\, , \dot{m}\_f > 0 \\; \text{and} \\; \dot{ws}\_g \geq 0 \\)
- Mathematical formulation:
$$ (\dot{m}\_a + \dot{m}\_{ws} + \dot{m}\_f \cdot (1-X_{CD,f})) \cdot h\_{g,o} + W\_l + \dot{m}\_{cv} \cdot h_{cv} $$ $$+ \dot{m}\_{bf} \cdot h_{bf} + (\dot{m}\_{cv} \cdot I_{CV} + \dot{m}\_{bf} \cdot I_{BF}) \cdot \text{HHV}\_c + W_s$$$$ = \dot{m}\_f \cdot (h_f + \text{LHV}) + \dot{m}\_a \cdot h\_{a,i} + \dot{m}\_{ws} \cdot h\_{ws,i} $$
- Comments:
This equation is used to compute the flue gases specific enthalpy after combustion \\( h_{g,o} \\).
### Energy balance equation (thermal power exchanged between the flue gases and the furnace wall)
- Validity domain:
\\( \forall T\_{g,o} \\; \text{and} \\; T\_{w,i} \\)
- Mathematical formulation:
$$ W\_s = \sum\_{i=1}^n \sigma \cdot \epsilon \cdot R\_{S,i} \cdot (T_{g,o}^4 - T_{w,i}^4) + \sum\_{i=1}^n h_c \cdot S_i \cdot R\_{S,i} \cdot (T_{g,o} - T_{w,i})
$$
### Momentum balance equation for the fluid (pressure losses)
- Validity domain:
\\( \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 domain:
\\( X_{H_20,a} < 1 \\; \\text{and} \\;\\ X_{O_2,a} > 0 \\)
- Mathematical formulation:
$$ E_X = M_O \cdot \frac{\frac{2 \cdot X_{C,f}}{M_C} + \frac{X_{H,f}}{2 \cdot M_H} + \frac{2 \cdot X_{S,f}}{M_S} - \frac{X_{O,f}}{M_O} - 2 \cdot \frac{\dot{m}\_{cv} \cdot I_{CV} + \dot{m}\_{bf} \cdot I\_{BF}}{M_C}}{\frac{X_{0_2,a}}{1 - X_{H_2O,a}}} $$
- Comments:
This formulation arises from the chemical reactions considered in the combustion:
$$ C + O_2 \longrightarrow CO_2 $$
$$ H + \frac{1}{4} 0_2 \longrightarrow H_2O $$
$$ S + O_2 \longrightarrow SO_2 $$
### \\( O_2 \\) mass fraction in the flue gases
- Validity domain:
\\( \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 domain:
\\( \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. 8.2. Springer Nature Switzerland AG.
Author Baligh El Hefni
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