# Simulation of Biomass Combustion with Modified Flue Gas Tract
## 2 Mathematical Simulation
### Combustion Process  
The combustion of biomass can be divided into three stages: moisture evaporation, devolatilization, and char combustion. Moisture evaporation was not included in the model.  
In real stoves, the devolatilization process occurs in the fixed bed in the retort burner. Products of devolatilization process were included in the model as part of mass flow in the burner inlet boundary condition. The amount of released gases was calculated based on fuel analysis and assumed power of the stove.  
Char combustion process was not considered in the model. To include heat and mass sources resulting from char combustion, the amount of main reaction products was calculated based on stoichiometry. Then, the combustion products were added into the burner as a volumetric mass source, and consumed oxygen was included as a negative mass source. Additionally, the heat released in the heterogeneous reaction was calculated and included in the model as a volumetric heat source in the burner. Such a simplification could be justified because the detailed analysis of heterogeneous reaction products was not a subject of this paper and because char combustion occurs in a fixed bed, the mass and heat source location is known and is independent of time for constant power of the stove. Values of volumetric sources are listed in Table 3.  
The combustion of volatiles is realized by two homogenous reactions described in Equations (7) and (8). As the exact composition as well as combustion reaction kinetics of volatiles is not known, it was assumed that volatiles were composed of methane and the amount of released gas was calculated to obtain an enthalpy source equal to the enthalpy of volatiles resulting from fuel analysis.  
\[2\,CH_{4}+3\,O_{2}\to 2\,CO+4\,H_{2}O \tag{7}\]  
\begin{table}
\begin{tabular}{c c c c c c} \hline  & & \multicolumn{4}{c}{**Particle Size [\(\upmu\)m]**} \\ \hline  & **Up to 20** & **20–50** & **50–100** & **100–150** & **150–250** & **250–500** \\ \hline
[\%] & 10.80 & 31.65 & 35.61 & 14.83 & 6.68 & 0.43 \\ \hline \end{tabular}
\end{table}
Table 2: Size distribution of particulate matter.  
\begin{table}
\begin{tabular}{c c c} \hline
**Source** & **Value** & **Unit** \\ \hline O\({}_{2}\) & \(-3.3\times 10^{-4}\) & kg/s \\ \hline CO\({}_{2}\) & \(4.59\times 10^{-4}\) & kg/s \\ \hline Heat & 5.491 & kW \\ \hline \end{tabular}
\end{table}
Table 3: Volumetric sources in the burner zone.  
\[2\;CO+\;O_{2}\to 2\;CO_{2} \tag{8}\]  
Turbulence-chemistry interaction was realized by using the Eddy Dissipation Concept (EDC) model. This model is an extension of the Eddy Dissipation model to involve all the necessary chemical relationships and bonds in the turbulent flow. In EDC, it is assumed that the reaction occurs in so-called fine structures and the reaction rate depends on mass transfer between the fine structures and surrounding gas. Reactions in Ansys Fluent compiled according to the Arrhenius Equation (9) were mutually interconnected using the numerical algorithm ISAT.  
\[k=A\cdot T^{\beta}\cdot e^{-\frac{E}{KT}}, \tag{9}\]  
where \(A\) is the pre-exponential factor; \(\beta\) is the temperature exponent; \(E\) is the activation energy for the reaction; and \(R\) is the universal gas constant [16].  
The kinetic parameters and temperature exponent for the homogenous reaction (7) are as follows: (I) the value of pre-exponential factor A is \(1.398762\times 10^{10}\); (II) the value of activation energy \(E\) is \(1.16712\times 10^{8}\) J. kmol\({}^{-1}\); and (III) the value of temperature exponent \(\beta\) is \(-0.062\). The kinetic parameters and temperature exponent for the homogenous reaction (8) are as follows: (I) the value of pre-exponential factor A is \(7.381123\times 10^{11}\); (II) the value of activation energy \(E\) is \(7.65969\times 10^{7}\) J. kmol\({}^{-1}\); and (III) the value of temperature exponent \(\beta\) is \(0.215\)[17].