# Biomass Combustion Modeling Using OpenFOAM: Development of a Simple Computational Model and Study of the Combustion Performance of Lippia origanoides Bagasse

^{1}

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## Abstract

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## 1. Introduction

_{2}excess values. Those models studied the combustion of wood pellets. As examples of analyses with other biomasses, we can mention the works of Karim and Naser published in 2018 [2,16], which report the modeling of two combustion systems: a small fixed bed combustor and an industrial moving grate boiler; they used them to study the combustion of the systems fueled by different kinds of lignocellulosic biomasses. A complete review of the subject is given in the works of Dernbecher et al. [11], Karim and Naser [17], Khodaei et al. [8], Bhuiyan et al. [6] and García et al. [18,19]. However, it is still a field in development due to its complexity; several submodels and high computational resources are required for simulations [11,17,20,21,22,23]. OpenFOAM is an advanced and robust open-source CFD package with rising adoption in industry and academia due to its advantages, such as a continuously growing set of features and the absence of license costs [24]. Nowadays, there are relatively few works about solid combustion modeling developed in OpenFOAM, although there has been a growing interest in the subject in recent years [19]. This work reports on the development of a bidimensional CFD model to study the combustion performance of several solid biomass fuels and its application in the analysis of Lippia origanoides bagasse combustion. The model was implemented in OpenFOAM and validated against experimental data of ignition front propagation velocity and the maximum temperature taken from a combustor tube fueled by three biomasses: wood pellets, olive stone and almond shell. The experimental data were taken from the work of Patiño [25]. The model uses an Eulerian–Lagrangian approach to simulate freeboard (continuous phase) and fuel bed (dispersed phase) behavior. In the continuous phase, governing equations are solved, and in the disperse phase, particles are tracked and the mass, momentum, species and energy transfer between those particles and the continuous phase are calculated. It employs the k-epsilon, P1 and partially stirred reactor (PaSR) submodels for turbulence, radiation and gas combustion, respectively. The novelty of this research lies in the development of a simple computational model to simulate solid combustion using OpenFOAM, and in the analysis of the combustion performance of a kind of residual biomass that had not been previously considered as a fuel.

## 2. Materials and Methods

#### 2.1. Fuel Properties

_{p}is the real density of the particles and ρ

_{a}is the bulk density of the biomass bed. The properties of the first three fuels which were used for validation were taken from the work of Patiño [25]. The elemental and proximate analyses and the densities of Lippia origanoides bagasse (LO) were determined experimentally in the laboratories of the Industrial University of Santander in Bucaramanga, Colombia, while the lower heating value was determined by Equation (2) [26]:

_{M}is the percentage by mass of moisture, X

_{H}is the percentage by mass of hydrogen and HHV is the higher heating value calculated from the proximate composition by Sheng and Azevedo’s [27] Equation (2).

#### 2.2. Experimental Setup and Computational Domain

#### 2.3. Mesh Independence Analysis

#### 2.4. Model Description

_{i}is the mass fraction of the species, R

_{g}is the Reynolds stress term and α

_{eff}and D

_{eff}are the effective thermal and mass diffusivities. The source terms can come from the combustion model (c), the Lagrangian particles (p) or the radiation model (r). The ones that come from the interaction with particles may be further decomposed according to the process they represent: drying (ev), devolatilization (dv), heat transfer by convection (cv) or the reaction to the particle drag force (dr). Therefore, the source terms may be decomposed as [29]:

_{p}), mass (m

_{p}) and temperature (T

_{p}) (Equations (11)–(13)) were solved and used to update their properties before each continuous phase time step.

_{dr}and F

_{grav}. The parcel’s mass variation (Equation (12)) is expressed as the sum of the variation during evaporation devolatilization, which comes from the respective drying and pyrolysis models. The temperature equation (Equation (13)) comes from the balance of energy; the rate of change in energy in the parcel is equal to the sum of the rate of change in specific enthalpy due to evaporation, devolatilization, radiation and convection.

#### 2.5. Submodels

#### 2.5.1. Drying

#### 2.5.2. Devolatilization

_{j}is the mass of the jth volatile component in biomass, E is the activation energy, A is the pre-exponential factor, R is the universal gas constant and T

_{p}is the parcel temperature. The volatile production rate was used to determine the source terms related to devolatilization in Equations (7)–(10) (${S}_{p,m}^{dv}$, ${S}_{p,h}^{dv}$, ${S}_{p,u}^{dv}$ and ${S}_{p,y}^{dv}$).

#### 2.5.3. Heat Transfer

_{p}is the emission contribution of the particles; σ is the Stefan–Boltzmann coefficient and T is the gas temperature. The source term in the gas phase energy equation can be expressed as:

_{p}is the incident radiation at the particle position and A

_{s}is the particle surface area. Convection was taken into account, employing the Ranz–Marshall correlation [32,33], with which the particle Nusselt number (Nu

_{p}) was calculated, and the rate of change in specific enthalpy due to convection (${\dot{h}}_{p}^{cv}$) and the source term due to convection in the energy equation (${S}_{p,h}^{cv}$) were determined:

_{s}and Pr

_{s}are the surface Reynolds and Prandlt numbers, h is the convective heat transfer coefficient, k is the particle thermal conductivity and V

_{c}is the volume of a cell with i particles inside it.

#### 2.5.4. Combustion

_{0}to a value c due to chemical reactions; in the second stage, the reactive mixture c is mixed with the unreactive one c

_{0}due to the turbulence during a mixing time τ

_{mix}, resulting in the averaged concentration c

_{1}. The reaction rate fm is defined as [34]:

_{c}is the chemical time and τ

_{mix}is obtained from the k-ε model:

_{mix}varies between 0.001 and 0.3 depending on the flow. In this work, it was taken as 0.03, as in other similar studies [35].

#### 2.5.5. Reaction Mechanism

## 3. Results

^{−2}s

^{−1}. As an example, Figure 3 shows the temperature profiles of wp combustion at 1000, 3500 and 7000 s, and an airflow rate of 0.2 kg.m

^{−2}s

^{−1}. The results of the ignition front velocities and maximum temperatures were compared with experimental data from the combustor fueled by the same fuels, which are presented in Figure 4 and Table 3. Table 3 shows the relative error between the calculated and experimental data (%E =|Experimental Value − Calculated Value|⁄Experimental Value).

## 4. Discussion

## 5. Conclusions

- This paper presents a two-dimensional model of solid biomass combustion. The model is useful for studying the performance of a combustion system fueled by different kinds of biomass and under different airflow rates. Unlike other similar studies, this is an efficient numerical model implemented in OpenFOAM, which is a popular computational tool rarely used in this type of application.
- The model was validated by comparing its results with those obtained in a cylindrical combustor fueled with three types of biomass, with relative error values lower than 13% in most cases, which is similar to the errors obtained in recent studies on this subject.
- The stems of Lippia origanoides bagasse show a similar performance to that of other biomass used as solid fuels, while the leaves and mixtures of the same plant present lower performance.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Temperature profiles for wood pellets (wp) at an airflow rate of 0.2 kg.m

^{−2}s

^{−1}, at three different moments: (

**a**) 1000 s; (

**b**) 3500 s and (

**c**) 7000 s. Temperatures are measured on the Kelvin scale.

**Figure 4.**Experimental and simulated curves of ignition front velocity and maximum temperature at different airflow rates: (

**a**) wood pellets (wp); (

**b**) olive stone (os) and (

**c**) almond shell (as).

**Figure 5.**Ignition front velocity and maximum temperature at different airflow rates for Lippia origanoides bagasse samples: (

**a**) stems (S); (

**b**) leaves (L) and (

**c**) mixture of stems and leaves (M).

Fuel | Empirical Formula | Proximate Analysis [wt%] | LHV [MJ/kg] | ρ_{p} [kg/m^{3}] | ρ_{a} [kg/m^{3}] | |||
---|---|---|---|---|---|---|---|---|

Water | Volat. | Char | Ash | |||||

Wood pellets (wp) | CH_{1.71}O_{0.70} | 7.3 | 69.0 | 23.0 | 0.7 | 16.6 | 1240 | 690 |

Olive stone (os) | CH_{1.50}O_{0.64} | 13 | 61.3 | 25.1 | 0.6 | 15.3 | 1070 | 620 |

Almond shell (as) | CH_{1.40}O_{0.68} | 11.9 | 64.1 | 23.4 | 0.6 | 15.6 | 920 | 360 |

LO leaves (L) | CH_{1.48}O_{0.92} | 9.5 | 66.4 | 14.8 | 9.4 | 14.5 | 120.9 | 23.1 |

LO stems (S) | CH_{1.32}O_{0.75} | 9.3 | 68.7 | 17.1 | 5.0 | 15.6 | 594.2 | 308.8 |

LO mixture (M) | CH_{1.39}O_{0.83} | 9.9 | 67.4 | 16.4 | 6.3 | 15.1 | 371.8 | 174.5 |

Homogeneous Reactions | |
---|---|

R1 | ${\mathrm{C}}_{6}{\mathrm{H}}_{6}+\frac{9}{2}{\mathrm{O}}_{2}\to 6\mathrm{C}\mathrm{O}+3{\mathrm{H}}_{2}\mathrm{O}$ |

R2 | $\mathrm{C}{\mathrm{H}}_{4}+\frac{3}{2}{\mathrm{O}}_{2}\to \mathrm{C}\mathrm{O}+2{\mathrm{H}}_{2}\mathrm{O}$ |

R3 | ${\mathrm{H}}_{2}+\frac{1}{2}{\mathrm{O}}_{2}\to {\mathrm{H}}_{2}\mathrm{O}$ |

R4 | $\mathrm{C}\mathrm{O}+\frac{1}{2}{\mathrm{O}}_{2}\to {\mathrm{C}\mathrm{O}}_{2}$ |

R5 | ${\mathrm{H}}_{2}\mathrm{O}+\mathrm{C}\mathrm{O}\to {\mathrm{C}\mathrm{O}}_{2}+{\mathrm{H}}_{2}$ |

R6 | ${\mathrm{C}\mathrm{O}}_{2}+{\mathrm{H}}_{2}\to {\mathrm{H}}_{2}\mathrm{O}+\mathrm{C}\mathrm{O}$ |

**Table 3.**Relative error (%E) of values of simulated ignition front velocity (F. Velocity) and maximum temperature (Tmax).

Airflow [kg/m ^{2}s] | wp | os | as | |||
---|---|---|---|---|---|---|

F. Velocity | Tmax. | F. Velocity | Tmax. | F. Velocity | Tmax. | |

0.1 | 12.69 | 11.77 | 1.16 | - | 4.43 | 12.71 |

0.2 | 12.80 | 9.19 | 9.74 | 23.48 | 12.62 | 4.64 |

0.3 | 1.29 | 12.62 | 9.21 | 30.97 | 26.46 | 6.32 |

0.4 | 5.88 | - | - | - | 51.19 | 21.86 |

0.45 | 14.54 | - | - | - | - | - |

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**MDPI and ACS Style**

García Sánchez, G.F.; Chacón Velasco, J.L.; Fuentes Díaz, D.A.; Rueda-Ordóñez, Y.J.; Patiño, D.; Rico, J.J.; Martínez Morales, J.R.
Biomass Combustion Modeling Using OpenFOAM: Development of a Simple Computational Model and Study of the Combustion Performance of *Lippia origanoides* Bagasse. *Energies* **2023**, *16*, 2932.
https://doi.org/10.3390/en16062932

**AMA Style**

García Sánchez GF, Chacón Velasco JL, Fuentes Díaz DA, Rueda-Ordóñez YJ, Patiño D, Rico JJ, Martínez Morales JR.
Biomass Combustion Modeling Using OpenFOAM: Development of a Simple Computational Model and Study of the Combustion Performance of *Lippia origanoides* Bagasse. *Energies*. 2023; 16(6):2932.
https://doi.org/10.3390/en16062932

**Chicago/Turabian Style**

García Sánchez, Gabriel Fernando, Jorge Luis Chacón Velasco, David Alfredo Fuentes Díaz, Yesid Javier Rueda-Ordóñez, David Patiño, Juan Jesús Rico, and Jairo René Martínez Morales.
2023. "Biomass Combustion Modeling Using OpenFOAM: Development of a Simple Computational Model and Study of the Combustion Performance of *Lippia origanoides* Bagasse" *Energies* 16, no. 6: 2932.
https://doi.org/10.3390/en16062932