# CFD Simulation of an Internally Cooled Biomass Fixed-Bed Combustion Plant

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Model

#### 2.1. Solid Phase

^{3}

_{solid}/m

^{3}

_{cell}), solid temperature (K), moisture density (kg/m

^{3}

_{solid}), dry wood density (kg/m

^{3}

_{solid}), char density (kg/m

^{3}

_{solid}), ash density (kg/m

^{3}

_{solid}) and third power of the particle average diameter (m

^{3}).

_{2}produced by the char oxidation (φ) is calculated by a temperature-dependent correlation [40,42].

#### 2.2. Gas Phase

_{2}and H

_{2}, consuming O

_{2}, CO

_{2}and H

_{2}O(v), respectively. To model the devolatilization, a simplified list of species is used. This includes CH

_{4}, C

_{6}H

_{6}, CO, CO

_{2}, H

_{2}and H

_{2}O(v). The methane and benzene represent the light hydrocarbons and tars, respectively. The composition of the emissions is estimated by a method based on an elemental and energy balance equation system that is closed with two experimental expressions [47]. In this case, experimental CO and CH

_{4}yields in the function of the temperature of pyrolysis are taken as the closure equations [48]. All the species generated and consumed in the solid fuel thermal processes are exchanged with the gas phase, using mass sources.

## 3. Methodology

#### 3.1. Experimental Plant

#### 3.2. Fuel and Operating Conditions

#### 3.3. Discretization and Boundary Conditions

^{3}/h of water, and the bed cooling system, when active, with 0.576 m

^{3}/h of water at an average temperature of 52 °C.

## 4. Results

_{4}and C

_{6}H

_{6}emissions.

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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Solid temperature | $\frac{\partial \left(\epsilon {\rho}_{P}{h}_{s}\right)}{\partial t}=\nabla \left({k}_{s.eff}\xb7\nabla {T}_{s}\right)+{S}_{{h}_{s}}$ | (1) |

Solid fraction | $\frac{\partial \epsilon}{\partial t}=\left(\frac{{\dot{\omega}}_{wood}^{\u2034}}{{\rho}_{wood}^{s}}+\frac{{\dot{\omega}}_{G,char}^{\u2034}-{\dot{\omega}}_{C,char}^{\u2034}}{{\rho}_{char}^{s}}\right)\epsilon $ | (2) |

Particle diameter | $\frac{\partial {d}_{eq}^{3}}{\partial t}=\left(\frac{-{\dot{\omega}}_{wood}^{\u2034}}{{\rho}_{wood}^{s}}+\frac{{\dot{\omega}}_{G,char}^{\u2034}-{\dot{\omega}}_{C,char}^{\u2034}}{{\rho}_{char}^{s}}\right){d}_{eq}^{3}$ | (3) |

Moisture density | $\frac{\partial \left(\epsilon {\rho}_{moisture}\right)}{\partial t}=-{\dot{\omega}}_{moisture}^{\u2034}\xb7\epsilon $ | (4) |

Wood density | $\frac{\partial \left(\epsilon {\rho}_{wood}\right)}{\partial t}=-{\dot{\omega}}_{wood}^{\u2034}\xb7\epsilon $ | (5) |

Char density | $\frac{\partial \left(\epsilon {\rho}_{char}\right)}{\partial t}=\left({\dot{\omega}}_{G,char}^{\u2034}-{\dot{\omega}}_{C,char}^{\u2034}\right)\epsilon $ | (6) |

Ash density | $\frac{\partial \left(\epsilon {\rho}_{ash}\right)}{\partial t}=0$ | (7) |

Drying rate | ${\dot{\omega}}_{moisture}^{\u2034}=\tau \frac{{\rho}_{P}{C}_{p}}{L{H}_{moisture}}\frac{\partial {T}_{S}}{\partial t},{T}_{S}\ge {T}_{evap}$ | (8) |

Devolatilization rate | ${\dot{\omega}}_{wood}^{\u2034}={\rho}_{wood}{\sum}_{i=1}^{3}{A}_{i}exp\left(-\frac{{E}_{i}}{R{T}_{S}}\right)$ | (9) |

Char consumption rate | ${\dot{\omega}}_{C,char}^{\u2034}={K}_{glob}^{ox}{A}_{v}\left[{O}_{2}\right]{M}_{C}+{K}_{glob}^{g,1}{A}_{v}\left[C{O}_{2}\right]{M}_{C}+{K}_{glob}^{g,2}{A}_{v}\left[{H}_{2}O\right]{M}_{C}$ | (10) |

Pyrolysis Reactions | A_{i} (s^{−1}) | E_{i} (kJ/mol) | References |

Dry wood → Gas | 1.11 × 10^{11} | 177 | [39] |

Dry wood → Tar | 9.28 × 10^{9} | 149 | [39] |

Dry wood → Char | 3.05 × 10^{7} | 125 | [39] |

Char Reactions | Kinetics | References | |

$C+\phi {O}_{2}\to 2\left(1-\phi \right)CO+\left(2\phi -1\right)C{O}_{2}$ | ${K}^{ox}=1.715\xb7{T}_{S}\xb7exp\left(\raisebox{1ex}{$-9000$}\!\left/ \!\raisebox{-1ex}{${T}_{S}$}\right.\right)$ | [40,41] | |

$C+C{O}_{2}\to 2CO$ | ${K}^{g,1}=3.42\xb7{T}_{S}\xb7exp\left(\raisebox{1ex}{$-15,600$}\!\left/ \!\raisebox{-1ex}{${T}_{S}$}\right.\right)$ | [40,41] | |

$C+{H}_{2}O\to CO+{H}_{2}$ | ${K}^{g,2}=5.7114\xb7{T}_{S}\xb7exp\left(\raisebox{1ex}{$-15,600$}\!\left/ \!\raisebox{-1ex}{${T}_{S}$}\right.\right)$ | [41] |

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

${C}_{6}{H}_{6}+\raisebox{1ex}{$9$}\!\left/ \!\raisebox{-1ex}{$2$}\right.{O}_{2}\to 6CO+3{H}_{2}O$ | ${R}_{R.1}=1.3496\times {10}^{9}\xb7exp\left(-\frac{1.256\times {10}^{8}}{RT}\right){\left[{C}_{6}{H}_{6}\right]}^{-0.1}{\left[{O}_{2}\right]}^{1.85}$ |

$C{H}_{4}+\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.{O}_{2}\to CO+2{H}_{2}O$ | ${R}_{R.2}=5.012\times {10}^{11}\xb7exp\left(-\frac{2\times {10}^{8}}{RT}\right){\left[C{H}_{4}\right]}^{0.7}{\left[{O}_{2}\right]}^{0.8}$ |

${H}_{2}+\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.{O}_{2}\to {H}_{2}O$ | ${R}_{R.3}=9.87\times {10}^{8}\xb7exp\left(-\frac{3.1\times {10}^{7}}{RT}\right)\left[{H}_{2}\right]\left[{O}_{2}\right]$ |

$CO+\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.{O}_{2}\to C{O}_{2}$ | ${R}_{R.4}=2.239\times {10}^{12}\xb7exp\left(-\frac{1.702\times {10}^{8}}{RT}\right)\left[CO\right]{\left[{O}_{2}\right]}^{0.25}{\left[{H}_{2}O\right]}^{0.5}$ |

${H}_{2}O+CO\to C{O}_{2}+{H}_{2}$ | ${R}_{R.5}=2.780\xb7exp\left(-\frac{1.255\times {10}^{7}}{RT}\right)\left[{H}_{2}O\right]\left[CO\right]$ |

$C{O}_{2}+{H}_{2}\to {H}_{2}O+CO$ | ${R}_{R.6}=93690\xb7exp\left(-\frac{4.659\times {10}^{7}}{RT}\right)\left[C{O}_{2}\right]\left[{H}_{2}\right]$ |

**Table 5.**Fuel characterization [19].

Proximate Analysis ^{a} | [wt%] |

Moisture | 5.23 |

Volatile | 71.57 |

Fixed carbon | 22.81 |

Ash | 0.39 |

Ultimate Analysis ^{b} | [wt%] |

C | 47.21 |

H | 6.34 |

O | 45.96 |

N | 0.08 |

Heating Values ^{a} | [MJ/kg] |

HHV | 18.19 |

LHV | 16.74 |

^{a}wet basis, as received.

^{b}dry basis, ash-free.

**Table 6.**Control variables defining the experiment sets [19].

Test Name | Total Airflow [kg/h] | Primary Air Ratio [%] | Bed Cooling |
---|---|---|---|

1.8 [kg/h] raw | 6 | 30 | OFF |

2.7 [kg/h] raw | 9 | 30 | OFF |

3 [kg/h] raw | 6 | 50 | OFF |

4.5 [kg/h] raw | 9 | 50 | OFF |

1.8 [kg/h] CB | 6 | 30 | ON |

2.7 [kg/h] CB | 9 | 30 | ON |

3 [kg/h] CB | 6 | 50 | ON |

4.5 [kg/h] CB | 9 | 50 | ON |

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**MDPI and ACS Style**

Álvarez-Bermúdez, C.; Chapela, S.; Varela, L.G.; Gómez, M.Á.
CFD Simulation of an Internally Cooled Biomass Fixed-Bed Combustion Plant. *Resources* **2021**, *10*, 77.
https://doi.org/10.3390/resources10080077

**AMA Style**

Álvarez-Bermúdez C, Chapela S, Varela LG, Gómez MÁ.
CFD Simulation of an Internally Cooled Biomass Fixed-Bed Combustion Plant. *Resources*. 2021; 10(8):77.
https://doi.org/10.3390/resources10080077

**Chicago/Turabian Style**

Álvarez-Bermúdez, César, Sergio Chapela, Luis G. Varela, and Miguel Ángel Gómez.
2021. "CFD Simulation of an Internally Cooled Biomass Fixed-Bed Combustion Plant" *Resources* 10, no. 8: 77.
https://doi.org/10.3390/resources10080077