# Lattice-Boltzmann and Eulerian Hybrid for Solid Burning Simulation

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## Abstract

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## 1. Introduction

- By separating combustion stages, we design governing equations for each stage.
- We introduce LBM for physical quantity exchanges in solid fuel, for example, microscopic heat exchange.
- We derive the Lattice-Boltzmann equation for physical quantity exchange in a porous material like wood.
- We apply the oxygen to control the combustion time and propagation.
- We propose an LBM and NSE hybrid simulator and a new method to exchange physical quantities.

## 2. Related Work

## 3. Burning Solid and Lattice-Boltzmann Method

#### 3.1. Burning Process

#### 3.2. Lattice Boltzmann Method

## 4. LBM Model for Porous Thermal Flow

## 5. NSE and LBM Interface Handling

#### 5.1. Exchanging Quantity between Solid (LBM) and Air (NSE) Domains

#### 5.2. Oxygen Considering

## 6. Experiments

#### 6.1. LBM Solver vs. NS Solver

#### 6.2. Porosity Comparison between LBM and NS Solver

#### 6.3. Pyrolysis: Wood into Charcoal

#### 6.4. Burning with Oxygen

#### 6.5. Wood Burning with Permeability

## 7. Conclusions and Future Work

## Supplementary Materials

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

## References

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**Figure 1.**Illustration of physical quantity exchanges across LBM and NSE interface. Upper row is the LBM domain and bottom row is the NSE domain. The macroscopic value (green row) from LBM is required for evolution of the NSE grid cell B. The value of the NSE grid cell has to decompose for the streaming of the LBM grid cell $\beta $.

**Figure 3.**Wood burning simulation in 3D. The wood is eroded by the collaboration of velocity fields computed in the NSE field, weighted streaming into solid domain (NSE to LBM) and solid-internal flows simulated by LBM.

**Figure 4.**The leftmost image is flow obtained by the NS solver that shows strong vorticity formation. The rest of the three images was done by porous LBM with a uniform porosity of 0.9 and a permeability coefficient of 1000, 1 and 0.001, respectively.

**Figure 5.**NS and LBM comparison experiment. Upper images are 3 s, 12 s and 30 s using NS solver. Lower images are 15 s, 40 s and 80 s using LBM solver.

**Figure 6.**Pyrolysis experiment. Solid fuel is burned by heat underneath and produces charcoal shown in black and gas fuel shown in green. On the right image, burnt wood, on the left, charcoal. However, the temperature is low enough so that gas fuel does not start the combustion process and charcoal smoldering is minimal. Note that the LBM domain includes charcoal in black color including heated in red near the heat source.

**Figure 7.**Upper row is burning with oxygen, where we can observe that the oxygen rich region burns first, while in the lower row where oxygen is not considered, burning is less natural and interesting.

**Figure 8.**Upper row has low permeability, where flow inside wood is minimal. In the lower row where permeability high, flow occurs naturally across the two simulation domains. We can observe that the proposed hybrid boundary handling enables smoke exchanging flows towards inside and outside woods, and the proposed porous LBM method generates natural flow inside the wood.

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**MDPI and ACS Style**

Jo, E.; Kim, B.; Song, O.-Y.
Lattice-Boltzmann and Eulerian Hybrid for Solid Burning Simulation. *Symmetry* **2019**, *11*, 1405.
https://doi.org/10.3390/sym11111405

**AMA Style**

Jo E, Kim B, Song O-Y.
Lattice-Boltzmann and Eulerian Hybrid for Solid Burning Simulation. *Symmetry*. 2019; 11(11):1405.
https://doi.org/10.3390/sym11111405

**Chicago/Turabian Style**

Jo, Eunchan, Byungmoon Kim, and Oh-Young Song.
2019. "Lattice-Boltzmann and Eulerian Hybrid for Solid Burning Simulation" *Symmetry* 11, no. 11: 1405.
https://doi.org/10.3390/sym11111405