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ABSTRACT
Modeling the propagation of smoldering fronts with forced air feeding in a porous medium remains a challenge to science. One of the main difficulties is to describe the carbon oxidation reaction that supports this self-sustained process. Pore scale approaches are required to tackle this complex coupled heat and mass transfer problem with chemistry. They, nevertheless, require high computation effort and still miss experimental validation. Furthermore, the heat loss at the walls of the cells inherent to every laboratory scale system adds another level of complexity in the understanding of the coupling between the phenomena at stake. Indeed, it induces a nonhomogeneous temperature field throughout the system. In this article, a 2D Darcy scale model is developed and validated by confrontation with experimental results from the literature, covering wide ranges of carbon content of the medium and forced air velocity. A reasonable description of the front temperature, velocity, and non-consumption oxygen amount is reached. The model finally enables understanding of the impact of heat loss, which controls the front shape and stability near the system walls.
Nomenclature
Latin symbols
| = | pre exponential factor(1/s) | |
| = | screen specific heat capacity (J/kg/K) | |
| = | carbon mass fraction in the solid phase | |
| = | mass diffusion coefficient (m | |
| = | effective mass diffusion coefficient (m | |
| = | sphere diameter (m) | |
| = | activation energy (J/mol) | |
| = | carbon monoxide fraction | |
| = | fraction of carbon oxidized by the combustion front | |
| = | fraction of oxygen consumed by the combustion front | |
| = | acceleration due to gravity (m/s | |
| = | solid gas convective heat transfer coefficient (W/m | |
| = | convective heat transfer coefficient (W/m | |
| = | molar mass (g/mol) | |
| = | Nusselt number | |
| = | pressure (Pa) | |
| = | Péclet number | |
| = | Prandtl number | |
| = | volumic flow rate (m | |
| = | ideal gas constant (J/mol/K) | |
| = | reacting medium radius (m) | |
| = | Reynolds number | |
| = | porous medium specific surface area (1/m) | |
| = | average macroscale temperature (K) | |
| = | time (s) | |
| = | velocity (m/s) | |
| = | mass fraction |
Greek symbols
| = | distribution coefficient for heat source | |
| = | dispersiviity (m) | |
| = | latent heat (J/kg) | |
| = | emissivity | |
| = | reaction rate (kg/m | |
| = | thermal conductivity (W/m/K) | |
| = | effective thermal conductivity (W/m/K) | |
| = | permeability (m | |
| = | density (kg/m | |
| = | Stefan-Boltzmann constant (W/m | |
| = | reaction heat (W/m | |
| = | dynamic viscosity (Pa.s) | |
| = | tortuosity | |
| = | porous media porosity |
Subscripts
| = | alumina | |
| = | bed | |
| = | chemical front | |
| = | gas phase | |
| = | insulating material | |
| = | accounting for the different gaseous species (N | |
| = | longitudinal | |
| = | pore | |
| = | solid phase | |
| = | surrounding | |
| = | transverse | |
| = | thermal | |
| = | top of the combustion cell |
Other symbols
| = | tensors | |
| = | vector | |
| = | nabla operator |
Acknowledgments
The authors would like to thank Bernard Auduc and Denis Marty for their technical support.
Funding
The author gratefully acknowlege the French Agence Nationale de la Recherche for financial support of the INSICOMB project ANR-11-BS009-005-01 in which this work was carried on.
Notes
1 Intel Core i7-4910 MQ Haswell at 2.90 MHz, 8 Go DDR3 1600 MHz.