http://orcid.org/0000-0003-2090-5109
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ABSTARCT
Upward flame spread over thin solids is numerically studied using an in-house three-dimensional transient numerical model with a two-stage solid pyrolysis. The simulation results reveal fundamentally different flame behaviors in different pressure conditions. At low pressures, conventional continuous flame spread is observed. Upon ignition, the flame grows and spreads upward until it reaches the end of the sample. At high pressures, the flame splits into two flames shortly after ignition. The two flames spread upward separately at different spread rates. In a transitional pressure region, cyclic flame splitting was observed. The flame splits periodically during the upward spreading process. In each splitting cycle, the bottom flame extinguishes shortly after splitting while the top flame continuously spreads upward and starts a new splitting cycle. This flame splitting phenomenon was previously observed experimentally, but to the authors’ knowledge is numerically captured for the first time in this study. The splitting process is presented in detail and compared with the continuous flame spread process. The numerical results indicate that the multi-stage pyrolysis is responsible for the flame splitting.
Acknowledgments
This work made use of the High Performance Computing Resource in the Core Facility for Advanced Research Computing at Case Western Reserve University. The authors would also like to acknowledge the support from Underwriters Laboratories.
Supplemental data
Supplemental data for this article can be accessed here.
Nomenclature
| As,i | = | Pre-exponential factor of the i th-step solid pyrolysis |
| Bg | = | Pre-exponential factor of the gas-phase reaction |
| Cp | = | Specific heat of the gas phase |
| Cp,F | = | Specific heat of the fuel vapor |
| Cs | = | Specific heat of the solid |
| Dj | = | Diffusion coefficient of species j |
| E | = | Activation energy of the gas-phase reaction |
| Es,i | = | Activation energy of the i th-step solid pyrolysis |
| g | = | Gravity acceleration |
| k | = | Thermal conductivity |
| Le,j | = | Lewis number of gas species j |
| LR | = | Reference length |
| ni | = | Reaction order of the i th-step solid pyrolysis |
| Ρ | = | Pressure |
| Pr | = | Prandtl number |
| T | = | Temperature |
| TL | = | Reference temperature of the solid phase |
| UR | = | Reference velocity |
| x | = | x-coordinate |
| XL | = | Latent heat of the solid at TL |
| y | = | y-coordinate |
| z | = | z-coordinate |
| = | Heat of combustion (at 300 K) of the gas-phase reaction | |
| α | = | Thermal diffusivity |
| μ | = | Viscosity |
| ρ | = | Density |
| τ | = | Thickness of the sample |
Subscripts
| flame | = | Adiabatic flame |
| holder | = | Properties for the sample holder |
| sample | = | Properties for the sample |
| s | = | Properties for solid |
| ∞ | = | Ambient |
Superscripts
| * | = | Properties evaluated at reference temperatures (1250 K for gas phase, 300 K for solid phase) |