Abstract
In wildland and other flame spread scenarios a spreading fire front often forms an elliptical shape, incorporating both forward and lateral spread. While lateral flame spread is much slower than forward rates of spread, it still contributes to the growth of the overall fire front. In this work, a small-scale experiment is performed to investigate the mechanisms causing this lateral spread in a simple, small-scale configuration. PMMA strips with thicknesses ranging from 1 mm to 3.1 mm and widths of 5 cm and 10 cm were ignited under forced flow in a laminar wind tunnel. Unlike traditional concurrent or opposed flame spread experiments, flames were allowed to progress from one side of the sample to the other, perpendicular to the wind direction. An infrared camera was used to track the progression of the pyrolysis front by estimating the surface temperature of the PMMA. The flame spread rate, depth of the burning region, thermal diffusion length, and radiant heat flux were determined and analyzed. Based on a theory of heat and mass transfer for a laminar diffusion flame, a thermal heat transfer model was developed for the preheating region to predict the lateral flame spread rate. Results show that the thermal diffusion length decreases with wind velocity, ranging from 4.5 mm to 3 mm. Convection dominates the flame-spread rate, accounting for more than 80% of the total heat flux. The theoretical flame spread rate agrees well with experimental data from all but the thinnest samples tested, overpredicting the lateral flame spread rate for 1 mm thick samples. The resulting model for lateral flame spread under concurrent flow works for forced-flow dominated flame spread over thermally-thin fuels and helps provide physical insight into the problem, aiding in future development of two-dimensional, elliptical fire spread models.
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Abbreviations
- a :
-
Average diffusion distance
- c s :
-
Specific heat of PMMA
- D :
-
Diffusion coefficient
- Da:
-
Damköhler number
- J z :
-
Diffusion velocity of gasified fuel
- k s :
-
The effective emission coefficient
- l m :
-
Flame mean beam length
- L :
-
The depth of burning region
- \(\dot{m}_{d}^{{\prime }}\) :
-
Mass flow of lateral diffusion
- P :
-
The perimeter of diffusion flame
- Pr:
-
Prandtl number
- \(\dot{q}^{{\prime }}\) :
-
Heat flux per unit width
- r :
-
The mass of fuel required to react with a unit of air
- R :
-
The radius of radiometer
- Re:
-
Reynolds number
- t :
-
Time
- \(T_{f}\) :
-
Flame temperature
- \(T_{rf}\) :
-
Effective flame radiation temperature
- \(T_{\text{g}}\) :
-
Film temperature of gas phase
- \(T_{p}\) :
-
Pyrolysis temperature
- \(T_{\infty }\) :
-
Ambient temperature
- \(u_{\infty }\) :
-
Wind velocity
- \(V_{f}\) :
-
Flame spread rate
- \(V_{b}\) :
-
Buoyant velocity of fire plume
- \(W\) :
-
Sample width
- \(Y_{fz}\) :
-
Fuel mass fraction
- \(Y_{fw}\) :
-
Fuel mass fraction at the solid surface
- \(\rho_{s}\) :
-
PMMA density
- \(\delta\) :
-
PMMA thickness
- \(\delta_{f}\) :
-
Flame stand-off distance
- \(\delta_{\text{g}}\) :
-
Lateral diffusion length
- \(\delta_{q}\) :
-
Quenching distance
- \(\delta_{d}\) :
-
Thermal penetration depth
- \(\lambda_{\text{g}}\) :
-
Thermal conductivity of the gas phase
- \(\lambda_{s}\) :
-
Thermal conductivity of PMMA
- \(\rho_{z}\) :
-
Density of diffusion flame
- \(\rho_{\infty }\) :
-
Ambient density
- \(v_{\infty }\) :
-
Kinematic viscosity
- η:
-
Similarity variable
- \(\alpha_{s}\) :
-
Surface absorptivity
- \(\varepsilon\) :
-
Emissivity
- \(\sigma\) :
-
Stefan-Boltzmann constant
- d:
-
Lateral diffusion
- f:
-
Flame
- p:
-
Pyrolysis
- g :
-
Gas phase
- s:
-
Solid phase
- ∞:
-
Ambient condition
- c:
-
Convective heat flux
- r:
-
Radiative heat flux
- rloss:
-
Radiative heat loss from solid surface
- w:
-
The value at the solid surface
- x, y, z:
-
Coordinate
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Acknowledgements
MG would like to thank Mark Finney for insightful discussions which inspired to the topic of the paper and acknowledge financial support for this work from the National Science Foundation under Grant No. CBET 1554026. KZ and LZY were supported by the Key project of National Natural Science Foundation of China (NSFC) under Grant No. 51636008, Key Research Program of Frontier Sciences, Chinese Academy of Science (CAS) under Grant No. QYZDB-SSW-JSC029, the Fundamental Research Funds for the Central Universities under Grant No. WK2320000035 and the Open Fund of State Key Laboratory of Fire Science under Grant No. HZ2019-KF09.
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Zhao, K., Gollner, M.J., Liu, Q. et al. Lateral Flame Spread over PMMA Under Forced Air Flow. Fire Technol 56, 801–820 (2020). https://doi.org/10.1007/s10694-019-00904-x
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DOI: https://doi.org/10.1007/s10694-019-00904-x