Abstract
In this second part of a two-part exploration into the dynamic behavior observed in wildland fires, time scales differentiating convective and radiative heat transfer are further explored. Scaling laws for the two different types of heat transfer were considered: radiation-driven fire spread and convection-driven fire spread, which can both occur during wildland fires. A new interpretation of the inertial forces introduced a downstream, time-dependent frequency ω, which captures the dynamic, vortex shedding behavior of flames due to the unstable nature of the turbulent flow created in the wake of the fire. Excelsior and paper strip experiments suggest many wildland fire scenarios fall into the convection-driven spread regime.
Keywords
- Inertial Force
- Strouhal Number
- Radiative Heat Transfer
- Diffusion Flame
- Flame Spread
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- Δθ 1 :
-
Temperature rise of air and gas
- Δθ 2 :
-
Temperature rise of fuel
- Δρ 1 :
-
Density change of air and gas
- c 2 :
-
Specific heat of fuel
- c p :
-
Specific heat of a gas at atmospheric pressure
- E :
-
Irradiance received by radiometer
- F b :
-
Buoyancy force of air and gas
- F i :
-
Inertial force
- F i :
-
Inertial force of air and gas
- Fr :
-
Froude number
- g :
-
Acceleration due to gravity
- H :
-
Fuel height
- H f :
-
Flame height
- I :
-
Fire intensity
- l 2 :
-
Fuel bed width
- L a :
-
Height of flame and fire plume
- L e :
-
Effective length over which the majority of heat transfer occurs (also effective length for vortex shedding)
- l H :
-
Characteristic length, height of fuel
- L w :
-
Flame zone thickness
- Ø:
-
Ratio of consumed fuel to the total available fuel
- Q :
-
Heat generated
- Q c1 :
-
Heat stored in the air and gas associated with the temperature rise
- Q c2 :
-
Heat stored in the unburned fuel
- q f :
-
Heat value per unit mass of fuel
- Q r :
-
Radiant heat received by the unburned fuel
- Q λ :
-
Latent heat of fuel (heat value per unit mass of fuel)
- R :
-
Spread velocity of flame front
- St :
-
Strouhal number
- t :
-
Characteristic time
- u :
-
Horizontal wind velocity
- α :
-
Fuel bed angle
- π:
-
pi number
- ρ 1 :
-
Gas density
- ρ f :
-
Fuel density
- ω:
-
Downstream, shedding frequency
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Acknowledgements
We acknowledge the late Professor Ichiro Emori and his former student Yasuo Iguchi for their pioneering work on scaling laws on flame spread. We also thank Professor Forman Williams for his invaluable discussions on the St–Fr correlation on wildland fires. This study was supported by USDA Forest Service under Collaboration Forest Service agreement: 12-CS-11221637-133.
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Adam, B.A., Akafuah, N.K., Finney, M.A., Forthofer, J., Saito, K. (2015). Section B Fire and Explosion - A Study of Flame Spread in Engineered Cardboard Fuel Beds Part II: Scaling Law Approach. In: Saito, K., Ito, A., Nakamura, Y., Kuwana, K. (eds) Progress in Scale Modeling, Volume II. Springer, Cham. https://doi.org/10.1007/978-3-319-10308-2_6
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DOI: https://doi.org/10.1007/978-3-319-10308-2_6
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