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Progress in Scale Modeling, Volume II pp 85–95Cite as

Section B Fire and Explosion - A Study of Flame Spread in Engineered Cardboard Fuel Beds Part II: Scaling Law Approach

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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.

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Abbreviations

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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Authors and Affiliations

  1. Institute of Research for Technology Development, University of Kentucky, Lexington, KY, 40506, USA

    Brittany A. Adam, Nelson K. Akafuah & Kozo Saito

  2. USDA Fire Science Laboratory, Missoula, MT, 59808, USA

    Mark A. Finney & Jason Forthofer

Authors
  1. Brittany A. Adam
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  2. Nelson K. Akafuah
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  3. Mark A. Finney
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  4. Jason Forthofer
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  5. Kozo Saito
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Corresponding author

Correspondence to Nelson K. Akafuah .

Editor information

Editors and Affiliations

  1. Dept. Mechanical Engineering, University of Kentucky, Lexington, Kentucky, USA

    Kozo Saito

  2. Hirosaki University, Hirosaki-shi, Aomori, Japan

    Akihiko Ito

  3. Toyohashi University of Technology, Toyohashi, Japan

    Yuji Nakamura

  4. Yamagata University, Yonezawa-shi, Yamagata, Japan

    Kazunori Kuwana

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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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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-10307-5

  • Online ISBN: 978-3-319-10308-2

  • eBook Packages: EngineeringEngineering (R0)

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