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Comparison of flame spread characteristics between dense and loose fuel arrays


This study investigates experimentally the fuel bed width effect on concurrent flame spread over discrete fuels. Two representative configurations, dense arrays spaced 3 mm and loose arrays spaced 6 mm, are concerned herein. Regular birch rod arrays were designed by varying five kinds of column numbers (denoted by n, 3, 5, 7, 9, and 11) and five slopes (θ, 0, 15°, 30°, 45°, and 60°). Results show that flame spread rate (FSR) of dense arrays is lower than that of loose arrays. A predicted model of FSR is also developed, which is in good agreement with experimental results. Moreover, compared with the loose arrays, the decay of heat flux in the thermal plume region behind the pyrolysis zone is more rapid for dense arrays. For dense arrays, with increasing inclination angle, maximum convective heat flux, mass loss rate, and flame length decrease first and then increase at n > 5, but have an increasing tendency for loose arrays. Furthermore, the fuel consumption efficiency of loose arrays has an obvious superiority over dense arrays when θ > 15˚. In addition, dimensionless correlations between flame length and heat release rate are proposed both for dense and loose arrays.

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A :

Coefficient in Eq. (2)

c p :

Specific heat (J g−1 K−1)

d :

Fuel thickness (mm)

D :

Flame thickness (mm)

D eq :

Equivalent diameter of burning zone (mm)

f :

Packing ratio

F :

View factor

h :

Convective heat transfer coefficient (W m−2 K)

∆H c :

Heat of combustion (kJ g−1)

ks :

Thermal conductivity (W m−1 k−1)

l :

Fuel length (mm)

l a :

Array length (mm)

L :

Characteristic length (mm)

L f :

Flame length (mm)

L f * :

Dimensionless flame length (mm)

m :

Row number

\(\dot{m}\) :

Mass loss rate (g s−1)

n :

Column number

Nu :

Nusselt number

\(\dot{q}^{\prime\prime}_{{{\text{in}}}}\) :

Incident heat flux (kW m−2)

\(\dot{q}^{\prime\prime}_{{\text{sur,rad}}}\) :

Radiant heat flux received by top surface (kW m−2)

\(\dot{q}_{{_{{\text{sur,conv}}} }}^{\prime \prime }\) :

Convective heat flux received by top surface (kW m−2)

\(\dot{q}_{{_{f} }}^{\prime \prime }\) :

Measured heat flux (kW m−2)

\(\dot{q}_{{_{f} }}^{\prime \prime *}\) :

Dimensionless heat flux

\(\dot{Q}\) :

Heat release rate (kW)

\(\dot{Q}^{*}\) :

Dimensionless heat release rate


Rayleigh number


Spacing (mm)

T :

Temperature (K)

t ig :

Ignition time (s)

t sp :

Spreading time (s)

t b :

Burnout time (s)

v f :

Flame spread rate (mm s−1)

W :

Array width (mm)

x :

Distance from the pyrolysis front (mm)

x py :

Pyrolysis length (mm)

α :

Thermal diffusivity (m2 s−1)

β :

Thermal expansion coefficient (K−1)

γ :

Included angle of pyrolysis front (°)

ɛ :

Flame emissivity

ϕ :

Included angle between flame and vertical direction (°)

θ :

Inclination angle (°)

θ f :

Included angle between flame plane and target (°)

v :

Kinematic viscosity (m2 s−1)

η :

Fuel consumption efficiency

ρ :

Density (kg m−3)

δ p :

Thermal penetration depth (mm)

f :


s :


p :





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This work was supported by the National Natural Science Foundation of China (Nos. 51804338, 51974361), Natural Science Foundation of Hunan Province (No. 2021JJ30860) and Fundamental Research Funds for the Central Universities of Central South University (No. 2021zzts0238).

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RB, YZ contributed to conceptualization; RB and YZ contributed to methodology; RB and XZ contributed to formal analysis and investigation; RB contributed to writing-original draft preparation; YZ and XZ contributed to writing review and editing; YZ and CF contributed to funding acquisition; YZ and CF contributed to resources; and YZ and CF supervised the study.

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Correspondence to Yang Zhou.

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Bu, R., Fan, C. & Zhou, Y. Comparison of flame spread characteristics between dense and loose fuel arrays. J Therm Anal Calorim 147, 13913–13924 (2022).

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  • Discrete fuels
  • Flame spread
  • Fuel bed width
  • Inclination angle
  • Heat flux