Soot Production and Radiative Heat Transfer in Opposed Flame Spread over a Polyethylene Insulated Wire in Microgravity

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Flame spread over an insulated electrical wire is identified as a fire scenario in space vehicles. In such microgravity configurations, the contribution of thermal radiation from gaseous participating species and soot to the wire burning rate and flame spread is not fully understood and the present paper addresses this question both experimentally and numerically. A non-buoyant opposed-flow flame spread configuration over a nickel–chrome wire coated by Low Density PolyEthylene (LDPE) is considered with an O2/N2 oxidizer composed of 19% of oxygen in volume and a flow velocity of 200 mm/s. Flame spread rate, pyrolysis rate, stand-off distance, soot volume fraction, and soot temperature are experimentally determined based on optical diagnostics that capture the flame spread in parabolic flights. The numerical model uses the measured spread and pyrolysis rates as input data and solves transport equations for mass, momentum, species, energy, and soot number density and mass fraction in an axisymmetric flame-fixed coordinate system in conjunction with a simple degradation model for the LDPE and a state-of-the-art radiation model. The model considers two assumptions. First, pure ethylene results from the decomposition of LDPE and, second, an acetylene/benzene based-soot model, initially validated for C1–C3 hydrocarbons, can be extended with minor modifications to model soot production of LDPE. Comparisons between model predictions and experimental data in terms of flame structure and soot volume fraction support these assumptions. The major finding of this study is that radiation contributes negatively to the surface heat balance along the LDPE molten surface and the coating ahead of the molten front. This shows that the convective heat transfer from the flame is the main contribution to sustain the pyrolysis process and the flame spread is mainly ensured owing to the combined contribution of convection from flame and conduction inside the condensed phase. The maximum incident radiative flux along the molten ball is 17.5 kW/m2 and is reached at the molten ball trailing edge whereas the radiant fraction is about 0.25. Neglecting flame self-absorption affects these values by less than 5%, showing that the optically-thin approximation is valid for this flame. In addition, soot radiation dominates the radiative heat transfer in this flame, contributing for about two-third of the total radiation. Finally, model results show that the usually-used thermally-thin assumption throughout the LDPE coating is not strictly valid.

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a :

Stretch function (–)

A S :

Soot surface area (m−1)

C a :

Agglomeration rate constant (–)

c :

Heat capacity (J kg−1 K−1)

f :

k-distribution function (m−1)

f S :

Soot volume fraction (–)

g :

Cumulative k-distribution function (–)

\({I}_{{g}} ,{I}\) :

Radiative intensity (W m−2 sr−1)

I b :

Blackbody intensity (Planck function) (W m−2 sr−1)

k :

Absorption coefficient variable (m−1)

k B :

Boltzmann constant (J kg−1)

L :

Heat of reaction (J kg−1)

\(\dot{m}_{pyr}\) :

Pyrolysis mass flow rate (kg s−1)

\(\dot{m}_{pyr}^{{{\prime \prime }}}\) :

Pyrolysis mass flow rate per unit area (kg m−2 s−1)

N A :

Avogadro number (part mol−1)

NC min :

Number of carbon atoms in the incipient soot particle (–)

N S :

Soot number density per unit mass of mixture (part kg−1)

\(\varvec{n}_{\varvec{q}}\) :

Unit surface normal (pointing away from surface into the medium)

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

Net heat flux (W m−2)

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

Radiative flux (W m−2)

\(\dot{q}_{R,inc}^{''}\) :

Incident radiative flux (W m−2)

\(\dot{q}_{R,net}^{{{\prime \prime }}}\) :

Net radiative flux (W m−2)

\(\dot{q}_{R,R}^{{{\prime \prime }}}\) :

Surface re-radiation (W m−2)

r :

Radial coordinate or radius (m)

\(\varvec{r}\) :

Position vector (m)

\(\hat{\varvec{s}}\) :

Unit vector into a given direction (–)

T :

Temperature (K)

u :

Velocity (m s−1)

\(u_{p}\) :

Spread rate (m s−1)

W i :

Molecular weight of the ith species (kg mol−1)

Y i :

Mass fraction of the ith species (–)

z :

Axial coordinate (m)

δ :

Stand-off distance (m)

\(\Delta \eta_{j}\) :

Narrow band spectral resolution (cm−1)

η :

Wavenumber (cm−1)

κ :

Absorption coefficient (m−1)

\(\lambda\) :

Thermal conductivity (W m−1 K−1)

ρ :

Density (kg m−3)

\(\dot{\omega }_{n}\) :

Reaction rate for soot nucleation (mol m−3 s−1)

\(\dot{\omega }_{sg}\) :

Reaction rate for soot surface growth (mol m−3 s−1)

\(\dot{\omega }_{{N_{S} }}\) :

Reaction rate for soot number density (part m−3 s−1)

\(\dot{\omega }_{{O_{2} }}\) :

Reaction rate for soot oxidation by O2 (kg m−3 s−1)

\(\dot{\omega }_{OH}\) :

Reaction rate for soot oxidation by OH (kg m−3 s−1)

\(\dot{\omega }_{{Y_{S} }}\) :

Source term for soot mass fraction (kg m−3 s−1)

\(\varOmega_{i}\) :

Solid angle around the direction \(s_{i}\)

b :

Molten ball


Metallic core

f :


F :


g :


inc :


m :

Molten phase

melt :




pyr :


PE :


R :

Radiation or radiative



ref :

Reference state

S :



Coated wire



η :

At a given wavenumber or per unit wavenumber




Full spectrum


Narrow band

g :


g-s :



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The authors feel grateful to the Centre National d’Etudes Spatiales for its financial support under Contract No. 130615.

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Correspondence to J. L. Consalvi.

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Guibaud, A., Consalvi, J.L., Orlac’h, J.M. et al. Soot Production and Radiative Heat Transfer in Opposed Flame Spread over a Polyethylene Insulated Wire in Microgravity. Fire Technol 56, 287–314 (2020).

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  • Insulated wire
  • Opposed-flow flame spread
  • Microgravity
  • Soot production
  • Heat transfer