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Study on the role of soot and heat fluxes in upward flame spread using a wall-resolved large eddy simulation approach

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Abstract

The present study aims to obtain further understandings of vertical flame spreading phenomena by analysing the influences of soot and individual heat flux components on PMMA walls using large eddy simulation. Total heat flux consists of convective and radiative components, but it is not clear which one has a significant role in fire spread. The computational code used is an in-house version of FireFOAM 2.2.x, which has recently undergone specific development and validation for flame spread studies by the authors. The present study has conducted numerical simulations for flame spread and full wall fire configurations. By scale-up of the PMMA size from 0.4 to 1.0 m, the convective heat flux decreased by 41.4% at the location of the pyrolysis front, radiative heat flux increased by 86.9%, and radiative heat flux due to soot grew by 215.2%. As the pyrolysis height increases from 0.3 to 1.0 m, the convective heat flux decreased by 26.8% at the location of the pyrolysis front. The radiative heat flux increased by 96.8%, and its components of combustion of the gaseous fuel and soot grew by 55.9% and 233.3%, respectively. Moreover, the ratio of radiative heat flux to total heat flux increased by 66.5%, and that of soot to radiative heat flux grew by 73.9%. The contribution of soot to radiative heat flux almost linearly increased against the pyrolysis height and that was higher at a higher pyrolysis height.

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Abbreviations

a rad :

Absorption coefficient (1 m−1)

A :

Frequency factor (unit is dependent on a equation)

Cp:

Specific heat at constant pressure (J K−1 kg−1)

C D2 :

Model constant of the eddy dissipation concept

C S :

Smagorinsky constant

C w :

Model constant of wall adapting local eddy viscosity model

d :

Wall thickness (m)

E :

Activation energy (kJ mol−1)

Err:

Error (%)

f v :

Soot volume fraction

h :

Enthalpy (J kg−1)

∆h :

Enthalpy of formation (J kg−1) or (J mol−1)

Δh comb :

Heat of combustion (J kg−1) or (J mol−1)

H :

PMMA height (m)

k :

(Total) turbulent kinetic energy (m2 s−2)

mʺ:

Local pyrolysis rate (kg s−1 m−2)

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

Mass transfer rate between fine structure and surrounding fluids (kg s−1)

p :

Pressure (Pa)

Pr t :

Turbulent Prandtl number

qʹ :

Heat release rate scaled by wall width (W m−1)

qʺ :

Heat flux (W m−2). Section 2.5.1 presents several definitions.

r rad :

Reflectivity

R :

Gas constant (kJ mol−1 K−1)

R 0 :

Criterion of flame volume

s :

Stoichiometric oxygen-fuel mass ratio

S S :

Soot particulate surface area (m2 kg−1)

Sc t :

Turbulent Schmidt number

t :

Time (s)

T :

Temperature (K)

T a :

Activation temperature (K)

W :

PMMA width (m)

x, y, z :

Coordinates (m) or the number of elements C, H, and O in a chemical equation

x p :

Pyrolysis height (m)

x f :

Flame height (m)

x wall :

Distance from the bottom leading edge of PMMA (m)

y standoff :

Standoff distance (m)

Y :

Mass fraction

Z:

Mixture fraction

γ :

Mass fraction of fine structures

ε :

(Total) dissipation rate (m2 s−3)

ε rad :

Emissivity

η rad :

Transmissivity

∆y wall :

Width of grid cell next to wall (mm)

λ :

Heat conductivity (W K−1 m−1)

ν :

Kinematic viscosity (m2 s−2)

ξ :

Criterion of flame regions

ω :

Reaction/pyrolysis rate (kg s−1 m−3)

ρ :

Density (kg m−3)

σ Stefan :

Stefan–Boltzmann constant (W m−2 K−4)

τ :

Timescale (s)

τ η :

Kolmogorov timescale (s)

\(\phi\) :

Equivalence ratio

χ :

Reaction fraction in the fine structures

chem:

Chemical reaction

conv:

Convection

diff:

Diffusion

EDC:

Eddy dissipation concept

em:

Emitted

fu:

Fuel

first:

First cell

gas:

Gas/gasification

integ:

Integral

inter:

Interface

J :

Chemical species

mel:

Melting

mod:

Modified

net:

Net

ox:

Oxidiser or oxygen

p:

Pyrolysis

pr:

Product

rad:

Radiation/radiative

refl:

Reflective

res:

Revolved

solid:

Solid

S/soot:

Soot

SGS:

Sub-grid scale

tot:

Total

vap:

Vaporisation

wall:

Wall

0:

Reference or standard value

*:

Fine structures

0:

Surrounding fluids

\(\overline{\phi }\) :

Time average variable

\(\tilde{\phi }\) :

Density-weighted average variable

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Acknowledgements

FireFOAM 2.2.x was built and distributed by FM Global, and the authors acknowledge technical and help supports from them. The in-house version of FireFOAM used in this study firstly developed in the project funded by the National key research and development program special for inter-governmental cooperation (No. 2016YFE0113400) and the European Commission FP7-PEOPLE-2012-IIF (Grant number 328784).

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Authors and Affiliations

  1. School of Civil Engineering, Hefei University of Technology, Hefei, 230009, China

    Kazui Fukumoto & Changjian Wang

  2. School of Engineering, University of Warwick, Coventry, CV4 7AL, UK

    Kazui Fukumoto & Jennifer X. Wen

  3. Anhui International Joint Research Centre On Hydrogen Safety, Hefei, 230009, China

    Changjian Wang

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  1. Kazui Fukumoto
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  2. Changjian Wang
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  3. Jennifer X. Wen
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Correspondence to Changjian Wang or Jennifer X. Wen.

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Appendix

Appendix

The readers can find a document about flame spread modelling and associated animation files from https://doi.org/10.17632/drtddfyvzc.1.

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Fukumoto, K., Wang, C. & Wen, J.X. Study on the role of soot and heat fluxes in upward flame spread using a wall-resolved large eddy simulation approach. J Therm Anal Calorim 147, 4645–4665 (2022). https://doi.org/10.1007/s10973-021-10791-6

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