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Effect of gas phase heat sink on suppression of downward flame spread over thin solid fuels

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Abstract

A two-dimensional numerical model of opposed flow flame spread over thin solid fuel is formulated and modeled to study effect of gas phase heat sink (a wire-mesh placed parallel to the fuel surface) on the flame spread rate and flame extinction. The work focuses on the performance of the wire-mesh in normal gravity environment of 21 % oxygen concentration. The simulations were carried out for various mesh parameters (wire diameter, ‘\( \overline{d}_{wr} \)’ and number of wires per unit length, ‘N’) and mesh distance perpendicular to fuel surface (Y mesh ). Experiments were carried out for wire mesh with \( \overline{d}_{wr} = 0.035\,{\text{cm}} \) and N = 5 and were found to complement numerical predictions. Both simulations and experiments show that wire mesh is effective in reducing flame spread rate when placed at distance less than flame width (which is about 0.50 cm). Mesh wire diameter is determined to not have major influence on heat transfer. However, smaller wire diameter is preferred on account better aerodynamics and for increasing heat transfer surface area (here prescribed by parameter ‘N’). Computations show that meshes with more number of wires per unit length are more effective heat sinks. However, the flame extinction occurs only if mesh is located very close to the fuel surface (of the order of 0.15 cm) and at this distance flame suppression is relatively insensitive to number of wires per unit length.

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Abbreviations

\( \bar{A}_{s} \) :

Solid phase pre-exponential factor (1.9 × 105 m/s)

AW :

Wire mesh heat transfer area

\( \bar{B}_{g} \) :

Gas phase pre-exponential factor (1.58 × 109 m3/kg/s)

\( Bo\, \) :

Boltzmann number \( ( = \rho^{*} c_{P}^{*} \bar{U}_{R} /(\sigma \bar{T}_{\infty }^{3} )) \)

\( c_{p}^{ * } \) :

Reference gas-phase specific heat (13.81 kJ/kg/K)

\( c_{p} \) :

Non-dimensional gas-phase specific heat \( ( = \bar{c}_{p} /c_{p}^{ * } ) \)

\( \bar{c}_{s} \) :

Solid-phase specific heat (12.55 kJ/kg/K)

c :

\( c_{p}^{ * } /\bar{c}_{s} \) (1.1)

C :

Correction factor

\( c_{p,i} \) :

Non-dimensional specific heat for species i

\( Da \) :

Damkohler number \( ( = \frac{{\bar{B}_{g} \rho^{ * } \alpha^{ * } }}{{\bar{U}_{R}^{2} }}) \)

\( D_{i} \) :

Diffusion coefficient of species i

\( \overline{d}_{wr} \) :

Mesh wire diameter

\( \bar{E}_{g} \) :

Gas-phase activation energy (87.31 × 104 J/g mol)

E g :

Non-dimensional gas-phase activation energy \( ( = \bar{E}_{g} /\bar{R}_{u} /\bar{T}_{\infty } = 35) \)

\( \bar{E}_{s} \) :

Solid-phase activation energy (13.70 × 104 J/g mol)

E s :

Non-dimensional solid-phase activation energy \( ( = \bar{E}_{s} /\bar{R}_{u} /\bar{T}_{\infty } = 55) \)

\( f_{i} \,\,\,\,\,\, \) :

Stoichiometric mass ratio of species i and fuel

\( \bar{g}_{e} \) :

Gravitational acceleration on surface of earth \( \left( {\bar{g}_{e} = 9.81\,\,{\text{m/s}}^{2} } \right) \)

\( \bar{g} \) :

Gravitational acceleration

g :

Gravitational acceleration (\( {{\overline{g} } \mathord{\left/ {\vphantom {{\overline{g} } {\overline{g}_{e} }}} \right. \kern-\nulldelimiterspace} {\overline{g}_{e} }} \))

\( h_{{_{i} }} \) :

Enthalpy of species i

h s :

Non-dimensional solid fuel thickness \( ( = \bar{h}_{s} /\bar{L}_{R} ) \)

h :

Non-dimensional fuel thickness (\( \bar{h}/\bar{\tau } \))

K:

Absorptivity of the medium

Le :

Lewis number of species \( i\;\left({Le_{\rm F}\,=\, 1,\,Le_{{\rm O_{2}}}\,=\, 1. 1 1,\,Le_{{\rm CO_{2}}}\,=\, 1. 3 9,\,Le_{{\rm H_{2}O}}\,=\,0. 8 3,\,Le_{\rm N2}\,=\, 1} \right) \)

\( \bar{l}_{P} \) :

Pyrolysis length

\( \bar{l}_{ph} \) :

Preheat length

\( \bar{L}_{R} \) :

Reference length (gas phase thermal length, \( \alpha^{ * } /\bar{U}_{R} \))

L :

Non-dimensional latent heat of solid \( (\bar{L}/\bar{c}_{s} /\bar{T}_{\infty } = - 2) \)

LW :

Length of wire

M i :

Molecular weight of species i

\( \dot{m} \) :

Non-dimensional mass flux from solid \( ( = \bar{\dot{m}}/\rho^{ * } /\bar{U}_{R} ) \)

N :

Number of wires per unit length

P :

Non-dimensional pressure \( ( = (\bar{P} - \bar{P}_{\infty } )/\rho^{*} /\bar{U}_{R}^{2} ) \)

P l :

Planck number

\( \bar{P}_{\infty } \) :

Ambient pressure

Pr :

Prandtl number

Qsink :

Heat taken by mesh

\( q_{c} \) :

Conduction heat flux

\( q_{r} \) :

Radiative heat flux

q y+ r , q y− r :

Positive and negative components of q r in y-direction

q y r :

Net radiative heat flux in y-direction

q x+, q x− r :

Positive and negative components of q r in x-direction

q x r :

Net radiative heat flux in x-direction

\( Re \) :

Reynolds number

\( \bar{R}_{u} \) :

Universal gas constant

Ra :

Rayleigh number

T* :

Reference temperature (1,250 K)

T :

Non-dimensional gas temperature \( ( = \bar{T}/\bar{T}_{\infty } ) \)

\( \overline{T}_{surface} \) :

Temperature of wire mesh (300 K)

\( T_{gas} \) :

Non-dimensional gas temperature

\( \bar{T}_{\infty } \) :

Ambient temperature (300 K)

\( T_{L} \) :

Non-dimensional temperature at which L is given \( ( = \bar{T}_{L} /\bar{T}_{\infty } = 1) \)

\( T_{s} \) :

Non-dimensional solid temperature \( ( = \bar{T}_{s} /\bar{T}_{\infty } ) \)

\( \bar{U}_{B} \) :

Reference buoyant velocity

\( \bar{U}_{R} \) :

Reference velocity (\( \max \,(\bar{U}_{\infty } + \bar{U}_{B} ) \))

\( \bar{U}_{\infty } \) :

Forced flow velocity

\( u \) :

Non-dimensional velocity in x-direction (\( = {{\overline{u} } \mathord{\left/ {\vphantom {{\overline{u} } {\overline{U}_{R} }}} \right. \kern-\nulldelimiterspace} {\overline{U}_{R} }} \))

v :

Non-dimensional velocity in y-direction (\( = {{\overline{v} } \mathord{\left/ {\vphantom {{\overline{v} } {\overline{U}_{R} }}} \right. \kern-\nulldelimiterspace} {\overline{U}_{R} }} \))

\( V_{f} \) :

Flame spread rate

\( x,\,X \) :

Non-dimensional x-coordinate (\( = {{\overline{x} } \mathord{\left/ {\vphantom {{\overline{x} } {\overline{L}_{R} }}} \right. \kern-\nulldelimiterspace} {\overline{L}_{R} }} \))

X i :

Mole fraction of species i

\( y,\,Y \) :

Non-dimensional y-coordinate (\( = {{\overline{y} } \mathord{\left/ {\vphantom {{\overline{y} } {\overline{L}_{R} }}} \right. \kern-\nulldelimiterspace} {\overline{L}_{R} }} \))

Y i :

Mass fraction of species i

Y mesh :

Mesh location

α* :

Reference gas thermal diffusivity (2.13 × 10−4 m2/s)

\( \bar{\alpha }_{s} \) :

Reference solid thermal diffusivity

α :

Solid absorptance (0.92)

β :

Extinction coefficient

ε :

Solid emittance (0.92)

κ* :

Reference gas thermal conductivity (8.07 × 10−5 W/m/K)

κ :

Non-dimensional gas thermal conductivity \( ( = \bar{k}/k^{ * } ) \)

κ :

Stefan–Boltzmann constant (5.6762 × 10−6 J/m2/s/K4)

μ* :

Reference gas viscosity (4.1 × 10−5 kg/m/s)

μ :

Non-dimensional gas viscosity \( ( = \bar{\mu }/\mu^{ * } ) \)

ρ* :

Reference gas density (0.275 kg/m3)

ρ :

Non-dimensional gas density \( ( = \bar{\rho }/\rho^{ * } ) \)

\( \bar{\rho }_{\infty } \) :

Ambient gas density (1.15 kg/m3)

\( \bar{\rho }_{s} \) :

Solid fuel density (750 kg/m3)

\( \bar{\tau } \) :

Solid half thickness (5.0 × 10−3 cm)

\( \omega^{\prime\prime\prime}_{F} \) :

Non-dimensional fuel source term \( ( = - Da\rho^{2} Y_{\text{F}} Y_{{{\text{O}}_{2} }} \exp ( - E_{g} /T)) \)

\( \omega^{\prime\prime\prime}_{i} \) :

Sink or source term for species i \( ( = f_{i} \omega^{\prime\prime\prime}_{F} ) \)

ω :

Scattering albedos

\( \xi ,\,\eta ,\,\mu \) :

Direction cosines in x, y and z directions

Г :

Non-dimensional solid parameter \( ( = \bar{\rho }_{s} \bar{c}_{s} \bar{V}_{F} /\rho^{ * } /c_{P}^{ * } /\bar{U}_{R} ) \)

\( \Upomega \) :

Ordinate direction (\( \xi ,\,\eta ,\,\mu \))

B :

Refers to buoyant

f :

Flame

F :

Refers to fuel

g :

Gas phase

i :

Species i (i = 1, N)

L :

Refers to latent heat

Max:

Maximum

Min:

Minimum

p :

Pyrolysis

R,r :

Reference

s :

Solid phase

w :

Value at wall

W:

Wire-mesh

x :

Along x-direction, or derivative with respect to x

y :

Along y-direction, or derivative with respect to y

∞:

Value at far field

*:

Evaluated at T*

–:

Dimensional quantity

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Acknowledgments

Authors would like to gratefully acknowledge and thank Chenthil Kumar, Doctoral Scholar in Department of Aerospace Engineering, Indian Institute of Technology Madras, for his valuable assistance and helpful discussions.

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Authors and Affiliations

  1. Department of Aerospace Engineering, Indian Institute of Technology, Madras, Chennai, 600036, Tamilnadu, India

    Vinayak Malhotra & Amit Kumar

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  1. Vinayak Malhotra
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  2. Amit Kumar
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Correspondence to Amit Kumar.

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Proceedings of 21st National and 10th ISHMT-ASME, December 2011.

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Malhotra, V., Kumar, A. Effect of gas phase heat sink on suppression of downward flame spread over thin solid fuels. Int J Adv Eng Sci Appl Math 4, 138–151 (2012). https://doi.org/10.1007/s12572-012-0064-0

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