Effects of Ambient Condition on Flame Spread over a Thin PMMA Sheet

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Effects of Ambient Condition on Flame Spread over
a Thin PMMA Sheet
Shuhei Takahashi, Takeshi Nagumo and Kazunori
Wakai Department of Mechanical and Systems
Engineering, Gifu University, JAPAN e-mail
takahash_at_mech.gifu-u.ac.jp Subrata
Bhattacharjee Department of Mechanical
Engineering, San Diego State University,
USA e-mail subrata_at_voyager5.sdsu.edu
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Background

• Spread rate over a thermally-thin PMMA sheet,
  where the thickness is less than 1mm, has not
  been investigated extensively.
• It is predicted that steady flame spread over
  PMMA in quiescent micro-gravity is achieved if
  the thickness is sufficiently thin.

Objective

• To measure the spread rate of thin PMMA sheets in
  normal- and micro-gravity with varying O2 level,
  pressure and opposed-flow velocity.

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Vf
Control Volumes in the gas and solid phases at
the leading edge
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Thermal-regime
if
Vg is not too high to cause kinetic effect and
not too low to cause radiative effect. Oxygen
level is high enough to allow fast reaction.
and
The dominant driving force of flame spread is the
conduction from the gas phase to the solid phase.
...(iii)
Scales of the control volume in the gas phase
where
...(iv)
Scales of the control volume in the solid phase
...(v)
Heat required to preheat the fuel
where
...(vi)
These expressions are identical to the analytical
solutions of de Ris 1 and Delichatsios 4.
Substituting Eqs. (i), (iv), (v) and (vi) into
Eq. (iii)
and
for thermally-thin fuel
for thermally-thick fuel
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The extended simplified theory (EST)
(S. Bhattacharjee et al. Proc. Combust. Inst.
26 1477-1485)
for thermally-thick fuel
for thermally-thin fuel
In the thermal-regime
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Fuel thick PMMA
The kinetic effect reduces the spread rate in low
oxygen level. (low Da effect)
Fuel thin ashless filter paper
This line corresponds to the Vr of 10cm/sec.
Thermal-region limit
The radiative loss reduces the spread rate with
low opposed-flow. (high R effect)
Blow off
Radiative extinction
Effect of Damköhler number and radiative loss on
spread rate (numerical simulation)
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Apparatus for normal-gravity experiments
Apparatus for micro-gravity experiments conducted
with the 4.5sec trop-tower (100meter-drop) of
MGLAB in Japan.
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where
and
for thermally-thin fuel
for thermally-thick fuel
Downward spread rate vs. fuel half-thickness in
normal-gravity
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where
Non-dimensional downward spread rate vs.
non-dimensional fuel half-thickness
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Spread rate in quiescent normal- and micro-gravity
Spread rate in mG
Spread rate in NG
O2 level 21 Pressure 1atm
Vr Vf Vg
Ratiative effect due to small Vf.
Thermal-regime spread due to large Vf
Spread rate in micro-gravity with varying
opposed-flow velocity, oxygen level and fuel
thickness
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Temperature diffusion layer
Mass diffusion layer
The unsteady spread observed when the oxygen
level is 50 and the fuel thickness is 125mm
Radiative loss
Scale of the temperature diffusion layer shrinks.
flame
0.00sec (Ignition)
0.918sec
1.836sec
2.584sec
2.720sec
2.754sec
2.822sec
3.400sec
Unsteady flame spread in micro-gravity (quiescent
condition)
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Conclusions

• The prediction, EST, can accurately predict the
  downward spread rate in the thermal-regime
  throughout thin and thick regimes.
• Low oxygen level and low opposed-flow velocity
  can cause the kinetics effect and the ratiative
  effect, respectively, to break thermal-regime.
• If the fuel is very thin (less than 50mm), the
  thermal-regime holds in a relatively wide range,
  even under a quiescent micro-gravity condition.