A Time-Scale Analysis of Opposed-Flow Flame Spread

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A Time-Scale Analysis of Opposed-Flow Flame
Spread The Foundations

• Subrata (Sooby) Bhattacharjee
• Professor, Mechanical Engineering Department
• San Diego State University, San Diego, USA

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Acknowledgement

• Profs. Kazunori Wakai and Shuhei Takahashi, Gifu
  University, Japan
• Dr. Sandra Olson, NASA Glenn Research Center.
• Team Members (graduate) Chris Paolini, Tuan
  Nguyen, Won Chul Jung, Cristian Cortes, Richard
  Ayala, Chuck Parme
• Team Members (undergraduate) Derrick, Cody,
  Isaac, Tahir and Mark.

(Support from NASA and Japan Government is
gratefully acknowledged)
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Overview

• What is opposed-flow flame spread?
• Flame spread in different environment.
• Mechanism of flame spread.
• Length scales and time scales.
• Spread rate in normal gravity.
• Spread rate in microgravity
• The quiescent limit

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Upward or any other flow-assisted flame spread
becomes large and turbulent very quickly.
Opposed-flow flame spread is also known as
laminar flame spread.
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Downward Spread Experiment, SDSU Combustion
Laboratory
PMMA 10 mm 0.06 mm/s
AFP 0.08 mm 1.8 mm/s
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Sounding Rocket Experiment Spread Over PMMA
Infrared Image at 2.7m

• Gravity Level 1.e-6g
• Environment 50-50 O2/N2 mixture at 1.0 atm.
• Flow Velocity 50 mm/s
• Fuel Thick PMMA (Black)
• Spread Rate 0.45 mm/s

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Experiments Aboard Shuttle O2 50 (Vol.), P1
atm.
Image sequence showing extinction
Fuel Thin AFP, 0.08 mm 4.4 mm/s
Vigorous steady propagation.
Thick PMMA
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Mechanism of Flame Spread
O2/N2 mixture
Fuel vapor
Virgin Fuel
The flame spreads forward by preheating the
virgin fuel ahead.
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Mechanism of Flame Spread
O2/N2 mixture
Vaporization Temperature,
Virgin Fuel
The rate of spread depends on how fast the flame
can heat up the solid fuel from ambient
temperature to vaporization temperature
.
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Forward Heat Transfer Pathways Domination of
Gas-to-solid Conduction (GSC)
The Leading Edge
Gas-to-Solid Conduction
Pyrolysis Layer
Preheat Layer
Solid-Forward Conduction
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The Leading Edge Length Scales
Gas-phase conduction being the driving force,
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Length Scales - Continued
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Heated Layer Thickness Gas Phase
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Heated Layer Thickness Solid Phase
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Energy Balance Characteristic Heating Rate
Sensible heating (sh) rate required to heat up
the unburned fuel from to
Flame Temperature,
Vaporization Temperature,
Heating rate due to gas-to-solid (gsc)
conduction
Ambient Temperature,
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Thick Fuel Spread Rate from Energy Equation
Conduction-limited or thermal spread rate
Vaporization Temperature,
For semi-infinite solid,
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Thin Fuel Spread Rate from Energy Equation
Conduction-limited spread rate
Vaporization Temperature,
For thermally thin solid,
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Parallel Heat Transfer Mechanisms
Gas to Environment Radiation (ger)
Gas to Solid Radiation (gsr)
Solid to Environment Radiation (ser)
Gas to Solid Conduction (gsc)
Solid Forward Conduction (sfc)
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Time Scales Relevant to Gas Phase
Gas to Environment Radiation (ger)

Available Time
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Time Scales Relevant to Gas Phase Thermal Regime
Solid to Env. Radiation (ser)
Gas to Solid Radiation (gsr)
Available Time in Gas Phase
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Time Scales Relevant to Solid Phase








Available Time
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Time Scales Relevant to Solid Phase Thermal
Regime








Available Time
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The Thermal Regime Governing Equation









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Time Scales Gas to Surface Conduction
The characteristic heat is the heat required to
raise the solid-phase control volume from to
.
Gas to Solid Conduction (gsc)
Gas-to-surface conduction time
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Thermal Regime Spread Rates Using Time Scales
Gas to Solid Conduction (gsc)
Substitute the two limits of
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Relative dominance of GSC over SFC
Gas to Solid Conduction (gsc)
Solid Forward Conduction (sfc)
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Radiative Term Becomes Important in Microgravity
Solid to Environment Radiation (ser)
The radiation number is inversely proportional to
the velocity scale. In the absence of buoyancy,
radiation can become important.
Gas to Solid Conduction (gsc)
Solid Residence Time
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Spread Rate in the Microgravity Regime
Solid to Environment Radiation (ser)
Include the radiative losses in the energy
balance equation
Gas to Solid Conduction (gsc)
Algebraic manipulation leads to
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Mild Opposing Flow Computational Results for
Thin AFP
As the opposing flow velocity decreases, the
radiative effects reduces the spread rate
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Mild Opposing Flow MGLAB Data for Thin PMMA
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The Quiescent Microgravity Limit Fuel Thickness
Solid to Environment Radiation (ser)
The minimum thickness of the heated layer can be
estimated as
Gas to Solid Conduction (gsc)
All fuels, regardless of physical thickness, must
be thermally thin in the quiescent limit.
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The Quiescent Microgravity Limit Spread Rate
Solid to Environment Radiation (ser)
The spread rate can be obtained from the energy
balance that includes radiation.
Gas to Solid Conduction (gsc)
reduces to
where,
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The Quiescent Limit Extinction Criterion
In a quiescent environment steady spread rate
cannot occur for
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The Quiescent Limit MGLAB Experiments
Extinction criterion proposed is supported by the
limited amount of data we have acquired thus far.

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Conclusions

• A phenomenological model for opposed flow flame
  spread is built around two residence times, one
  in the gas phase and one in the solid.
• Theoretical solutions in the thermal regime are
  reproduced using the time scale analysis.
• Deviation from the thermal regime can be
  quantified by comparing the time scale of the
  added physics with the appropriate residence
  time.
• In the quiescent microgravity environment all
  fuels behave like thin fuels.
• A critical thickness is proposed beyond which a
  spreading flame cannot be sustained in such
  environment.