Wrinkled flame propagation in narrow channels: What Darrieus

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Wrinkled flame propagation in narrow channels
What Darrieus Landau didnt tell you

• http//cpl.usc.edu/HeleShaw
• M. Abid, J. A. Sharif, P. D. Ronney
• Dept. of Aerospace Mechanical Engineering
• University of Southern California
• Los Angeles, CA 90089-1453 USA

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Introduction

• Models of premixed turbulent combustion dont
  agree with experiments nor each other!

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Introduction - continued...

• whereas in liquid flame experiments, ST/SL in
  4 different flows is consistent with Yakhots
  model with no adjustable parameters

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Why are gaseous flames harder to model compare
(successfully) to experiments?

• One reason self-generated wrinkling due to flame
  instabilities
• Thermal expansion (Darrieus-Landau, DL)
• Rayleigh-Taylor (buoyancy-driven, RT)
• Viscous fingering (Saffman-Taylor, ST) in
  Hele-Shaw cells when viscous fluid displaced by
  less viscous fluid
• Diffusive-thermal (DT) (Lewis number)
• Joulin Sivashinsky (1994) - combined effects of
  DL, ST, RT heat loss (but no DT effect - no
  damping at small l)

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Objectives

• Use Hele-Shaw flow to study flame instabilities
  in premixed gases
• Flow between closely-spaced parallel plates
• Described by linear 2-D equation (Darcys law)
• 1000's of references
• Practical application flame propagation in
  cylinder crevice volumes
• Measure
• Wrinkling characteristics
• Propagation rates

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Apparatus

• Aluminum frame sandwiched between Lexan windows
• 40 cm x 60 cm x 1.27 or 0.635 cm test section
• CH4 C3H8 fuel, N2 CO2 diluent - affects Le,
  Peclet
• Upward, horizontal, downward orientation
• Spark ignition (1 or 3 locations)

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Results - videos - baseline case

• 6.8 CH4-air, horizontal, 12.7 mm cell

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Results - videos - upward propagation

• 6.8 CH4-air, upward, 12.7 mm cell

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Results - videos - downward propagation

• 6.8 CH4-air, downward, 12.7 mm cell

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Results - videos - high Lewis number

• 3.2 C3H8-air, horizontal, 12.7 mm cell (Le 1.7)

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Results - videos - low Lewis number

• 8.0 CH4 - 32.0 O2 - 60.0 CO2, horizontal, 12.7
  mm cell (Le 0.7)

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Results - videos - low Peclet number

• 5.8 CH4- air, horizontal, 6.3 mm cell (Pe
  26(!))

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Results - qualitative

• Orientation effects
• Horizontal propagation - large wavelength wrinkle
  fills cell
• Upward propagation - more pronounced large
  wrinkle
• Downward propagation - globally flat front
  (buoyancy suppresses large-scale wrinkles)
  oscillatory modes, transverse waves
• Consistent with Joulin-Sivashinsky predictions
• Large-scale wrinkling observed even at high Le
  small scale wrinkling suppressed at high Le
• For practical range of conditions, buoyancy
  diffusive-thermal effects cannot prevent
  wrinkling due to viscous fingering thermal
  expansion
• Evidence of preferred wavelengths, but selection
  mechanism unclear (DT ?)

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Results - propagation rates

• 3-stage propagation
• Thermal expansion - most rapid
• Quasi-steady
• Near-end-wall - slowest - large-scale wrinkling
  suppressed
• Quasi-steady propagation rate (ST) always larger
  than SL - typically 3SL even though u/SL 0!

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Results - orientation effect

• Horizontal - ST/SL independent of Pe SLw/a
• Upward - ST/SL ? as Pe ? (decreasing benefit of
  buoyancy) highest propagation rates
• Downward - ST/SL ? as Pe ? (decreasing penalty of
  buoyancy) lowest propagation rates
• ST/SL converges to constant value at large Pe

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Results - Lewis effect

• ST/SL generally slightly higher at lower Le
• CH4-air (Le 0.9) - ST/SL independent of Pe
• C3H8-air (Le 1.7) - ST/SL ? as Pe ?
• CH4-O2-CO2 (Le 0.7) - ST/SL ? as Pe ?
• ST/SL independent of Le at higher Pe
• Fragmented flames at low Le Pe

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Results - orientation effect revisited
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Results - orientation effect revisited
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Results - pressure characteristics

• Initial pressure rise after ignition
• Pressure constant during quasi-steady phase
• Pressure rise higher for faster flames
• Slow flame Fast flame

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Conclusions

• Flame propagation in quasi-2D Hele-Shaw cells
  reveals effects of
• Thermal expansion - always present
• Viscous fingering - narrow channels, long
  wavelengths
• Buoyancy - destabilizing/stabilizing at long
  wavelengths for upward/downward propagation
• Lewis number affects behavior at small
  wavelengths but propagation rate large-scale
  structure unaffected
• Heat loss (Peclet number) little effect

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Remark

• Most experiments conducted in open flames
  (Bunsen, counterflow, ...) - gas expansion
  relaxed in 3rd dimension
• but most practical applications in confined
  geometries, where unavoidable thermal expansion
  (DL) viscous fingering (ST) instabilities cause
  propagation rates 3 SL even when heat loss,
  Lewis number buoyancy effects are negligible
• DL ST effects may affect propagation rates
  substantially even when strong turbulence is
  present - generates wrinkling up to scale of
  apparatus
• (ST/SL)Total (ST/SL)Turbulence x
  (ST/SL)ThermalExpansion ?

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Remark

• Computational studies suggest similar conclusions
• Early times, turbulence dominates
• Late times, thermal expansion dominates
• H. Boughanem and A. Trouve, 27th Symposium, p.
  971.
• Initial u'/SL 4.0 (decaying turbulence)
  integral-scale Re 18