wrinkled flame propagation in narrow channels: what darrieus & landau didn’t tell you
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Wrinkled flame propagation Wrinkled flame propagation in narrow channels: in narrow channels:
What Darrieus & Landau What Darrieus & Landau didn’t tell youdidn’t tell you
http://cpl.usc.edu/HeleShaw
M. Abid, J. A. Sharif, P. D. RonneyDept. of Aerospace & Mechanical Engineering
University of Southern CaliforniaLos Angeles, CA 90089-1453 USA
IntroductionIntroduction Models of premixed turbulent combustion don’t agree
with experiments nor each other!
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x
Turbulence Intensity (u'/S L)
Yakhot
Gouldin (ReT=1,000)
Experiment(Re
T=1,000)
Bray (zero heat release) (large heat release)
Pope & Anand (zero heat release) (large heat release)
Sivashinsky
Introduction - continued...Introduction - continued... …whereas in “liquid flame” experiments, ST/SL in 4 4
different flowsdifferent flows is consistent with Yakhot’s model with no adjustable parametersno adjustable parameters
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0.1 1 10 100 1000
Hele-ShawCapillary waveTaylor-CouetteVibrating grid (Shy et al. )Theory (Yakhot)Power law fit to expts.
"Turbulence" intensity (u'/S L)
Power law fit (u'/S L > 2):
ST/SL = 1.61 (u'/S L).742
Why are gaseous flames harder to model & Why are gaseous flames harder to model & compare (successfully) to experiments?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 )
Ω2 +(1+Λ)Ω− 1−ε2
4ε +1+ε4 F+G( )Λ
⎧ ⎨ ⎩ ⎪
⎫ ⎬ ⎭ ⎪ =0;
Ω≡σ(1+ε)2kU ; Λ≡ fav
ρuUk; F≡ fb −εfu
εfav;
G≡ρu(1−ε)gfavU
; ε≡ρbρu
; fav≡fu +fb
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UpwardHorizontalDownwardDL only
Dimensioness waveength (fav/ρ
uUk)
ObjectivesObjectives Use Hele-Shaw flow to study flame instabilities in
premixed gases Flow between closely-spaced parallel plates Described by linear 2-D equation (Darcy’s law) 1000's of references Practical application: flame propagation in cylinder
crevice volumes Measure
Wrinkling characteristics Propagation rates
ApparatusApparatus
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)
Lexan sheets
Burned gas
Ballvalve
Flame front
Exhaust
Video camera
Sparkgenerator
Sparkelectrode(1 of 2)
Mixing chamber
Partial pressuregas mixing system
OxidizerDiluentFuel
Exhaust manifold
Aluminum plate
Unburned gas
Computer
Results - videos - “baseline” caseResults - videos - “baseline” case
6.8% CH4-air, horizontal, 12.7 mm cell
QuickTime™ and aVideo decompressorare needed to see this picture.
Results - videos - upward propagationResults - videos - upward propagation
6.8% CH4-air, upward, 12.7 mm cell
QuickTime™ and aVideo decompressorare needed to see this picture.
Results - videos - downward propagationResults - videos - downward propagation
6.8% CH4-air, downward, 12.7 mm cell
QuickTime™ and aVideo decompressorare needed to see this picture.
Results - videos - high Lewis numberResults - videos - high Lewis number
3.2% C3H8-air, horizontal, 12.7 mm cell (Le ≈ 1.7)
QuickTime™ and aVideo decompressorare needed to see this picture.
Results - videos - low Lewis numberResults - videos - low Lewis number
8.0% CH4 - 32.0% O2 - 60.0% CO2, horizontal, 12.7 mm cell (Le ≈ 0.7)
QuickTime™ and aVideo decompressorare needed to see this picture.
Results - videos - low Peclet numberResults - videos - low Peclet number
5.8% CH4- air, horizontal, 6.3 mm cell (Pe ≈ 26(!))
QuickTime™ and aVideo decompressorare needed to see this picture.
Results - qualitativeResults - 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 & For practical range of conditions, buoyancy &
diffusive-thermal effects cannot prevent wrinkling diffusive-thermal effects cannot prevent wrinkling due to viscous fingering & thermal expansiondue to viscous fingering & thermal expansion
Evidence of preferred wavelengths, but selection mechanism unclear (DT + ?)
Results - propagation ratesResults - 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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7.8% methane/air12.5% methane/air
Time (seconds)
Thermalexpansion
region
Quasi-steadyregion
Near-wallregion
Results - orientation effectResults - 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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0 50 100 150 200 250
HorizontalUpwardDownwardHorizontal (6.35 mm cell)
Peclet number ≡ SLw/a
CH4-aiρ mixtuρes (Le ≈ 0.9)
Results - Lewis # effectResults - 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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0 50 100 150 200 250 300
CH4-air
C3H
8-air
CH4-O
2-CO
2
CH4-air (6.35 mm cell)
C3H
8-air (6.35 mm cell)
Peclet number ≡ SLw/a
Hoρizonta oρientation ony
ConclusionsConclusions 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
RemarkRemark 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 ?
RemarkRemark 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
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