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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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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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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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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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