Wrinkled flame propagation in narrow channels: What Darrieus & Landau didn’t tell you M. Abid, J. A. Sharif, P. D. Ronney Dept. of Aerospace & Mechanical Engineering University of Southern California Los Angeles, CA USA

Introduction Models of premixed turbulent combustion don’t agree with experiments nor each other!

Introduction - continued... 4 different flows no adjustable parameters …whereas in “liquid flame” experiments, S T /S L in 4 different flows is consistent with Yakhot’s model with no adjustable parameters

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 )

Objectives n 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

Apparatus Aluminum frame sandwiched between Lexan windows 40 cm x 60 cm x 1.27 or cm test section CH 4 & C 3 H 8 fuel, N 2 & CO 2 diluent - affects Le, Peclet # Upward, horizontal, downward orientation Spark ignition (1 or 3 locations)

Results - videos - “baseline” case 6.8% CH 4 -air, horizontal, 12.7 mm cell

Results - videos - upward propagation 6.8% CH 4 -air, upward, 12.7 mm cell

Results - videos - downward propagation 6.8% CH 4 -air, downward, 12.7 mm cell

Results - videos - high Lewis number 3.2% C 3 H 8 -air, horizontal, 12.7 mm cell (Le ≈ 1.7)

Results - videos - low Lewis number 8.0% CH % O % CO 2, horizontal, 12.7 mm cell (Le ≈ 0.7)

Results - videos - low Peclet number 5.8% CH 4 - air, horizontal, 6.3 mm cell (Pe ≈ 26(!))

Results - qualitative n Orientation effects u Horizontal propagation - large wavelength wrinkle fills cell u Upward propagation - more pronounced large wrinkle u Downward propagation - globally flat front (buoyancy suppresses large-scale wrinkles); oscillatory modes, transverse waves u Consistent with Joulin-Sivashinsky predictions n 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 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 + ?)

Results - propagation rates 3-stage propagation  Thermal expansion - most rapid  Quasi-steady  Near-end-wall - slowest - large-scale wrinkling suppressed Quasi-steady propagation rate (S T ) always larger than S L - typically 3S L even though u’/S L = 0!

Results - orientation effect Horizontal - S T /S L ≈ independent of Pe = S L w/  n Upward - S T /S L  as Pe  (decreasing benefit of buoyancy); highest propagation rates n Downward - S T /S L  as Pe  (decreasing penalty of buoyancy); lowest propagation rates n S T /S L converges to ≈ constant value at large Pe

Results - Lewis # effect n S T /S L generally slightly higher at lower Le n CH 4 -air (Le ≈ 0.9) - S T /S L ≈ independent of Pe n C 3 H 8 -air (Le ≈ 1.7) - S T /S L  as Pe  n CH 4 -O 2 -CO 2 (Le ≈ 0.7) - S T /S L  as Pe  n S T /S L ≈ independent of Le at higher Pe n Fragmented flames at low Le & Pe

Results - orientation effect revisited

Results - pressure characteristics n Initial pressure rise after ignition n Pressure ≈ constant during quasi-steady phase n Pressure rise higher for faster flames Slow flameFast flame

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

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 S L 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  (S T /S L ) Total = (S T /S L ) Turbulence x (S T /S L ) ThermalExpansion ?

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