Wrinkled flame propagation in narrow channels: What Darrieus & Landau didn’t tell you

1. Wrinkled flame propagation in narrow channels: What Darrieus & Landau didn’t 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

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

3. Introduction - continued... • …whereas in “liquid flame” experiments, ST/SL in 4 different flows is consistent with Yakhot’s model with no adjustable parameters

4. 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)

5. Objectives • 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

6. 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)

7. Results - videos - “baseline” case 6.8% CH4-air, horizontal, 12.7 mm cell

8. Results - videos - upward propagation 6.8% CH4-air, upward, 12.7 mm cell

9. Results - videos - downward propagation 6.8% CH4-air, downward, 12.7 mm cell

10. Results - videos - high Lewis number 3.2% C3H8-air, horizontal, 12.7 mm cell (Le ≈ 1.7)

11. Results - videos - low Lewis number 8.0% CH4 - 32.0% O2 - 60.0% CO2, horizontal, 12.7 mm cell (Le ≈ 0.7)

12. Results - videos - low Peclet number 5.8% CH4- air, horizontal, 6.3 mm cell (Pe ≈ 26(!))

13. 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 + ?)

14. 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!

15. 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

16. 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

17. 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

18. 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 ?

19. 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