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Dynamics of Front Propagation in Narrow Channels

Dynamics of Front Propagation in Narrow Channels. Mohammed Abid, Jamal A. Sharif, Paul D. Ronney Department of Aerospace & Mechanical Engineering University of Southern California Los Angeles, CA 90089-1453. Motivation.

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Dynamics of Front Propagation in Narrow Channels

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  1. Dynamics of Front Propagation in Narrow Channels Mohammed Abid, Jamal A. Sharif, Paul D. Ronney Department of Aerospace & Mechanical Engineering University of Southern California Los Angeles, CA 90089-1453

  2. Motivation • Premixed gas flame instabilities & buoyancy effects not well understood due to • Large Dr/r - baroclinic production of vorticity • n, a, D increase ≈ 25x across flame • 3d hydrodynamics with large Re • Effects most pronounced near extinction, but couple strongly to flame stretch & heat losses • Practical applications • Accidental explosions - laminar flame ® wrinkled flame ® turbulent flame ® detonation • Industrial furnaces - large Grashof # • Fire safety in spacecraft

  3. Approach • Hele-Shaw flow • 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 • Premixed-gas flames, PLUS propagating chemical fronts in aqueous solution • d º Dr/r << 1 - No baroclinicity, Bousinnesq approximation valid • DT ≈ 3 K - no change in transport properties • Not affected by heat loss • Large Schmidt # - front stays "thin” even at high Re • Simpler chemistry than gaseous flames

  4. Types of flame instabilities • Thermal expansion (Darrieus-Landau, DL) • Rayleigh-Taylor (buoyancy-driven, RT) • Viscous fingering (Saffman-Taylor, ST) (flow in narrow channels when viscous fluid displaced by less viscous fluid) • Diffusive-thermal (Lewis number) • Joulin & Sivashinsky (1994) - combined effects of DL, ST, RT & heat loss (but no diffusive-thermal effect - no damping at small l)

  5. Objectives • Study behavior of flame propagation in Hele-Shaw cells • Wrinkling characteristics • Propagation rates • Buoyancy effects • Compare variable-density flames & nearly constant-density aqueous chemical fronts

  6. Chemical considerations • Iodate-hydrosulfite system IO3- + 6 H+ + 6 e- ® I- + 3 H2O S2O42- + 4 H2O ® 6 e- + 8 H+ + 2 SO42- ----------------------------------------------------- IO3- + S2O42- + H2O ® I- + 2 SO42- + 2 H+ Autocatalytic in H+ • Simple solutions • Non-toxic • "Lightning fast" (up to 0.05 cm/sec)

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

  8. Apparatus (liquid flames) • 25cm x 20cm; 0.04cm < W < 0.2cm; 0.2 < Grw < 25 • Color-changing or fluorescent pH indicators • Initiate at a point using acid solution

  9. Results - gaseous flames - 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 + ?)

  10. Results - gas flames - propagation rates • Propagation rate (ST) always larger than SL • 3-stage propagation • Thermal expansion - most rapid • Quasi-steady • Near-end-wall - slowest - large-scale wrinkling suppressed

  11. Results - gas flames - 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

  12. Results - gas flames - Lewis # effect • ST/SL generally higher at lower Le • CH4-air (Le ≈ 1) - 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 convergence at large Pe uncertain

  13. Results - liquid flames - fingering • FINGERING (???) for upward propagation • No wrinkling for downward or horizontal propagation - unlike gaseous flames • Wavelength (l) nearly independent of SL & width

  14. Results - fingering - continued • Saffman & Taylor (1958) • No wavelength selection without surface tension! • Dµ = 0, S ≠ 0: • l independent of U (~SL) & K (~w2) but depends on cell angle q - consistent with experiments

  15. Results - fingering - continued • Zhu (1998) - wavelength selection due to curvature (Markstein) effect on SL: ls=max = 48πnD/gw2cos(q)d- much too small (≈0.1 mm) & not correct effect of w, q • Surface tension issues • Can miscible interfaces have a surface tension? • l = 1 cm S ≈ 5 x 10-3 dyne/cm ≈ 7 x 10-5Swater-air • Is this S reasonable? • Davis (1988): miscible systems S ~ C/t; t = interface thickness, C = 2 x 10-6 dyne S ≈ 7 x 10-3 dyne/cm • If S ~ 1/t, t = D/SL for chemical front, Swater-air = 70 dyne/cm, twater-air ≈ 10-7cm, Sliquid flame ≈ 7 x 10-3 dyne/cm •  Probably reasonable value - need rotating drop or capillary wave experiment to check • Unlike a diffusing passive interface between miscible fluids, chemical fronts have constant thickness  constant S

  16. Results - liquid flames - propagation rates • Wrinkled fronts propagate quasi-steadily with rate ST >> SL • Can ST be related to a “turbulence intensity”? Estimated buoyant velocity ub ≈ smax/ks=max

  17. Results - liquid flames - propagation rates • ST of rising fronts in Hele-Shaw cells (K = w2/12) consistent with Yakhot (1988) renormalization-group model for Huygens’ propagation with U = u’/SL (!)

  18. Results - liquid flames - propagation rates • Data on ST/SL in 5 different flows consistent with Yakhot’s model with no adjustable parameters

  19. Conclusions • Flame propagation in quasi-2D Hele-Shaw cells reveals effects of • Thermal expansion • Viscous fingering • Buoyancy • Lewis number • Surface tension (!?) • Fronts in Hele-Shaw cells enable rational comparisons of models & experiments • Flame propagation in cylinder crevice volumes may be quite different from expectations based on unconfined flame experiments • Rich dynamics observed even for aqueous 2d system much simpler than freely propagating gaseous flames

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